C A S R I L A N K A C U R R I C U L U M 2 0 2 0

S T U D Y T E X T

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First edition 2019 ISBN 9781 5097 3120 6 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Published by BPP Learning Media Ltd BPP House, Aldine Place 142-144 Uxbridge Road London W12 8AA www.bpp.com/learningmedia The copyright in this publication is owned by BPP Learning Media Ltd. The publishers are grateful to the IASB for permission to reproduce extracts from the International Financial Reporting Standards including all International Accounting Standards, SIC and IFRIC Interpretations (the Standards). The Standards together with their accompanying documents are issued by: The International Accounting Standards Board (IASB) 30 Cannon Street, London, EC4M 6XH, United Kingdom. Email: info@ifrs.org Web: www.ifrs.org Disclaimer: The IASB, the International Financial Reporting Standards (IFRS) Foundation, the authors and the publishers do not accept responsibility for any loss caused by acting or refraining from acting in reliance on the material in this publication, whether such loss is caused by negligence or otherwise to the maximum extent permitted by law. Copyright © IFRS Foundation All rights reserved. Reproduction and use rights are strictly limited. No part of this publication may be translated, reprinted or reproduced or utilised in any form either in whole or in part or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without prior permission in writing from the IFRS Foundation. Contact the IFRS Foundation for further details. The IFRS Foundation logo, the IASB logo, the IFRS for SMEs logo, the "Hexagon Device", "IFRS Foundation", "eIFRS", "IAS", "IASB", "IFRS for SMEs", "IASs", "IFRS", "IFRSs", "International Accounting Standards" and "International Financial Reporting Standards", "IFRIC" "SIC" and "IFRS Taxonomy" are Trade Marks of the IFRS Foundation. Further details of the Trade Marks including details of countries where the Trade Marks are registered or applied for are available from the Licensor on request.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright holder. The contents of this book are intended as a guide and not professional advice and every effort has been made to ensure that the contents of this book are correct at the time of going to press by CA Sri Lanka, BPP Learning Media, the Editor and the Author. Every effort has been made to contact the copyright holders of any material reproduced within this publication. If any have been inadvertently overlooked, CA Sri Lanka and BPP Learning Media will be pleased to make the appropriate credits in any subsequent reprints or editions. We are grateful to CA Sri Lanka for permission to reproduce the Learning Outcomes and past examination questions, the copyright of which is owned by CA Sri Lanka, and to the Association of Chartered Certified Accountants and Chartered Institute of Management Accountants for use of past examination questions in which they hold the copyright. © BPP Learning Media Ltd 2019

Draft Version

Introduction iii

Contents

Page Introduction iv Chapter features vi Learning outcomes vii Action verbs checklist xiv Business Level II – Management Accounting Part A Cost Accounting Chapter 1 Introduction to Management Accounting 3 Chapter 2 Cost Classification 25 Chapter 3 Accounting for Labour Costs 77 Chapter 4 Accounting for Overhead Costs 93 Chapter 5 Pricing 125 Chapter 6 Integrated Accounting 141 Chapter 7 Job, Batch, Contract and Service Costing 159 Chapter 8 Process Costing 195 Chapter 9 Marginal & Absorption Costing 255 Part B Planning and Controlling Chapter 10 Standard Costing and Variance Analysis 279 Chapter 11 Budgeting; Preparation and Control 331 Part C Decision Making Chapter 12 Short-Term Decision Making 407 Chapter 13 Long-Term Decision Making 457 Part D Risk and Uncertainty Chapter 14 Risk and Uncertainty 491 Part E Working Capital Management Chapter 15 Inventory Control 563 Index

Draft Version

Business Level II – Management Accounting iv

Introduction

Business Level II – Management Accounting The Business II Level course module for Management Accounting aims to provide a firm understanding of fundamentals of cost and management accounting and a blended learning by coupling business mathematics relevant to the subject. Accordingly, Management Accounting covers a number of mathematical fundamentals and their application to cost and management accounting.

Syllabus structure

Main syllabus areas Weightings A. Cost Accounting 35% B. Planning and Controlling 20% C. Decision Making 25% D. Risk and Uncertainty 10% E. Working Capital Management 10% One of the key elements in examination success is practice. It is important that not only you fully understand the topics by reading carefully the information contained in this Study Text, but it is also vital that you practise the techniques and apply the principles that you have learned. In order to do this, you should: Work through all the examples provided within the chapters and review the solutions, ensuring that you understand them; Complete the progress test for each chapter. In addition, you should use the Practice and Revision Kit. These questions will provide you with excellent examination practice when you are in the revision phase of your studies.

Draft Version

Introduction v

Pillar structure The Chartered Accountant Curriculum is structured around four progressively ascending levels of competency, namely, Business I, Business II, Corporate and Strategic Levels. Business Level II provides the fundamentals of accounting and harnesses the skills and professional values needed to mould a Certified Business Accountant. The Curriculum is also subdivided into specific subject areas or knowledge pillars and learning material is delivered to meet the knowledge requirements. These Knowledge Pillars focus on imparting the technical knowledge required of a competent CA and comprise of five pillars that focus on the following subject areas: Knowledge Pillar 1: Audit, Assurance and Ethics (AA&E) Knowledge Pillar 2: Financial Accounting and Reporting (FA&R) Knowledge Pillar 3: Performance Measurement and Risk (PM&R) Knowledge Pillar 4: Taxation and Law (T&L) Knowledge Pillar 5: Business Management and Strategy (BM&S)

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Business Level II – Management Accounting vi

Chapter features

Each chapter contains a number of helpful features to guide you through each topic. Topic list This tells you what you will be studying in the chapter. The topic items form the numbered headings within the chapter. Chapter introduction

The introduction puts the chapter topic into perspective and explains why it is important, both within your studies and within your practical working life. Learning Outcomes

The learning outcomes issued for the module by CA Sri Lanka are listed at the beginning of the chapter, with reference to the chapter section within which coverage will be found. Key terms

These are definitions of important concepts that you really need to know and understand before the exam. Examples These are illustrations of particular techniques or concepts with a worked solution or explanation provided immediately afterwards. Case study

Often based on real world scenarios and contemporary issues, these examples or illustrations are designed to enrich your understanding of a topic and add practical emphasis. Questions

These are questions that enable you to practise a technique or test your understanding. You will find the answer underneath the question. Formula to learn

These are the formula that you are required to learn for the exam. Section introduction

This summarises the key points to remember from each section. Chapter roundup This provides a recap of the key areas covered in the chapter. Progress Test Progress tests at the end of each chapter are designed to test your memory. Bold text Throughout the Study Text you will see that some of the text is in bold type. This is to add emphasis and to help you to grasp the key elements within a sentence or paragraph.

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Introduction

vii

Lear

ning

out

com

es

CA Sri Lanka'

s Learning out

comes for the

Module are se

t out on the fol

lowing pages.

They are cros

s-referenced t

o the chapter

in the Study T

ext where the

y are covere

d. Sy

llabu

s Ar

ea

Kno

wle

dge

Com

pone

nt

Lear

ning

Out

com

es

Spec

ific

Kno

wle

dge

Chap

ter

A. C

ost

Acco

unti

ng

1.1

Intr

oduc

tion

to

Cost

and

M

anag

emen

t Ac

coun

ting

1.1.1 Explain

the difference

between

the role of a m

anagement acc

ountant

and the financ

ial accountant

Definit

ions of manag

ement accoun

ting and

cost accountin

g, nature of m

anagement

accounting inf

ormation

1

1.1.2 Explain

the role of ma

nagement

accountant to

support plan

ning, contro

lling and decis

ion making

Objective and

scope of man

agement

accounting, po

licies and plan

s to achieve

desired object

ives of manag

ement, levels

of plannin

g and controll

ing (operation

al, manag

ement and co

rporate level)

1

1.

2 Co

st

Clas

sific

atio

n 1.2.1 Id

entify key com

ponents of

production co

st Compo

nents classifie

d under produ

ction and ser

vice cost

2

1.2.2 Explain

different cost

classifi

cations and id

entify differen

t cost ca

tegories

2

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Cost cl

assifications:

• by nature (

material, labo

ur, other cost

) • for

profit measure

ment and stoc

k valuati

on (direct cos

t, indirect cos

t, manufa

cturing cost an

d non-manufa

cturing cost, p

roduct cost,

periodic cost)

• by b

ehaviour, for

decision maki

ng and

controlling (v

ariable cost, fi

xed cost,

semi-variable

cost, relevan

t cost, irrelev

ant cost, contr

ollable cost, n

on-contro

llable cost)

1.2.3 Calculat

e appropriate c

ost estima

tions having i

dentified the

cost behavi

our Cost es

timation using

high-low meth

od, scatter

diagram and

regression me

thod, compu

te and interpr

et correlation

coeffici

ent, rank corre

lation 2

1.

3 La

bour

Cos

ts

1.3.1 Comput

e labour costs

using differe

nt remunerat

ion methods

Time-based pa

y (concept of o

vertime, idle

time), perform

ance-based pa

y, guaranteed

remun

eration, bonus

schemes

3

1.3.2 Comput

e labour cost f

or a produc

tion organisat

ion Direct

and indirect la

bour costs

3

1.

4 O

verh

ead

Cost

s 1.4.1 P

repare an ove

rhead cost

statement

Definition and

components u

nder overhead

cost, ov

erhead allocat

ion and

apportionmen

t, reapportionm

ent under

reciprocal serv

icing (repeate

d distribution

method

, elimination m

ethod)

4

1.4.2 Comput

e the full cost o

f produc

ts, services an

d activities

under absorp

tion costing a

nd margin

al costing

Treatment of d

irect and indir

ect costs in

ascertaining th

e full cost of a p

roduct

Overhead abso

rption (single

O.A.R, depart

mental O.A.R)

Over/u

nder absorptio

n of overhead

s 4

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1.

5 Pr

icin

g 1.5.1 A

pply cost infor

mation in

pricing decisio

ns Margin

al cost plus pr

icing and full c

ost pricing

to achieve sp

ecified targets

(eg, return

on investment

, margin, mark

-up) 5

1.

6 In

tegr

ated

Ac

coun

ting

1.6.1 E

xplain the inte

gration of cost

accoun

ts with the fin

ancial accoun

ting system

Explain the ad

vantages and

disadvantage

s of integ

rated account

ing 6

1.6.2 P

repare accoun

ts for inventor

y, labour

, overheads, w

ork-in-progre

ss, finishe

d goods flowi

ng up to incom

e statem

ent Invento

ry control a/c

s (material, wo

rk in progre

ss, finished go

ods), wages co

ntrol a/c, pr

oduction and n

on-production

overhe

ad control a/c

, accounting fo

r overhe

ad under abso

rption/over

absorption, co

st of sales con

trol a/c, incom

e statem

ent

6

1.

7 Sp

ecifi

c O

rder

Co

stin

g 1.7.1 C

ompute and a

ccount for the

costs o

f a specific ord

er using job

costing and ba

tch costing

Specific order

costing (job c

osting and ba

tch costing

) Charac

teristics of job

costing and b

atch costing

Job cos

t card Accoun

ting for jobs

7

1.7.2 Comput

e and account

for the

costs of a spec

ific order usin

g contrac

t costing

Contract costi

ng (characteri

stics, prepar

ation contract

accounts and

recognising p

rofits) 7

1.7.3 Comput

e the cost of a s

pecific order u

sing service co

sting Service

costing with

composite cos

t units Charac

teristics of a s

ervice vs prod

uct 7

1.

8 Pr

oces

s Co

stin

g1.8.1 Id

entify stages o

f a process and

accoun

t for process c

osts Losses

and gains, cos

t entries in pro

cess accoun

ts 8

1.8.2 Interpret

and apply the

concept

of equivalent

units of produ

ct costing Equiva

lent unit conc

ept for WIP, F

IFO method

and weighted

average meth

od for WIP

8

1.8.3 Comput

e the cost of jo

int produc

ts and by-pro

ducts Joint an

d by-product c

osting 8

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1.

9 M

argi

nal a

nd

Abso

rpti

on C

osti

ng1.9.1 C

ompute inven

tory value and

profit u

nder absorptio

n costing and

margin

al costing

Inventory valu

ation and pro

fit statement

under margin

al and absorp

tion costing

Arguments 'fo

r' and 'against

' each method;

marginal and

absorption co

sting 9

1.9.2 Prepare

reconciliation

for the

differences in

profit calcula

ted under

absorption co

sting and mar

ginal costing

system

Profit reconcil

iations

9

B. P

lann

ing

and

Cont

rolli

ng

2.1

Intr

oduc

tion

to

Stan

dard

Cos

ting

an

d Va

rian

ce

Anal

ysis

2.1.1 Explain

the importance

of standa

rd costing

Definitions an

d purposes of

standard

costing

Different type

s of standards

(ideal,

attainable and

current)

Preparation o

f the standard

cost card

10

2.1.2 Comput

e and interpre

t varianc

es related to s

ales and costs

Calculate and

interpret basi

c variances;

Cost variances

: material (tot

al, price and

usage) / labou

r (total, rate, e

fficiency and

idle time) / va

riable overhea

d (total,

expenditure an

d efficiency) v

ariances

Note: Material

variances with

raw material

stocks need to

be computed

Sales variance

s: sales price v

ariance/ sales

volume

contribution v

ariance

10

2.1.3 Prepare

a statement th

at reconc

iles budgeted c

ontribution

with the actua

l contribution

calcula

ted using mar

ginal costing

The use of var

iances to reco

ncile the

budgeted and

actual contrib

ution that has

been ca

lculated using

marginal costi

ng Accoun

ting for varian

ces in the inte

grated accoun

ting system

10

2.2

Budg

etin

g;

Prep

arat

ion

and

Cont

rol

2.2.1 Explain

how and why

organisations

prepare budg

ets Definit

ions and purp

oses of budge

ting, budget

preparation p

rocess (budge

t period,

budget centre

, budget comm

ittee, budget

manual, princ

ipal budget fa

ctor) 11

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2.2.2 P

repare functio

nal budgets

Functional bud

gets (sales, pro

duction,

material usag

e/purchases,

labour, overh

ead budget

s) 11

2.2.3 P

repare cash b

udgets and

explain the sol

utions for bud

geted cash de

ficits and surpl

uses in the

short and long

run Cash b

udget. Tools f

or short term

and long term

cash deficits

and surpluses

11

2.2.4 Explain

the master bu

dget Linkag

e between bu

dgeted incom

e statem

ent, balance s

heet and cash

flow statem

ent in the mas

ter budget

11

2.2.5 Calculat

e projected sa

les volume

s, revenue and

costs using

forecasting tec

hniques

Time series fo

recasting (reg

ression metho

d and mo

ving average m

ethod), adjust

ing for

seasonality (a

dditive and m

ultiplicative

methods)

11

2.2.6 Explain

feedback and

feed forwar

d controls and

their behavi

oural implicatio

ns Feed fo

rward vs feed

back control

11

2.2.7 Identify d

isadvantages o

f budget

ing including

budget slack

Disadvantage

s of budgeting

including

budget slack

11

2.2.8 Explain

budgeting at d

ifferent

levels of plann

ing of the orga

nisation Strateg

ic, tactical and

operational p

lanning

11

2.2.9 Prepare

and interpret

a flexible

budget and bu

dget variance

Fixed v

s flexible budg

et Budget

ary control sta

tement

11

C. D

ecis

ion

Mak

ing

3.1

Cost

-Vol

ume-

Prof

it A

naly

sis

3.1.1 Comput

e the contribut

ion from

products, serv

ices and activ

ities Concep

t of contributio

n and C:S ratio

12

3.1.2 Comput

e breakeven p

oint and

identify volum

e required for

a given

profit target

Single produc

t: breake

ven analysis /

target profit /

margin

of safety / bre

akeven charts

(traditional,

contribution, p

rofit-volume)

12

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3.

2 Si

ngle

Lim

itin

g Fa

ctor

Dec

isio

ns

3.2.1 Identify t

he optimum

production/sa

les mix for a s

ingle limitin

g factor scena

rio Limitin

g factor analy

sis (contributio

n per limitin

g factor) for a

multi-produc

t company

with one scarc

e resource

12

3.

3 Re

leva

nt

Cost

ing

3.3.1 Identify t

he relevant co

st for short-t

erm decision m

aking Releva

nt (opportunit

y cost, avoida

ble cost,

incremental c

ost) vs non-re

levant costs

(sunk cost, com

mitted cost, n

on-cash flow

cost, common

cost, notional c

osts) 12

3.3.2 Apply re

levant costing

to prepar

e a cost sheet

for decision

making

Relevant cost

of material, la

bour, variable

OH, fix

ed OH 12

3.

4 Lo

ng-T

erm

D

ecis

ion

Mak

ing

3.4.1 Explain

the purpose of

investm

ent appraisal

Objectives of i

nvestment app

raisals,

investment app

raisal process,

time value of

money

13

3.4.2 Comput

e the financia

l feasibility

using differen

t investment a

ppraisal

techniques

Investment app

raisal techniq

ues: Non-di

scounted cash

flow techniqu

es (accoun

ting rate of ret

urn , payback p

eriod) Time va

lue of money –

discounted cash

flow, perpetu

ity Discou

nted cash flow

techniques (d

iscounted

payback perio

d, NPV, IRR)

Working capita

l in investmen

t appraisals

NPV vs IRR

Non-financial f

actors in inve

stment

appraisals

13

D. R

isk

and

Unc

erta

inty

4.

1 In

trod

ucti

on

to R

isk

and

Unc

erta

inty

4.1.1 Explain

the concept of

risk and

uncertainty

Risk and unce

rtainty

14

4.

2 Ba

sic

Dec

isio

n-M

akin

g To

ols

Und

er R

isk

4.2.1 Calculat

e summary me

asures of

central tenden

cy and dispers

ion for

both grouped

and ungroupe

d data Arithm

etic mean, me

dian, mode, ra

nge, varianc

e, standard dev

iation and coe

fficient

of variation for

both ungroup

ed and

grouped data

14

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4.2.2 Demons

trate the use o

f probab

ility in decisio

n making

Probability (co

mplementary

law, addition

law and multi

plication law)

Normal distrib

ution 14

4.2.3 Analyse

outcomes usin

g the basic d

ecision tools u

nder risk

Maxi-max, max

i-min, mini-max

regret

criteria

Expected valu

e and pay off t

able Limitat

ions of expect

ed values

14

E. W

orki

ng

Capi

tal

Man

agem

ent

5.1

Mat

eria

l M

anag

emen

t 5.1.1 Il

lustrate the in

ventory contr

ol proces

s Invento

ry control ove

rview; orderin

g, purcha

sing, receiving

, storing and i

ssuing,

storing metho

ds; centralised

vs decent

ralised storing

, periodic vs pe

rpetual

stock taking

15

5.1.2 Calculat

e inventory re

lated costs fo

r a manufactur

ing organis

ation Purcha

sing cost, orde

ring cost, hold

ing cost,

stock-out cost

15

5.1.3 Calculat

e inventory co

ntrol levels a

nd EOQ

Inventory cont

rol levels (re-o

rder level,

maximum sto

ck level, minim

um stock leve

l) Econom

ic order quant

ity 15

5.1.4 Calculat

e the cost of iss

ued stocks

and closing in

ventory using

FIFO, L

IFO and weigh

ted average co

st method

s Issuing

and valuation

: FIFO method,

LIFO method

, weighted ave

rage cost meth

ods 15

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Business Level II – Management Accounting xiv

Action verbs checklist

Knowledge Process Verb List Verb Definitions

Define Describe exactly the nature, scope or meaning Draw Produce (a picture or diagram) Identify Recognise, establish or select after consideration List Write the connected items one below the other Relate To establish logical or causal connections

Tier – 1 Remember Recall important information

State Express something definitely or clearly Calculate/Compute Make a mathematical computation Discuss Examine in detail by argument showing different aspects, for the purpose of arriving at a conclusion Explain Make a clear description in detail revealing relevant facts Interpret Present in understandable terms or to translate Recognise To show validity or otherwise, using knowledge or contextual experience Record Enter relevant entries in detail

Tier – 2 Comprehension Explain important information

Summarise Give a brief statement of the main points (in facts or figures)

Draft Version

Introduction xv

Knowledge Process Verb List Verb Definitions

Apply Put to practical use Assess Determine the value, nature, ability or quality Demonstrate Prove, especially with examples Graph Represent by means of a graph Prepare Make ready for a particular purpose Prioritise Arrange or do in order of importance Reconcile Make consistent with another

Tier – 3 Application Use knowledge in a setting other than the one in which it was learned/solve close-ended problems

Solve To find a solution through calculations and/or explanations Analyse Examine in detail in order to determine the solution or outcome Compare Examine for the purpose of discovering similarities Contrast Examine in order to show unlikeness or differences Differentiate Constitute a difference that distinguishes something

Tier – 4 Analysis Draw relations among ideas and to compare and contrast/solve open-ended problems Outline Make a summary of significant features

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Business Level II – Management Accounting xvi

Knowledge Process Verb List Verb Definitions

Advise Offer suggestions about the best course of action in a manner suited to the recipient Convince To persuade others to believe something using evidence and/or argument Criticise Form and express a judgment Evaluate To determine the significance by careful appraisal Recommend A suggestion or proposal as to the best course of action Resolve Settle or find a solution to a problem or contentious matter

Tier – 5 Evaluate Formation of judgments and decisions about the value of methods, ideas, people or products

Validate Check or prove the accuracy Compile Produce by assembling information collected from various sources Design Devise the form or structure according to a plan Develop To disclose, discover, perfect or unfold a plan or idea

Tier – 6 Synthesis Solve unfamiliar problems by combining different aspects to form a unique or novel solution Propose To form or declare a plan or intention for consideration or adoption

Draft Version

Draft Version

2 CA Sri Lanka

Draft Version

3

Knowledge Component A Cost accounting 1.1 Introduction to cost and management accounting

1.1.1 Explain the difference between the role of a management accountant and the financial accountant 1.1.2 Explain the role of management accountant to support planning, controlling and decision making

INTRODUCTION This chapter provides an introduction to Management Accounting. We look at data and information and introduce you to cost accounting and the differences between financial accounting and management accounting. We also outline the managerial processes of planning, control and decision making. Please note that this section is for reference only and will not be tested in the examination.

C H

A P

T E

R

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BL6 | Chapter 1: Introduction to Management Accounting

4 CA Sri Lanka

CHAPTER CONTENTS

LEARNING OUTCOME1 Definitions of management accounting and cost accounting 1.1.12 Nature of management accounting information 1.1.13 Objective and scope of management accounting, policies and plans to achieve desired objectives of management 1.1.2

4 Levels of planning and controlling (operational, management and corporate level) 1.1.2

1 Definitions of management accounting and cost accounting

1.1 Financial accounts and management accounts

Financial accounting systems ensure that the assets and liabilities of a business are properly accounted for and provide information about profits and so on to shareholders and to other interested parties. Management accounting systems provide information specifically for the use of managers within an organisation. Financial management information provides a common source from which information is drawn for two groups of people. (a) Financial accounts are prepared for individuals external to an organisation: shareholders, customers, suppliers, tax authorities, employees. (b) Management accounts are prepared for internal managers of an organisation. The data used to prepare financial accounts and management accounts is the same. The differences between the financial accounts and the management accounts arise because the data is analysed differently.

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1.2 Financial accounts versus management accounts

Financial accounts Management accounts Financial accounts detail the performance of an organisation over a defined period and the state of affairs at the end of that period. Management accounts are used to aid management to record, plan and control the organisation's activities and to help the decision-making process. Limited liability companies must, by law, prepare financial accounts. There is no legal requirement to prepare management accounts. The format of published financial accounts is determined by local law, by International Accounting Standards and International Financial Reporting Standards. In principle the accounts of different organisations can therefore be easily compared.

The format of management accounts is entirely at management discretion: no strict rules govern the way they are prepared or presented. Each organisation can devise its own management accounting system and format of reports. Financial accounts concentrate on the business as a whole, aggregating revenues and costs from different operations, and are an end in themselves. Management accounts can focus on specific areas of an organisation's activities. Information may be produced to aid a decision rather than to be an end-product of a decision. Most financial accounting information is of a monetary nature. Management accounts incorporate non-monetary measures. Management may need to know, for example, tons of aluminium produced, monthly machine hours, or miles travelled by sales people. Financial accounts present an essentially historic picture of past operations. Management accounts are both an historical record and a future planning tool.

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QUESTION Management accounts

Identify which of the following statements about management accounts is/are true. (i) There is a legal requirement to prepare management accounts. (ii) The format of management accounts is largely determined by law. (iii) They serve as a future planning tool and are not used as a historical record. A (i) and (ii) B (ii) and (iii) C (iii) only D None of the statements are correct. ANSWER The answer is D. Statement (i) is incorrect. Limited liability companies must, by law, prepare financial accounts. The format of published financial accounts is determined by law. Statement (ii) is therefore incorrect. Management accounts do serve as a future planning tool but they are also useful as a historical record of performance. Therefore all three statements are incorrect and D is the correct answer. 1.3 Cost accounts Cost accounting and management accounting are terms which are often used interchangeably. It is not correct to do so. Cost accounting is part of management accounting. Cost accounting provides a bank of data for the management accountant to use. Cost accounting is concerned with the following. Preparing statements (eg budgets, costing) Cost data collection Applying costs to inventory, products and services Cost accounting involves gathering cost information and assigning costs to various objects or entities. Cost accounting includes devising budgets and standard costs, and analysing variances associated with these.

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Management accounting is concerned with the following. Using financial data and communicating it as information to users Management accounting focuses on the use of accounting techniques to create value, for example through better informed decision-making, rather than to comply with regulation.

1.3.1 Uses of cost accounts Below is a list of the possible uses of cost accounts: (a) The cost of goods produced or services provided. (b) The cost of a department or work section. (c) What revenues have been received. (d) The profitability of a product, a service, a department, or the organisation in total. (e) Setting prices when based on the costs of sales. (f) The value of inventories of goods (raw materials, work-in-progress, finished goods) that are still held in store at the end of a period, thereby aiding the preparation of a statement of financial position of the company's assets and liabilities. (g) Future costs of goods and services (costing is an integral part of budgeting (planning) for the future). (h) How actual costs compare with budgeted costs. If an organisation plans for its revenues and costs to be a certain amount, but they actually turn out differently, the differences can be measured and reported. Management can use these reports as a guide to whether corrective action (or 'control' action) is needed to sort out a problem revealed by these differences between budgeted and actual results. This system of control is often referred to as budgetary control. It would be wrong to suppose that cost accounting systems are restricted to manufacturing operations, although they are probably more fully developed in this area of work. Service industries, government departments and welfare activities can all make use of cost accounting information. Within a manufacturing organisation, the cost accounting system should be applied not only to manufacturing but also to administration, selling and distribution, research and development and all other departments.

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2 Nature of management accounting information

2.1 Data and information

Data is the raw material for data processing. Data relates to facts, events and transactions and so forth. Information is data that has been processed in such a way as to be meaningful to the person who receives it. Information is anything that is communicated. Information is sometimes referred to as processed data. The terms 'information' and 'data' are often used interchangeably. It is important to understand the difference between these two terms. Researchers who conduct market research surveys might ask members of the public to complete questionnaires about a product or a service. These completed questionnaires are data; they are processed and analysed in order to prepare a report on the survey. This resulting report is information and may be used by management for decision-making purposes. 2.2 Qualities of good information Good information should be relevant, complete, accurate, clear; it should inspire confidence, it should be appropriately communicated, its volume should be manageable, it should be timely and its cost should be less than the benefits it provides. Let us look at those qualities in more detail. (a) Relevance. Information must be relevant to the purpose for which a manager wants to use it. In practice, far too many reports fail to 'keep to the point' and contain irrelevant paragraphs which only annoy the managers reading them. (b) Completeness. Information users should have all the information they need to do their job properly. If they do not have a complete picture of the situation, they might well make bad decisions. (c) Accuracy. Information should obviously be accurate; using incorrect information could have serious and damaging consequences. However, information should only be accurate enough for its purpose. There is no need to go into unnecessary detail for pointless accuracy. (d) Clarity. Information must be clear to the user. If the user does not understand it properly, he or she cannot use it properly. Lack of clarity is one of the causes of a breakdown in communication. It is, therefore, important to choose the most appropriate presentation medium or channel of communication.

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(e) Confidence. Information must be trusted by the managers who are expected to use it. However, not all information is certain. Some information has to be certain, especially operating information, for example, related to a production process. Strategic information, especially relating to the environment, is uncertain. However, if the assumptions underlying it are clearly stated, this might enhance the confidence with which the information is perceived. (f) Communication. Within any organisation, individuals are given the authority to do certain tasks, and they must be given the information they need to do them. Office managers might be made responsible for controlling expenditures in the office, and given a budget expenditure limit for the year. As the year progresses, the managers might try to keep expenditure in check but unless they are told throughout the year the current total expenditure to date, they will find it difficult to judge whether they are keeping within budget or not. (g) Volume. There are physical and mental limits to what a person can read, absorb and understand properly before taking action. An enormous mountain of information, even if it is all relevant, cannot be handled. Reports to management must therefore be clear and concise; in many systems, control action works basically on the 'exception' principle. (h) Timing. Information which is not available until after a decision is made will be useful only for comparisons and longer-term control, and may serve no purpose even then. Information prepared too frequently can be a serious disadvantage. If, for example, a decision is taken at a monthly meeting about a certain aspect of a company's operations, information to make the decision is only required once a month; weekly reports would be a time-consuming waste of effort. (i) Channel of communication. There are occasions when using one particular method of communication will be better than others. For example, job vacancies should be announced in a medium where they will be brought to the attention of the people most likely to be interested. The channel of communication might be the company's in-house journal, a national or local newspaper, a professional magazine, a job centre or school careers office. Some internal memoranda may be better sent by email. Some information is best communicated informally by telephone or word-of-mouth, whereas other information ought to be formally communicated in writing or figures. (j) Cost. Information should have some value, otherwise it would not be worth the cost of collecting and filing it. The benefits obtainable from the information must also exceed the costs of acquiring it. Whenever management is trying to decide whether or not to produce information for a

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particular purpose (for example, whether to computerise an operation or to build a financial planning model) a cost/benefit study ought to be made. You may find this graph helpful. The point is that perfect information probably isn't worth paying for. Rs Marginal cost

Marginal benefit

Perfect informationOptimum

Quality of information Figure 2.1: Cost/benefit of obtaining information

QUESTION Value of information The value of information lies in the action taken as a result of receiving it. Required

List the questions you might ask in order to make an assessment of the value of information. ANSWER (a) What information is provided? (b) What is it used for? (c) Who uses it? (d) How often is it used? (e) Does the frequency with which it is used coincide with the frequency with which it is provided? (f) What is achieved by using it? (g) What other relevant information is available which could be used instead?

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An assessment of the value of information can be derived in this way, and the cost of obtaining it should then be compared against this value. On the basis of this comparison, it can be decided whether certain items of information are worth having. It should be remembered that there may also be intangible benefits which may be harder to quantify. 2.3 Why is information important? Consider the following problems and the information which management needs to solve them. (a) A company wishes to launch a new product. The company's pricing policy is to charge cost plus 20%. What should the price of the product be? (b) An organisation's widget-making machine has a fault. The organisation has to decide whether to repair the machine, buy a new machine or hire a machine. What does the organisation do if its aim is to control costs? (c) A firm is considering offering a discount of 2% to those customers who pay an invoice within seven days of the invoice date and a discount of 1% to those customers who pay an invoice within eight to fourteen days of the invoice date. How much will this discount offer cost the firm? In solving these and a wide variety of other problems, management need information. (a) In problem (a) above, management would need information about the cost

of the new product. (b) Faced with problem (b), management would need information on the cost of repairing, buying and hiring the machine. (c) To calculate the cost of the discount offer described in (c), information would be required about current sales settlement patterns and expected changes to the pattern if discounts were offered. The successful management of any organisation depends on information: non-profit seeking organisations such as charities, clubs and local authorities need information for decision making and for reporting the results of their activities, just as multi-nationals do. For example, a tennis club needs to know the cost of undertaking its various activities so that it can determine the amount of annual subscription it should charge its members.

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2.4 What type of information is needed? Most organisations require the following types of information. Financial Non-financial A combination of financial and non-financial information 2.4.1 Example: Financial and non-financial information Suppose that the management of ABC Co have decided to provide a canteen for their employees. (a) The financial information required by management might include canteen staff costs, costs of subsidising meals, capital costs, costs of heat and light and so on. (b) The non-financial information might include management comment on the effect on employee morale of the provision of canteen facilities, details of the number of meals served each day, meter readings for gas and electricity and attendance records for canteen employees. ABC Co could now combine financial and non-financial information to calculate the average cost to the company of each meal served, thereby enabling them to predict total costs depending on the number of employees in the work force. 2.4.2 Non-financial information Most people probably consider that management accounting is only concerned with 'financial information' and that 'people' do not matter. This is, nowadays, a long way from the truth. For example, managers of business organisations need to know whether employee morale has increased due to introducing a canteen, whether the bread from particular suppliers is fresh and the reason why the canteen staff are demanding a new dishwasher. This type of non-financial information will play its part in planning, controlling and decision making and is therefore just as important to management as financial information. Non-financial information must therefore be monitored as carefully, recorded as accurately and taken into account as fully as financial information. There is little point in a careful and accurate recording of total canteen costs if the recording of the information on the number of meals eaten in the canteen is uncontrolled and therefore produces inaccurate information. While management accounting is mainly concerned with the provision of financial information to aid planning, control and decision making, the management accountant cannot ignore non-financial influences and should qualify the information provided with non-financial matters as appropriate.

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3 Objective and scope of management accounting, policies and plans to achieve desired objectives of management

3.1 Objectives of organisations An objective is the aim or goal of an organisation (or an individual). Note that, in practice, the terms objective, goal and aim are often used interchangeably. A strategy is a possible course of action that might enable an organisation (or an individual) to achieve its objectives. The two main types of organisation that you are likely to come across in practice are as follows. Profit making Non-profit seeking The main objective of profit-making organisations is to maximise profits. A secondary objective of profit-making organisations might be to increase output of its goods/services. The main objective of non-profit seeking organisations is usually to provide goods and services. A secondary objective of non-profit seeking organisations might be to minimise the costs involved in providing the goods/services. In conclusion, the objectives of an organisation might include one or more of the following. Maximise profits Maximise revenue Maximise shareholder value Increase market share Minimise costs Remember that the type of organisation concerned will have an impact on its objectives. 3.2 Strategy and organisational structure There are two schools of thought on the link between strategy and organisational structure. Structure follows strategy Strategy follows structure Let's consider the first idea that structure follows strategy. What this means is that organisations develop a structure in order to implement a strategy. Or do they? The second school of thought suggests that strategy follows structure. This side of the argument suggests that the strategy of an organisation is determined or influenced by the structure of the organisation. The structure of the organisation therefore limits the number of strategies available.

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We could explore these ideas in much more detail, but for the purposes of your management accounting studies, you really just need to be aware that there is a link between strategy and the structure of an organisation. 3.3 Long-term strategic planning Long-term strategic planning, also known as corporate planning, involves selecting appropriate strategies so as to prepare a long-term plan to attain the objectives.

The time span covered by a long-term plan depends on the organisation, the industry in which it operates and the particular environment involved. Typical periods are 2, 5, 7 or 10 years although longer periods are frequently encountered. Long-term strategic planning is a detailed, lengthy process, essentially incorporating three stages and ending with a corporate plan. Figure 2.2 provides an overview of the process and shows the link between short-term and long-term planning. 3.4 Short-term tactical planning The long-term corporate plan serves as the long-term framework for the organisation as a whole; for operational purposes it is necessary to convert the corporate plan into a series of short-term plans, usually covering one year, which relate to sections, functions or departments. The annual process of short-term planning should be seen as stages in the progressive fulfilment of the corporate plan: each short-term plan steers the organisation towards its long-term objectives. It is, therefore, vital that, to obtain the maximum advantage from short-term planning, some sort of long-term plan exists.

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The planning process

THE

ASSESSMENT

STAGE

THE

OBJECTIVE

STAGE

THE

EVALUATION

STAGE

THE

CORPORATE

PLAN

Assess the

external

environment

Assess the

organisationAssess the

future

Assess

expectations

Evaluate

corporate

objectives

Consider

alternative

ways of achieving

objectives

Agree a

corporate

plan

Production

planning

Resource

planning

Product

planning

Research and

development

planning

Detailed operational plans which implement the corporate plan on a monthly,

quarterly or annual basis. Operational plans include short-term budgets,

standards and objectives.

LONG-

TERM

STRATEGY

PLANNING

SHORT-

TERM

PLANNING

Figure 2.2: The planning process

3.5 Types of information

Information within an organisation can be analysed into the three levels assumed in Anthony's hierarchy: strategic, tactical and operational. 3.6 Strategic information Strategic information is used by senior managers to plan the objectives of their organisation, and to assess whether the objectives are being met in practice. Such information includes overall profitability, the profitability of different segments of the business, capital equipment needs and so on. Strategic information, therefore, has the following features. It is derived from both internal and external sources. It is summarised at a high level. It is relevant to the long term. It deals with the whole organisation (although it might go into some detail).

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It is often prepared on an ad hoc basis. It is both quantitative and qualitative. It cannot provide complete certainty, given that the future cannot be predicted. 3.6.1 Tactical information

Tactical information is used by middle management to decide how the resources of the business should be employed, and to monitor how they are being and have been employed. Such information includes productivity measurements (output per man hour or per machine hour), budgetary control or variance analysis reports, and cash flow forecasts and so on. Tactical information therefore has the following features. It is primarily generated internally. It is summarised at a lower level. It is relevant to the short and medium term. It describes or analyses activities or departments. It is prepared routinely and regularly. It is based on quantitative measures. 3.6.2 Operational information

Operational information is used by 'front-line' managers such as foremen or head clerks to ensure that specific tasks are planned and carried out properly within a factory or office and so on. In the payroll office, for example, information at this level will relate to day-rate labour and will include the hours worked each week by each employee, the rate of pay per hour, details of the deductions; and, for the purpose of wages analysis, details of the time each person spent on individual jobs during the week. In this example, the information is required weekly, but more urgent operational information, such as the amount of raw materials being input to a production process, may be required daily, hourly or, in the case of automated production, second-by-second. Operational information has the following features. It is derived almost entirely from internal sources. It is highly detailed, being the processing of raw data. It relates to the immediate term, and is prepared constantly, or very frequently. It is task-specific and largely quantitative.

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4 Levels of planning and controlling (operational, management and corporate level)

4.1 Planning

Information for management is likely to be used for planning, control and decision making. An organisation should never be surprised by developments which occur gradually over an extended period of time because the organisation should have implemented a planning process. Planning involves the following. Establishing objectives Selecting appropriate strategies to achieve those objectives Planning, therefore, forces management to think ahead systematically in both the short term and the long term. 4.2 Control Remember that we said that information for management is likely to be used for planning, control and decision making. We have just looked at planning. Now we'll look at control. There are two stages in the control process. (a) The performance of the organisation, as set out in the detailed operational plans, is compared with the actual performance of the organisation on a regular and continuous basis. Any deviations from the plans can then be identified and corrective action taken. (b) The corporate plan is reviewed in the light of the comparisons made and any changes in the parameters on which the plan was based (such as new competitors, government instructions and so on) to assess whether the objectives of the plan can be achieved. The plan is modified as necessary before any serious damage to the organisation's future success occurs.

Effective control is therefore not practical without planning, and planning without control is pointless. An established organisation should have a system of management reporting that produces control information in a specified format at regular intervals. Smaller organisations may rely on informal information flows or ad hoc reports, produced as required.

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4.3 Decision making Management is decision taking. Managers of all levels within an organisation take decisions. Decision making always involves a choice between alternatives and it is the role of the management accountant to provide information so that management can reach an informed decision. It is, therefore, vital that the management accountant understands the decision-making process so that he/she can supply the appropriate type of information. 4.3.1 Decision-making process

Make the choice/decision.

State the expected outcome

and check that the expected

outcome is in keeping with

the overall goals or objectives.

Identify goals,

objectives or problems.

Identify alternative solutions/

opportunities which might

contribute towards achieving

them.

Collect and analyse relevant

data about each alternative.

Implement the decision.

Obtain data about actual results.

Compare actual results with

the expected outcome.

Evaluate achievements.

PLANNING

CONTROL

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7 Figure 2.3: The decision-making process

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4.4 Anthony's view of management activity Anthony divides management activities into strategic planning, management control and operational control. R N Anthony, a leading writer on organisational control, has suggested that the activities of planning, control and decision making should not be separated since all managers make planning and controlling decisions. He has identified three types of management activity. (a) Strategic planning: 'the process of deciding on objectives of the organisation, on changes in these objectives, on the resources used to attain these objectives, and on the policies that are to govern the acquisition, use and disposition of these resources.' (b) Tactical (or management) control: 'the process by which managers assure that resources are obtained and used effectively and efficiently in the accomplishment of the organisation's objectives.' (c) Operational control: 'the process of assuring that specific tasks are carried out effectively and efficiently.' 4.4.1 Strategic planning

Strategic plans are those which set or change the objectives, or strategic targets of an organisation. They would include such matters as the selection of products and markets, the required levels of company profitability, the purchase and disposal of subsidiary companies or major non-current assets and so on. 4.4.2 Tactical/management control Whilst strategic planning is concerned with setting objectives and strategic targets, management control is concerned with decisions about the efficient and effective use of an organisation's resources to achieve these objectives or targets. (a) Resources, often referred to as the '4 Ms' (manpower, materials, machines and money). (b) Efficiency in the use of resources means that optimum output is achieved from the input resources used. It relates to the combinations of manpower, land and capital (for example how much production work should be automated) and to the productivity of labour, or material usage. (c) Effectiveness in the use of resources means that the outputs obtained are in line with the intended objectives or targets.

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4.4.3 Operational control The third, and lowest, tier in Anthony's hierarchy of decision making consists of operational control decisions. As we have seen, operational control is the task of ensuring that specific tasks are carried out effectively and efficiently. Just as 'management control' plans are set within the guidelines of strategic plans, so too are 'operational control' plans set within the guidelines of both strategic planning and management control. Consider the following. (a) Senior management may decide that the company should increase sales by 5% per annum for at least five years – a strategic plan. (b) The sales director and senior sales managers will make plans to increase sales by 5% in the next year, with some provisional planning for future years. This involves planning direct sales resources, advertising, sales promotion and so on. Sales quotas are assigned to each sales territory – a

tactical plan (management control). (c) The manager of a sales territory specifies the weekly sales targets for each sales representative. This is operational planning: individuals are given tasks which they are expected to achieve. Although we have used an example of selling tasks to describe operational control, it is important to remember that this level of planning occurs in all aspects of an organisation's activities, even when the activities cannot be scheduled nor properly estimated because they are non-standard activities (such as repair work, answering customer complaints). The scheduling of unexpected or ad hoc work must be done at short notice, which is a feature of much operational planning. In the repairs department, for example, routine preventive maintenance can be scheduled, but breakdowns occur unexpectedly and repair work must be scheduled and controlled 'on the spot' by a repairs department supervisor. 4.5 Management control systems A management control system is a system which measures and corrects the performance of activities of subordinates in order to make sure that the objectives of an organisation are being met and the plans devised to attain them are being carried out. The management function of control is the measurement and correction of the activities of subordinates in order to make sure that the goals of the organisation, or planning targets, are achieved.

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The basic elements of a management control system are as follows. Planning: deciding what to do and identifying the desired results Recording the plan, which should incorporate standards of efficiency or targets Carrying out the plan and measuring actual results achieved Comparing actual results against the plans Evaluating the comparison, and deciding whether further action is necessary Where corrective action is necessary, this should be implemented Traditional cost accounting information is, in general, unsuitable for decision making. The information required for decision making is different from the information provided by conventional cost accounts. Decision-making information should be relevant. However, absorption costing (a widely-used method of costing products and services which we will be looking at later) provides information that in many situations is misleading and irrelevant. All decision making is concerned with the future and so there will always be some degree of uncertainty surrounding the possible outcomes of a decision. Information for decision making should therefore incorporate uncertainty in some way. The methods of incorporating uncertainty are outside the scope of this syllabus, but you should realise that if cost accounting information does not take account of uncertainty it is unsuitable for decision making. If an attempt to incorporate uncertainty is made the information should be more suitable for decision making but can never be risk free. QUESTION Uncertainty

State any factors which contribute to the uncertainty an organisation might face. ANSWER Here are a few suggestions. You probably thought of others. The actions of competitors Inflation Interest rate changes New government legislation Possible shortages of material or labour Possible industrial disputes

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Data is the raw material for data processing. Data relates to facts, events and transactions and so forth. Information is data that has been processed in such a way as to be meaningful to the person who receives it. Information is anything that is communicated. Good information should be relevant, complete, accurate, clear; it should

inspire confidence, it should be appropriately communicated, its volume should be manageable, it should be timely and its cost should be less than the benefits it provides. Information for management is likely to be used for planning, control and

decision making. An objective is the aim or goal of an organisation (or an individual). Note that, in practice, the terms objective, goal and aim are often used interchangeably. A

strategy is a possible course of action that might enable an organisation (or an individual) to achieve its objectives. Anthony divides management activities into strategic planning, management

control and operational control. A management control system is a system which measures and corrects the performance of activities of subordinates in order to make sure that the objectives of an organisation are being met and the plans devised to attain them are being carried out. Information within an organisation can be analysed into the three levels assumed in Anthony's hierarchy: strategic, tactical and operational. Financial accounting systems ensure that the assets and liabilities of a business are properly accounted for, and provide information about profits and so on to shareholders and to other interested parties. Management accounting systems provide information specifically for the use of managers within an organisation. Cost accounting and management accounting are terms which are often used interchangeably. It is not correct to do so. Cost accounting is part of

management accounting. Cost accounting provides a bank of data for the management accountant to use.

Cost accounting information is, in general, unsuitable for decision making.

CHA

PTER

RO

UN

DU

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1 Define the terms data and information. 2 The four main qualities of good information are:

………………………. ………………………. ………………………. ……………………….

3 In terms of management accounting, information is most likely to be used for: (1) ………………………. (2) ………………………. (3) ………………………. 4 A strategy is the aim or goal of an organisation. True False 5 State the main objective of the following organisations: A Profit-making B Non-profit seeking 6 List the three types of management activity identified by R N Anthony. (1) ………………………. (2) ………………………. (3) ………………………. 7 A management control system is A A possible course of action that might enable an organisation to achieve its objectives B A collective term for the hardware and software used to drive a database system C A set up that measures and corrects the performance of activities of subordinates in order to make sure that the objectives of an organisation are being met and their associated plans are being carried out D A system that controls and maximises the profits of an organisation 8 List six differences between financial accounts and management accounts. 9 Information provided by conventional cost accounts is ideal for decision making. True or false?

PRO

GR

ESS

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1 Data is the raw material for data processing. Information is data that has been processed in such a way as to be meaningful to the person who receives it. Information is anything that is communicated.

2 Relevance Accuracy Completeness Clarity

3 (1) Planning (2) Control (3) Decision making 4 False. This is the definition of an objective. A strategy is a possible course of action that might enable an organisation to achieve its objectives. 5 A Profit-making = maximise profits B Non-profit seeking = provide goods and services 6 (1) Strategic planning (2) Management control (3) Operational control 7 The answer is C. 8 See Section 3.2 9 False

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Knowledge Component A Cost accounting 1.2 Cost classification 1.2.1 Identify key components of production cost 1.2.2 Explain different cost classifications and identify different cost categories 1.2.3 Calculate appropriate cost estimations having identified the cost behaviour

INTRODUCTION The classification of costs as either direct or indirect, for example, is essential in the costing method used by an organisation to determine the cost of a unit of product or service. The fixed and variable cost classifications, on the other hand, are important in absorption and marginal costing, and behaviour. We will cover behaviour in this chapter, and you will meet the other topics as we progress through the Study Text. This chapter therefore acts as a foundation stone for a number of other chapters and hence an understanding of the concepts covered in it is vital before you move on.

C H

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CHAPTER CONTENTS

LEARNING OUTCOME1 Components classified under production and service cost 1.2.12 Direct and indirect costs 1.2.13 Cost classification for profit measurement and stock valuation (manufacturing and non-manufacturing cost) 1.2.2

4 Cost classification for profit measurement and stock valuation (product cost and periodic cost) 1.2.25 Behavioural cost classification – fixed, variable and semi-variable costs 1.2.26 Cost classification for decision making – relevant cost and non-relevant cost 1.2.27 Cost classification for decision making – controllable cost and non-controllable cost 1.2.28 Cost estimation using high-low method 1.2.39 Cost estimation using scatter diagrams and regression method 10 Cost estimation using correlation coefficient and rank correlation 1.2.31.2.3

1 Components classified under production and service cost The total cost of making a product or providing a service consists of the following elements. (a) Cost of materials (b) Cost of the wages and salaries (labour costs) (c) Cost of other expenses (i) Rent and rates (ii) Electricity and gas bills (iii) Depreciation

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2 Direct and indirect costs

2.1 Direct costs – materials, labour and direct expenses A direct cost is a cost that can be traced in full to the product, service or department that is being costed. Materials, labour costs and other expenses can be classified as either direct costs or indirect costs. (a) Direct material costs are the costs of materials that are known to have been used in making and selling a product (or even providing a service). (b) Direct labour costs are the specific costs of the workforce used to make a product or provide a service. Direct labour costs are established by measuring the time taken for a job, or the time taken in 'direct production work'. (c) Other direct expenses are those expenses that have been incurred in full as a direct consequence of making a product, providing a service or running a department. 2.2 Indirect costs – production overheads An indirect cost (or overhead) is a cost that is incurred in the course of making a product, providing a service or running a department, but which cannot be traced directly and in full to the product, service or department. Examples of indirect costs include supervisors' wages, cleaning materials and buildings insurance. These overheads can be incurred in the following categories as follows: Variable production overheads are indirect costs of manufacture which increase as production volumes increase. Indirect costs can be materials, labour or other types of cost. An example is electricity used to run production machinery. Fixed production overheads are indirect costs of manufacture which remain unchanged as production volume increases. These overheads are generally incurred at the beginning of production. Examples include factory rent and rates. Variable non-production overheads are indirect costs incurred after manufacture which increase as production volumes increase. Example are distribution costs. Fixed non-production overheads are indirect costs incurred after manufacture which remain the same as production volumes increase. Examples are a sales manager or marketing department.

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2.3 Analysis of total cost

Cost category Example Direct materials Components Direct labour Assembly Direct expenses Packaging Total direct costs of production Variable production overheads Machine running costs Fixed production overheads Factory canteen or production director Total direct and indirect costs of production Variable non-production overheads Delivery cost Fixed non-production overheads Sales director Total cost Each of these cost categories is discussed in more detail in the next section. In summary, Total direct cost of production = direct materials + direct labour + direct expenses Total cost of production = Total direct costs of production (as above) + variable production overheads + fixed production overheads Total cost = Total cost of production (as above) + variable non-production overheads + fixed non-production overheads

3 Cost classification for profit measurement and stock valuation (manufacturing and non-manufacturing cost)

3.1 Classification by function

Classification by function involves classifying costs as production/ manufacturing costs, administration costs or marketing/selling and distribution costs. Direct expenses are any expenses which are incurred on a specific product other than direct material cost and direct wages. Direct material is all material becoming part of the product (unless used in negligible amounts and/or having negligible cost).

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Direct material costs are charged to the product as part of the prime cost. Examples of direct material are as follows. (a) Component parts, specially purchased for a particular job, order or process. (b) Part-finished work which is transferred from department 1 to department 2. This becomes finished work of department 1 and a direct material cost in department 2. (c) Primary packing materials such as cartons and boxes. Direct expenses are charged to the product as part of the prime cost. Examples of direct expenses are as follows. The hire of tools or equipment for a particular job Maintenance costs of tools, fixtures and so on Direct expenses are also referred to as chargeable expenses. Direct wages are all wages paid for labour (either as basic hours or as overtime) expended on work on the product itself.

Direct wages costs are charged to the product as part of the prime cost. Examples of groups of labour receiving payment as direct wages are as follows. (a) Workers engaged in altering the condition or composition of the product. (b) Inspectors, analysts and testers specifically required for such production. (c) Foremen, shop clerks and anyone else whose wages are specifically

identified. Two trends may be identified in direct labour costs. The ratio of direct labour costs to total product cost is falling, as the use of machinery increases; depreciation charges hence increase. Skilled labour costs and sub-contractor costs are increasing, as unskilled labour costs decrease. 3.2 Production overhead Production includes all indirect material costs, indirect wages and indirect expenses incurred in the factory from receipt of the order until its completion.

Production overhead includes the following. (a) Indirect materials which cannot be traced in the finished product. Consumable stores, eg material used in negligible amounts

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(b) Indirect wages, meaning all wages not charged directly to a product. Wages of non-productive personnel in the production department, eg foremen (c) Indirect expenses (other than material and labour) not charged directly to production. (i) Rent, rates and insurance of a factory (ii) Depreciation, fuel, power, maintenance of plant, machinery and buildings In a 'traditional' costing system for a manufacturing organisation, costs are classified as follows. (a) Production or manufacturing costs. These are costs associated with the factory. (b) Administration costs. These are costs associated with general office departments. This is all indirect material costs, wages and expenses incurred in the direction, control and administration of an undertaking. Examples of administration overhead are as follows. Depreciation of office buildings and equipment Office salaries, including salaries of directors, secretaries and accountants Rent, rates, insurance, lighting, cleaning, telephone charges and so on (c) Marketing or selling and distribution costs. These are costs associated with sales, marketing, warehousing and transport departments. Classification in this way is known as classification by function. Expenses that do not fall fully into one of these classifications might be categorised as

general overheads or even listed as a classification on their own (for example, research and development costs). Selling overhead is all indirect materials, costs, wages and expenses incurred in promoting sales and retaining customers. Examples of selling overhead are as follows. Printing and stationery, such as catalogues and price lists Salaries and commission of salesmen, representatives and sales department staff Advertising and sales promotion, market research Rent, rates and insurance of sales offices and showrooms, bad debts and so on Distribution overhead is all indirect material costs, wages and expenses incurred in making the packed product ready for despatch and delivering it to the customer.

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Examples of distribution overhead are as follows. Cost of packing cases Wages of packers, drivers and despatch clerks Insurance charges, rent, rates, depreciation of warehouses and so on QUESTION Direct labour cost A direct labour employee's wage in week 5 consists of the following. Rs (a) Basic pay for normal hours worked, 36 hours at Rs. 400 per hour =14,400 (b) Pay at the basic rate for overtime, 6 hours at Rs. 400 per hour = 2,400 (c) Overtime shift premium, with overtime paid at time-and-a-quarter ¼ 6 hours Rs. 400 per hour = 600 (d) A bonus payment under a group bonus (or 'incentive') scheme: bonus for the month = 3,000 Total gross wages in week 5 for 42 hours of work 20,400 Required

Calculate the direct labour cost for this employee in week 5. A Rs. 14,400 B Rs. 16,800 C Rs. 19,800 D Rs. 20,400 ANSWER Let's start by considering a general approach to answering multiple-choice questions (MCQs). In a numerical question like this, the best way to begin is to ignore the available options and work out your own answer from the available data. If your solution corresponds to one of the four options, then mark this as your chosen answer and move on. Don't waste time working out whether any of the other options might be correct. If your answer does not appear among the available options, then check your workings. If it still does not correspond to any of the options then you need to take a calculated guess. Do not make the common error of simply selecting the answer which is closest to yours. The best thing to do is to first eliminate any answers which you know or suspect are incorrect. For example you could eliminate C and D because you know that group bonus schemes are usually indirect costs. You are then left with a choice between A and B, and at least you have now improved your chances if you really are guessing. The correct answer is B because the basic rate for overtime is a part of direct wages cost. It is only the overtime premium that is usually regarded as an overhead or indirect cost.

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3.3 Full cost of sales In costing a small product made by a manufacturing organisation, direct costs are usually restricted to some of the production costs. A commonly found build-up of costs is therefore as follows. Rs Production costs Direct materials A Direct wages B Direct expenses C Prime cost A+B+C Production overheads D Full factory cost A+B+C+D Administration costs E Selling and distribution costs F Full cost of sales A+B+C+D+E+F 3.4 Functional costs (a) Production costs are the costs which are incurred by the sequence of operations beginning with the supply of raw materials and ending with the completion of the product ready for warehousing as a finished goods item. Packaging costs are production costs where they relate to 'primary' packing (boxes, wrappers and so on). (b) Administration costs are the costs of managing an organisation, that is, planning and controlling its operations, but only insofar as such administration costs are not related to the production, sales, distribution or research and development functions. (c) Selling costs, sometimes known as marketing costs, are the costs of creating demand for products and securing firm orders from customers. (d) Distribution costs are the costs of the sequence of operations with the receipt of finished goods from the production department and making them ready for despatch and where appropriate ending with the reconditioning for reuse of empty containers. (e) Research costs are the costs of searching for new or improved products, whereas development costs are the costs incurred between the decision to produce a new or improved product and the commencement of full manufacture of the product. (f) Financing costs are costs incurred to finance the business, such as loan interest.

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QUESTION Cost classification Within the costing system of a manufacturing company the following types of expense are incurred. Reference number 1 Cost of oils used to lubricate production machinery 2 Motor vehicle licences for lorries 3 Depreciation of factory plant and equipment 4 Cost of chemicals used in the laboratory 5 Commission paid to sales representatives 6 Salary of the secretary to the finance director 7 Trade discount given to customers 8 Holiday pay of machine operatives 9 Salary of security guard in raw material warehouse 10 Fees to advertising agency 11 Rent of finished goods warehouse 12 Salary of scientist in laboratory 13 Insurance of the company's premises 14 Salary of supervisor working in the factory 15 Cost of typewriter ribbons in the general office 16 Protective clothing for machine operatives Required Identify the correct cost classification of the above expenses and state the reference number of the expenditure item in the following table. Cost classification Reference number Production costs Selling and distribution costs Administration costs Research and development costs Each type of expense should appear only once in your answer. You may use the reference numbers in your answer.

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ANSWER Cost classification Reference number Production costs 1 3 8 9 14 16 Selling and distribution costs 2 5 7 10 11 Administration costs 6 13 15 Research and development costs 4 12

4 Cost classification for profit measurement and stock valuation (product cost and periodic cost)

For the preparation of financial statements, costs are often classified as production costs and period costs. Production costs are costs identified with goods produced or purchased for resale. Period costs are costs deducted as expenses during the current period. Production costs are all the costs involved in the manufacture of goods. In the case of manufactured goods, these costs consist of direct material, direct labour and manufacturing overhead. Period costs are taken directly to the statement of profit or loss as expenses in the period in which they are incurred; such costs consist of selling and administrative expenses. 4.1 Production and period costs The distinction between production and period costs is the basis of valuing inventory. 4.2 Example A business has the following costs for a period: Rs '000 Materials 600 Labour 1,000 Production overheads 500 Administration overheads 700 2,800 During the period 100 units are produced. If all of these costs were allocated to production units, each unit would be valued at Rs. 28,000.

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This would be incorrect. Only production costs are allocated to units of inventory. Administrative overheads are period costs. So, each unit of inventory should be valued at Rs. 21,000, which was calculated as (600,000 + 1,000,000 + 500,000)/100 This affects both gross profit and the valuation of closing inventory. If during the period 80 units are sold at Rs. 40,000 each, the gross profit will be: Rs '000 Sales (80 40,000) 3,200 Cost of sales (80 21,000) (1,680) Gross profit 1,520 The value of closing (unsold) inventory will be Rs. 420,000 (20 21,000). 5 Behavioural cost classification – fixed, variable and semi-

variable costs

5.1 Introduction to fixed cost and variable cost

Cost behaviour is the way in which costs are affected by changes in the volume of output. There are many factors which may influence costs. The major influence is volume of output, or the level of activity. The level of activity may refer to one of the following. Number of units produced Number of invoices issued Value of items sold Number of units of electricity consumed Number of items sold The basic principle of cost behaviour is that as the level of activity rises, costs will usually rise. It will cost more to produce 2,000 units of output than it will cost to produce 1,000 units. However, some costs rise with production output (variable costs) and some costs remain unchanged (fixed costs). Many items of expenditure are part-fixed and part-variable and hence are termed step-fixed or semi-variable costs. Therefore, an important way of analysing and classifying costs is into fixed costs and variable costs, as follows. A fixed cost is a cost which is incurred for a particular period of time and which, within certain activity levels, is unaffected by changes in the level of production activity. A variable cost is a cost which tends to vary with the level of production activity.

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5.2 Examples of fixed cost and variable cost (a) Direct material costs are variable costs because they rise as more units of a product are manufactured. (b) Sales commission is often a fixed percentage of sales turnover, and so is a variable cost that varies with the level of sales. (c) Telephone call charges are likely to increase if the volume of business expands, but there is also a fixed element of line rental, and so they are a semi-fixed or semi-variable overhead cost. (d) The rental cost of business premises is a constant amount, at least within a stated time period, and so it is a fixed cost.

5.3 Fixed costs A fixed cost is a cost which tends to be unaffected by increases or decreases in the volume of output. Fixed costs are a period charge, in that they relate to a span of time; as the time span increases, so too will the fixed costs (which are sometimes referred to as period costs for this reason). It is important to understand that fixed costs always have a variable element, since an increase or decrease in production may also bring about an increase or decrease in fixed costs. A sketch graph of fixed cost would look like this.

RsTotal cost

Volume of output (level of activity)

Total fixed cost

Figure 3.1: Fixed costs Examples of a fixed cost would be as follows. The salary of the managing director (per month or per annum) The rent of a single factory building (per month or per annum) Straight line depreciation of a single machine (per month or per annum)

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5.3.1 Step fixed costs A step fixed cost is a cost which is fixed in nature but only within certain levels of activity. Consider the depreciation of a machine which may be fixed if production remains below 1,000 units per month. If production exceeds 1,000 units, a second machine may be required, and the cost of depreciation (on two machines) would go up a step. A sketch graph of a step fixed cost could look like this. Cost

Rs

Step �ixed cost

Volume of output Figure 3.2: Step fixed costs Other examples of step fixed costs are as follows. (a) Rent is a step fixed cost in situations where accommodation requirements increase as output levels get higher. (b) Basic pay of employees is nowadays usually fixed, but as output rises, more employees (direct workers, supervisors, managers and so on) are required. (c) Royalties. 5.4 Variable costs A variable cost is a cost which tends to vary directly with the volume of output. The variable cost per unit is the same amount for each unit produced.

Rs

Cost

Graph of variable cost (1)

Volume of output

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Figure 3.3: Variable costs (1) A constant variable cost per unit implies that the price per unit of, say, material purchased is constant, and that the rate of material usage is also constant. (a) The most important variable cost is the cost of raw materials (where there is no discount for bulk purchasing, since bulk purchase discounts reduce the cost of purchases). (b) Direct labour costs are, for very important reasons, classed as a variable cost even though basic wages are usually fixed. (c) Sales commission is variable in relation to the volume or value of sales. (d) Bonus payments for productivity to employees might be variable once a certain level of output is achieved, as the following diagram illustrates. Rs

Cost

Graph of variable cost (2)

Volume of outputA

Bonus

Figure 3.4: Variable costs (2) Up to output A, no bonus is earned. Imagine if, up to a given level of activity, the purchase price per unit of raw material is constant. After that point, a quantity discount is given so the price per unit is lower for further purchases and also retrospectively to all units already purchased. The graph would be as follows.

Rs

Cost

Level of activity

Graph of variable cost (3)

Figure 3.5: Variable costs (3) Imagine if, up to a given level of activity, the purchase price per unit of raw material is constant. After that point, a discount is given so that the price per unit

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is lower for further purchases but not for the units already purchased. The graph would be as follows. Rs

Cost

Level of activity Figure 3.6: Variable costs (4)

5.4.1 Non-linear or curvilinear variable costs If the relationship between total variable cost and volume of output can be shown as a curved line on a graph, the relationship is said to be curvilinear. Two typical relationships are as follows. (a) (b) CostRs

Volume of output

CostRs

Volume of output

Figure 3.7: Variable costs – curvilinear and non-linear Each extra unit of output in graph (a) causes a less than proportionate increase in cost whereas in graph (b), each extra unit of output causes a more than proportionate increase in cost. The cost of a piecework scheme for individual workers with differential rates could behave in a curvilinear fashion if the rates increase by small amounts at progressively higher output levels.

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5.5 Semi-variable costs (or semi-fixed costs or mixed costs) A semi-variable/semi-fixed/mixed cost is a cost which contains both fixed and variable components and so is partly affected by changes in the level of activity. Examples of these costs include the following. (a) Electricity and gas bills (i) Fixed cost = standing charge (ii) Variable cost = charge per unit of electricity used (b) Salesperson's salary (i) Fixed cost = basic salary (ii) Variable cost = commission on sales made (c) Costs of running a car (i) Fixed cost = road tax, insurance (ii) Variable costs = petrol, oil, repairs (which vary with miles travelled) 5.6 Other cost behaviour patterns Other cost behaviour patterns may be appropriate to certain cost items. Examples of two other cost behaviour patterns are shown below. (a) Cost behaviour pattern (1) (b) Cost behaviour pattern (2)

CostRs

Maximum

cost

Volume of output

CostRs

Minimum

charge

Output Figure 3.8: Cost behaviour patterns

Graph (a) represents an item of cost which is variable with output up to a certain maximum level of cost. Graph (b) represents a cost which is variable with output, subject to a minimum (fixed) charge.

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5.7 Cost behaviour and cost per unit The following table relates to different levels of production of the zed. The variable cost of producing a zed is Rs. 5,000; fixed costs are Rs. 5,000,000. 1 zed 10 zeds 50 zeds Rs '000 Rs '000 Rs '000 Total variable cost 5 50 250 Variable cost per unit 5 5 5 Total fixed cost 5,000 5,000 5,000 Fixed cost per unit 5,000 500 100 Total cost (fixed and variable) 5,005 5,050 5,250 Total cost per unit 5,005 505 105 What happens when activity levels rise can be summarised as follows. The variable cost per unit remains constant The fixed cost per unit falls The total cost per unit falls This may be illustrated graphically as follows. Cost per

unit

Rs '000

Number of units

Variable cost

Number of units

Fixed cost Total cost

Number of units

Cost per

unit

Rs '000

Cost per

unit

Rs '000

Figure 3.9: Cost behaviours

5.8 Example: cost behaviour and activity level Hans Bratch has a fleet of company cars for sales representatives. Running costs have been estimated as follows. (a) Cars cost Rs. 1,200,000 when new and have a guaranteed trade-in value of Rs. 600,000 at the end of two years. Depreciation is charged on a straight-line basis. (b) Petrol and oil cost Rs. 15 per km. (c) Tyres cost Rs. 30,000 per set to replace; replacement occurs after 30,000 km. (d) Routine maintenance costs Rs. 20,000 per car (on average) in the first year and Rs. 45,000 in the second year. (e) Repairs average Rs. 40,000 per car over two years and are thought to vary with distance travelled. The average car travels 25,000 km per annum. (f) Tax, insurance, membership of motoring organisations and so on cost Rs. 40,000 per annum per car.

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Required

Calculate the average cost per annum of cars which travel (a) 15,000 km per annum and (b) 30,000 km per annum. Solution Costs may be analysed into fixed, variable and step fixed cost items; a step fixed cost is a cost which is fixed in nature but only within certain levels of activity. (a) Fixed costs Rs '000 per

annum Depreciation Rs. (1,200,000 600,000) ÷ 2 300 Routine maintenance Rs. (20,000 + 45,000) ÷ 2 32.5 Tax, insurance etc 40 372.5 (b) Variable costs Rs per km Petrol and oil 15.0 Repairs (Rs. 40,000 ÷ 50,000 km)* 0.8 15.8 * If the average car travels 25,000 km per annum, it will be expected to travel 50,000 km over two years (this will correspond with the repair bill of Rs. 40,000 over two years). (c) Step fixed costs are tyre replacement costs, which are Rs. 30,000 at the end of every 30,000 km. (i) If the car travels less than or exactly 30,000 km in two years, the tyres will not be changed. Average cost of tyres per annum = Rs. 0. (ii) If a car travels more than 30,000 km and up to (and including) 60,000 km in two years, there will be one change of tyres in the period. Average cost of tyres per annum = Rs. 15,000 (Rs. 30,000 2). (iii) If a car exceeds 60,000 km in two years (up to 90,000 km) there will be two tyre changes. Average cost of tyres per annum = Rs. 30,000 (Rs. 60,000 ÷ 2). The estimated costs per annum of cars travelling 15,000 km per annum and 30,000 km per annum would therefore be as follows. 15,000 km 30,000 km per annum per annum Rs '000 Rs '000 Fixed costs 372.5 372.5 Variable costs (Rs. 15.80 per km) 237 474 Tyres – 15 Cost per annum 609.5 861.5

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QUESTION Fixed, variable, mixed costs

Identify whether the following are likely to be fixed, variable or mixed costs. (a) Telephone bill (b) Annual salary of the chief accountant (c) The accountant's annual membership fee to CA Sri Lanka (paid by the company) (d) Cost of materials used to pack 20 units of product X into a box (e) Wages of warehousemen ANSWER (a) Mixed (b) Fixed (c) Fixed (d) Variable (e) Variable 5.9 Assumptions about cost behaviour Assumptions about cost behaviour include the following. (a) Within the normal or relevant range of output, costs are often assumed to be either fixed, variable or semi-variable (mixed). (b) Departmental costs within an organisation are assumed to be mixed costs, with a fixed and a variable element. (c) Departmental costs are assumed to rise in a straight line as the volume of activity increases. In other words, these costs are said to be linear. The high-low method of determining fixed and variable elements of mixed costs relies on the assumption that mixed costs are linear. We shall now go on to look at this method of cost determination.

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6 Cost classification for decision making – relevant cost and non-relevant cost

6.1 Relevant costs

Relevant costs are future cash flows arising as a direct consequence of a decision. Relevant costs are future costs Relevant costs are cash flows Relevant costs are incremental costs Decision making should be based on relevant costs. (a) Relevant costs are future costs. A decision is about the future and it cannot alter what has been done already. Costs that have been incurred in the past are totally irrelevant to any decision that is being made 'now'. Such costs are

past costs or sunk costs. Costs that have been incurred include not only costs that have already been paid, but also costs that have been committed. A committed cost is a future cash flow that will be incurred anyway, regardless of the decision taken now. (b) Relevant costs are cash flows. Only cash flow information is required. This means that costs or charges which do not reflect additional cash spending (such as depreciation and notional costs) should be ignored for the purpose of decision making. (c) Relevant costs are incremental costs. For example, if an employee is expected to have no other work to do during the next week, but will be paid his basic wage (of, say, Rs. 3000 per week) for attending work and doing nothing, his manager might decide to give him a job which earns the organisation Rs. 1000. The net gain is Rs. 1000 and the Rs. 3000 is irrelevant to the decision because, although it is a future cash flow, it will be incurred anyway whether the employee is given work or not. Decision making is based only on relevant costs which are future, incremental cashflows. The following aspects fulfil the definition of a relevant cost, so should be included when decision making. Avoidable costs are those costs which can change as a result of a decision ie, a production cost. Specific fixed costs are additional costs which may be required to increase production. For example. a new machine may be required to increase production capacity. The cost of this machine is relevant to the decision to increase production as it represents an additional incremental, future, cash outflow.

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Opportunity costs may be incurred where there is a resource constraint or production is at full capacity. If materials are scarce or if labour is working at full capacity, these resources will have to be taken away from another activity in order to switch resources to a new project. This will create a relevant opportunity cost which must be included during the decision-making process. For example, as a result of a production decision to increase output of Product B, material and labour resources must be switched from Product A and as a result Product A production volume reduces, resulting in lost sales of Product A. The opportunity cost represents the fall in cashflows relating to lower Product A sales and should be included in decision making concerning Product B. 6.2 Non-relevant costs Non-relevant costs are costs which would not be incurred if the activity to which they relate did not exist.

One of the situations in which it is necessary to identify the irrelevant costs is in deciding whether or not to discontinue a product. The only costs which would be saved are the relevant costs which are usually the variable costs and sometimes some specific costs. Costs which would be incurred whether or not the product is discontinued are known as non-relevant costs. The following types of non-relevant costs are excluded from decision making. A sunk cost is a cost that has been irreversibly incurred in the past or committed. A sunk cost cannot be changed so fails the required future cash flow requirement in the relevant cost definition. An example of a sunk cost are research costs already incurred, before the decision to proceed with production was made. A committed cost is a future cash outflow that will be incurred anyway, whatever decision is taken. Committed costs may exist because of legal contracts already entered into by the organisation that it cannot avoid paying in the future. A non-cashflow cost, such as depreciation or other non-cash accounting cost adjustments, fails the required cash flow definition of a relevant cost, so is excluded from decision making. A notional cost is a cost used in product evaluation, decision-making and performance measurement to reflect the use of resources which carry no actual cashflow. An example is the notional rent of a machine, which is actually owned, in order to understand the full cost of production which reflects all assets and resources required to manufacture a product.

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A general fixed overhead or one which is estimated (absorbed) into production fail the incremental requirement of a relevant cost. A fixed overhead is excluded from decision making as the cost does not change as a result of the decision. An example is a machine maintenance overhead which must always be incurred. 7 Cost classification for decision making – controllable cost

and non-controllable cost

7.1 Controllable and uncontrollable costs A controllable cost is a cost which can be influenced by management decisions and actions. An uncontrollable cost is a cost which cannot be affected by management within a given time span. Most variable costs within a department are thought to be controllable in the

short term because managers can influence the efficiency with which resources are used, even if they cannot do anything to raise or lower price levels. A cost which is not controllable by a junior manager might be controllable by a senior manager. For example, there may be high direct labour costs in a department caused by excessive overtime working. The junior manager may feel obliged to continue with the overtime to meet production schedules, but the senior manager may be able to reduce costs by hiring extra full-time staff, thereby reducing the requirements for overtime. A cost which is not controllable by a manager in one department may be controllable by a manager in another department. For example, an increase in material costs may be caused by buying at higher prices than expected (controllable by the purchasing department) or by excessive wastage (controllable by the production department) or by a faulty machine producing rejects (controllable by the maintenance department). Some costs are non-controllable, such as increases in expenditure due to inflation. Other costs are controllable, but in the long term rather than the short term. For example, production costs might be reduced by the introduction of new machinery and technology but, in the short term, management must attempt to do the best they can with the resources and machinery at their disposal.

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8 Cost estimation using high-low method

8.1 Analysing costs The fixed and variable elements of semi-variable costs can be determined by the high-low method. It is generally assumed that costs are one of the following. Variable Semi-variable Fixed Cost accountants tend to separate semi-variable costs into their variable and fixed elements. They therefore generally tend to treat costs as either fixed or variable. There are several methods for identifying the fixed and variable elements of semi-variable costs. Each method is only an estimate, and each will produce different results. One of the principal methods is the high-low method. 8.2 High-low method Follow the steps below to estimate the fixed and variable elements of semi-variable costs. Step 1 Review records of costs in previous periods.

Select the period with the highest activity level. Select the period with the lowest activity level.

Step 2 Determine the following. Total cost at high activity level Total cost at low activity level Total units at high activity level Total units at low activity level

Step 3 Calculate the following. level activitylow at units total _ level activity high at units Total level activitylow at cost total _ level activity high at cost Total = variable cost per unit (v)

Step 4 The fixed costs can be determined as follows. (Total cost at high activity level) – (total units at high activity level × variable cost per unit)

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The following graph demonstrates the high-low method. Rs

Total Cost

Demonstration of high-low

method

Low High Level of activity

Assumed total costa

Fixed costs (same at all

levels of output

Variable costs

Figure 3.10: High-low method

8.3 Example: The high-low method DG Co has recorded the following total costs during the last five years. Year

Output volume

Total cost Units Rs '000 20X0 65,000 145,000 20X1 80,000 162,000 20X2 90,000 170,000 20X3 60,000 140,000 20X4 75,000 160,000

Required

Calculate the total cost that should be expected in 20X5 if output is 85,000 units. Solution

Step 1 Period with highest activity = 20X2 Period with lowest activity = 20X3

Step 2 Total cost at high activity level = 170,000,000 = Rs. 170 million Total cost at low activity level = 140,000,000 = Rs. 140 million Total units at high activity level = 90,000,000 = 90 million units Total units at low activity level = 60,000,000 = 60 million units

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Step 3 Variable cost per unit = _total cost at high activity level total cost at low activity level_total units at high activity level total units at low activity level =

170 million 140 million90,000 60,000 = 30 million30,000 = Rs. 1,000 per unit

Step 4 Fixed costs = (total cost at high activity level) – (total units at high activity level × variable cost per unit) = 170,000,000 – (90,000 × 1,000) = 170,000,000 – 90,000,000 = Rs. 80,000,000 Therefore the costs in 20X5 for output of 85,000 units are as follows. Rs million Variable costs = 85,000 × Rs. 1,000 85 Fixed costs 80 165

8.4 Example: The high-low method with stepped fixed costs The following data relates to the overhead expenditure of contract cleaners (for industrial cleaning) at two activity levels. Square metres cleaned 12,750 15,100 Overheads Rs. 73,950 Rs. 83,585 When more than 14,000 square metres are industrially cleaned, there will be a step up in fixed costs of Rs. 4,700. Required

Calculate the estimated total cost if 14,500 square metres are to be industrially cleaned. Solution Before we can compare high output costs with low output costs in the normal way, we must eliminate the part of the high output costs that are due to the step up in fixed costs: Total cost for 15,100 without step up in fixed costs = Rs. 83,585 – Rs. 4,700 = Rs. 78,885 We can now proceed in the normal way using the revised cost above.

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Units Rs High output 15,100 Total cost 78,885 Low output 12,750 Total cost 73,950 2,350 4,935 Variable cost = Rs. 4, 9352, 350 = Rs. 2.10 per square metre Before we can calculate the total cost for 14,500 square metres we need to find the fixed costs. As the fixed costs for 14,500 square metres will include the step up of Rs. 4,700, we can use the activity level of 15,100 square metres for the fixed cost calculation: Rs Total cost (15,100 square metres) (this includes the step up in fixed costs) 83,585 Total variable costs (15,100 × Rs. 2.10) 31,710 Total fixed costs 51,875 Estimated overhead expenditure if 14,500 square metres are to be industrially cleaned: Rs Fixed costs 51,875Variable costs (14,500 Rs. 2.10) 30,450 82,3258.5 Example: The high-low method with a change in the variable

cost per unit Using the same data as the previous question, but with this extra information: a round of wage negotiations has just taken place, which will cost an additional Rs. 1 per square metre. Required Calculate the estimated total cost if 14,500 square metres are to be industrially cleaned. Solution Estimated overheads to clean 14,500 square metres. Per square

metre Rs Variable cost 2.10 Additional variable cost 1.00 Total variable cost 3.10

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Cost for 14,500 square metres: Rs Fixed 51,875 Variable costs (14,500 Rs. 3.10) 44,950 96,825 QUESTION High-low method The Valuation Department of a large firm of surveyors wishes to develop a method of predicting its total costs in a period. The following past costs have been recorded at two activity levels.

Number of valuations

Total cost (V) (TC) Period 1 420 82,200 Period 2 515 90,275

Required

Identify which of the following would represent the total cost model for a period. A TC = Rs. 46,500 + 85V C TC = Rs. 46,500 – 85V B TC = Rs. 42,000 + 95V D TC = Rs. 51,500 – 95V ANSWER The correct answer is A. Valuations Total cost V Rs Period 2 515 90,275 Period 1 420 82,200 Change due to variable cost 95 8,075 Variable cost per valuation = Rs. 8,075/95 = Rs. 85. Period 2: fixed cost = Rs. 90,275 – (515 Rs. 85) = Rs. 46,500 Using good MCQ technique, you should have managed to eliminate C and D as incorrect options straightaway. The variable cost must be added to the fixed cost, rather than subtracted from it. Once you had calculated the variable cost as Rs. 85 per valuation (as shown above), you should have been able to select option A without going on to calculate the fixed cost (we have shown this calculation above for completeness).

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The high-low method is a simple forecasting technique. 8.6 High-low method (a) Records of costs in previous periods are reviewed and the costs of the following two periods are selected. (i) The period with the highest volume of activity (ii) The period with the lowest volume of activity (b) The difference between the total cost of these two periods will be the

variable cost of the difference in activity levels (since the same fixed cost is included in each total cost). (c) The variable cost per unit may be calculated from this (difference in total costs difference in activity levels), and the fixed cost may then be determined by substitution. (d) This method may be applied to annual sales figures or any other activity as well as costs. So be prepared to use this outside the context of costs.

8.7 Example: the high-low method using revenues The following information concerning sales revenues for a development, Cool Blue, for the last four months have been as follows.

Month Sales revenues Website 'hits' Rs 1 110,000 70,000 2 115,000 80,000 3 111,000 77,000 4 97,000 60,000 Required

Calculate the revenues that should be expected in month five when 'hits' is expected to be 75,000 units. Ignore inflation. 8.8 Solution Revenue (a) Hits Rs High activity 80,000 115,000 Low activity 60,000 97,000 20,000 18,000 Variable revenue per hit Rs. 18,000/20,000 = Rs. 0.90

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(b) Substituting in either the high or low volume activity: High Low Rs Rs Total revenue 115,000 97,000 Variable revenue (80,000 × Rs. 0.90) 72,000 (60,000 × Rs. 0.90) 54,000 Fixed revenue 43,000 43,000 (c) Estimated revenues when there are 75,000 hits: Rs Fixed revenues 43,000 Variable revenues (75,000 × Rs. 0.90) 67,500 Total revenues 110,500

8.9 Example: the high-low method with inflation You may be asked to use the high-low method when cost inflation is included. You need to deflate (reduce) all of the costs to a base year before the high-low method can be applied. Year 1 Year 2 Year 3 Year 4 Sales/production (units) 85,000 93,400 95,800 94,300Total costs Rs. 337,500 Rs. 365,670 Rs. 379,080 Rs. 382,395Cost inflation index 100 102 104 106

Required

State a linear equation for total costs per annum (at year 1 prices) using the high-low method. 8.10 Solution Cost data has to be reduced by dividing by the inflation index before the high-low method can be applied.

Year 1 Year 2 Year 3 Year 4 Cost/ inflation index Rs. 337,500 Rs. 365,670/1.02 Rs. 379,080/1.04 Rs. 382,395/1.06 = Rs. 337,500 = Rs. 358,500 = Rs. 364,500 = Rs. 360,750

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After adjusting for inflation, the year of highest output (Year 3) is now also the year of the highest cost. Using the high-low method for Year 1 and Year 3: Cost Units Rs High 95,800 364,500 Low 85,000 337,500 10,800 27,000

variable cost per unit = Rs. 27,000/10,800 = Rs. 2.50 Fixed cost = Rs. 337,500 – (85,000 × Rs. 2.50) = Rs. 125,000 Total cost (y) = Rs. 2.50 x + Rs. 125,000 (where x is the number of units) 8.11 Advantages and disadvantages of the high-low method Advantages

It is easy to use and understand It needs just two activity levels Disadvantages

It uses two extreme data points which may not be representative of normal conditions Using only two points to determine a formula may mean that the formula is not very accurate

9 Cost estimation using scatter diagrams and regression method

9.1 Introduction Two variables are said to be correlated if a change in the value of one variable is accompanied by a change in the value of another variable. This is what is meant by correlation. Examples of variables which might be correlated are as follows. A person's height and weight The distance of a journey and the time it takes to make it

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9.2 Scattergraphs One way of showing the correlation between two related variables is on a scattergraph or scatter diagram, plotting a number of pairs of data on the graph. For example, a scattergraph showing monthly selling costs against the volume of sales for a 12-month period might be as follows.

Selling

costs, Rs

Sales volume Figure 18.1: Scattergraph/scatter diagram This scattergraph suggests that there is some correlation between selling costs and sales volume, so that as sales volume rises, selling costs tend to rise as well. A 'line of best fit', which is a line drawn by judgement to pass through the middle of the points, thereby having as many points above the line as below it, can then be drawn. 9.3 Degrees of correlation Two variables might be perfectly correlated, partly correlated or uncorrelated. Correlation can be positive or negative. The differing degrees of correlation can be illustrated by scatter diagrams. 9.3.1 Perfect correlation

(a) (b)YY

X X Figure 18.2: Perfect correlation All the pairs of values lie on a straight line. An exact linear relationship exists between the two variables.

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9.3.2 Partial correlation (a) (b)

YY

X X Figure 18.3: Partial correlation In (a), although there is no exact relationship, low values of X tend to be associated with low values of Y, and high values of X with high values of Y. In (b) again, there is no exact relationship, but low values of X tend to be associated with high values of Y and vice versa. 9.3.3 No correlation

(c)Y

X Figure 18.4: No correlation The values of these two variables are not correlated with each other. 9.3.4 Positive and negative correlation Correlation, whether perfect or partial, can be positive or negative. Positive correlation means that low values of one variable are associated with low values of the other; and high values of one variable are associated with high values of the other. Negative correlation means that low values of one variable are associated with high values of the other; and high values of one variable with low values of the other.

9.4 Linear regression

Linear regression analysis (the least squares method) is one technique for estimating a line of best fit. Once an equation for a line of best fit has been determined, forecasts can be made.

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FORMULA TO LEARN The least squares method of linear regression analysis involves using the following formulae for a and b in Y = a + bX. b = 2X2Xn YXXYn

a = nXbnY where n is the number of pairs of data The line of best fit that is derived represents the regression of Y upon X. A different line of best fit could be obtained by interchanging X and Y in the formulae. This would then represent the regression of X upon Y (X = a + bY) and it would have a slightly different slope. For examination purposes, always use the regression of Y upon X, where X is the independent variable, and Y is the dependent variable whose value we wish to forecast for given values of X. In a time series, X will represent time. 9.4.1 Example: the least squares method (a) Calculate an equation to determine the expected level of costs, for any given volume of output, using the least squares method. You may assume the variables X (output) and Y (total cost). Time period 1 2 3 4 5 Output ('000 units) 20 16 24 22 18 Total cost (Rs. 000) 82 70 90 85 73 (b) Prepare a budget for total costs, if output is 22,000 units. (c) Calculate the correlation coefficient and state whether there is a high degree of correlation between output and costs. Solution (a) WORKINGS

X Y XY X2 Y2 20 82 1,640 400 6,724 16 70 1,120 256 4,900 24 90 2,160 576 8,100 22 85 1,870 484 7,225 18 73 1,314 324 5,329 X = 100 Y = 400 XY = 8,104 X2 = 2,040 Y2 = 32,278 n = 5 (There are five pairs of data for x and y values)

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b = 22 X)(Xn YXXYn = 21002,0405 400)(1008,104)(5

= 10,00010,200 40,00040,520 = 200520 = 2.6 a = nXbnY = 5400 – 2.6

5100 = 28 Y = 28 + 2.6X where Y = total cost, in thousands of Rs.; X = output, in thousands of units. Note that the fixed costs are Rs. 28,000 (when X = 0 costs are Rs. 28,000) and the variable cost per unit is Rs. 2.60. (b) If the output is 22,000 units, we would expect costs to be 28 + 2.6 22 = 85.2 = Rs. 85,200. (c) r = 240032,2785200 520

= 1,390200520

= 527.3520 = +0.99

9.5 Regression lines and time series The same technique can be applied to calculate a regression line (a trend line) for a time series. This is particularly useful for purposes of forecasting. As with correlation, years can be numbered from 0 upwards. QUESTION Trend line

Calculate the trend line of sales and forecast sales in 20Y2 and 20Y3 using the data in the question entitled 'Correlation'. ANSWER Using workings from the question entitled 'Correlation': b =

210305 78101345

= 100150 780670 = –2.2

a = nXbnY = 5 102.2578 = 20 Y = 20 – 2.2X where X = 0 in 20X7, X = 1 in 20X8 and so on. Using the trend line, predicted sales in 20Y2 (year 5) would be: 20 – (2.2 5) = 9 ie 9,000 units and predicated sales in 20Y3 (year 6) would be: 20 – (2.2 6) = 6.8 ie 6,800 units.

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QUESTION Regression analysis Regression analysis was used to find the equation Y = 300 – 4.7X, where X is time (in quarters) and Y is sales level in thousands of units. Required Given that X = 0 represents 20X0 quarter 1, calculate the forecast sales levels for 20X5 quarter 4. ANSWER X = 0 corresponds to 20X0 quarter 1 Therefore X = 23 corresponds to 20X5 quarter 4 Forecast sales = 300 – (4.7 × 23) = 191.9 = 191,900 units

QUESTION Forecasting Over a 36-month period, sales have been found to have an underlying regression line of Y = 14.224 + 7.898X where Y is the number of items sold and X represents the month. Required

Calculate the forecast number of items to be sold in month 37. ANSWER Y = 14.224 + 7.898X = 14.224 + (7.898 × 37) = 306.45 = 306 units

9.6 The reliability of regression analysis forecasts As with all forecasting techniques, the results from regression analysis will not be wholly reliable. There are a number of factors which affect the reliability of forecasts made using regression analysis. (a) It assumes a linear relationship exists between the two variables (since linear regression analysis produces an equation in the linear format) whereas a non-linear relationship might exist. (b) It assumes that the value of one variable, Y, can be predicted or estimated from the value of one other variable, X. In reality the value of Y might depend on several other variables, not just X.

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(c) When it is used for forecasting, it assumes that what has happened in the past will provide a reliable guide to the future. (d) When calculating a line of best fit, there will be a range of values for X. In the example in section 4.2, the line Y = 28 + 2.6X was predicted from data with output values ranging from X = 16 to X = 24. Depending on the degree of correlation between X and Y, we might safely use the estimated line of best fit to predict values for Y in the future, provided that the value of X remains within the range 16 to 24. We would be on less safe ground if we used the formula to predict a value for Y when X = 10, or 30, or any other value outside the range 16 to 24, because we would have to assume that the trend line applies outside the range of X values used to establish the line in the first place. (i) Interpolation means using a line of best fit to predict a value within the two extreme points of the observed range. (ii) Extrapolation means using a line of best fit to predict a value outside the two extreme points. When linear regression analysis is used for forecasting a time series (when the X values represent time) it assumes that the trend line can be extrapolated into the future. This might not necessarily be a good assumption to make. (e) As with any forecasting process, the amount of data available is very important. Even if correlation is high, if we have fewer than about ten pairs of values, we must regard any forecast as being somewhat unreliable. (It is likely to provide more reliable forecasts than the scattergraph method, however, since it uses all of the available data.) (f) The reliability of a forecast will depend on the reliability of the data collected to determine the regression analysis equation. If the data is not collected accurately or if data used is false, forecasts are unlikely to be acceptable. A check on the reliability of the estimated line Y= 28 + 2.6X can be made, however, by calculating the coefficient of correlation. From the answer to the example in section 4.2, we know that r = 0.99. This is a high positive correlation, and r2 = 0.9801, indicating that 98.01% of the variation in cost can be explained by the variation in volume. This would suggest that a fairly large degree of reliance can probably be placed on estimates. If there is a perfect linear relationship between X and Y (r = 1) then we can predict Y from any given value of X with great confidence. If correlation is high (for example r = 0.9) the actual values will all lie quite close to the regression line and so predictions should not be far out. If correlation is below about 0.7, predictions will only give a very rough guide as to the likely value of Y.

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9.7 Advantages of regression analysis (a) It gives a definitive line of best fit, taking account of all of the data. (b) Linear regression makes efficient use of data and good results can be obtained with relatively small data sets. (c) The significance/reliability of the relationship between variables can be statistically tested (but you don't need to know the details of this for KE2.) (d) Many processes are linear, so are well described by regression analysis. Even many non-linear relationships can be well-approximated by a linear model over a short range. 10 Cost estimation using correlation coefficient and rank

correlation

10.1 The correlation coefficient The degree of linear correlation between two variables is measured by the Pearsonian (product moment) correlation coefficient, r. The nearer r is to +1 or –1, the stronger the relationship. When we have measured the degree of correlation between two variables we can decide, using actual results in the form of pairs of data, whether two variables are perfectly or partially correlated, and if they are partially correlated, whether there is a high or low degree of partial correlation.

FORMULA TO LEARN

Correlation coefficient, r =

n XY - X Y2 22 2[n X - X ] [n Y - Y ] where X and Y represent pairs of data for two variables X and Y n = the number of pairs of data used in the analysis The correlation coefficient, r, must always fall between –1 and +1. If you get a value outside this range you have made a mistake. r = +1 means that the variables are perfectly positively correlated r = –1 means that the variables are perfectly negatively correlated r = 0 means that the variables are uncorrelated

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10.2 Example: the correlation coefficient formula The cost of output at a factory is thought to depend on the number of units produced. Data has been collected for the number of units produced each month in the last six months, and the associated costs, as follows. Month Output Cost '000s of units Rs'000 X Y 1 2 9 2 3 11 3 1 7 4 4 13 5 3 11 6 5 15

Required

Assess whether there is any correlation between output and cost. Solution r =

n XY - X Y2 22 2[n X - X ] [n Y - Y ] We need to find the values for the following. (a) XY Multiply each value of X by its corresponding Y value, so that there are six values for XY. Add up the six values to get the total. (b) X Add up the six values of X to get a total. (X)2 will be the square of this total. (c) Y Add up the six values of Y to get a total. (Y)2 will be the square of this total. (d) X2 Find the square of each value of X, so that there are six values for X2. Add up these values to get a total. (e) Y2 Find the square of each value of Y, so that there are six values for Y2. Add up these values to get a total. WORKINGS X Y XY X2 Y2 2 9 18 4 81 3 11 33 9 121 1 7 7 1 49 4 13 52 16 169 3 11 33 9 121 5 15 75 25 225 X = 18 Y = 66 XY = 218 X2 = 64 Y2 = 766

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(X)2 = 182 = 324 (Y)2 = 662 = 4,356 n = 6 r =

(6 × 218) - 18 × 666 × 64 - 324 × 6 × 766 - 4,356 =

1,308 -1,188384 -324 × 4,596 - 4,356

= 120 120 120= = 12060×240 14,400 = 1 There is perfect positive correlation between the volume of output at the factory and costs, which means that there is a perfect linear relationship between output and costs. 10.3 Example: the correlation coefficient without the formula If you are given a question with relatively simple numbers as variables, you may be able to estimate the correlation coefficient without using the formula at all. The following data is available for the number of materials purchased and the total cost. Number of units purchased Total cost

x y Rs 1 10 2 20 3 30 4 40 5 50 Required

State the correlation coefficient between the two variables without using the formula. Solution A correlation coefficient of +1 means that there is a perfect linear relationship between the two variables. The equation relating the two variables would be of the form y = a + bx. If you plotted a graph, it would be a straight line. You can see fairly easily that y is ten times the value of x. So the equation is y = 10x. This means that there is perfect positive correlation and the correlation coefficient is +1.

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Look at the following data. x y 0.0 60 0.1 50 0.2 40 0.3 30 0.4 20 0.5 10 Required

State the correlation coefficient between the two variables without using the formula. Solution You could draw a quick sketch of the graph as follows.

**

**

**

y

x0.1 0.2 0.3 0.4 0.5 0.6

10

20

30

40

50

60

70

0 Figure 18.5 This graph slopes downwards from left to right and therefore has a negative gradient. It is a straight line so we are looking at perfect negative correlation with a correlation coefficient of -1. Note that the gradient is -10/0.1 = -100 and the intercept is 60. The equation of the line is therefore y = -100x + 60. 10.4 Correlation in a time series Correlation exists in a time series if there is a relationship between the period of time and the recorded value for that period of time. The correlation coefficient is calculated with time as the X variable, although it is convenient to use simplified values for X instead of year numbers. For example, instead of having a series of years 2011 to 2015, we could have values for X from 0 (2011) to 4 (2015). Note that whatever starting value you use for X (be it 0, 1, 2 ... 721, ... 953), the value of r will always be the same.

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QUESTION Correlation Sales of product A between 20X7 and 20Y1 were as follows. Year Units sold ('000s) 20X7 20 20X8 18 20X9 15 20Y0 14 20Y1 11 Required

Identify whether there is a trend in sales. In other words, state whether there is any correlation between the year and the number of units sold. ANSWER WORKINGS Let 20X7 to 20Y1 be years 0 to 4.

X Y XY X2 Y2 0 20 0 0 400 1 18 18 1 324 2 15 30 4 225 3 14 42 9 196 4 11 44 16 121 X = 10 Y = 78 XY = 134 X2 = 30 Y2 = 1,266 (X)2 = 100 (Y)2 = 6,084 n = 5 r =

6,0841,2665100305 78)(10134)(5

=

6,0846,330100150 780670

= 24650110

= 12,300110 = 110.90537110 = –0.992 There is partial negative correlation between the year of sale and units sold. The value of r is close to –1, therefore a high degree of correlation exists, although it is not quite perfect correlation. This means that there is a clear downward trend in sales.

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10.5 The coefficient of determination, r2 The coefficient of determination, r2 (alternatively R2) measures the proportion of the total variation in the value of one variable that can be explained by variations in the value of the other variable. It denotes the strength of the linear association between two variables. Unless the correlation coefficient r is exactly or very nearly +1, –1 or 0, its meaning or significance is a little unclear. For example, if the correlation coefficient for two variables is +0.8, this would tell us that the variables are positively correlated, but the correlation is not perfect. It would not really tell us much else. A more meaningful analysis is available from the square of the correlation coefficient, r, which is called the coefficient of determination. The question above entitled 'Correlation' shows that r = –0.992, therefore r2 = 0.984. This means that over 98% of variations in sales can be explained by the passage of time, leaving 0.016 (less than 2%) of variations to be explained by other factors. Similarly, if the correlation coefficient between a company's output volume and maintenance costs was 0.9, r2 would be 0.81, meaning that 81% of variations in maintenance costs could be explained by variations in output volume, leaving only 19% of variations to be explained by other factors (such as the age of the equipment). Note, however, that if r2 = 0.81, we would say that 81% of the variations in y can be explained by variations in x. We do not necessarily conclude that 81% of variations in y are caused by the variations in x. We must beware of reading too much significance into our statistical analysis. 10.6 Correlation and causation If two variables are well correlated, either positively or negatively, this may be due to pure chance or there may be a reason for it. The larger the number of pairs of data collected, the less likely it is that the correlation is due to chance, though that possibility should never be ignored entirely. If there is a reason, it may not be causal. For example, monthly net income is well-correlated with monthly credit to a person's bank account, for the logical (rather than causal) reason that for most people the one equals the other. Even if there is a causal explanation for a correlation, it does not follow that variations in the value of one variable cause variations in the value of the other. For example, sales of ice cream and of sunglasses are well correlated, not because of a direct causal link but because the weather influences both variables.

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10.7 Coefficient of rank correlation In the examples considered above, the data were given in terms of the values of the relevant variables, such as the number of hours. Sometimes however, they are given in terms of order or rank rather than actual values. Spearman's rank correlation coefficient is used when data is given in terms of order or rank, rather than actual values. FORMULA TO LEARN

Coefficient of rank correlation, R = 1 – )

Σ

−

226 dn(n 1 Formula here (Body text style) Where n = number of pairs of data d = the difference between the rankings in each set of data. The coefficient of rank correlation can be interpreted in exactly the same way as the ordinary correlation coefficient. Its value can range from –1 to +1. 10.7.1 Example: The rank correlation coefficient The examination placings of seven students were as follows.

Statistics Economics Student placing placing A 2 1 B 1 3 C 4 7 D 6 5 E 5 6 F 3 2 G 7 4

Required Judge whether the placings of the students in statistics correlate with their placings in economics. Solution Correlation must be measured by Spearman's coefficient because we are given the placings of students, and not their actual marks. R = 1 –

)

Σ−

226 dn(n 1 where d is the difference between the rank in statistics and the rank in economics for each student.

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Rank Rank Student Statistics Economics d d 2 A 2 1 1 1 B 1 3 2 4 C 4 7 3 9 D 6 5 1 1 E 5 6 1 1 F 3 2 1 1 G 7 4 3 9 d2 = 26 R = 1 –

)×

× −6 267 (49 1 = 1 – 156336 = 0.536 The correlation is positive, 0.536, but the correlation is not strong.

10.7.2 Tied ranks If in a problem some of the items tie for a particular ranking, these must be given an average place before the coefficient of rank correlation is calculated. Here is an example. Position of students in examination Express as A 1 = average of 1 and 2 1.5 B 1 = 1.5 C 3 3 D 4 4 E 5 = 6 F 5 = average of 5, 6 and 7 6 G 5 = 6 H 8 8

QUESTION Rank Correlation Five artists were placed in order of merit by two different judges as follows. Judge P Judge Q

Artist Rank Rank A 1 4 = B 2 = 1 C 4 3 D 5 2 E 2 = 4 =

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Required Assess how the two sets of rankings are correlated Five artists were placed in order of merit by two different judges as follows. Judge P Judge Q

Artist Rank Rank A 1 4 = B 2 = 1 C 4 3 D 5 2 ANSWER Judge P Judge Q Rank Rank d d 2 A 1.0 4.5 3.5 12.25 B 2.5 1.0 1.5 2.25 C 4.0 3.0 1.0 1.00 D 5.0 2.0 3.0 9.00 E 2.5 4.5 2.0 4.00 28.50 R = 1 –

)×

× −6 28.55 (25 1 = – 0.425 There is a slight negative correlation between the rankings.

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In practice, most cost accounting transactions are recorded at historic cost, but costs can be measured in terms of economic cost. Economic value is the amount someone is willing to pay. A direct cost is a cost that can be traced in full to the product, service or department being costed. An indirect cost (or overhead) is a cost that is incurred in the course of making a product, providing a service or running a department, but which cannot be traced directly and in full to the product, service or department. Total direct cost of production = direct materials + direct labour + direct expenses Total cost of production = Total direct costs of production (as above) + variable production overheads + fixed production overheads Total cost = Total cost of production (as above) + variable non-production overheads + fixed non-production overheads Classification by function involves classifying costs as production/ manufacturing costs, administration costs or marketing/selling and distribution costs. A different way of analysing and classifying costs is into fixed costs and variable

costs. Many items of expenditure are part-fixed and part-variable and hence are termed semi-fixed or semi-variable costs. For the preparation of financial statements, costs are often classified as

production costs and period costs. Production costs are costs identified with goods produced or purchased for resale. Period costs are costs deducted as expenses during the current period. Cost centres are collecting places for costs before they are further analysed. Costs are further analysed into cost units once they have been traced to cost centres. A cost unit is a unit of product or service to which costs can be related. The cost unit is the basic control unit for costing purposes. A cost object is any activity for which a separate measurement of costs is desired. A responsibility centre is a department or organisational function whose performance is the direct responsibility of a specific manager. Profit centres are similar to cost centres but are accountable for both costs and

revenues. Revenue centres are similar to cost centres and profit centres but are accountable for revenues only. Revenue centre managers should normally have control over how revenues are raised.

CHA

PTER

RO

UN

DU

P

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An investment centre is a profit centre with additional responsibilities for capital investment and possibly for financing; its performance is measured by its return on investment. Relevant costs are future cash flows arising as a direct consequence of a decision. • Relevant costs are future costs • Relevant costs are cash flows • Relevant costs are incremental costs Relevant costs are also differential costs and opportunity costs. Differential costs are the difference in total cost between alternatives. An opportunity cost is the value of the benefit sacrificed when one course of action is chosen in preference to an alternative. A sunk cost is a past cost which is not directly relevant in decision making. Cost behaviour is the way in which costs are affected by changes in the volume of output. The basic principle of cost behaviour is that as the level of activity rises, costs

will usually rise. It will cost more to produce 2,000 units of output than it will to produce 1,000 units. A fixed cost is a cost which tends to be unaffected by increases or decreases in the volume of output. A step fixed cost is a cost which is fixed in nature but only within certain levels of activity. A variable cost is a cost which tends to vary directly with the volume of output. The variable cost per unit is the same amount for each unit produced. If the relationship between total variable cost and volume of output can be shown as a curved line on a graph, the relationship is said to be curvilinear. A semi-variable/semi-fixed/mixed cost is a cost which contains both fixed and variable components and so is partly affected by changes in the level of activity. The fixed and variable elements of semi-variable costs can be determined by the

high-low method. When decision making, only include relevant costs which are defined as future, incremental cashflows. Examples of relevant costs include opportunity costs, avoidable costs and specific fixed costs. Two variables are said to be correlated if a change in the value of one variable is accompanied by a change in the value of another variable. This is what is meant by

correlation. Two variables might be perfectly correlated, partly correlated or uncorrelated. Correlation can be positive or negative.

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The degree of linear correlation between two variables is measured by the Pearsonian (product moment) correlation coefficient, r. The nearer r is to +1 or to –1, the stronger the relationship.

The coefficient of determination, r2 (alternatively R2) measures the proportion of the total variation in the value of one variable that can be explained by variations in the value of the other variable. It denotes the strength of the linear association between two variables. The high-low method is a simple forecasting technique. Linear regression analysis (the least squares method) is one technique for estimating a line of best fit. Once an equation for a line of best fit has been determined, forecasts can be made. As with all forecasting techniques, the results from regression analysis will not be wholly reliable. There are a number of factors which affect the reliability of forecasts made using regression analysis. Spearman's rank correlation coefficient is used when data is given in terms of order or rank, rather than actual values.

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1 State two examples of direct expenses. 2 State an example of an administration overhead, a selling overhead and a distribution overhead. 3 List the types of functional costs. 4 Explain the distinction between fixed and variable costs. 5 Define production costs and non-production costs. 6 Define the term 'cost centre'. 7 Define the term 'cost unit'. 8 Define the term 'profit centre'. 9 Define the term 'investment centre'. 10 Cost behaviour is ………………………………………………………………………………………. . 11 The basic principle of cost behaviour is that as the level of activity rises, costs will usually …………… . (a) rise (b) fall.

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12 Identify the title for each graph given below and state an example. Rs

Cost

Rs

Cost

Rs

Cost

Rs

Cost

Activity

Activity

Activity

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(b)

(c)

(d)

Graph of a cost

Example:

Graph of a cost

Example:

Graph of a cost

Example:

Graph of a cost

Example:

13 Costs are assumed to be either fixed, variable or semi-variable within the normal or relevant range of output. True False

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14 The costs of operating the canteen at 'Eat a lot Company' for the past three months is as follows. Month Cost Employees Rs '000 1 72,500 1,250 2 75,000 1,300 3 68,750 1,175

Calculate (a) Variable cost (per employee per month) (b) Fixed cost per month

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1 The hire of tools or equipment for a particular job Specific costs of the workforce used to make a product

2 Administration overhead = Depreciation of office buildings and equipment Selling overhead = Printing and stationery (catalogues, price lists) Distribution overhead = Wages of packers, drivers and despatch clerks

3 Functional costs are classified as follows. Production or manufacturing costs Administration costs Marketing or selling and distribution costs

4 A fixed cost is a cost which is incurred for a particular period of time and which, within certain activity levels, is unaffected by changes in the level of activity. A variable cost is a cost which tends to vary with the level of activity. 5 Production costs are costs identified with a finished product. Such costs are initially identified as part of the value of inventory. They become expenses only when the inventory is sold.

Non-production costs are costs that are deducted as expenses during the current period without ever being included in the value of inventory held. 6 A cost centre acts as a collecting place for certain costs before they are analysed further. 7 A cost unit is a unit of product or service to which costs can be related. The cost unit is the basic control unit for costing purposes. 8 A profit centre is similar to a cost centre but is accountable for costs and

revenues. 9 An investment centre is a profit centre with additional responsibilities for capital investment and possibly financing. 10 The variability of input costs with activity undertaken. 11 Rise

12 (a) Step cost. Example: rent, supervisors' salaries (b) Variable cost. Example: raw materials, direct labour (c) Semi-variable cost. Example: electricity and telephone (d) Fixed. Example: rent, depreciation (straight-line) 13 True

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14 (a) Variable cost = Rs. 50,000 per employee per month (b) Fixed costs = Rs. 10,000,000 per month Activity Cost Rs '000 High 1,300 75,000 Low 1,175 68,750 125 6,250 Variable cost per employee = Rs. 6,250,000/125 = Rs. 50,000 For 1,175 employees, total cost = Rs. 68,750,000 Total cost = variable cost + fixed cost Rs. 68,750,000 = (1,175 Rs. 50,000) + fixed cost Fixed cost = Rs. 68,750,000 – Rs. 58,750,000 = Rs. 10,000,000

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Knowledge Component A Cost accounting 1.3 Labour costs 1.3.1 Compute labour costs using different remuneration methods 1.3.2 Compute labour cost for a production organisation

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INTRODUCTION Just as management need to control inventories and operate an appropriate valuation policy in an attempt to control material costs, so too must they be aware of the most suitable remuneration policy for their organisation. We will be looking at a number of methods of remuneration and will consider the various types of bonus/incentive schemes that exist. The last part of this chapter recaps direct and indirect labour costs.

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CHAPTER CONTENTS

LEARNING OUTCOME1 Time-based pay 1.3.12 Timesheets 1.3.13 Guaranteed remuneration 1.3.14 Bonus schemes 1.3.15 Recap – direct and indirect labour 1.3.2

1 Time-based pay

There are three basic groups of remuneration method: time work, piecework schemes and bonus/incentive schemes. Labour remuneration methods have an effect on the following. The cost of finished products and services The morale and efficiency of employees 1.1 Time-based pay 1. Time Based Pay 2. Performance Based Pay --> No example questions 3. Guaranteed Remuneration --> Not covered 4. Bonus Schemes --> No example questions The most common form of time work is a day-rate system in which wages are calculated by the following formula. Wages = Hours worked rate of pay per hour

1.1.1 Overtime premiums If an employee works for more hours than the basic daily requirement he may be entitled to an overtime payment. Hours of overtime are usually paid at a premium rate. For instance, if the basic day-rate is Rs. 400 per hour and overtime is paid at time-and-a-quarter, eight hours of overtime would be paid the following amount.

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Rs Basic pay (8 Rs. 400) 3,200 Overtime premium (8 Rs. 100) 800 Total (8 Rs. 500) 4,000 The overtime premium is the extra rate per hour which is paid, not the whole of the payment for the overtime hours. If employees work unsocial hours, for instance overnight, they may be entitled to a shift premium. The extra amount paid per hour, above the basic hourly rate, is the shift premium. Overtime premium is usually regarded as an overhead expense (indirect cost), because it is 'unfair' to charge the items produced in overtime hours with the premium. Why should an item made in overtime be more costly just because, by chance, it was made after the employee normally clocks off for the day? However, if the overtime was specifically asked for by the customer then this expense become a ‘Direct’ cost. Overtime premium paid to both direct and indirect workers is an indirect cost, except in two particular circumstances. (i) If overtime is worked at the specific request of a customer to get his order completed, the overtime premium paid is a direct cost of the order. (ii) If overtime is worked regularly by a production department in the normal course of operations, the overtime premium paid to direct workers could be incorporated into the (average) direct labour hourly rate. 1.1.2 Summary of day-rate systems (a) They are easy to understand. (b) They do not lead to very complex negotiations when they are being revised. (c) They are most appropriate when the quality of output is more important than the quantity, or where there is no basis for payment by performance. (d) There is no incentive for employees who are paid on a day-rate basis to improve their performance. 1.1.3 Idle time

Idle time has a cost because employees will still be paid their basic wage or salary for these unproductive hours and so there should be a record of idle time.

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Idle time occurs when employees cannot get on with their work, through no fault of their own. Examples are as follows. Machine breakdowns Shortage of work A record of idle time may simply comprise an entry on time sheets coded to 'idle time' generally, or separate idle time cards may be prepared. A supervisor might enter the time of a stoppage, its cause, its duration and the employees made idle on an idle time record card. Each stoppage should have a reference number which can be entered on time sheets or job cards. 1.1.4 Wages department Responsibilities of the payroll department include the following. Preparation of the payroll and payment of wages Maintenance of employee records Summarising wages cost for each cost centre Summarising the hours worked for each cost centre Summarising other payroll information, eg bonus payment, pensions etc Providing an internal check for the preparation and pay-out of wages Attendance cards are the basis for payroll preparation. For time workers, the gross wage is the product of time attended and rate of pay. To this is added any overtime premium or bonus. For piece workers, gross wages are normally obtained by the product of the number of good units produced and the unit rate, with any premiums, bonuses and allowances for incomplete jobs added. After calculation of net pay, a pay slip is prepared showing all details of earnings and deductions. The wage envelope or the attendance card may be used for this purpose. When the payroll is complete, a coin and note analysis is made and a cheque drawn to cover the total amount. On receipt of the cash, the pay envelopes are made up and sealed. A receipt is usually obtained on pay-out (the attendance card can be used). Wages of absentees are retained until claimed by an authorised person. Internal checks are necessary to prevent fraud. One method is to distribute the payroll work so that no person deals completely with any transaction. All calculations should be checked on an adding machine where possible. Makeup of envelopes should not be done by persons who prepare the payroll. The cashier should reconcile his analysis with the payroll summary.

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1.1.5 Idle time ratio

FORMULA TO LEARN

Idle time ratio = Idle hoursTotal hours 100% The idle time ratio is useful because it shows the proportion of available hours which were lost as a result of idle time. 1.2 Performance based pay: Piecework schemes

FORMULA TO LEARN In a piecework scheme, wages are calculated by the following formula. Wages = Units produced Rate of pay per unit Suppose for example, an employee is paid Rs. 100 for each unit produced and works a 40-hour week. Production overhead is added at the rate of Rs. 200 per direct labour hour. Weekly Pay Conversion Conversion

production (40 hours) Overhead cost cost per unit Units Rs '000 Rs '000 Rs '000 Rs 40 4 8 12 300 50 5 8 13 260 60 6 8 14 233 70 7 8 15 214 As his output increases, his wage increases and at the same time unit costs of output are reduced. It is normal for pieceworkers to be offered a guaranteed minimum wage, so that they do not suffer loss of earnings when production is low through no fault of their own. If an employee makes several different types of product, it may not be possible to add up the units for payment purposes. Instead, a standard time allowance is given for each unit to arrive at a total of piecework hours for payment. QUESTION Weekly pay Penny Pincher is paid Rs. 25 for each towel she weaves, but she is guaranteed a minimum wage of Rs. 3,000 for a 40 hour week. In a series of four weeks, she makes 100, 120, 140 and 160 towels.

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Required

Calculate her pay each week, and the conversion cost per towel if production overhead is added at the rate of Rs. 250 per direct labour hour. ANSWER

Unit Production Conversion conversion

Week Output Pay overhead cost cost units Rs '000 Rs '000 Rs '000 Rs 1 100 (minimum) 3 5 8 80 2 120 3 5 8 66 3 140 3.5 5 8.5 60 4 160 4 5 9 56 There is no incentive to Penny Pincher to produce more output unless she can exceed 120 units in a week. The guaranteed minimum wage in this case is too high to provide an incentive. 1.2.1 Example: Piecework An employee is paid Rs. 50 per piecework hour produced. In a standard week he produces the following output. Piecework time allowed per unit 3 units of product A 2.5 hours 5 units of product B 8.0 hours Required

Calculate the employee's pay for the week. Solution Piecework hours produced are as follows. Product A 3 2.5 hours 7.5 hours Product B 5 8 hours 40.0 hours Total piecework hours 47.5 hours Therefore employee's pay = 47.5 Rs. 50 = Rs. 2,375 for the week. 1.2.2 Differential piecework scheme

Differential piecework schemes offer an incentive to employees to increase their output by paying higher rates for increased levels of production. For example: Up to 80 units per week, rate of pay per unit = Rs. 20 80 to 90 units per week, rate of pay per unit = Rs. 24 Above 90 units per week, rate of pay per unit = Rs. 26

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Employers should obviously be careful to make it clear whether they intend to pay the increased rate on all units produced, or on the extra output only. 1.2.3 Summary of piecework schemes

They enjoy fluctuating popularity. They are occasionally used by employers as a means of increasing pay levels. They are often seen to drive employees to work too hard to earn a satisfactory wage. Careful inspection of output is necessary to ensure that quality doesn't fall as production increases. 1.3 High day-rate system A high day-rate system is a system where employees are paid a high hourly wage rate in the expectation that they will work more efficiently than similar employees on a lower hourly rate in a different company.

1.3.1 Example: High day-rate system For example, if an employee would make 100 units in a 40-hour week if he were paid Rs. 20 per hour, but 120 units if he were paid Rs. 25 per hour, and if production overhead is added to cost at the rate of Rs. 20 per direct labour hour, costs per unit of output would be as follows. (a) Costs per unit of output on the low day-rate scheme would be: 40 × Rs. 40100 = Rs. 16 per unit (b) Costs per unit of output on the high day-rate scheme would be: 40 × Rs. 45120 = Rs. 150 per unit (c) The labour cost per unit is lower in the first scheme (Rs. 80) than in the second (Rs. 83.33), but the unit conversion cost (labour plus production overhead) is higher: overhead costs per unit are higher at Rs. 80 than with the high day-rate scheme (Rs. 66.67). (d) In this example, the high day-rate scheme would reward both employer (a lower unit cost by Rs. 10) and employee (an extra Rs. 50 earned per hour).

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1.3.2 Advantages and disadvantages of high day rate schemes There are two advantages of a high day-rate scheme over other incentive schemes. (a) It is simple to calculate and easy to understand. (b) It guarantees the employee a consistently high wage. The disadvantages of such schemes are as follows. (a) Employees cannot earn more than the fixed hourly rate for their extra effort. In the previous example, if the employee makes 180 units instead of 120 units in a 40-hour week on a high day-rate pay scheme, the cost per unit would fall to Rs. 1 but his wage would be the same – 40 hours at Rs. 4.50. All the savings would go to benefit the company and none would go to the employee. (b) There is no guarantee that the scheme will work consistently. The high wages may become the accepted level of pay for normal working, and supervision may be necessary to ensure that a high level of productivity is maintained. Unit costs would rise. (c) Employees may prefer to work at a normal rate of output, even if this entails accepting the lower wage paid by comparable employers.

2 Timesheets Even though salaried staff are paid a flat rate monthly, they may be required to prepare timesheets. The reasons are as follows. (a) Timesheets provide management with information (eg product costs). (b) Timesheet information may provide a basis for billing for services provided (eg service firms where clients are billed based on the number of hours work done). (c) Timesheets are used to record hours spent and so support claims for overtime payments by salaried staff.

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An example of a timesheet (as used in the service sector) is shown as follows. WEEKLY TIME SHEET

NAME

CLIENT or NON-

CHARGEABLE

TIME DESCRIPTION

Staff NumberWEEK end dateD D M M Y Y

HOURS WORKED O/T

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Sun M T W T FTotal HrsIncl O/T

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Client Number Charge A/C

Number

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TOTAL

AuthorisedSigned Date

TOTAL

Weekly service sector timesheet

3 Guaranteed remuneration

3.1 Guaranteed remuneration Guaranteed remuneration is a fixed monetary amount paid by an employer to an employee. The most common form of guaranteed renumeration is a base level salary. Guaranteed renumeration may also include holiday and sick pay and excludes variable pay such as overtime, bonuses or other discretionary incentives. The basic element of guaranteed remuneration is base salary which may be paid on an hourly, daily, weekly, or monthly rate. Base salary is provided for doing the job the employee is hired to do. Guaranteed remuneration is a fixed cost as represents the minimum amount which must be paid regardless of production volume. Therefore, guaranteed remuneration is not relevant for decision making. For example, each employee is guaranteed a weekly salary of 30 hours. Weekly production requires 40 hours per employee. Therefore, only the additional 10 hours of variable labour cost per employee is relevant for decision making.

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4 Bonus schemes

4.1 Bonus schemes In general, bonus schemes were introduced to compensate workers paid under a time-based system for their inability to increase earnings by working more efficiently. Various types of incentive and bonus schemes have been devised which encourage greater productivity. The characteristics of such schemes are as follows. (a) Employees are paid more for their efficiency. (b) The profits arising from productivity improvements are shared between employer and employee. (c) Morale of employees is likely to improve since they are seen to receive extra reward for extra effort. A bonus scheme must satisfy certain conditions to operate successfully. (a) Its objectives should be clearly stated and attainable by the employees. (b) The rules and conditions of the scheme should be easy to understand. (c) It must win the full acceptance of everyone concerned. (d) It should be seen to be fair to employees and employers. (e) The bonus should ideally be paid soon after the extra effort has been made by the employees. (f) Allowances should be made for external factors outside the employees' control which reduce their productivity (machine breakdowns, material shortages). (g) Only those employees who make the extra effort should be rewarded. (h) The scheme must be properly communicated to employees. We shall be looking at the following types of incentive schemes in detail.

High day-rate system Profit-sharing schemes Individual bonus schemes Incentive schemes involving shares Group bonus schemes Value-added incentive schemes Some organisations employ a variety of incentive schemes. A scheme for a production labour force may not necessarily be appropriate for white-collar workers. An organisation's incentive schemes may be regularly reviewed, and altered as circumstances dictate. 4.2 Individual bonus schemes An individual bonus scheme is a remuneration scheme whereby individual employees qualify for a bonus on top of their basic wage, with each person's bonus being calculated separately.

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(a) The bonus is unique to the individual. It is not a share of a group bonus. (b) The individual can earn a bonus by working at an above-target standard of efficiency. (c) The individual earns a bigger bonus the greater his efficiency, although the bonus scheme might incorporate quality safeguards, to prevent individuals from sacrificing quality standards for the sake of speed and more pay. To be successful, however, an individual bonus scheme must take account of the following factors. (a) Each individual should be rewarded for the work done by that individual. This means that each person's output and time must be measured separately. Each person must therefore work without the assistance of anyone else. (b) Work should be fairly routine, so that standard times can be set for jobs. (c) The bonus should be paid soon after the work is done, to provide the individual with the incentive to try harder. QUESTION Bonus Employees work on the production line for 8 hours per day and the basic rate of pay is Rs 50 per hour. The standard time to produce one unit is 2 minutes. A bonus is earned where employees exceed the expected daily production target. It is calculated as 75% of time saved at the basic rate of Rs 50 per hour. What is the bonus earned where one employee produces 340 units in one day? ANSWER Production time available in minutes = 8 hours x 60 minutes = 480 minutes Expected production = 480 minutes /2 minutes per unit = 240 units One employee produced 340 units in 8 hours, which is 100 units (340 units – 240 units) higher than expectation. 100 units should have taken an additional 200 minutes (100 units 2 minutes per unit). Performance based pay = 75% 200 minutes saved = 150 minutes Performance based pay = 2.5 hours Rs 50 per hour = Rs 125.

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4.3 Group bonus schemes A group bonus scheme is an incentive plan which is related to the output performance of a group of workers, a department, or even the whole factory. Where individual effort cannot be measured, and employees work as a team, an individual incentive scheme is impracticable, but a group bonus scheme would be feasible. The other advantages of group bonus schemes are as follows. (a) They are easier to administer because they reduce the clerical effort required to measure output and calculate individual bonuses. (b) They increase co-operation between fellow workers. (c) They have been found to reduce accidents, spoilage, waste and absenteeism. Serious disadvantages would occur in the following circumstances. (a) The employee groups demand low efficiency standards as a condition of accepting the scheme. (b) Individual employees are browbeaten by their fellow workers for working too slowly.

QUESTION Bonus An employee has agreed to pay an annual group bonus as follows, based on production activity in the year. This bonus will be split equally amongst production employees. Between 100,000 and 120,000 units = Rs 25,000 Between 125,000 and 150,000 units = Rs 40,000 Greater than 150,000 units = Rs 50,000 8 production employees have produced, on average, 15,000 units per month. What is the group bonus payable per employee. ANSWER Total annual production = 12 months x 15,000 units = 180,000 units Group bonus payable is therefore Rs 50,000 This represents a bonus of Rs 100,000/8 = Rs 6,250 per employee

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5 Recap – direct and indirect labour We had a brief look at direct and indirect labour costs in Chapter 2. Have a go at the following question to remind yourself about the classification of labour costs. QUESTION Direct and indirect costs A direct labour employee's wage in week 5 consists of the following. Rs (a) Basic pay for normal hours worked, 36 hours at Rs. 40 per hour = 1,440 (b) Pay at the basic rate for overtime, 6 hours at Rs. 40 per hour = 240 (c) Overtime shift premium, with overtime paid at time-and-a-quarter ¼ 6 hours Rs. 40 per hour = 60 (d) A bonus payment under a group bonus (or 'incentive') scheme: bonus for the month = 300 Total gross wages in week 5 for 42 hours of work 2,040 Required

Assess which costs are direct costs and which are indirect costs. ANSWER Items (a) and (b) are direct labour costs of the items produced in the 42 hours worked in week 5. Overtime premium, item (c), is usually regarded as an overhead expense, because it is 'unfair' to charge the items produced in overtime hours with the premium. Why should an item made in overtime be more costly just because, by chance, it was made after the employee normally clocks off for the day? Group bonus scheme payments, item (d), are usually overhead costs, because they cannot normally be traced directly to individual products or jobs. In this example, the direct labour employee costs were Rs. 1,680 in direct costs and Rs. 360 in indirect costs. QUESTION Overtime Jaffa Co employs two types of labour: skilled workers, considered to be direct workers, and semi-skilled workers considered to be indirect workers. Skilled workers are paid Rs. 100 per hour and semi-skilled Rs. 50 per hour. The skilled workers have worked 20 hours overtime this week, 12 hours on specific orders and 8 hours on general overtime. Overtime is paid at a rate of time and a quarter.

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The semi-skilled workers have worked 30 hours overtime, 20 hours for a specific order at a customer's request and the rest for general purposes. Overtime again is paid at time and a quarter. Required

Calculate the total overtime pay considered to be a direct cost for this week. A Rs. 2,750 C Rs. 3,750 B Rs. 3,550 D Rs. 4,375 ANSWER Direct

cost Indirect

cost Rs Rs Skilled workers Specific overtime (12 hours Rs. 100 1.25) 1,500 General overtime (8 hours Rs. 100 1) 800 (8 hours Rs. 100 0.25) 200 Semi-skilled workers Specific overtime (20 hours Rs. 500 1.25) 1,250 General overtime (10 hours Rs. 500 1.25) 625 3,550 825 The correct answer is therefore B. If you selected option A, you forgot to include the direct cost of the general overtime of Rs. 800 for the skilled workers. If you selected option C, you included the overtime premium for skilled workers' general overtime of Rs. 200. If you selected option D, you calculated the total of direct cost + indirect cost instead of the direct cost.

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There are three basic groups of remuneration method: time work, piecework

schemes and bonus/incentive schemes. Idle time has a cost because employees will still be paid their basic wage or salary for these unproductive hours and so there should be a record of idle time.

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1 Explain briefly the term 'idle time' by using an example. 2 State the idle time ratio.

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1 Idle time occurs when employees cannot get on with their work, through no fault of their own, for example when machines break down or there is a shortage of work. 2 Idle time ratio = Idle hoursTotal hours 100%

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Knowledge Component A Cost accounting 1.4 Overhead costs 1.4.1 Prepare an overhead cost statement 1.4.2 Compute the full cost of products, services and activities under absorption costing and marginal costing

INTRODUCTION This chapter begins by explaining the meaning over Overheads and looks at how they are treated under Absorption costing, this is a method of accounting for overheads. It is basically a method of sharing out overheads incurred amongst units produced. This chapter then explains why absorption costing might be necessary and provides an overview of how the cost of a unit of product is built up under a system of absorption costing. A detailed analysis of this costing method is then provided, covering the three stages of absorption costing: allocation, apportionment and absorption.

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LEARNING OUTCOME1 Overheads 1.4.12 Overhead allocation 1.4.13 Overhead apportionment 1.4.14 Reapportionment under reciprocal servicing 1.4.15 Overhead absorption 1.4.26 Ledger entries relating to overheads 1.4.2

1 Overheads

Overhead is the cost incurred in the course of making a product, providing a service or running a department, which cannot be traced directly and in full to the product, service or department. Overhead is actually the total of the following. Indirect materials Indirect expenses Indirect labour The total of these indirect costs is usually split into the following categories. Production Selling and distribution Administration In cost accounting there are two schools of thought as to the correct method of dealing with overheads. Absorption costing Marginal costing (This is covered in Chapter 11)

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2 Overhead allocation

2.1 Introduction

Allocation is the process by which whole cost items are charged direct to a cost unit or cost centre. Cost centres may be one of the following types. (a) A production department, to which production overheads are charged (b) A production area service department, to which production overheads are charged (c) An administrative department, to which administration overheads are charged (d) A selling or a distribution department, to which sales and distribution overheads are charged (e) An overhead cost centre, to which items of expense which are shared by a number of departments, such as rent and rates, heat and light and the canteen, are charged The following costs would therefore be charged to cost centres through the process of allocation. Direct labour will be charged to a production cost centre. The cost of a warehouse security guard will be charged to the warehouse cost centre. Paper (recording computer output) will be charged to the computer department. Costs such as the canteen are charged direct to various overhead cost centres. 2.2 Example: Overhead allocation Consider the following costs of a company. Wages of the foreman of department A Rs. 40,000 Wages of the foreman of department B Rs. 30,000 Indirect materials consumed in department A Rs. 10,000 Rent of the premises shared by departments A and B Rs. 60,000 The cost accounting system might include three overhead cost centres. Cost centre: 101 Department A 102 Department B 201 Rent

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Overhead costs would be allocated directly to each cost centre, ie Rs. 40,000 + Rs. 10,000 to cost centre 101, Rs. 30,000 to cost centre 102 and Rs. 60,000 to cost centre 201. The rent of the factory will be subsequently shared between the two production departments, but for the purpose of day-to-day cost recording, the rent will first of all be charged in full to a separate cost centre. 3 Overhead apportionment

Apportionment is a procedure whereby indirect costs are spread fairly between cost centres. Service cost centre costs may be apportioned to production cost centres by using the reciprocal method. The following question will be used to illustrate the overhead apportionment process. 3.1 Example: Overhead apportionment – Gihan LLC Gihan LLC has two production departments (A and B) and two service departments (maintenance and stores). Details of next year's budgeted overheads are shown below. Total (Rs '000) Total (Rs '000) Heat and light 19,200 Rent and rates 38,400 Repair costs 9,600 Canteen 9,000 Machinery depreciation 54,000 Machinery insurance 25,000 Details of each department are as follows. A B Maintenance Stores Total Floor area (m2) 6,000 4,000 3,000 2,000 15,000 Machinery book value (Rs '000) 48,000 20,000 8,000 4,000 80,000 Number of employees 50 40 20 10 120 Allocated overheads (Rs '000)

15,000 20,000 12,000 5,000 50,000

Service departments' services were used as follows. A B Maintenance Stores Total Maintenance hours worked 5,000 4,000 ---- 1,000 10,000 Number of stores requisitions 3,000 1,000 ---- ---- 4,000

3.2 Stage 1: Apportioning general overheads Overhead apportionment follows on from overhead allocation. The first stage of overhead apportionment is to identify all overhead costs as production department, production service department, administration or selling and

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distribution overhead. The costs for heat and light, rent and rates, the canteen and so on (ie costs allocated to general overhead cost centres) must therefore be shared out between the other cost centres. 3.2.1 Bases of apportionment It is considered important that overhead costs should be shared out on a fair basis. You will appreciate that because of the complexity of items of cost it is rarely possible to use only one method of apportioning costs to the various departments of an organisation. The bases of apportionment for the most usual cases are given below. Overhead to which the basis applies Basis Rent, rates, heating and light, repairs and depreciation of buildings Floor area occupied by each cost centre Depreciation, insurance of equipment Cost or book value of equipment Personnel office, canteen, welfare, wages and cost offices, first aid Number of employees, or labour hours worked in each cost centre Note that heating and lighting may also be apportioned using volume of space occupied by each cost centre. 3.2.2 Example: Gihan LLC Using the Gihan LLC information above, demonstrate how overheads should be apportioned between the four departments (to the nearest '000). Solution

Item of cost Basis of Department apportionment Mainte

-nance

A B Stores Total Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Heat and light Floor area (W1) 7,680 5,120 3,840 2,560 19,200Repair costs Floor area (W1) 3,840 2,560 1,920 1,280 9,600Machine dep'n Machinery value (W2) 32,400 13,500 5,400 2,700 54,000Rent and rates Floor area (W1) 15,360 10,240 7,680 5,120 38,400Canteen No of employees (W3) 3,750 3,000 1,500 750 9,000Machine insurance Machinery value (W2) 15,000 6,250 2,500 1,250 25,000Total 78,030 40,670 22,840 13,660

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WORKINGS (1) Overhead apportioned by floor area Overhead apportioned to department = area floor Total departmentbyoccupied area Floor total overhead For example: Heat and light apportioned to Dept A = 15,0006,000 19,200,000 = Rs. 7,680,000 (2) Overheads apportioned by machinery value Overheads apportioned to department = machinery of value Total machinery s'department of Value total overhead (3) Overheads apportioned by number of employees Overheads apportioned to department = employees of no Total departmentinemployees of No total overhead 3.3 Stage 2 – Reapportion service department costs Only production departments produce goods that will ultimately be sold. In order to calculate a correct price for these goods, we must determine the total cost of producing each unit – that is, not just the cost of the labour and materials that are directly used in production, but also the indirect costs of services provided by such departments as maintenance, stores and canteen. Our aim is to reapportion all the service department costs to the production departments, in one of three ways. (a) The direct method, where the service centre costs are apportioned to production departments only. (b) The step-down method, where each service centre's costs are not only apportioned to production departments but to some (but not all) of the other service centres that make use of the services provided. (c) The repeated distribution (or reciprocal) method, where service centre costs are apportioned to both the production departments and service departments that use the services. The service centre costs are then gradually apportioned to the production departments. This method is used only when service departments work for each other – that is, service

departments use each other's services (for example, the maintenance department will use the canteen, whilst the canteen may rely on the maintenance department to ensure its equipment is functioning properly, or

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to replace bulbs, plugs, and so on). Your syllabus states that only a discussion is expected on reciprocal servicing. 3.3.1 Basis of apportionment Whichever method is used to apportion service cost centre costs, the basis of apportionment must be fair. A different apportionment basis may be applied for each service cost centre. This is demonstrated in the following table. Service cost centre Possible basis of apportionment Stores Number or cost value of material requisitions Maintenance Hours of maintenance work done for each cost centre Production planning Direct labour hours worked in each production cost centre 3.3.2 Direct method of reapportionment The direct method of reapportionment involves apportioning the costs of each service cost centre to production cost centres only. This method is most easily explained by working through the following example. 3.3.3 Example: Gihan LLC direct method (ignores inter-service department

work)

A B Maintenance Stores Rs '000 Rs '000 Rs '000 Rs '000 Allocated costs (from Section 4.1) 15,000 20,000 12,000 5,000 General costs (from Section 4.2.2) 78,030 40,670 22,840 13,660 93,030 60,670 34,840 18,660 Service departments' services were used as follows. A B Maintenance Stores Total Maintenance hours used 5,000 4,000 – 1,000 10,000 Number of stores requisitions 3,000 1,000 1,000 – 5,000

Required

Calculate the total production overhead costs of Departments A and B, using the direct method of reapportionment (to the nearest '000).

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Solution

Service department

Basis of apportionment Total cost

Dept A Dept B Rs '000 Rs '000 Rs '000 Maintenance Maintenance hours (W1) 34,840 19,356 15,484 Stores Number of requisitions (W2) 18,660 13,995 4,665 53,500 33,351 20,149 Previously allocated costs 153,700 93,030 60,670 Total overhead 207,200 126,381 80,819 WORKINGS (1) Maintenance department overheads These are reapportioned as follows. Total hours worked in Departments A and B = 5,000 + 4,000 = 9,000 hours Reapportioned to Department A = 5,0009,000 Rs. 34,840,000 = Rs. 19,356,000 Reapportioned to Department B = 4,0009,000 Rs. 34,840,000 = Rs. 15,484,000

(2) Stores department overheads These are reapportioned as follows. Total number stores requisitions = 3,000 + 1,000 (for Departments A and B) = 4,000 Reapportioned to Department A = 3,0004,000 Rs. 18,660,000 = Rs. 13,995,000 Reapportioned to Department B = 1,0004,000 Rs. 18,660,000 = Rs. 4,665,000 The total overhead has now been shared, on a fair basis, between the two production departments.

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QUESTION Reapportionment (1) The following table shows the overheads apportioned to the five departments in Kusum LLC. Machine shop

Machine shop

Total A B Assembly Canteen Maintenance Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Indirect wages 78,560 8,586 9,190 15,674 29,650 15,460 Consumable Materials 16,900 6,400 8,700 1,200 600 – Rent and rates 16,700 3,711 4,453 5,567 2,227 742 Insurance 2,400 533 640 800 320 107 Power 8,600 4,730 3,440 258 – 172 Heat and light 3,400 756 907 1,133 453 151 Depreciation 40,200 20,100 17,900 2,200 – – 166,760 44,816 45,230 26,832 33,250 16,632

Other information: Machine Machine Total shop A shop B Assembly Canteen MaintenancePower usage – technical estimates (%) 100 55 40 3 – 2 Direct labour (hours) 35,000 8,000 6,200 20,800 – – Machine usage (hours) 25,200 7,200 18,000 – – – Area (m2) 45,000 10,000 12,000 15,000 6,000 2,000 Required

Calculate overhead totals for Kusum LLC’s three production departments: Machine Shop A, Machine Shop B and Assembly using the bases which you consider to be the most appropriate. ANSWER Basis of Mainte- appor- Total A B Assembly Canteen nance tionment Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Total overheads 166,760 44,816 45,230 26,832 33,250 16,632 Reapportion (W1) – 7,600 5,890 19,760 (33,250) – Dir labour Reapportion (W2) – 4,752 11,880 – – (16,632) Mac usage Totals 166,760 57,168 63,000 46,592 – –

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WORKINGS (1) Canteen overheads Total direct labour hours = 35,000 Machine shop A = 35,0008,000 Rs. 33,250,000 = Rs. 7,600,000 Machine shop B = 35,0006,200 Rs. 33,250,000 = Rs. 5,890,000 Assembly = 35,00020,800 Rs. 33,250,000 = Rs. 19,760,000 (2) Maintenance overheads Total machine hours = 25,200 Machine shop A = 25,2007,200 Rs. 16,632,000 = Rs. 4,752,000 Machine shop B = 25,20018,000 Rs. 16,632,000 = Rs. 11,880,000 The total overhead has now been shared, on a fair basis, between the three production departments.

3.3.4 Elimination method of reapportionment This method works as follows. Step 1 Reapportion one of the service cost centre's overheads to all of the other centres which make use of its services (production and service). Step 2 Reapportion the overheads of the remaining service cost centre to the production departments only. The other service cost centre is ignored. 3.3.5 Example: Gihan LLC elimination method

A B Maintenance Stores Rs '000 Rs '000 Rs '000 Rs '000 Allocated costs (from Section 4.1) 15,000 20,000 12,000 5,000 General costs (from Section 4.2.2) 78,030 40,670 22,840 13,660 93,030 60,670 34,840 18,660

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Service departments' services were used as follows. A B Maintenance Stores TotalMaintenance hours used 5,000 (50%)* 4,000 (40%) – 1,000(10%) 10,000 (100%) Number of stores requisitions 3,000** (60%) 1,000 (20%) 1,000 (20%) – 5,000(100%)* 5,000/10,000 100% = 50%, 4,000/10,000 = 40%, 1,000/10,000 = 10%** 3,000/5,000 100% = 60%, 1,000/5,000 = 20%

Required

Prepare the overhead schedule to show the apportionment of the service department overhead costs using the elimination method of apportionment, starting with the stores department (to the nearest '000). Solution

A B Maintenance Stores Rs '000 Rs '000 Rs '000 Rs '000 Overhead costs (general and allocated) 93,030 60,670 34,840 18,660 Apportion stores (60%/20%/20%) 11,196 3,732 3,732 (18,660) 38,572 Apportion maintenance (5/9 / 4/9) 21,429 17,143 (38,572) 125,655 81,545 – – If the first apportionment had been the maintenance department, then the overheads of Rs. 34,840,000 would have been apportioned as follows. A B Maintenance Stores Rs '000 Rs '000 Rs '000 Rs '000 Overhead costs (general and allocated) 93,030 60,670 34,840 18,660 Apportion maintenance (50%/40%/10%) 17,420 13,936 (34,840) 3,484 - 22,144Apportion stores (3/4 / 1/4) 16,608 5,536 (22,144) 127,058 80,142 - -

Note. Notice how the final results differ, depending upon whether the stores department or the maintenance department is apportioned first. If one service cost centre, compared with the other(s), has higher overhead costs and carries out a bigger proportion of work for the other service cost centre(s), then the overheads of this service centre should be reapportioned first.

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QUESTION Reapportionment (2) Sadikka LLC has two service departments serving two production departments. Overhead costs apportioned to each department are as follows. Production 1 Production 2 Service 1 Service 2 Rs Rs Rs Rs 97,428,000 84,947,000 9,384,000 15,823,000 Service 1 department is expected to work a total of 40,000 hours for the other departments, divided as follows.

Hours Production 1 20,000 Production 2 15,000 Service 2 5,000 Service 2 department is expected to work a total of 12,000 hours for the other departments, divided as follows. Hours Production 1 3,000 Production 2 8,000 Service 1 1,000

Required The finance director has asked you to reapportion the costs of the two service departments using the direct method of apportionment. Prepare the overhead reapportionment schedule (to the nearest '000). ANSWER

Direct apportionment method

Production 1

Production 2

Service 1 Service 2 Rs '000 Rs '000 Rs '000 Rs '000 97,428 84,947 9,384 15,823 Apportion Service 1 costs (20:15) 5,362 4,022 (9,384) – 102,790 88,969 – 15,823Apportion Service 2 costs (3:8) 4,315 11,508 – (15,823) 107,105 100,477 – –

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QUESTION Elimination method When you show the finance director how you have reapportioned the costs of the two service departments, he says 'Did I say that we used the direct method? Well, I meant to say the elimination method.' Required Prepare the overhead apportionment schedule using the elimination method. (Note. Apportion the overheads of service department 1 first.) The calculation should be presented to the nearest '000. ANSWER

Elimination method Production 1

Production 2

Service 1 Service 2 Rs '000 Rs '000 Rs '000 Rs '000 97,428 84,947 9,384 15,823 Apportion Service 1 costs (20:15:5) 4,692 3,519 (9,384) 1,173 102,120 88,466 – 16,996 Apportion Service 2 costs (3:8) 4,635 12,361 – (16,996) 106,755 100,827 – – 4 Reapportionment under reciprocal servicing Now that we have looked at the 'simple' scenario of only one service department making use of the other service department's services, we can move onto the more complicated situation of 'reciprocal' servicing. This is where each service department makes use of the other service department (in the Gihan LLC example, stores would use maintenance and maintenance would use stores).

4.1 Example: Gihan LLC using repeated distribution method A B Maintenance Stores Rs '000 Rs '000 Rs '000 Rs '000 Allocated costs (from Section 4.1) 15,000 20,000 12,000 5,000 General costs (from Section 4.2.2) 78,030 40,670 22,840 13,660 93,030 60,670 34,840 18,660

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A B Maintenance Stores Total Maintenance hours used 5,000 4,000 – 1,000 10,000 Number of stores requisitions 3,000 1,000 1,000 – 5,000 Required

Calculate the total overheads for each of the production departments showing how the Maintenance and Stores departments' overheads would be apportioned to the two production departments (to the nearest '000). Solution Remember to apportion both the general and allocated overheads. The bases of apportionment for Maintenance and Stores are the same as for the previous examples (that is, maintenance hours worked and number of stores requisitions).

A B Maintenance Stores Rs '000 Rs '000 Rs '000 Rs '000 Total overheads (general and allocated) 93,030 60,670 34,840 18,660 Apportion maintenance (note (a)) 17,420 13,936 (34,840) 3,484 NIL 22,144 Apportion stores (note (b)) 13,286 4,429 4,429 (22,144) 4,429 NIL Apportion maintenance 2,215 1,772 (4,429) 442 NIL 442 Apportion stores (note (c)) 332 110 NIL (442) Total overheads 126,283 80,917 NIL NIL Notes (a) It does not matter which department you choose to apportion first. Apportioned as follows:

worked hours emaintenanc Total departmentinworked hours eMaintenanc Rs. 34,840,000 Production department A = 10,0005,000 Rs. 34,840,000 = Rs. 17,420,000 Production department B = 10,0004,000 Rs. 34,840,000 = Rs. 13,936,000 Stores department = 10,0001,000 Rs. 34,840,000 = Rs. 3,484,000

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(b) Stores overheads are apportioned as follows: nsrequisitio stores of number Total departmentfornsrequisitio stores of Number Rs. 22,144,000

Production department A = 3,0005,000 Rs. 22,144,000 = Rs. 13,286,000 Production department B = 1,0005,000 Rs. 22,144,000 = Rs. 4,429,000 Maintenance = 1,0005,000 Rs. 22,144,000 = Rs. 4,429,000 (c) The problem with the repeated distribution method is that you can keep performing the same calculations many times. When you are dealing with a small number (such as Rs. 442,000 above) you can take the decision to apportion the figure between the production departments only. In this case, we ignore the stores requisitions for Maintenance and base the apportionment on the total stores requisitions for the production departments (that is, 4,000). The amount apportioned to production department A was calculated as follows.

B)(A nsrequisitio stores Total Afornsrequisitio Stores

Stores overheads = 4,0003,000 Rs. 442,000 = Rs. 332,000 5 Overhead absorption

The objective of absorption costing is to include in the total cost of a product an appropriate share of the organisation's total overhead. 'An appropriate share' is generally taken to mean an amount which reflects the amount of time and effort that has gone into producing a unit or completing a job. An organisation with one production department that produces identical units will divide the total overheads among the total units produced. Absorption costing is a method for sharing overheads between different products on a fair basis.

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5.1 Is absorption costing necessary? Suppose that a company makes and sells 100 units of a product each week. The prime cost per unit is Rs. 600 and the unit sales price is Rs. 1,000. Production overhead costs Rs. 20,000 per week and administration, selling and distribution overhead costs Rs. 15,000 per week. The weekly profit could be calculated as follows. Rs '000 Rs '000 Sales (100 units Rs. 1,000) 100 Prime costs (100 Rs. 600) 60 Production overheads 20 Administration, selling and distribution costs 15 95 Profit 5 In absorption costing, overhead costs will be added to each unit of product manufactured and sold. Rs per unit Prime cost per unit 600 Production overhead (Rs. 20,000 per week for 100 units) 200 Full factory cost 800 The weekly profit would be calculated as follows. Rs '000 Sales 100 Less factory cost of sales 80 Gross profit 20 Less administration, selling and distribution costs 15 Net profit 5 Sometimes, but not always, the overhead costs of administration, selling and distribution are also added to unit costs, to obtain a full cost of sales. Rs per unit Prime cost per unit 600 Factory overhead cost per unit 200 Administration, selling and distribution costs per unit 150 Full cost of sales 950 The weekly profit would be calculated as follows. Rs Sales 1,000 Less full cost of sales 950 Profit 50 It may already be apparent that the weekly profit is Rs. 50, no matter how the figures have been presented. So, how does absorption costing serve any useful purpose in accounting? The theoretical justification for using absorption costing is that all production overheads are incurred in the production of the organisation's output and so each unit of the product receives some benefit from these costs. Each unit of output should therefore be charged with some of the overhead costs.

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5.1.1 Practical reasons for using absorption costing The main reasons for using absorption costing are for inventory valuations, pricing decisions, and establishing the profitability of different products. (a) Inventory valuations. Inventory in hand must be valued for two reasons. (i) For the closing inventory figure in the statement of financial position (ii) For the cost of sales figure in the statement of profit or loss The valuation of inventory will affect profitability during a period because of the way in which the cost of sales is calculated. The cost of goods produced + the value of opening inventories – the value of closing inventories = the cost of goods sold. In our example, closing inventories might be valued at prime cost (Rs. 6), but in absorption costing, they would be valued at a fully absorbed factory cost, Rs. 8 per unit. (They would not be valued at Rs. 9.50, the full cost of sales, because the only costs incurred in producing goods for finished inventory are factory costs.) (b) Pricing decisions. Many companies attempt to fix selling prices by calculating the full cost of production or sales of each product, and then adding a margin for profit. In our example, the company might have fixed a gross profit margin at 25% on factory cost, or 20% of the sales price, in order to establish the unit sales price of Rs. 10. 'Full cost-plus pricing' can be particularly useful for companies which do jobbing or contract work, where each job or contract is different, so that a standard unit sales price cannot be fixed. Without using absorption costing, a full cost is difficult to ascertain. (c) Establishing the profitability of different products. This argument in favour of absorption costing is more contentious but is worthy of mention here. If a company sells more than one product, it will be difficult to judge how profitable each individual product is, unless overhead costs are shared on a fair basis and charged to the cost of sales of each product. 5.1.2 International Accounting Standard 2 (LKAS 2)

Absorption costing is recommended in financial accounting by IAS 2 Inventories, which deals with financial accounting systems. The cost accountant is (in theory) free to value inventories by whatever method seems best, but where companies integrate their financial accounting and cost accounting systems into a single system of accounting records, the valuation of closing inventories will be determined by IAS 2.

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IAS 2 states that costs of all inventories should comprise those costs which have been incurred in the normal course of business in bringing the inventories to their 'present location and condition'. These costs incurred will include all related production overheads, even though these overheads may accrue on a time basis. In other words, in financial accounting, closing inventories should be valued at full factory cost, and it may therefore be convenient and appropriate to value inventories by the same method in the cost accounting system. 5.1.3 Absorption costing stages The three stages of absorption costing are: 1 Allocation 3 Absorption 2 Apportionment We have looked at Allocation and Apportionment and shall now begin our study of Absorption costing. 5.2 Overhead Absorption

Overhead absorption is the process whereby overhead costs allocated and apportioned to production cost centres are added to unit, job or batch costs. Overhead absorption is sometimes called overhead recovery. Having allocated and/or apportioned all overheads, the next stage in the costing treatment of overheads is to add them to, or absorb them into, cost units. Overheads are usually added to cost units using a predetermined overhead absorption rate, which is calculated using figures from the budget. 5.2.1 Calculation of overhead absorption rates

Step 1 Estimate the overhead likely to be incurred during the coming period. Step 2 Estimate the activity level for the period. This could be total hours, units, or direct costs or whatever it is upon which the overhead absorption rates are to be based. Step 3 Divide the estimated overhead by the budgeted activity level. This produces the overhead absorption rate. Step 4 Absorb the overhead into the cost unit by applying the calculated absorption rate.

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5.2.2 Example: The basics of absorption costing Athena Co makes two products, the Greek and the Roman. Greeks take 2 labour hours each to make and Romans take 5 labour hours. What is the overhead cost per unit for Greeks and Romans respectively if overheads are absorbed on the basis of labour hours? Solution Step 1 Estimate the overhead likely to be incurred during the coming period Athena Co estimates that the total overhead will be Rs. 50,000,000 Step 2 Estimate the activity level for the period Athena Co estimates that a total of 100,000 direct labour hours will be worked Step 3 Divide the estimated overhead by the budgeted activity level Absorption rate = Rs. 50, 000, 000100, 000 hrs = Rs. 500 per direct labour hour Step 4 Absorb the overhead into the cost unit by applying the calculated absorption rate

Greek Roman Labour hours per unit 2 5 Absorption rate per labour hour Rs. 500 Rs. 500 Overhead absorbed per unit Rs. 1,000 Rs. 2,500 It should be obvious to you that, even if a company is trying to be 'fair', there is a great lack of precision about the way an absorption base is chosen. This arbitrariness is one of the main criticisms of absorption costing; if absorption costing is to be used (because of its other virtues) then it is important that the methods used are kept under regular review. Changes in working conditions should, if necessary, lead to changes in the way in which work is accounted for. For example, a labour-intensive department may become mechanised. If a direct labour hour rate of absorption had been used previous to the mechanisation, it would probably now be more appropriate to change to the use of a machine hour rate. 5.2.3 Choosing the appropriate absorption base The different bases of absorption (or 'overhead recovery rates') are as follows. A percentage of direct materials cost A percentage of direct labour cost A percentage of prime cost A rate per machine hour

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A rate per direct labour hour A rate per unit A percentage of factory cost (for administration overhead) A percentage of sales or factory cost (for selling and distribution overhead) The choice of an absorption basis is a matter of judgement and common sense; what is required is an absorption basis which realistically reflects the characteristics of a given cost centre and which avoids undue anomalies. Many factories use a direct labour hour rate or machine hour rate in preference to a rate based on a percentage of direct materials cost, wages or prime cost. (a) A direct labour hour basis is most appropriate in a labour-intensive environment. (b) A machine hour rate would be used in departments where production is controlled or dictated by machines. (c) A rate per unit would be effective only if all units were identical. 5.2.4 Example: Overhead absorption The budgeted production overheads and other budget data of Bridge Cottage LLC are as follows. Production Production Budget dept A dept B Overhead cost Rs. 36,000,000 Rs. 5,000,000 Direct materials cost Rs. 32,000,000 Direct labour cost Rs. 40,000,000 Machine hours 10,000 Direct labour hours 18,000 Units of production 1,000 Required

Calculate the absorption rate using the various bases of apportionment. Solution Department A (i) Percentage of direct materials cost Rs.36, 000, 000Rs. 32, 000, 000 100% = 112.5% (ii) Percentage of direct labour cost Rs. 36, 000, 000Rs. 40, 000, 000 100% = 90% (iii) Percentage of prime cost Rs. 36, 000, 000Rs. 72, 000, 000 100% = 50%

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(iv) Rate per machine hour Rs. 36, 000, 00010, 000 hrs = Rs. 3,600/machine hour (v) Rate per direct labour hour Rs. 36, 000, 00018, 000 hrs = Rs. 2,000/direct labour hour The department B absorption rate will be based on units of output. Rs. 5, 000, 0001, 000 units = Rs. 5,000 per unit produced 5.2.5 Bases of absorption The choice of the basis of absorption is significant in determining the cost of individual units, or jobs, produced. Using the previous example, suppose that an individual product has a material cost of Rs. 80,000, a labour cost of Rs. 85,000, and requires 36 labour hours and 23 machine hours to complete. The overhead cost of the product would vary, depending on the basis of absorption used by the company for overhead recovery. (a) As a percentage of direct material cost, the overhead cost would be 112.5% Rs. 80,000 = Rs. 90,000 (b) As a percentage of direct labour cost, the overhead cost would be 90% Rs. 85,000 = Rs. 76,500 (c) As a percentage of prime cost, the overhead cost would be 50% Rs. 165,000 = Rs. 82,500 (d) Using a machine hour basis of absorption, the overhead cost would be 23 hrs Rs. 3,600 = Rs. 82,800 (e) Using a labour hour basis, the overhead cost would be 36 hrs Rs. 2,000 = Rs. 72,000 In theory, each basis of absorption would be possible, but the company should choose a basis for its own costs which seems to be 'fairest'.

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5.3 Blanket absorption rates and departmental absorption rates 5.3.1 Introduction A blanket overhead absorption rate is an absorption rate used throughout a factory and for all jobs and units of output, irrespective of the department in which they were produced. For example, if total overheads were Rs. 500,000 and there were 250,000 direct machine hours during the period, the blanket overhead rate would be Rs. 2 per direct machine hour and all jobs passing through the factory would be charged at that rate. Blanket overhead rates are not appropriate in the following circumstances. There is more than one department. Jobs do not spend an equal amount of time in each department. If a single factory overhead absorption rate is used, some products will receive a higher overhead charge than they ought 'fairly' to bear, whereas other products will be under-charged. If a separate absorption rate is used for each department, charging of overheads will be fair and the full cost of production of items will represent the amount of the effort and resources put into making them. 5.3.2 Example: Separate absorption rates Barca has two production departments, for which the following budgeted information is available. Department A Department B Total Budgeted overheads Rs. 360,000,000 Rs. 200,000,000 Rs. 560,000,000Budgeted direct labour hours 200,000 hrs 40,000 hrs 240,000 hrs If a single factory overhead absorption rate is applied, the rate of overhead recovery would be: Rs. 560, 000, 000240, 000 hours = Rs. 2,330 per direct labour hour If separate departmental rates are applied, these would be:

Department A = Rs. 360, 000, 000200, 000 hours = Rs. 1,800 per direct labour hour

Department B =Rs. 200, 000, 00040, 000 hours = Rs. 5,000 per direct labour hour

Department B has a higher overhead rate of cost per hour worked than department A.

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Now let us consider two separate jobs. Job X has a prime cost of Rs. 100,000, takes 30 hours in department B and does not involve any work in department A. Job Y has a prime cost of Rs. 100,000, takes 28 hours in department A and 2 hours in department B. Required

Calculate the factory cost of each job, using the following rates of overhead recovery. (a) A single factory rate of overhead recovery (b) Separate departmental rates of overhead recovery Solution Job X Job Y (a) Single factory rate Rs '000 Rs '000 Prime cost 100 100 Factory overhead (30 Rs. 2,330) 70 70 Factory cost 170 170 (b) Separate

departmental rates Rs '000 Rs '000 Prime cost 100 100.00 Factory overhead: department A 0 (28 Rs. 1,800) 50.40 department B (30 Rs. 5,000) 150 (2 Rs. 5,000) 10.00 Factory cost 250 160.40 Using a single factory overhead absorption rate, both jobs would cost the same. However, since job X is done entirely within department B, where overhead costs are relatively higher (whereas job Y is done mostly within department A, where overhead costs are relatively lower) it can be argued that job X should cost more than job Y. This will occur if separate departmental overhead recovery rates are used to reflect the work done on each job in each department separately. If all jobs do not spend approximately the same time in each department then, to ensure that all jobs are charged with their fair share of overheads, it is necessary to establish separate overhead rates for each department.

QUESTION Machine hour absorption rate The following data relate to one year in department A. Budgeted machine hours 25,000 Actual machine hours 21,875 Budgeted overheads Rs. 350,000,000 Actual overheads Rs. 350,000,000

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Required

Calculate the machine hour absorption rate for the above data using the conventional method. A Rs. 12,000 B Rs. 14,000 C Rs. 16,000 D Rs. 18,000 ANSWER The correct answer in this case is B. Overhead absorption rate Don't forget, if your calculations produce a solution which does not correspond with any of the options available, then eliminate the unlikely options and make a guess from the remainder. Never leave out a multiple-choice question. A common pitfall is to think 'we haven't had answer A for a while, so I'll guess that'. The examiner is not required to produce an even spread of A, B, C and D answers in the examination. There is no reason why the answer to every question cannot be D! 5.4 Over and under absorption of overheads 5.4.1 Introduction

Over and under-absorption of overheads occurs because the predetermined overhead absorption rates are based on estimates. The rate of overhead absorption is based on estimates (of both numerator and denominator) and it is quite likely that either one or both of the estimates will not agree with what actually occurs. (a) Over-absorption means that the overheads charged to the cost of sales are greater then the overheads actually incurred. (b) Under-absorption means that insufficient overheads have been included in the cost of sales. It is almost inevitable that at the end of the accounting year there will have been an over-absorption or under-absorption of the overhead actually incurred.

= hours machine Budgeted overheads Budgeted = Rs. 350, 000, 00025, 000 = Rs. 14,000 per machine hour

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5.4.2 Example: Over and under-absorption Suppose that the budgeted overhead in a production department is Rs. 80,000,000 and the budgeted activity is 40,000 direct labour hours. The overhead recovery rate (using a direct labour hour basis) would be Rs. 2,000 per direct labour hour. Actual overheads in the period are, say, Rs. 84,000,000 and 45,000 direct labour hours are worked. Rs '000 Overhead incurred (actual) 84,000 Overhead absorbed (45,000 Rs. 2,000) 90,000 Over-absorption of overhead 6,000 In this example, the cost of produced units or jobs has been charged with Rs. 6,000,000 more than was actually spent. An adjustment to reconcile the overheads charged to the actual overhead is necessary and the over-absorbed overhead will be credited to the profit and loss account at the end of the accounting period. 5.4.3 The reasons for under/over-absorbed overhead

The overhead absorption rate is predetermined from budget estimates of overhead cost and the expected volume of activity. Under or over-recovery of overhead will occur in the following circumstances. Actual overhead costs are different from budgeted overheads The actual activity level is different from the budgeted activity level Actual overhead costs and actual activity level differ from the budgeted costs and level 5.4.4 Example: Reasons for under/over-absorbed overhead Hashini LLC has a budgeted production overhead of Rs. 50,000,000 and a budgeted activity of 25,000 direct labour hours; it has, therefore, a recovery rate of Rs. 2,000 per direct labour hour. Required

Calculate the under/over-absorbed overhead, and the reasons for the under/over-absorption, in the following circumstances. (a) Actual overheads cost Rs. 47,000,000 and 25,000 direct labour hours are worked. (b) Actual overheads cost Rs. 50,000,000 and 21,500 direct labour hours are worked. (c) Actual overheads cost Rs. 47,000,000 and 21,500 direct labour hours are worked.

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Solution (a) Rs '000 Actual overhead 47,000 Absorbed overhead (25,000 Rs. 2,000) 50,000 Over-absorbed overhead 3,000 The reason for the over-absorption is that although the actual and budgeted direct labour hours are the same, actual overheads cost less than expected. (b) Rs '000 Actual overhead 50,000 Absorbed overhead (21,500 Rs. 2,000) 43,000 Under-absorbed overhead 7,000 The reason for the under-absorption is that although budgeted and actual overhead costs were the same, fewer direct labour hours were worked than expected. (c) Rs '000 Actual overhead 47,000 Absorbed overhead (21,500 Rs. 2,000) 43,000 Under-absorbed overhead 4,000 The reason for the under-absorption is a combination of the reasons in (a) and (b). The distinction between overheads incurred (actual overheads) and overheads absorbed is an important one which you must learn and understand. The difference between them is known as under or over-absorbed overheads. QUESTION Under/over-absorbed overhead The budgeted and actual data for River Arrow Products LLC for the year to 31 March 20X5 are as follows. Budgeted Actual Direct labour hours 9,000 9,900 Direct wages Rs. 34,000,000 Rs. 35,500,000 Machine hours 10,100 9,750 Direct materials Rs. 55,000,000 Rs. 53,900,000 Units produced 120,000 122,970 Overheads Rs. 63,000,000 Rs. 61,500,000 The cost accountant of River Arrow Products Co has decided that overheads should be absorbed on the basis of labour hours. Required Calculate the amount of under or over-absorbed overheads for River Arrow Products LLC for the year to 31 March 20X5.

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ANSWER Overhead absorption rate Rs. 63,000,000= = Rs. 7, 000 per hour9,000 Overheads absorbed by production = 9,900 Rs. 7,000 = Rs. 69,300,000 Rs '000 Actual overheads 61,500 Overheads absorbed 69,300 Over-absorbed overheads 7,800 You may find the following graph helpful to your understanding. Rs

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Activity Figure 10.1: Identifying under/over-absorbed overhead You can see from the graph that when we absorb overheads, we are really treating them as variable costs. They are, however, fixed costs. The graph highlights the fact that if we treat fixed costs as variable costs, this will result in under- or over-absorption. QUESTION Budgeted overhead absorption rate A management consultancy recovers overheads on chargeable consulting hours. Budgeted overheads were Rs. 615,000,000 and actual consulting hours were 32,150. Overheads were under-recovered by Rs. 35,000,000. Required

Calculate the budgeted overhead absorption rate per hour if actual overheads were Rs. 694,075,000. A Rs. 19,130 B Rs. 20,500 C Rs. 21,590 D Rs. 22,680

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ANSWER Rs '000 Actual overheads 694,075 Under-recoverable overheads 35,000 Overheads recovered for 32,150 hours at budgeted overhead absorption rate (x) 659,075 32,150x = 659,075,000 x = 32,150 0659,075,00 = Rs. 20,500 The correct option is B. 6 Ledger entries relating to overheads

6.1 Introduction The bookkeeping entries for overheads are not as straightforward as those for materials and labour. We shall now consider the way in which overheads are dealt with in a cost accounting system. When an absorption costing system is in use we now know that the amount of overhead included in the cost of an item is absorbed at a predetermined rate. The entries made in the cash book and the nominal ledger, however, are the actual amounts. You will remember that it is highly unlikely that the actual amount and the predetermined amount will be the same. The difference is called under or over-absorbed overhead. To deal with this in the cost accounting books, therefore, we need to have an account to collect under or over-absorbed amounts for each type of overhead. 6.2 Example: The under/over-absorbed overhead account Mariott's Motorcycles absorbs production overheads at the rate of Rs. 500 per operating hour and administration overheads at 20% of the production cost of sales. Actual data for one month was as follows. Administration overheads Rs. 32,000,000 Production overheads Rs. 46,500,000 Operating hours 90,000 Production cost of sales Rs. 180,000,000 Required

Record the entries that need to be made for overheads in the ledgers.

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Solution PRODUCTION OVERHEADS DR CR Rs '000 Rs '000 Cash 46,500 Absorbed into WIP (90,000 Rs. 500) 45,000 Under-absorbed overhead 1,500 46,500 46,500 ADMINISTRATION OVERHEADS DR CR Rs '000 Rs '000 Cash 32,000 To cost of sales (180 million 0.2) 36,000 Over-absorbed overhead 4,000 36,000 36,000 UNDER/OVER-ABSORBED OVERHEADS DR CR Rs '000 Rs '000 Production overhead 1,500 Administration overhead 4,000 Balance to profit and loss account 2,500 4,000 4,000 Less production overhead has been absorbed than has been spent, so there is under-absorbed overhead of Rs. 1,500,000. More administration overhead has been absorbed (into cost of sales, note, not into WIP) and so there is over-absorbed overhead of Rs. 4,000,000. The net over-absorbed overhead of Rs. 2,500,000 is a credit in the statement of profit or loss.

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Overhead is the cost incurred in the course of making a product, providing a service or running a department, but which cannot be traced directly and in full to the product, service or department. The objective of absorption costing is to include in the total cost of a product an appropriate share of the organisation's total overhead. An appropriate share is generally taken to mean an amount which reflects the amount of time and effort that has gone into producing a unit or completing a job. The main reasons for using absorption costing are for inventory valuations,

pricing decisions and establishing the profitability of different products.

The three stages of absorption costing are: 1 Allocation 3 Absorption 2 Apportionment Allocation is the process by which whole cost items are charged direct to a cost unit or cost centre. Apportionment is a procedure whereby indirect costs are spread fairly between cost centres. Service cost centre costs may be apportioned to production cost centres by using the reciprocal method. A blanket overhead absorption rate is an absorption rate used throughout a factory and for all jobs and units of output irrespective of the department in which they were produced. Over and under-absorption of overheads occurs because the predetermined overhead absorption rates are based on estimates. Overhead absorption is the process whereby overhead costs allocated and apportioned to production cost centres are added to unit, job or batch costs. Overhead absorption is sometimes called overhead recovery.

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1 Define the term 'allocation'. 2 List the three stages in charging overheads to units of output. 3 Match the following overheads with the most appropriate basis of apportionment.

Overhead Basis of apportionment (a) Depreciation of equipment (1) Direct machine hours (b) Heat and light costs (2) Number of employees (c) Canteen (3) Book value of equipment (d) Insurance of equipment (4) Floor area 4 State in which of the following environments a direct labour hour basis is most appropriate. A Machine-intensive C When all units produced are identical B Labour-intensive D None of the above 5 Explain briefly the problem with using a single factory overhead absorption rate. 6 Explain briefly the accounting treatment for under/over-absorbed overhead. 7 Explain briefly the reasons for the occurrence of under or over-absorbed overhead.

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1 The process whereby whole cost items are charged direct to a cost unit or cost centre. 2 Allocation Absorption

Apportionment 3 a/3 c/2 b/4 d/3 4 The answer is B. 5 Because some products will receive a higher overhead charge than they ought 'fairly' to bear and other products will be undercharged. 6 Under/over-absorbed overhead is written as an adjustment to the statement of profit or loss at the end of an accounting period.

Over-absorbed overhead credit in statement of profit or loss Under-absorbed overhead debit in statement of profit or loss

7 Actual overhead costs are different from budgeted overheads The actual activity level is different from the budgeted activity level Actual overhead costs and actual activity level differ from the budgeted costs and level

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Knowledge Component A Cost accounting 1.5 Pricing 1.5.1 Apply cost information in pricing decisions

INTRODUCTION This chapter looks at calculating mark-up and margin to arrive at the amount in rupees for given mark-up/margin percentages in different scenario. The costing method that we shall be looking at is Cost plus Pricing. We will see how mark-up and margin % are used to determine the profit from either selling price or unit cost.

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CHAPTER CONTENTS

LEARNING OUTCOME1 Concepts of mark-up and margin 1.5.12 Principles of marginal costing 3 Cost-plus pricing 4 Full cost-plus pricing 5 Marginal cost-plus pricing

1.5.11.5.11.5.11.5.1

1 Concepts of mark-up and margin You may be required in your assessment to calculate profit, selling price or cost of sale of an item or number of items from certain information. To do this you need to remember the following crucial formula. % Cost of sales 100 Plus Profit 25 Equals Sales 125 Profit may be expressed either as a percentage of cost of sales (such as 25% (25/100) mark-up) or as a percentage of sales (such as 20% (25/125) margin). When you have this information, you can then use it in 2 different ways: Cost Mark Up – this is where you know the cost of an introductory product so you can add the element of profit required to the cost to calculate the selling price. Or Profit Margin – which is what you would use for an established product and the market price can be used to calculate the profit element to give you a target cost. 1.1 Profit margins If profit is expressed as a percentage of sales (margin) the following formula is also useful. % Selling price 100 Profit 20 Cost of sales 80

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It is best to think of the selling price as 100% if profit is expressed as a margin (percentage of sales). On the other hand, if profit is expressed as a percentage of cost of sales (mark-up) it is best to think of the cost of sales as being 100%. The following examples should help to clarify this point. 1.2 Example: Margin Delilah's Dresses sells a dress at a 10% margin. The dress cost the shop Rs. 1,000. Required

Calculate the profit made by Delilah's Dresses. Solution The margin is 10% (ie 10/100) Let selling price = 100% Profit = 10% Cost = 90% = Rs. 1,000 1% = Rs.1,00090 10% = profit = ×

Rs. 1,000 90 10 = Rs. 111.11 (and the selling price is Rs. 1,000 + Rs. 111.11 = Rs. 1,111.11) 1.3 Example: mark-up Trevor's Trousers sells a pair of trousers for Rs. 800 at a 15% mark-up. Required

Calculate the profit made by Trevor's Trousers. Solution The mark-up is 15%. Let cost of sales = 100% Profit = 15% Selling price = 115% = Rs. 800 1% = Rs. 800115 15% = profit = ×15

Rs. 800115 = Rs. 104.35

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QUESTION Profits A skirt which cost the retailer Rs. 750 is sold at a profit of 25% on the selling price. Required

Calculate the profit. A Rs. 187.50 B Rs. 200.00 C Rs. 250.00 D Rs. 300.00 ANSWER Let selling price = 100% Profit = 25% of selling price Cost = 75% of selling price Cost = Rs. 750 = 75% 1% = Rs. 75075 25% = profit =

Rs. 75075 25 = Rs. 250.00 The correct answer is C.

2 Principles of marginal costing

2.1 Introduction The marginal costing philosophy is that profit measurement should be based on an analysis of total contribution; that is, sales value less the variable cost of sales. Supporters of marginal costing argue that the valuation of closing inventories should be at variable production cost (direct materials, direct labour, direct expenses (if any) and variable production overhead) because these are the only costs properly attributable to the product. The principles of marginal costing (also known as variable costing) are as follows: (a) Period fixed costs are the same for any volume of sales and production (provided that the level of activity is within the 'relevant range'). Therefore, by selling an extra item of product or service the following will happen: (i) Revenue will increase by the sales value of the item sold (ii) Costs will increase by the variable cost per unit (iii) Profit will increase by the amount of contribution earned from the extra item

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(b) Similarly, if the volume of sales falls by one item, the profit will fall by the amount of contribution earned from the item. (c) Since fixed costs relate to a period of time, and do not change with increases or decreases in sales volume, it is misleading to charge units of sale with a share of fixed costs. (d) When a unit of product is made, the extra costs incurred in its manufacture are the variable production costs. Fixed costs are unaffected, and no extra fixed costs are incurred when output is increased. Before reviewing marginal costing principles any further, it will be helpful to remind yourself of the basics by looking at a numerical example. 2.2 Example Water and Sons makes a product, the Splash, which has a variable production cost of Rs. 60 per unit and a sales price of Rs 100 per unit. At the beginning of September 20X0, there were no opening inventories and production during the month was 20,000 units. Fixed costs for the month were Rs. 300,000 for production and Rs. 150,000 for administration, sales and distribution. There were no variable marketing costs. Required Calculate the contribution and profit for September, using marginal costing principles, if sales were as follows: (a) 10,000 Splashes (b) 15,000 Splashes (c) 20,000 Splashes The first stage in the profit calculation must be to identify the variable costs, and then the contribution. Fixed costs are deducted from the total contribution to derive the profit. All closing inventories are valued at marginal production cost (Rs. 60 per unit). Production during the month in all 3 cases is 20,000 units.

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10,000 Splashes 15,000 Splashes 20,000 Splashes Rs'000 Rs'000 Rs'000 Rs'000 Rs'000 Rs'000 Sales (at Rs. 100) 1,000 1,500 2,000 Opening inventory 0 0 0 Variable prod’n cost 1,200 1,200 1,200 1,200 1,200 1,200 Less value of closing Inventory (at marginal cost) 600 300 0 Variable cost of sales 600 900 1,200 Contribution 400 600 800 Less fixed costs 450 450 450 Profit/(loss) (50) 150 350 Profit/(loss) per unit (5) 10 17.50 Contribution per unit 40 40 40 The conclusions that may be drawn from this example are as follows: (a) The profit per unit varies at differing levels of sales, because the average fixed overhead cost per unit changes with the volume of output and sales. (b) The contribution per unit is constant at all levels of output and sales. Total contribution, which is the contribution per unit multiplied by the number of units sold, increases in direct proportion to the volume of sales. (c) Since the contribution per unit does not change, the most effective way of calculating the expected profit at any level of output and sales would be as follows: (i) Calculate the total contribution (ii) Deduct fixed costs as a period charge in order to find the profit (d) In our example, the expected profit from the sale of 17,000 Splashes would be as follows: Rs’000 Total contribution (17,000 Rs. 40) 680 Less fixed costs 450 Profit 230 The marginal costing philosophy is that profit measurement should be based on an analysis of total contribution; that is, sales value less the variable cost of sales.

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3 Cost-plus pricing

The usual method of establishing prices in a jobbing concern is cost-plus pricing. Cost-plus pricing means that a desired profit margin is added to total costs to arrive at the selling price. The estimated profit will depend on the particular circumstance of the job and organisation in question. In competitive situations the profit may be small, but if the organisation is sure of securing the job the margin may be greater. In general terms, the profit earned on each job should conform to the requirements of the organisation's overall business plan. The final price quoted will, of course, be affected by what competitors charge and what the customer will be willing to pay. 3.1.1 Example: Selling price and unit cost Product CT's unit cost is Rs. 150. A selling price is set based on a margin of 20%. Required

Calculate the selling price. Solution Rs % Cost 150 80 Profit ? 20 Selling price ? 100 Therefore selling price = Rs. 150 ÷ 80% = Rs. 187.50 3.1.2 Example: Selling price and unit cost (2) Product HM's unit cost is Rs. 650. The mark up is 20%. Required

Calculate the selling price. Solution Rs % Cost 650 100 Profit ? 20 Selling price ? 120 Therefore selling price = Rs. 650 × 120% = Rs. 780

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3.1.3 Example: Selling price and unit cost (3) Product JT's selling price is Rs. 935. The mark up is 10%. Required

Calculate the unit cost. Solution Rs % Cost ? 100 Profit ? 10 Selling price 935 110 Therefore unit cost = Rs. 935 ÷ 110% = Rs. 850

4 Full cost-plus pricing

In full cost-plus pricing the sales price is determined by calculating the full cost of the product and then adding a percentage mark-up for profit. The most important criticism of full cost-plus pricing is that it fails to recognise that since sales demand may be determined by the sales price, there will be a profit maximising combination of price and demand. Full cost-plus pricing is a method of determining the sales price by calculating the full cost of the product and adding a percentage mark-up for profit. 4.1 Setting full cost-plus prices The 'full cost' may be a fully absorbed production cost only, or it may include some absorbed administration, selling and distribution overhead. A business might have an idea of the percentage profit margin it would like to earn, and so might decide on an average profit mark-up as a general guideline for pricing decisions. This would be particularly useful for businesses that carry out a large amount of contract work or jobbing work, for which individual job or contract prices must be quoted regularly to prospective customers. However, the percentage profit mark-up does not have to be rigid and fixed, but can be varied to suit the circumstances. In particular, the percentage mark-up can be varied to suit demand conditions in the market.

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QUESTION Full Cost-plus pricing A business has begun to produce a new product, product X, for which the following cost estimates have been made. Rs Direct materials 270 Direct labour: 4 hours at Rs. 50 per hour 200 Variable production overheads: machining, ½ hr at Rs. 60 per hour 30 500 Production fixed overheads are budgeted at Rs. 3,000,000 per month and, because of the shortage of available machining capacity, the company will be restricted to 10,000 hours of machine time per month. The absorption rate will be a direct labour rate, however, and budgeted direct labour hours are 25,000 per month. It is estimated that the company could obtain a minimum contribution of Rs. 100 per machine hour on producing items other than product X. The direct cost estimates are not certain as to material usage rates and direct labour productivity, and it is recognised that the estimates of direct materials and direct labour costs may be subject to an error of 15%. Machine time estimates are similarly subject to an error of 10%. The company wishes to make a profit of 20% on full production cost from product X. Required Ascertain the full cost-plus based price. Even for a relatively 'simple' cost-plus pricing estimate, some problems can arise, and certain assumptions must be made and stated. In this example, we can identify two problems: (a) Should the opportunity cost of machine time be included in cost or not? (b) What allowance, if any, should be made for the possible errors in cost estimates? Different assumptions could be made. ANSWER (a) Exclude machine time opportunity costs: ignore possible costing errors Rs Direct materials 270 Direct labour (4 hours) 200 Variable production overheads 30 Fixed production overheads (at Rs. 3,000,00025,000 = Rs.120 per direct labour hour) 480 Full production cost 980 Profit mark-up (20%) 196 Selling price per unit of product X 1,176

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(b) Include machine time opportunity costs: ignore possible costing errors

Rs Full production cost as in (a) 980 Opportunity cost of machine time: contribution forgone (½ hr Rs.100) 50 Adjusted full cost 1,030 Profit mark-up (20%) 206 Selling price per unit of product X 1,236 (c) Exclude machine time opportunity costs but make full allowance for possible underestimates of cost Rs Rs Direct materials 270.0 Direct labour 200.0 470.0 Possible error (15%) 70.5 540.5 Variable production overheads 30.0 Possible error (10%) 3.0 33.0 Fixed production overheads (4 hours Rs 120) 480.0 Possible error (labour time) (15%) 72.0 552.0 Potential full production cost 1,125.5 Profit mark-up (20%) 225.1 Selling price per unit of product X 1,350.6 (d) Include machine time opportunity costs and make a full allowance for possible underestimates of cost Rs Potential full production cost as in (c) 1,125.5 Opportunity cost of machine time: potential contribution forgone (½ hour Rs. 100 110%) 55.0 Adjusted potential full cost 1,180.5 Profit mark-up (20%) 236.1 Selling price per unit of product X 1,416.6 Using different assumptions, we could arrive at any of four different unit prices in the range Rs 1,176.0 to Rs 1,416.6.

4.2 Problems with and advantages of full cost-plus pricing There are several serious problems with relying on a full cost approach to pricing. (a) It fails to recognise that since demand may be determining price, there will be a profit-maximising combination of price and demand. (b) There may be a need to adjust prices to market and demand conditions.

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(c) Budgeted output volume needs to be established. Output volume is a key factor in the overhead absorption rate. (d) A suitable basis for overhead absorption must be selected, especially where a business produces more than one product. However, it is a quick, simple and cheap method of pricing which can be delegated to junior managers (which is particularly important with jobbing work where many prices must be decided and quoted each day) and, since the size of the profit margin can be varied, a decision based on a price in excess of full cost should ensure that a company working at normal capacity will cover all of its fixed costs and make a profit. 5 Marginal cost-plus pricing

Marginal cost-plus pricing involves adding a profit margin to the marginal cost of production/sales. A marginal costing approach is more likely to help with identifying a profit-maximising price. Marginal cost-plus pricing/mark-up pricing is a method of determining the sales price by adding a profit margin onto either marginal cost of production or marginal cost of sales. QUESTION Marginal cost-plus pricing A product has the following costs: Rs Direct materials 50 Direct labour 30 Variable overheads 70 Fixed overheads are Rs. 100,000 per month. Budgeted sales per month are 400 units to allow the product to break even. Required Fill in the blank in the sentence below. The mark-up which needs to be added to marginal cost to allow the product to break even is ...... %.

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ANSWER

The correct answer is 166 2/3%. Breakeven point is when total contribution equals fixed costs. At breakeven point, Rs.100,000 = 400 (price – Rs. 150) Rs. 250 = price – Rs. 150 Rs 400 = price Mark-up = ((400 – 150) /150) 100% = 166 2/3% 5.1 The advantages and disadvantages of a marginal cost-plus

approach to pricing The main advantages are as follows: (a) It is a simple and easy method to use. (b) The mark-up percentage can be varied, and so mark-up pricing can be adjusted to reflect demand conditions. (c) It draws management attention to contribution, and the effects of higher or lower sales volumes on profit. In this way, it helps to create a better awareness of the concepts and implications of marginal costing and cost-volume-profit analysis. For example, if a product costs Rs.100 per unit and a mark-up of 150% is added to reach a price of Rs. 250 per unit, management should be clearly aware that every additional Rs. 10 of sales revenue would add Rs. 6 to contribution and profit. (d) In practice, mark-up pricing is used in businesses where there is a readily identifiable basic variable cost. Retail industries are the most obvious example, and it is quite common for the prices of goods in shops to be fixed by adding a mark-up (20% or 33.3%, say) to the purchase cost. There are, of course, drawbacks to marginal cost-plus pricing. (a) Although the size of the mark-up can be varied in accordance with demand conditions, it does not ensure that sufficient attention is paid to demand conditions, competitors' prices and profit maximisation. (b) It ignores fixed overheads in the pricing decision, but the sales price must be sufficiently high to ensure that a profit is made after covering fixed costs.

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The usual method of fixing prices within a jobbing concern is cost-plus pricing. In full cost-plus pricing the sales price is determined by calculating the full cost of the product and then adding a percentage mark-up for profit. The most important criticism of full cost-plus pricing is that it fails to recognise that since sales demand may be determined by the sales price, there will be a profit-maximising combination of price and demand. Marginal cost-plus pricing involves adding a profit margin to the marginal cost of production/sales. A marginal costing approach is more likely to help with identifying a profit-maximising price. The marginal costing philosophy is that profit measurement should be based on an analysis of total contribution; that is, sales value less the variable cost of sales. Supporters of marginal costing argue that the valuation of closing inventories should be at variable production cost (direct materials, direct labour, direct expenses (if any) and variable production overhead) because these are the only costs properly attributable to the product.

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1 The cost of a job is Rs. 100,000 (a) If profit is 25% of the job cost, the price of the job = Rs……………… (b) If there is a 25% margin, the price of the job = Rs………………… 2 Fill in the blanks. (a) One of the problems with relying on a full cost-plus approach to pricing is that it fails to recognise that since price may be determining demand, there will be a …………………….. combination of …………. and ……………. (b) An advantage of the full cost-plus approach is that, because the size of the profit margin can be varied, a decision based on a price in excess of full cost should ensure that a company working at …………….. capacity will cover …………….… and make a ……………….. 3 Pricing based on mark-up per unit of limiting factor is particularly useful if an organisation is not working to full capacity.

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1 (a) Rs. 100,000 + (25% Rs. 100,000) = Rs. 100,000 + Rs. 25,000 = Rs. 125,000 (b) Let price of job = x Profit = 25% x (selling price) If profit = 0.25x x – 0.25x = cost of job 0.75x = Rs. 100,000 x = Rs. 100,0000.75 = Rs. 133,333 2 (a) profit-maximising combination of price and demand (b) working at normal capacity will cover all of its fixed costs and make a profit 3 False. It is useful if the organisation is working at full capacity. A

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Knowledge Component A Cost accounting 1.6 Integrated accounting 1.6.1 Explain the integration of cost accounts with the financial accounting system 1.6.2 Prepare accounts for inventory, labour, overheads, work in progress, finished goods flowing up to income statement

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INTRODUCTION We need to consider how management accounting impacts on the financial accounting of a business. We will look at Inventory Control A/cs, Wages Control A/cs and Cost of Control A/cs. We will also examine the accounting for under / over absorption of overheads and finally the Profit and Loss Statement.

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CHAPTER CONTENTS

LEARNING OUTCOME1 Inventory control account 1.6.22 WIP control account 3 Finished goods control account 1.6.21.6.24 Wages control account 1.6.25 Accounting for under/over absorption of overheads 6 Cost of sales control account and P&L statements 1.6.21.6.27 Profit and loss statements 8 Advantages and disadvantages of integrated accounting 1.6.21.6.1

1 Inventory control account

The purpose of this is to control the value of the inventory being recorded in the general ledger and ultimately the financial statements of the business. We will now use an example to illustrate how to account for the purchase and issue of raw materials. 1.1 Example – material control account Bossy Co manufactures a single product and has the following transactions for material during a particular period: (1) Raw materials of Rs. 500,000 were purchased on credit from a supplier (Timid Co). (2) Raw materials costing Rs. 10,000 were returned to the same supplier, due to defects. (3) The total stores requisitions for direct material for the period were Rs. 400,000. (4) Total issues for indirect materials during the period were Rs. 15,000. (5) Rs. 5,000 of unused material was returned to stores from production. Required

Record the transactions in the material control account for the period, showing clearly how each transaction is treated.

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Solution Notes on transactions: (1) All raw material purchases are entered into the material control account as a debit entry – the corresponding credit goes to the payables control account. (2) Any returns of material are treated in the opposite way to purchases of material. (3) Direct material is directly related to production. The material control account will be reduced (credited) by the amount of material being issued. Ongoing production is represented by a Work in Progress account in the ledger system. (4) Indirect materials are not directly related to production so will not affect the Work in Progress account. Such materials are classed as factory overheads and will therefore be entered into a Factory Overheads account. (5) The unused material returned to stores (inventory) will increase materials inventory and will therefore be a debit entry in the material control account. As it is being returned from production, the corresponding credit entry will be in the Work in Progress account. MATERIAL CONTROL ACCOUNT Rs Rs (1) Payables control (2) Payables control account 500,000 account 10,000 (2) Work in progress (3) Work in progress account 5,000 account 400,000 (4) Factory overheads account 15,000 Closing inventory (bal. figure) 80,000 505,000 505,000 Any increases in materials inventory will result in a debit entry in the material control account whilst any reductions in materials inventory will be shown as a credit entry in the material control account. QUESTION Accounting for materials Doodaa Co issued Rs. 100,000 of material from stores, 25% of which did not relate directly to production. Required

Identify how the transaction would be recorded in Doodaa's ledger accounts. A Debit: Work in Progress Rs. 100,000 Credit: Material Control Account Rs. 100,000

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B Debit: Material Control Account Rs. 100,000 Credit: Work in Progress Rs. 100,000 C Debit: Work in Progress Rs. 75,000 Credit: Material Control Account Rs. 100,000 Debit: Factory Overheads Rs. 25,000 D Debit: Material Control Account Rs. 100,000 Credit: Work in Progress Rs. 75,000 Credit: Factory Overheads Rs. 25,000 ANSWER The correct answer is C. Materials inventory is being reduced as materials are being issued, therefore the Material Control Account is credited with Rs. 100,000. 25% of the total (Rs. 25,000) did not relate to production and should therefore be debited to Factory Overheads. The remaining Rs. 75,000 which relates directly to production should be debited to Work in Progress. The total debit entries equal the total credit entries, which should always be the case.

2 WIP control account

The purpose of this is to control the value of the work in progress being recorded in the general ledger and ultimately the financial statements of the business. This follows on from the Material Control Account. The purpose of this account is to control the value of Work in Progress of the business. We will now continue to the above example to illustrate how to account for the receipt of WIP and completion / issue of WIP. 2.1 Example – WIP Control Account Bossy Co manufactures a single product and has the following transactions for WIP during a particular period: Points from the above example: (3) The total stores requisitions for direct material for the period were Rs. 400,000. (5) Rs. 5,000 of unused material was returned to stores from production. At the start of the period there was a balance b/d on the account of Rs. 50,000. During the period Rs. 390,000 was completed and transferred to finished goods.

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Required

Record the transactions in the WIP control account for the period, showing clearly how each transaction is treated. Solution Notes on transactions: (3) Direct material is directly related to production. The WIP control account is increased (debited) by the amount of material being issued into production. (5) The unused material returned to stores (inventory) will increase materials inventory and will therefore be a debit entry in the material control account. As it is being returned from production, the corresponding credit entry will be in the Work in Progress account. WIP CONTROL ACCOUNT Rs Rs Balance b/d (3) Materials Control 50,000 (5) Materials Control account 400,000 account 5,000 Finished Goods Control account 390,000 Closing WIP (bal. figure) 55,000 450,000 450,000 Any increases in WIP will result in a debit entry in the WIP control account whilst any reductions in WIP will be shown as a credit entry in the WIP control account. QUESTION Accounting for WIP Doodaa Co transferred Rs. 150,000 of WIP to finished goods. Required

Identify how the transaction would be recorded in Doodaa's ledger accounts. A Debit: Work in Progress Rs. 150,000 Credit: Finished Goods Control A/c Rs. 150,000 B Debit: Finished Goods Control A/c Rs. 150,000 Credit: Work in Progress Rs. 150,000 ANSWER The correct answer is B.

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3 Finished goods control account

The purpose of this is to control the value of the finished goods being recorded in the general ledger and ultimately the financial statements of the business. This follows on from the WIP Control Account. The purpose of this account is to control the value of finished goods of the business. We will now continue to the above example to illustrate how to account for the receipt of completed production and issue / sales of finished goods. 3.1 Example – Finished goods control account Bossy Co manufactures a single product and has the following transactions for finished goods during a particular period: Points from the above example: During the period Rs. 390,000 was completed and transferred to finished goods. At the start of the period Bossy already had a finished goods stock to the value of Rs. 435,000. During the period Bossy made sales of the finished goods to the value of Rs. 495,000 on credit. Required

Record the transactions in the Finished Goods control account for the period, showing clearly how each transaction is treated. Solution FINISHED GOODS CONTROL ACCOUNT Rs Rs Balance b/d WIP Control 435,000 Trade Receivables - Sales 495,000 account 390,000 Closing Finished Goods 330,000 (bal. figure) 825,000 825,000

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QUESTION Accounting for finished goods Doodaa Co sold Rs. 185,000 of finished goods on credit. Required

Identify how the transaction would be recorded in Doodaa's ledger accounts. A Debit: Trade Receivables Rs. 185,000 Credit: Finished Goods Control A/c Rs. 185,000 B Debit: Finished Goods Control A/c Rs. 185,000 Credit: Trade Receivables Rs. 185,000 ANSWER The correct answer is A.

4 Wages control account

The purpose of this is to control the cost of wages being recorded in the general ledger and ultimately the statement of profit or loss of the business. We have already looked at labour costs in Chapter 4. Now we will use an example to briefly review the principal bookkeeping entries for wages. 4.1 Example: The wages control account The following details were extracted from a weekly payroll for 750 employees at a factory. Analysis of gross pay Direct Indirect workers workers Total Rs '000 Rs '000 Rs '000 Ordinary time 36,000 22,000 58,000 Overtime: basic wage 8,700 5,430 14,130 premium 4,350 2,715 7,065 Shift allowance 3,465 1,830 5,295 Sick pay 950 500 1,450 Idle time 3,200 – 3,200 56,665 32,475 89,140 Net wages paid to employees Rs. 45,605,000 Rs. 24,220,000 Rs. 69,825,000Required

Record the above payroll details in the wages control account for the week.

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Solution (a) The wages control account acts as a sort of 'collecting place' for net wages paid and deductions made from gross pay. The gross pay is then analysed between direct and indirect wages. (b) The first step is to determine which wage costs are direct and which are indirect. The direct wages will be debited to the work in progress account and the indirect wages will be debited to the production overhead account. (c) There are in fact only two items of direct wages cost in this example: the ordinary time (Rs. 36 million) and the basic overtime wage (Rs. 8.7 million) paid to direct workers. All other payments (including the overtime premium) are indirect wages. (d) The net wages paid are debited to the control account, and the balance then represents the deductions which have been made for tax, social insurance, and so on. WAGES CONTROL ACCOUNT Rs '000 Rs '000 Bank: net wages paid 69,825 Work in progress – direct labour 44,700 Deductions control accounts* Production overhead control: (89,140 69,825) 19,315 Indirect labour 27,430 Overtime premium 7,065 Shift allowance 5,295 Sick pay 1,450 Idle time 3,200 89,140 89,140 * In practice there would be a separate deductions control account for each type of deduction made (for example, tax and social insurance).

5 Accounting for under/over absorption of overheads We have already looked at under / over absorption of overheads in Chapter 5 so we will now look at the accounting for these. 5.1 Introduction The bookkeeping entries for overheads are not as straightforward as those for materials and labour. We shall now consider the way in which overheads are dealt with in a cost accounting system. When an absorption costing system is in use we now know that the amount of overhead included in the cost of an item is absorbed at a predetermined rate. The entries made in the cash book and the nominal ledger, however, are the actual amounts.

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You will remember that it is highly unlikely that the actual amount and the predetermined amount will be the same. The difference is called under or over-absorbed overhead. To deal with this in the cost accounting books, therefore, we need to have an account to collect under or over-absorbed amounts for each type of overhead. 5.1.1 Example: The under/over-absorbed overhead account Mariott's Motorcycles absorbs production overheads at the rate of Rs. 500 per operating hour and administration overheads at 20% of the production cost of sales. Actual data for one month was as follows. Administration overheads Rs. 32,000,000 Production overheads Rs. 46,500,000 Operating hours 90,000 Production cost of sales Rs. 180,000,000 Required

Record the entries that need to be made for overheads in the ledgers. Solution PRODUCTION OVERHEADS DR CR Rs '000 Rs '000 Cash 46,500 Absorbed into WIP (90,000 Rs. 500) 45,000 Under-absorbed overhead 1,500 46,500 46,500 NON-PRODUCTION OVERHEADS DR CR Rs '000 Rs '000 Cash 32,000 To cost of sales (180 million 0.2) 36,000 Over-absorbed overhead 4,000 36,000 36,000 UNDER/OVER-ABSORBED OVERHEADS DR CR Rs '000 Rs '000 Production overhead 1,500 Administration overhead 4,000 Balance to profit and loss account 2,500 4,000 4,000

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Less production overhead has been absorbed than has been spent, so there is under-absorbed overhead of Rs. 1,500,000. More administration overhead has been absorbed (into cost of sales, note, not into WIP) and so there is over-absorbed overhead of Rs. 4,000,000. The net over-absorbed overhead of Rs. 2,500,000 is a credit in the statement of profit or loss.

6 Cost of sales control account and P&L statements

The purpose of this is to control the cost of the goods being recorded in the general ledger and ultimately the statement of profit or loss of the business. Cost of Sales Control Account When finished goods are sold a transfer is made from the Finished Goods Control A/c (CR) into the Cost of Sales Control A/c (DR). This is then transferred into the Statement of P&L – so that nothing is left in the Cost of Sales Control A/c. You can see how this works in the example in Section 7 below. Any adjustment for under or over absorbed overheads is made as a debit / credit to the costing statement of profit or loss. If we have under absorbed overheads then we need to increase the costs as we have not put enough into the statement of profit or loss when we used the budgeted overhead absorption rate. Rs Revenue X Less: Cost of sales (using budgeted overhead absorption rates) X Gross Profit X Less: Under-absorption of overheads X Adjusted Gross Profit X If we have over absorbed overheads then we need to decrease the costs as we have put too much into the statement of profit or loss when we used the budgeted overhead absorption rate. Rs Revenue X Less: Cost of sales (using budgeted overhead absorption rates) X Gross Profit X Add: Over-absorption of overheads X Adjusted Gross Profit X

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7 Profit and loss statements Throughout this module we will be reviewing the impact where relevant with the Profit and Loss Statements. You can now see a comprehensive example with notes explaining below: Example Using the information given below for October, you are required to prepare the following accounts. Raw materials control Work in progress control Finished goods control Production overhead control Wages and salaries control Selling and administration overhead control Cost of sales Trading and income statement Balances as at 1 October Rs'000 Raw materials control 100 Work in progress control 150 Finished goods control 180 Transactions for October Rs'000 Materials received from suppliers on credit 500 Materials issued to production 420 Materials issued to production service departments 50 Direct wages incurred 300 Production indirect wages incurred 130 Selling and administration salaries incurred 120 Production expenses paid as incurred 80 Selling and administration expenses paid as incurred 90 Allowance for depreciation: production equipment 30 selling and administration equipment 20 Wages and salaries paid: direct wages 280 production indirect wages 130 selling and administration salaries 120 Production completed and transferred to finished goods store 900 Production cost of goods sold 970 Sales on credit 1,450 Production overhead is absorbed at the rate of 80 per cent of direct wages incurred.

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Solution The figures in brackets refer to the explanations which follow after the ledger accounts. RAW MATERIALS CONTROL Rs'000 Rs'000 Balance b/d 100 Work in progress (1) 420 Accounts payable 500 Production overhead control (1) 50 Balance c/d 130 600 600 Balance b/d 13

WORK IN PROGRESS CONTROL Rs'000 Rs'000 Balance b/d 150 Finished goods control (4) 900 Raw materials control (1) 420 Balance c/d (4) 210 Wages and salaries control (2) 300 Production overhead control (3) 240 1,110 1,110 Balance b/d 210 FINISHED GOODS CONTROL Rs'000 Rs'000 Balance b/d 180 Cost of sales (5) 970 Work in progress control (4) 900 Balance c/d (5) 110 1,080 1,080 Balance b/d 110 PRODUCTION OVERHEAD CONTROL Rs'000 Rs'000 Raw materials control (1) 50 Work in progress control (3) 240 Wages and salaries control (2) 130 Under absorption to SPL(8) 50 Bank (6) 80 Allowance for depreciation (6) 30 290 290 WAGES AND SALARIES CONTROL Rs'000 Rs'000 Bank (7) 530 Work in progress control (2) 300 Balance c/d (7) 20 Production overhead control (2) 130 Selling and admin o/h control (2) 120 550 550 Balance b/d 20

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SELLING AND ADMINISTRATION OVERHEAD CONTROL Rs'000 Rs'000 Bank (6) 90 SPL 230 Wages and salaries control (2) 120 Allowance for depreciation (6) 20 230 230 COST OF SALES Rs'000 Rs'000 Finished goods control (5) 970 SPL 970 STATEMENT OF PROFIT OR LOSS Rs'000 Rs'000 Cost of sales (5) 970 Sales – receivables 1,450 Gross profit c/d 480 1,450 1,450 Under-absorbed overhead (8) 5 Gross profit b/d 480 Selling and admin o/h 230 Net profit for October 200 480 480 Notes 1 The materials issued to production are charged as direct materials to work in progress. The materials issued to production service departments are

indirect materials. The cost of indirect materials is 'collected' in the production overhead control account, pending its later absorption, along with all the other production overheads, into the value of work in progress. 2 The wages and salaries incurred are debited to the relevant control accounts: direct wages to work in progress indirect wages to production overhead control selling and administration salaries to selling and administration overhead control The credit entry for wages incurred is made in the wages and salaries control account. 3 Once the direct material and direct wages have been debited to work in progress, the next step is to absorb production overheads, using the predetermined overhead absorption rate. The work in progress account is charged with 80 per cent of wages incurred: Rs300,000 80% = Rs240,000. 4 Now that all of the elements of production cost have been charged to work in progress, the production cost of goods completed can be transferred to the finished goods control account.

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5 The production cost of goods sold is transferred from the finished goods account to the cost of sales account. The balance on the finished goods account represents the inventory at the end of October. 6 The production expenses incurred and the depreciation on production machinery are debited in the production overhead control account. Thus they are 'collected' with the other production overheads, for later absorption into work in progress. 7 The total amount of wages paid (Rs. 280,000 + Rs. 130,000 + Rs. 120,000) is debited to the wages and salaries control account. The balance remaining on the account is the difference between the wages paid and the wages incurred. This represents a Rs20,000 accrual for wages, which is carried down into next month's accounts. 8 The balance remaining on the production overhead control account is the difference between the production overhead incurred, and the amount absorbed into work in progress. On this occasion the overhead is underabsorbed and is transferred as a debit in the SPL.

8 Advantages and disadvantages of integrated accounting An integrated accounting system only operates one set of accounts and so it has the following advantages: (i) Eliminates rekeying information – where a business operates separate financial and management accounting systems – information will need to entered into each system. (ii) Only maintaining 1 set of accounts – a business would only be producing one set of accounts and there would be no need for any reconciliations between the systems. (iii) Greater accuracy – if the data is being entered twice then human errors are more likely to occur. (iv) Can reduce the number of employees required due to reduced duplication of workload. (v) Accounting process is simplified due to there only being one system. The main disadvantage of operating an integrated accounting system is that a single system is used to produce information for both external and internal users. The information that management require is different to that required of shareholders or the bank. It can be a more complicated system so trained and competent staff are essential.

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The purpose of this is to control the value of the inventory being recorded in the general ledger and ultimately the financial statements of the business. Any increases in materials inventory will result in a debit entry in the material control account whilst any reductions in materials inventory will be shown as a

credit entry in the material control account. The purpose of this is to control the value of the work in progress being recorded in the general ledger and ultimately the financial statements of the business. Any increases in WIP will result in a debit entry in the WIP control account whilst any reductions in WIP will be shown as a credit entry in the WIP control account. The purpose of this is to control the value of the finished goods being recorded in the general ledger and ultimately the financial statements of the business. The purpose of this is to control the cost of wages being recorded in the general ledger and ultimately the statement of profit or loss of the business. The purpose of this is to control the cost of the goods being recorded in the general ledger and ultimately the statement of profit or loss of the business.

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1 The following details were extracted from a weekly payroll for 20 employees at a factory. Analysis of gross pay Direct Indirect workers workers Total Rs Rs Rs Ordinary time 46,000 20,000 66,000 Overtime: basic wage 10,700 2,430 13,130 premium 3,350 3,715 7,065 Shift allowance 5,465 2,830 8,295 Sick pay 1,950 1,500 3,450 Idle time 2,200 – 2,200 69,665 30,475 100,140 Net wages paid to employees Rs. 54,339 Rs. 23,770 Rs. 78,109 Required Prepare the wages control account for the week.

2 Fruity Coffee manufactures a single product and has the following transactions for material during a particular period: (1) Raw materials of Rs. 350,000 were purchased on credit from a supplier. (2) Raw materials costing Rs. 2,500 were returned to the same supplier, due to defects. (3) The total stores requisitions for direct material for the period were Rs. 320,000. (4) Total issues for indirect materials during the period were Rs. 9,000. (5) Rs. 5,000 of unused material was returned to stores from production. Required

Record the transactions in the material control account for the period, showing clearly how each transaction is treated.

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1 WAGES CONTROL ACCOUNT Rs Rs Bank: net wages paid 78,109 WIP – direct labour 56,700Deductions control accounts* Production overhead control: (Rs100,140 Rs78,109) 22,031 Indirect labour 22,430 Overtime premium 7,065 Shift allowance 8,295 Sick pay 3,450 Idle time 2,200 100,140 100,140 2 MATERIAL CONTROL ACCOUNT Rs Rs Payables control a/c 350,000 Payables control a/c 2,500 Work in Progress a/c 5,000 Work in Progress a/c 320,000 Factory Overheads a/c 9,000 Closing inventory (bal. figure) 23,500 355,000 355,000

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Knowledge Component A Cost accounting 1.7 Specific order costing 1.7.1 Compute and account for the costs of a specific order using job costing and batch costing 1.7.2 Compute and account for the costs of a specific order using contract costing 1.7.3 Compute the cost of a specific order using service costing

INTRODUCTION The first costing method that we shall be looking at is job costing. We will see the circumstances in which job costing should be used and how the costs of jobs are calculated. We will look at how the costing of individual jobs fits in with the recording of total costs in control accounts and then we will move on to batch costing, the procedure for which is similar to job costing. Service costing deals with specialist services supplied to third parties or an internal service supplied within an organisation.

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LEARNING OUTCOME1 Costing methods 1.7.12 Job costing 1.7.13 Batch costing 4 Differences between job costing and batch costing 1.7.11.7.15 Contract costing 1.7.26 Service costing 1.7.3

1 Costing methods

A costing method is designed to suit the way goods are processed or manufactured or the way services are provided. Each organisation's costing method will have unique features but costing methods of firms in the same line of business will more than likely have common aspects. Organisations involved in completely different activities, such as hospitals and car part manufacturers, will use very different methods. We will be considering these important costing methods in this chapter. Job Contract Batch Service

2 Job costing

2.1 Introduction

Job costing is a costing method applied where work is undertaken to customers' special requirements and each order is of comparatively short duration. A job is a cost unit which consists of a single order or contract, which is customised to a customer’s specific requirements. A job is a cost unit that consists of a single order or contract. A job has the following characteristics.

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Each job is separately identifiable and costs can be attributed to each job, for example, construction of a new rail link. The work relating to a job moves through processes and operations as a

continuously identifiable unit. Job costing is most commonly applied where all stages of production happen within the factory or workshop. A job is customised to specific customer requirements and is usually a heterogenous product, as it is unique, and differs to the other products manufactured by the same organisation A job is generally completed in one accounting period. Accounting for job costing projects: (a) All job costs are coded to a unique job code, so job costs can be separately aggregated and analysed by job. (b) The relevant costs of materials issued, direct labour performed and direct expenses incurred are charged to a job account in the work in progress ledger. The work in progress ledger records the cost of all work in progress (WIP). A separate WIP control account exists for each job. (c) Some labour costs, such as overtime premium, might be charged either directly to a job or else as an overhead cost, depending on the circumstances in which the costs have arisen. (d) The job account is allocated with the job's share of the factory overhead, based on the absorption rate(s) in operation. If the job is incomplete at the end of an accounting period, it is valued at factory cost in the closing statement of financial position (where a system of absorption costing is in operation). (e) On completion of the job, the job account is charged with the appropriate administration, selling and distribution overhead, after which the total cost of the job can be ascertained. The job is transferred to finished goods. (f) The difference between the agreed selling price and the total actual cost will be the supplier's profit (or loss). (g) When delivery is made to the customer, the collective job costs become a

cost of sale.

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2.2 Procedure for the performance of jobs The normal procedure in jobbing concerns involves: (a) The prospective customer approaches the supplier and indicates the requirements of the job. (b) A representative sees the prospective customer and agrees with him the precise details of the items to be supplied. For example, the quantity, quality, size and colour of the goods, the date of delivery and any special requirements. (c) The estimating department of the organisation then prepares an estimate for the job. This will be based on the cost of the materials to be used, the labour expense expected, the cost overheads, the cost of any additional equipment needed specially for the job, and finally the supplier's profit margin. The total of these items will represent the quoted selling price. (d) If the estimate is accepted the job can be scheduled. All materials, labour and equipment required will be 'booked' for the job. In an efficient organisation, the start of the job will be timed to ensure that, while it will be ready for the customer by the promised date of delivery, it will not be loaded or put into production too early, otherwise storage space will have to be found for the product until the date it is required by (and was promised to) the customer.

2.3 Job cost sheets/cards Costs for each job are collected on a job cost sheet or job card. With other methods of costing, it is usual to produce for inventory; this means that management must decide in advance how many units of each type, size, colour, quality and so on will be produced during the coming year, regardless of the identity of the customers who will eventually buy the product. In job costing, because production is usually carried out in accordance with the special requirements of each customer, it is usual for each job to differ in one or more respects from another job. A separate record must therefore be maintained to show the details of individual jobs. Such records are often known as job cost sheets or job cost cards. An example is shown in Figure 6.1. Either the detail of relatively small jobs or a summary of direct materials, direct labour and so on for larger jobs will be shown on a job cost sheet.

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2.4 Job cost information

Material costs for each job are determined from material requisition notes. Labour times on each job are recorded on a job ticket, which is then costed and recorded on the job cost sheet. Some labour costs, such as overtime premium or the cost of rectifying sub-standard output, might be charged either directly to a job or else as an overhead cost, depending on the circumstances in which the costs have arisen. Overhead is absorbed into the cost of jobs using the predetermined overhead absorption rates. Information for the direct and indirect costs will be gathered as follows. 2.4.1 Direct material cost (a) The estimated cost will be calculated by valuing all items on the bill of

materials. Materials that have to be specially purchased for the job in question will need to be priced by the purchasing department. (b) The actual cost of materials used will be calculated by valuing materials issues notes for those issues from store for the job, and/or from invoices for materials specially purchased. All documentation should indicate the job number to which it relates. 2.4.2 Direct labour cost (a) The estimated labour time requirement will be calculated from past experience of similar types of work, or work study engineers may prepare estimates following detailed specifications. Labour rates will need to take account of any increases, overtime and bonuses. (b) The actual labour hours will be available from either timesheets or job tickets/cards, using job numbers where appropriate to indicate the time spent on each job. The actual labour cost will be calculated using the hours information and current labour rates (plus bonuses, overtime payments and so on). 2.4.3 Direct expenses (a) The estimated cost of any expenses likely to be incurred can be obtained from a supplier. (b) The details of actual direct expenses incurred can be taken from invoices.

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JOB COST CARD

Customer Mr J White

Job Description Repair damage to offside front door

Estimate Ref. 2599Quotedprice Rs338.68

Customer’s Order No.

Invoice No.Invoiceprice Rs355.05

Job No. B641

Vehiclemake Peugot 205 GTEVehiclereg. no. G 614 SOX

Vehiclecollect 14.6.00

Material Labour Overheads

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Qty. PriceCost

DateEmp-loyee Cost

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Cost

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12.6 36815 1 75.49 75 49 12.6 018 B 1.98 6.50 - 12 87 7.9 2.50 19 75

12.6 36816 1 33.19 33 19 13.6 018 B 5.92 6.50 - 38 48

12.6 36842 5 6.01 30 05 13.65 13 65

13.6 36881 5 3.99 19 95

Total C/F 158 68 Total C/F 65 00 Total C/F 19 75

Expenses Job Cost Summary

Date Ref. DescriptionCost

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Direct Materials B/F 158 68 158 68

Direct Expenses B/F 50 00

Direct Labour B/F 65 00 180 00

Direct Cost 273 68

Overheads B/F 19 75

Total C/F 50 -

293 43

Admin overhead (add 10%) 29 34

= Total Cost 322 77 338 68

Invoice Price 355 05

Job Profit/Loss 32 28

Comments

Job Cost Card Completed by

Actual Estimate

Rs cts Rs cts

Figure 6.1: Typical job card (Note that the abbreviations of B/F and C/F in the above cost card mean 'brought forward' and 'carried forward'.)

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2.4.4 Production overheads (a) The estimated production overheads to be included in the job cost will be calculated from overhead absorption rates in operation and the estimate of the basis of the absorption rate (for example, direct labour hours). This assumes the job estimate is to include overheads (in a competitive environment management may feel that if overheads are to be incurred irrespective of whether or not the job is taken on, the minimum estimated quotation price should be based on variable costs only). (b) The actual production overhead to be included in the job cost will be calculated from the overhead absorption rate and the actual results (such as labour hours coded to the job in question). Inaccurate overhead absorption rates can seriously harm an organisation; if jobs are over-priced, customers will go elsewhere; if jobs are under-priced, revenue will fail to cover costs.

2.4.5 Administration, selling and distribution overheads The organisation may absorb non-production overheads using any one of a variety of methods (percentage on full production cost, for example) and estimates of these costs and the actual costs should be included in the estimated and actual job cost. 2.5 Rectification costs If the finished output is found to be sub-standard, it may be possible to rectify the fault. The sub-standard output will then be returned to the department or cost centre where the fault arose. Rectification costs can be treated in two ways. (a) If rectification work is not a frequent occurrence, but arises on occasions with specific jobs to which it can be traced directly, then the rectification costs should be charged as a direct cost to the jobs concerned. (b) If rectification is regarded as a normal part of the work carried out generally in the department, then the rectification costs should be treated as

production overheads. This means that they would be included in the total of production overheads for the department and absorbed into the cost of all jobs for the period, using the overhead absorption rate.

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2.6 Work in progress At the year end, the value of work in progress (WIP) is simply the sum of the costs incurred on incomplete jobs (provided that the costs are lower than the net realisable value of the customer order). 2.7 Pricing the job The usual method of establishing prices in a jobbing concern is cost-plus pricing. Cost-plus pricing means that a desired profit margin is added to total costs to arrive at the selling price. The estimated profit will depend on the particular circumstances of the job and organisation in question. In competitive situations the profit may be small, but if the organisation is sure of securing the job the margin may be greater. In general terms, the profit earned on each job should conform to the requirements of the organisation's overall business plan. The final price quoted will, of course, be affected by what competitors charge and what the customer will be willing to pay. 2.7.1 Example: Selling price and unit cost Product CT's unit cost is Rs. 15000. A selling price is set based on a margin of 20%. Required

Calculate the selling price. Solution Rs % Cost 15000 80Profit ? 20Selling price ? 100Therefore, selling price = Rs. 15000 ÷ 80% = Rs. 18750 2.7.2 Example: Selling price and unit cost (2) Product HM's unit cost is Rs. 650. The mark up is 20%. Required

Calculate the selling price.

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Solution Rs % Cost 650 100 Profit ? 20 Selling price ? 120 Therefore selling price = Rs. 650 × 120% = Rs. 780

2.7.3 Example: Selling price and unit cost (3) Product JT's selling price is Rs. 935. The mark up is 10%. Required

Calculate the unit cost. Solution Rs % Cost ? 100 Profit ? 10 Selling price 935 110 Therefore unit cost = Rs. 935 ÷ 110% = Rs. 850

2.8 Job costing and computerisation Job cost sheets exist in manual systems, but it is increasingly likely that in large organisations the job costing system will be computerised, using accounting software specifically designed to deal with job costing requirements. A computerised job accounting system is likely to contain the following features. (a) Every job will be given a job code number, which will determine how the data relating to the job is stored. (b) A separate set of codes will be given for the type of costs that any job is likely to incur. Thus, 'direct wages', say, will have the same code whichever job they are allocated to. (c) In a sophisticated system, costs can be analysed both by job (for example all costs related to Job 456), but also by type (for example direct wages incurred on all jobs). It is thus easy to perform control analysis and to make comparisons between jobs. (d) A job costing system might have facilities built into it which incorporate other factors relating to the performance of the job. In complex jobs, sophisticated planning techniques might be employed to ensure that the job is performed in the minimum time possible: time management features may be incorporated into job costing software.

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2.9 Example: Job costing Fateful Morn is a jobbing company. On 1 June 20X2, there was one uncompleted job in the factory. The job card for this work is summarised as follows. Job Card, Job No 6832 Costs to date Rs Direct materials 15,750 Direct labour (120 hours) 8,750 Factory overhead (Rs. 2 per direct labour hour) 6,000 Factory cost to date 30,500 During June, three new jobs were started in the factory, and costs of production were as follows.

Direct materials Rs Issued to: Job 6832 59,750 Job 6833 42,000 Job 6834 98,750 Job 6835 110,500 Damaged inventory written off from stores 57,500 Material transfers Rs Job 6834 to Job 6833 6,250 Job 6832 to 6834 15,500 Materials returned to store Rs From Job 6832 21,750 From Job 6835 4,250 Direct labour hours recorded Job 6832 430 hrs Job 6833 650 hrs Job 6834 280 hrs Job 6835 410 hrs The cost of labour hours during June 20X2 was Rs.70 per hour, and production overhead is absorbed at the rate of Rs.50 per direct labour hour. Production overheads incurred during the month amounted to Rs. 95,000. Completed jobs were delivered to customers as soon as they were completed, and the invoiced amounts were as follows. Rs Job 6832 137,500 Job 6834 200,000 Job 6835 187,500 Administration and marketing overheads are added to the cost of sales at the rate of 7.5% of factory cost. Actual costs incurred during June 20X2 amounted to Rs. 32,000.

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Required (a) Prepare the job accounts for each individual job during June 20X2; (the accounts should only show the cost of production, and not the full cost of sale). (b) Prepare the summarised job cost cards for each job, and calculate the profit on each completed job. Solution (a) Job accounts JOB 6832 Rs Rs Balance b/f 30,500 Job 6834 a/c 15,500 Materials (stores a/c) 59,750 (materials transfer) Stores a/c (materials Labour (wages a/c) 51,100 returned) 21,750 Production overhead (o'hd a/c) 21,500 Cost of sales a/c (balance) 125,600 162,850 162,850 JOB 6833 Rs Rs Materials (stores a/c) 42,000 Balance c/f 126,250 Labour (wages a/c) 45,500 Production overhead (o'hd a/c) 32,500 Job 6834 a/c (materials transfer) 6,250 126,250 126,250 JOB 6834 Rs Rs Job 6833 a/c (materials Materials (stores a/c) 98,750 transfer) 6,250 Labour (wages a/c) 19,600 Production overhead (o'hd a/c) 14,000 Cost of sales a/c (balance) 141,600 Job 6832 a/c (materials transfer) 15,500 147,850 147,850

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JOB 6835 Rs Rs Stores a/c (materials Materials (stores a/c) 110,500 returned) 4,250 Labour (wages a/c) 28,700 Production overhead (o'hd a/c) 20,500 Cost of sales a/c (balance) 155,450 159,700 159,700 (b) Job cards, summarised Job 6832 Job 6833 Job 6834 Job 6835 Rs Rs Rs Rs Materials 38,250* 42,000 108,000** 106,250 Labour 59,850 45,500 19,600 28,700 Production overhead 27,500 32,500 14,000 20,500 Factory cost 125,600 120,000 (c/f) 141,600 155,450 Admin & marketing o'hd (7.5%) 9,420 10,620 11,659 Cost of sale 135,020 152,220 167,109 Invoice value 137,500 200,000 187,500 Profit/(loss) on job 2480 47,780 20,391 *Rs. (15,750 + 59,750 – 15,500 – 21,750) **Rs. (98,750 + 15,500 – 6,250)

2.10 Job costing for internal services It is possible to use a job costing system to control the costs of an internal service department, such as the maintenance department or the printing department. If a job costing system is used it is possible to charge the user departments for the cost of specific jobs carried out, rather than apportioning the total costs of these service departments to the user departments using an arbitrarily determined apportionment basis. An internal job costing system for service departments will have the following advantages.

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Advantages Comment

Realistic pportionment

The identification of expenses with jobs and the subsequent charging of these to the department(s) responsible means that costs are borne by those who incurred them. Increased responsibility and awareness

User departments will be aware that they are charged for the specific services used and may be more careful to use the facility more efficiently. They will also appreciate the true cost of the facilities that they are using and can take decisions accordingly. Control of service department costs

The service department may be restricted to charging a standard cost to user departments for specific jobs carried out or time spent. It will then be possible to measure the efficiency or inefficiency of the service department by recording the difference between the standard charges and the actual expenditure. Planning information

This information will ease the planning process, as the purpose and cost of service department expenditure can be separately identified. QUESTION Total job cost A furniture-making business manufactures quality furniture to customers' orders. It has three production departments (A, B and C) which have overhead absorption rates (per direct labour hour) of Rs. 50, Rs. 55 and Rs. 60 respectively. Two pieces of furniture are to be manufactured for customers. Direct costs are as follows. Job XYZ Job MNO Direct material Rs. 154 Rs. 108 Direct labour 20 hours dept A 16 hours dept A 12 hours dept B 10 hours dept B 10 hours dept C 14 hours dept C Labour rates are as follows: Rs. 75(A); Rs. 70 (B); Rs. 65 (C) Required

Calculate the total cost of each job.

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ANSWER Job XYZ Job MNO Rs Rs Direct material 555,154 5,108 Direct labour: dept A (20 75) 1,500 (16 75) , 1,200 dept B (12 70) 840 (10 70) 700 dept C (10 65) 650 (14 65) 915 Total direct cost 8,144 7,923 Overhead: dept A (20 50) 1,000 (16 50) 800 dept B (12 55) 655 (10 55) 550 dept C (10 60) 600 (14 60) 840 Total cost 10,399 10,113

QUESTION Closing work in progress A firm uses job costing and recovers overheads on direct labour. Three jobs were worked on during a period, the details of which are as follows. Job 1 Job 2 Job 3 Rs Rs Rs Opening work in progress 8,500 0 46,000 Material in period 17,150 29,025 0 Labour for period 12,500 23,000 4,500 The overheads for the period were exactly as budgeted, Rs. 140,000. Jobs 1 and 2 were the only incomplete jobs. Required

Calculate the value of closing work in progress. A Rs. 81,900 B Rs. 90,175 C Rs. 140,675 D Rs. 214,425 ANSWER Total labour cost = Rs. 12,500 + Rs. 23,000 + Rs. 4,500 = Rs. 40,000 Overhead absorption rate = Rs. 140,000Rs. 40,000 100% = 350% of direct labour cost Closing work in progress valuation

Job 1 Job 2 Total Rs Rs Rs Costs given in question 38,150 52,025 90,175 Overhead absorbed (12,500 350%) 43,750 (23,000 350%) 80,500 124,250 214,425 The correction answer is D.

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We can eliminate option B because Rs. 90,175 is simply the total of the costs allocated to Jobs 1 and 2, with no absorption of overheads. Option A is an even lower cost figure, therefore it can also be eliminated. Option C is wrong because it is a simple total of all allocated costs, including Job 3 which is not incomplete.

3 Batch costing

3.1 Introduction

Batch costing is similar to job costing in that each batch of similar articles is separately identifiable. The cost per unit manufactured in a batch is the total batch cost divided by the number of units in the batch. A batch is a group of similar articles which maintains its identity during one or more stages of production and is treated as a cost unit. In general, the procedures for costing batches are very similar to those for

costing jobs. (a) The batch is treated as a job during production and the costs are collected in the manner already described in this chapter. (b) Once the batch has been completed, the cost per unit can be calculated as the total batch cost divided into the number of units in the batch. 3.1.1 Set-up costs During batch costing there will often be a 'set-up' cost incurred. For example, this could be the cost incurred for setting up machinery ready to process a different batch of goods. A set-up cost is considered to be a non-value-added cost and the aim would be to keep that cost to a minimum. Examples of Set-up Costs • Costs of changing tools or setting up specific requirements of machinery. • Preparing and moving materials or components to the equipment. • Running specific tests on the initial output to check the equipment meets the jobs requirements. There are also additional costs such as labour costs of setting up the machinery.

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In addition to this there may be a lost opportunity cost. This cost is based on the 'lost opportunity' to manufacture profitable output during the time that the equipment is being set up. The larger the batch size then the smaller the overall set-up costs would be as the changes in machinery set-up and associated costs would be less often, whereas the smaller the batch then the more frequent the changes will need to be made adding more cost to the process. 3.2 Example: Batch costing Rio manufactures Brazils to order and has the following budgeted overheads for the year, based on normal activity levels. Production departments Budgeted overheads Budgeted activity Rs Welding 1,200,000 3,000 labour hours Assembly 2,000,000 2,000 labour hours Selling and administrative overheads are 10% of factory cost. An order for 500 Brazils, made as Batch 38, incurred the following costs. Materials Rs. 240,000 Labour 200 hours in the Welding Department at Rs. 60 per hour 400 hours in the Assembly Department at Rs. 100 per hour Rs. 10,000 was paid for the hire of x-ray equipment for testing the accuracy of the welds. Required

Calculate the cost per unit for Batch 38. Solution The first step is to calculate the overhead absorption rate for the production departments. Welding = Rs. 1, 200, 0003, 000 = Rs. 400 per labour hour Assembly = Rs. 2, 000, 0002, 000 = Rs. 1000 per labour hour

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Total cost – Batch 38 Rs Rs Direct material 240,000 Direct expense 10,000 Direct labour 200 Rs. 60 = 12,000 400 Rs. 100 = 40,000 52,000 Prime cost 302,000 Overheads 200 Rs. 400 = 80,000 400 Rs. 1000 = 400,000 480,000 Factory cost 782,000 Selling and administrative cost (10% of factory cost) 78,200 Total cost 860,200 Cost per unit = Rs. 860, 200500 = Rs. 1,720

4 Differences between job costing and batch costing To compare job costing and batch costing let's look at some examples of specific orders: Job Costing Batch Costing Making 1 specific loaf. Making a batch of loaves to a standard recipe. Printing a specific poster for a business. Printing a batch of posters to be put up around town. Installing an alarm in a house. Installing alarms in block of flats.

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5 Contract costing

Contract costing is a form of job costing which applies where the job is on a large scale and for a long duration. The majority of costs relating to a contract are direct costs. Imagine trying to build up job costs on a job ticket in the way described in the previous chapter during the excavation of the tunnel under the English Channel or the construction of a skyscraper. It would be impossible. In industries such as building and construction work, civil engineering and shipbuilding, job costing is not usually appropriate. Contract costing is. A contract is a cost unit or cost centre which is charged with the direct costs of production and an apportionment of head office overheads. Contract costing is the name given to a method of job costing where the job to be carried out is of such magnitude that a formal contract is made between the customer and supplier. It applies where work is undertaken to customers' special requirements and each order is of long duration (compared with the time to which job costing applies). The work is usually constructional; the method is broadly similar to job costing, although there are, of course, a few differences.

5.1 Features of contract costing (a) A formal contract is made between customer and supplier. (b) Work is undertaken to customers' special requirements. (c) The work is for a relatively long duration. Large jobs may take a long time to complete, perhaps two or three years. Even when a contract is completed within less than twelve months, it is quite possible that the work may have begun during one financial year and ended during the supplier's next financial year; therefore the profit on the contract will relate to more than one accounting period. (d) The work is frequently constructional in nature. (e) The method of costing is similar to job costing. (f) The work is frequently based on site. (g) It is not unusual for a site to have its own cashier and time-keeper.

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The problems which may arise in contract costing are as follows. Problem Comment

Identifying direct costs Because of the large size of the job, many cost items which are usually thought of as production overhead are charged as direct costs of the contract (for example, supervision, hire of plant, depreciation or loss in value of plant which is owned, sub-contractors' fees or charges and so on). Low indirect costs Because many costs normally classed as overheads

are charged as direct costs of a contract, the absorption rate for overheads should only apply a share of the cost of those cost items which are not already direct costs. For most contracts the only item of indirect cost would be a charge for head office expenses.

Difficulties of cost control Because of the size of some contracts and some sites, there are often cost control problems (material usage and losses, pilferage, labour supervision and utilisation, damage to (and loss of) plant and tools, vandalism and so on). 5.2 Overhead costs Overhead costs are added periodically (for example, at the end of an accounting period) and are based on predetermined overhead absorption rates for the period. You may come across examples where a share of head office general costs is absorbed as an overhead cost to the contract, but this should not happen if the contract is unfinished at the end of the period: only production overheads should be included in the value of any closing work in progress. 5.3 Contract accounts The account for a contract is a job account, or work in progress account, and is a record of the direct materials, direct labour, direct expenses and overhead charges on the contract. A typical contract account might appear as shown below. Check the items in the account carefully and notice how the cost (or value) of the work done emerges as work in progress. On an unfinished contract, where no profits are taken mid-way through the contract, this cost of work in progress is carried forward as a closing inventory balance.

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5.4 Example: a contract account CONTRACT 794 – TEN-LANE MOTORWAY Rs'000 Rs'000 Book value of plant on site b/d 14,300 Materials returned to stores or Materials requisition from stores 15,247 transferred to other sites 2,100 Materials and equipment purchased 36,300 Proceeds from sale of materials Maintenance and operating costs on site and jobbing work for of plant and vehicles 14,444 other customers 600 Hire charges for plant and Book value of plant transferred 4,800 vehicles not owned 6,500 Materials on site c/d 7,194 Tools and consumables 8,570 Book value of plant on site c/d 6,640 Direct wages 23,890 21,334 Supervisors' and engineers' salaries Cost of work done c/d (proportion relating to time spent (balancing item) 139,917 on the contract) 13,000 Other site expenses 12,000 Overheads (apportioned perhaps on the basis of direct labour hours) 17,000 161,251 161,251 Materials on site b/d 7,194 Book value of plant on site b/d 6,640 Cost of work done b/d 139,917 6 Service costing

6.1 What is service costing?

Service costing can be used by companies operating in a service industry or by companies wishing to establish the cost of services carried out by some of their departments. Service organisations do not make or sell tangible goods. Service costing (or function costing) is a costing method concerned with establishing the costs, not of items of production, but of services rendered.

Service costing is used in the following circumstances. (a) A company operating in a service industry will cost its services, for which sales revenue will be earned; examples include electricians, car hire services, road, rail or air transport services and hotels. (b) A company may wish to establish the cost of services carried out by some of its departments; for example, the costs of the vans or lorries used in distribution, the costs of the computer department or the staff canteen.

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6.2 Service costing versus product costing (such as job or process costing) (a) With many services, the cost of direct materials consumed will be relatively small compared to the labour, direct expenses and overheads cost. In product costing the direct materials are often a greater proportion of the total cost. (b) Although many services are revenue-earning, others are not (such as the distribution facility or the staff canteen). This means that the purpose of service costing may not be to establish a profit or loss (nor to value closing inventories for the statement of financial position); it may be to provide management information about the comparative costs or efficiency of the services, with a view to helping managers to budget for their costs using historical data as a basis for estimating costs in the future and to control the costs in the service departments. (c) The procedures for recording material costs, labour hours and other expenses will vary according to the nature of the service.

6.3 Specific characteristics of services Specific characteristics of services Simultaneity Intangibility Heterogeneity Perishability Consider the service of providing a haircut. (a) The production and consumption of a haircut are simultaneous, and therefore it cannot be inspected for quality in advance, nor can it be returned if it is not what was required. (b) A haircut is heterogeneous and so the exact service received will vary each time: not only will two hairdressers cut hair differently, but a hairdresser will not consistently deliver precisely the same standard of haircut. (c) A haircut is intangible in itself; the performance of the service comprises many other intangible factors, such as the music in the salon, the personality of the hairdresser, the quality of the coffee. (d) Haircuts are perishable, that is, they cannot be stored. You cannot buy them in bulk, and the hairdresser cannot do them in advance and keep them stocked away in case of heavy demand. The incidence of work in progress in service organisations is less frequent than in other types of organisation. Note the mnemonic SHIP for remembering the specific characteristics of services.

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6.4 Unit cost measures The main problem with service costing is the difficulty in defining a realistic cost unit that represents a suitable measure of the service provided. Frequently, a composite cost unit may be deemed more appropriate. Hotels, for example, may use the 'occupied bed/night' as an appropriate unit for cost ascertainment and control. Typical cost units used by companies operating in a service industry are shown below. Service Road, rail and air transport services Hotels Education Hospitals Catering establishment

Cost unit Passenger/mile or kilometre, tonne/mile, tonne/kilometre Occupied bed-night Full-time student Patient Meal served

QUESTION Internal services

List examples of cost units for internal services such as canteens, distribution and maintenance. ANSWER

Service Canteen Maintenance Vans and lorries used in distribution Cost unit Meal served Man hour Mile or kilometre, tonne/mile, tonne/kilometre Each organisation will need to ascertain the cost unit most appropriate to its activities. If a number of organisations within an industry use a common cost unit, then valuable comparisons can be made between similar establishments. This is particularly applicable to hospitals, educational establishments and local authorities. Whatever cost unit is decided upon, the calculation of a cost per unit is as follows.

FORMULA TO LEARN

Cost per service unit = Total costs for periodNumber of service units in the period

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6.5 Service cost analysis

Service cost analysis should be performed in a manner which ensures that the following objectives are attained. (a) Planned costs should be compared with actual costs. Differences should be investigated and corrective action taken as necessary. (b) A cost per unit of service should be calculated. If each service has a number of variations (such as maintenance services provided by plumbers, electricians and carpenters) then the calculation of a cost per unit of each service may be necessary. (c) The cost per unit of service should be used as part of the control function. For example, costs per unit of service can be compared, month by month, period by period, year by year and so on and any unusual trends can be investigated. (d) Prices should be calculated for services being sold to third parties. The procedure is similar to job costing. A mark-up is added to the cost per unit of service to arrive at a selling price. (e) Costs should be analysed into fixed, variable and semi-variable costs to help assist management with planning, control and decision making. 6.6 Service cost analysis in internal service situations

Service department costing is also used to establish a specific cost for an internal service which is a service provided by one department for another, rather than sold externally to customers, eg canteen, maintenance. 6.6.1 Transport costs

'Transport costs' is a term used here to refer to the costs of the transport services used by a company, rather than the costs of a transport organisation, such as a rail network. If a company has a fleet of lorries or vans which it uses to distribute its goods, it is useful to know how much the department is costing, for a number of reasons. (a) Management should be able to budget for expected costs, and to control actual expenditure on transport, by comparing actual costs with budgeted costs. (b) The company may charge customers for delivery or 'carriage outwards' costs, and a charge based on the cost of the transport service might be appropriate.

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(c) If management knows how much its own transport is costing, a comparison can be made with alternative forms of transport – to decide, for example, whether a cheaper or better method of delivery can be found. (d) Similarly, if a company uses, say, a fleet of lorries, knowledge of how much transport by lorry costs should help management to decide whether another type of vehicle, say vans, would be cheaper to use. Transport costs may be analysed to provide the cost of operating one van or lorry each year, but it is more informative to analyse costs as follows. (a) The cost per mile or kilometre travelled. (b) The cost per tonne/mile or tonne/kilometre (the cost of carrying one tonne of goods for one kilometre distance) or the cost per kilogram/metre. For example, suppose that a company lorry makes five deliveries in a week. Distance Tonnes (one way) Tonne/kilometres Delivery carried Kilometres carried 1 0.4 180 72 2 0.3 360 108 3 1.2 100 120 4 0.8 250 200 5 1.0 60 60 560 If the costs of operating the lorry during the week are known to be Rs. 840, the cost per tonne/kilometre would be: Rs. 840560 tonne / kilometre = Rs. 1.50 per tonne/kilometre Transport costs might be collected under five broad headings. (a) Running costs, such as petrol, oil, drivers' wages (b) Loading costs (the labour costs of loading the lorries with goods for delivery) (c) Servicing, repairs, spare parts and tyre usage (d) Annual direct expenses, such as insurance and depreciation (e) Indirect costs of the distribution department, such as the wages of managers The role of the cost accountant is to provide a system for recording and analysing costs. Just as production costs are recorded by means of material requisition notes, labour timesheets and so on, so too must transport costs be recorded by means of log sheets or timesheets, and material supply notes.

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The purpose of a lorry driver's log sheet is to record distance travelled, or the number of tonne/kilometres and the drivers' time. 6.6.2 Canteen costs Another example of service costing is the cost of a company's canteen services. A feature of canteen costing is that some revenue is earned when employees pay for their meals, but the prices paid will be insufficient to cover the costs of the canteen service. The company will subsidise the canteen and a major purpose of canteen costing is to establish the size of the subsidy. If the costs of the canteen service are recorded by a system of service cost accounting, the likely headings of expense would be as follows. (a) Food and drink: separate canteen stores records may be kept, and the consumption of food and drink recorded by means of 'materials issues' notes. (b) Labour costs of the canteen staff: hourly paid staff will record their time at work on a time card or timesheet. Salaried staff will be a 'fixed' cost each month. (c) Consumable stores, such as crockery, cutlery, glassware, table linen and cleaning materials, will also be recorded in some form of inventory control system. (d) The cost of gas and electricity may be separately metered; otherwise an apportionment of the total cost of such utilities for the building as a whole will be made to the canteen department. (e) Asset records will be kept and depreciation charges made for major items of equipment such as ovens and furniture. (f) An apportionment of other overhead costs of the building (rent and rates, building insurance and maintenance and so on) may be charged against the canteen. Cash income from canteen sales will also be recorded.

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6.6.3 Example: Service cost analysis Suppose that a canteen recorded the following costs and revenue during the month. Rs Food and drink 11,250 Labour 11,250 Heating and lighting 1,875 Repairs and consumable stores 1,125 Financing costs 1,000 Depreciation 750 Other apportioned costs 875 Revenue 22,500 The canteen served 37,500 meals in the month. The size of the subsidy could be easily identified as follows: Rs The total costs of the canteen 28,125 Revenue 22,500 Loss, to be covered by the company 5,625 The cost per meal averages 75c and the revenue per meal 60c. If the company decided that the canteen should pay its own way, without a subsidy, the average price of a meal would have to be raised by 15 cents. 6.7 The usefulness of costing services that do not earn revenue 6.7.1 Purposes of service costing The techniques for costing services are similar to the techniques for costing products, but why should we want to establish a cost for 'internal' services, services that are provided by one department for another, rather than sold externally to customers? In other words, what is the purpose of service costing for non-revenue-earning services? Service costing has two basic purposes. (a) To control the costs in the service department. If we establish a distribution cost per tonne/kilometre, a canteen cost per employee, or job costs of repairs, we can establish control measures in the following ways. (i) Comparing actual costs against a target or standard (ii) Comparing current actual costs against actual costs in previous periods

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(b) To control the costs of the user departments, and prevent the unnecessary use of services. If the costs of services are charged to the user departments in such a way that the charges reflect the use actually made by each department, then the following will occur. (i) The overhead costs of user departments will be established more accurately; indeed some service department variable costs might be identified as directly attributable costs of the user department. (ii) If the service department's charges for a user department are high, the user department might be encouraged to consider whether it is making an excessively costly and wasteful use of the service department's service. (iii) The user department might decide that it can obtain a similar service at a lower cost from an external service company. 6.7.2 Example: costing internal services (a) If maintenance costs in a factory are costed as jobs (that is, if each bit of repair work is given a job number and costed accordingly) repair costs can be charged to the departments on the basis of repair jobs actually undertaken, instead of on a more generalised basis (such as apportionment according to machine hour capacity in each department). Departments with high repair costs could then consider their high incidence of repairs; they could consider the age and reliability of their machines, or the skills of the machine operatives. (b) If IT costs are charged to a user department on the basis of a cost per hour, the user department would assess whether it was getting good value from its use of the IT department and whether it might be better to outsource some of its IT work. 6.8 Service cost analysis in service industry situations 6.8.1 Distribution costs

Example: service cost analysis in the service industry This example shows how a rate per tonne/kilometre can be calculated for a distribution service. Rick Shaw operates a small fleet of delivery vehicles. Standard costs have been established as follows. Loading 1 hour per tonne loaded Loading costs: Labour (casual) Rs. 70 per hour Equipment depreciation Rs. 800 per week

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Supervision Rs. 4,000 per week Drivers' wages (fixed) Rs. 3,000 per driver per week Petrol Rs. 2 per kilometre Repairs Rs. 1 per kilometre Depreciation Rs. 800 per week per vehicle Supervision Rs. 5,000 per week Other general expenses (fixed) Rs. 5,000 per week There are two drivers and two vehicles in the fleet. During a slack week, only six journeys were made. Tonnes

carried One-way distance

Journey (one way) of journey Kilometres 1 5 100 2 8 20 3 2 60 4 4 50 5 6 200 6 5 300 Required Calculate the expected average full cost per tonne/kilometre for the week. Solution Variable costs Journey 1 2 3 4 5 6 Rs Rs Rs Rs Rs Rs Loading labour 350 560 140 280 420 350Petrol (both ways) 200 40 120 100 400 600Repairs (both ways) 100 20 60 50 200 300 650 620 320 430 1,020 1,250Total costs Rs Variable costs (total for journeys 1 to 6) 4,290 Loading equipment depreciation 800 Loading supervision 4,000 Drivers' wages 6,000 Vehicles depreciation 1,600 Drivers' supervision 5,000 Other costs 5,000 26,690

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One way distance Journey Tonnes Kilometres Tonne/kilometres 1 5 100 500 2 8 20 160 3 2 60 120 4 4 50 200 5 6 200 1,200 6 5 300 1,500 3,680

Cost per tonne/kilometre Rs. 26, 6903, 680 = Rs. 7.253 Note that the large element of fixed costs may distort this measure; however, a variable cost per tonne/kilometre of Rs. 4,290/3,680 = Rs. 1.166 may be useful for budgetary control. 6.8.2 Education The techniques described in the preceding paragraphs can be applied, in general, to any service industry situation. Attempt the following question about education. QUESTION Suitable cost unit A university with annual running costs of Rs. 30 million has the following students. Attendance weeks Hours Classification Number per annum per week 3-year 2,700 30 28 4-year 1,500 30 25 Sandwich 1,900 35 20 Required

Calculate a cost per suitable cost unit for the university, to the nearest cent.

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ANSWER We need to begin by establishing a cost unit for the university. Since there are three different categories of students we cannot use 'a student' as the cost unit. Attendance hours would seem to be the most appropriate cost unit. The next step is to calculate the number of units. Total hours per Number of students Weeks Hours annum 2,700 30 28 = 2,268,000 1,500 30 25 = 1,125,000 1,900 35 20 = 1,330,000 4,723,000 The cost per unit is calculated as follows. Cost per unit = Total costNumber of units = Rs.

30,000,0004,723,000 = Rs. 6.35

QUESTION Service costing

State which of the following are characteristics of service costing. (i) High levels of indirect costs as a proportion of total costs (ii) Use of composite cost units (iii) Use of equivalent units A (i) only C (ii) only B (i) and (ii) only D (ii) and (iii) only ANSWER The answer is B. In service costing it is difficult to identify many attributable direct costs. Many costs must be shared over several cost units, therefore characteristic (i) does apply. Composite cost units such as tonne/mile or room/night are often used, therefore characteristic (ii) does apply. Equivalent units are more often used in costing for tangible products, therefore characteristic (iii) does not apply. The correct answer is therefore B.

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A costing method is designed to suit the way goods are processed or manufactured or the way services are provided. Job costing is a costing method applied where work is undertaken to customers' special requirements and each order is of comparatively short duration. Costs for each job are collected on a job cost sheet or job card. Material costs for each job are determined from material requisition notes.

Labour times on each job are recorded on a job ticket, which is then costed and recorded on the job cost sheet. Some labour costs, such as overtime premium or the cost of rectifying sub-standard output, might be charged either directly to a job or else as an overhead cost, depending on the circumstances in which the costs have arisen. Overhead is absorbed into the cost of jobs using the predetermined overhead absorption rates. The usual method of fixing prices within a jobbing concern is cost-plus pricing. It is possible to use a job costing system to control the costs of an internal

service department, such as the maintenance department or the printing department. Batch costing is similar to job costing in that each batch of similar articles is separately identifiable. The cost per unit manufactured in a batch is the total batch cost divided by the number of units in the batch. Contract costing is a form of job costing which applies where the job is on a large scale and for a long duration. The majority of costs relating to a contract are direct costs. Service costing can be used by companies operating in a service industry or by companies wishing to establish the cost of services carried out by some of their departments. Service organisations do not make or sell tangible goods. Specific characteristics of services – Simultaneity – Heterogeneity – Intangibility – Perishability

The main problem with service costing is the difficulty in defining a realistic cost unit that represents a suitable measure of the service provided. Frequently, a composite cost unit may be deemed more appropriate. Hotels, for example, may use the 'occupied bed/night' as an appropriate cost unit for ascertainment and control.

Service department costing is also used to establish a specific cost for an internal service which is a service provided by one department for another, rather than sold externally to customers, eg canteen, maintenance.

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1 Identify the documents that are used in calculating the material cost for each job. 2 Which of the following are not characteristics of job costing? I Customer-driven production II Complete production possible within a single accounting period III Homogeneous products A I and II only C II and III only B I and III only D III only 3 The cost of a job is Rs. 100,000 (a) If profit is 25% of the job cost, the price of the job = Rs……………… (b) If there is a 25% margin, the price of the job = Rs………………… 4 Define the term 'batch'. 5 State briefly the method of calculating the cost per unit of a completed batch. 6 Define service costing. 7 Match up the following services with their typical cost units

Service Cost unit Hotels Patient-day Education ? Meal served Hospitals Full-time student Catering organisations Occupied bed-night 8 State the advantage of organisations within an industry using a common cost unit. 9 Cost per service unit = ................................................... 10 Service department costing is used to establish a specific cost for an 'internal service' which is a service provided by one department for another. True False

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11 The following information is available for contract AF3. Contract price Rs. 15 million Cost of work to date Rs. 5,040,000 Estimated costs to completion Rs. 3,960,000 The amount of profit to be recognised on the contract is A Rs. 0 B Rs. 3,360,000 C Rs. 6,000,000 D Rs. 8,400,000

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1 Materials requisition notes, or from suppliers' invoices if materials are purchased specifically for a particular job. 2 The answer is D. 3 (a) Rs. 100,000 + (25% Rs. 100,000) = Rs. 100,000 + Rs. 25,000 = Rs. 125,000 (b) Let price of job = x Profit = 25% x (selling price) If profit = 0.25x x – 0.25x = cost of job 0.75x = Rs. 100,000 x = Rs. 100,0000.75 = Rs. 133,333 4 A group of similar articles which maintains its identity during one or more stages of production and is treated as a cost unit. 5 Total batch costNumber of units in the batch 6 Cost accounting for services or functions eg canteens, maintenance, personnel (service centres/functions). 7 Service Cost unit Hotels Patient-day Education Meal served Hospitals Full-time student Catering organisations Occupied bed-night 8 It is easier to make comparisons. 9 Cost per service unit = Total costs for periodNumber of service units in the period 10 True

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11 The answer is B. Total cost to completion = Rs. 5,040,000 + Rs. 3,960,000 = Rs. 9,000,000 Percentage of total cost incurred to date = Rs. 5,040,000/Rs. 9,000,000 = 56% Therefore it is acceptable to recognise a profit. This eliminates option A. Profit to be recognised = Cost of work doneEstimated total cost of contract estimated total profit = Rs. 5, 040, 000Rs. 9, 000, 000 Rs. (15,000,000 – 9,000,000) = Rs. 3,360,000

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Knowledge Component A Cost accounting 1.8 Process costing 1.8.1 Identify stages of a process and account for process costs 1.8.2 Interpret and apply the concept of equivalent units of product costing 1.8.3 Compute the cost of joint products and by-products

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INTRODUCTION In this chapter we will consider process costing. The chapter will consider the topic from basics, looking at how to account for the most simple of processes. We then move on to how to account for any losses which might occur, as well as what to do with any scrapped units which are sold. We also consider how to deal with any closing work in progress and then look at two methods of valuing opening work in progress. Valuation of both opening and closing work in progress hinges on the concept of equivalent units, which will be explained in detail. We then take the subject further by looking at the more complex decisions and accounting connected with process costing. These relate to processes that produce more than one product, and situations where it may not be profitable to undertake further processing.

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CHAPTER CONTENTS

LEARNING OUTCOME1 The basics of process costing, losses and gains 1.8.12 Losses with scrap value and disposal costs 1.8.13 Valuing closing work in progress 1.8.24 Valuing opening work in progress: FIFO method 1.8.25 Valuing opening work in progress: weighted average cost method (AVCO) 1.8.2

6 Joint products costing 1.8.37 By-products costing 1.8.3

1 The basics of process costing, losses and gains

1.1 Introduction to process costing

Process costing is a costing method used where it is not possible to identify separate units of production or jobs, usually because of the continuous nature of the production processes involved. It is common to identify process costing with continuous production such as the following. Oil refining Foods and drinks Paper Chemicals Process costing may also be associated with the continuous production of large volumes of low-cost items, such as cans or tins. 1.2 Features of process costing (a) The output of one process becomes the input to the next until the finished product is made in the final process. (b) The continuous nature of production in many processes means that there will usually be closing work in progress (WIP) which must be valued. In process costing it is not possible to build up cost records of the cost per unit of output or the cost per unit of closing inventory because production in progress is an indistinguishable homogeneous mass.

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(c) There is often a loss in process due to spoilage, wastage, evaporation and so on. (d) Output from production may be a single product, but there may also be a by-product (or by-products) and/or joint products. The aim of this chapter is to describe how cost accountants keep a set of accounts to record the costs of production in a processing industry. The aim of the set of accounts is to derive a cost, or valuation, for output and closing inventory.

1.3 Process accounts Where a series of separate processes is required to manufacture the finished product, the output of one process becomes the input to the next until the final output is made in the final process. If two processes are required the accounts would look like this. PROCESS 1 ACCOUNT Units Rs’000 Units Rs’000 Direct materials 1,000 50,000 Output to process 2 1,000 90,000 Direct labour 20,000 Production overhead 20,000 1,000 90,000 1,000 90,000 PROCESS 2 ACCOUNT Units Rs’000 Units Rs’000 Materials from process 1 1,000 90,000 Output to finished goods 1,000 150,000Added materials 30,000 Direct labour 15,000 Production overhead 15,000 1,000 150,000 1,000 150,000Note that direct labour and production overhead may be treated together in an examination question as conversion cost. Added materials, labour and overhead in process 2 are added gradually throughout the process. Materials from process 1, in contrast, will often be introduced in full at the start of process 2. The 'units' columns in the process accounts are for memorandum purposes only and help you to ensure that you do not miss out any entries.

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1.4 Framework for dealing with process costing Process costing is centred around four key steps. The exact work done at each step will depend on whether there are normal losses, scrap, opening or closing work in progress. Step 1 Determine output and losses Step 2 Calculate cost per unit of output, losses and WIP Step 3 Calculate total cost of output, losses and WIP Step 4 Complete accounts Let's look at these steps in more detail Step 1 Determine output and losses. This step involves the following.

Determining expected output Calculating normal loss and abnormal loss and gain Calculating equivalent units if there is closing or opening work in progress

Step 2 Calculate cost per unit of output, losses and WIP. This step involves calculating cost per unit or cost per equivalent unit. Step 3 Calculate total cost of output, losses and WIP. In some examples this will be straightforward; however, in cases where there is closing and/or opening work-in-progress, a statement of evaluation will have to be prepared. Step 4 Complete accounts. This step involves the following.

Completing the process account Writing up the other accounts required by the question

1.5 Losses and gains in process costing 1.5.1 Introduction

Losses may occur in process. If a certain level of loss is expected, this is known as normal loss. If losses are greater than expected, the extra loss is abnormal loss. If losses are less than expected, the difference is known as abnormal gain.

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Normal loss is the loss expected during a process. It is not given a cost. Abnormal loss is the extra loss resulting when actual loss is greater than normal or expected loss; it is given a cost. Abnormal gain is the gain resulting when actual loss is less than the normal or expected loss; it is given a 'negative cost'.

Since normal loss is not given a cost, the cost of producing these units is borne by the 'good' units of output. Abnormal loss and gain units are valued at the same unit rate as 'good' units. Abnormal events do not, therefore, affect the cost of good production. Their costs are analysed separately in an abnormal loss or abnormal gain account. 1.5.2 Example: abnormal losses and gains Suppose that input to a process is 1,000 units at a cost of Rs. 4,500. Normal loss is 10% and there are no opening or closing stocks. Required

Prepare the accounting entries for the cost of output and the cost of the loss if actual output were as follows. (a) 860 units (so that actual loss is 140 units) (b) 920 units (so that actual loss is 80 units) Solution Before we demonstrate the use of the 'four-step framework' we will summarise the way that the losses are dealt with. (i) Normal loss is given no share of cost. (ii) The cost of output is therefore based on the expected units of output, which in our example amount to 90% of 1,000 = 900 units. (iii) Abnormal loss is given a cost, which is written off to the profit and loss account via an abnormal loss/gain account. (iv) Abnormal gain is treated in the same way, except that being a gain rather than a loss, it appears as a debit entry in the process account (whereas a loss appears as a credit entry in this account).

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(a) Output is 860 units

Step 1 Determine output and losses If actual output is 860 units and the actual loss is 140 units: Units Actual loss 140 Normal loss (10% of 1,000) 100 Abnormal loss 40 Step 2 Calculate cost per unit of output and losses The cost per unit of output and the cost per unit of abnormal loss are based on expected output. Costs incurredExpected output = Rs. 45, 000900 units = Rs. 50 per unit Step 3 Calculate total cost of output and losses Normal loss is not assigned any cost. Rs Cost of output (860 Rs. 50) 43,000 Normal loss 0 Abnormal loss (40 Rs. 50) 2,000 45,000 Step 4 Complete accounts PROCESS ACCOUNT Units Rs Units Rs Cost incurred 1,000 45,000 Normal loss 100 0 Output (finished goods a/c) 860 ( Rs. 50) 4,300 Abnormal loss 40 ( Rs. 50) 2,000 1,000 45,000 1,000 45,000 ABNORMAL LOSS ACCOUNT Units Rs Units Rs Process a/c 40 2,000 Statement of profit or loss 40 2,000

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(b) Output is 920 units

Step 1 Determine output and losses If actual output is 920 units and the actual loss is 80 units: Units Actual loss 80 Normal loss (10% of 1,000) 100 Abnormal gain 20 Step 2 Calculate cost per unit of output and losses The cost per unit of output and the cost per unit of abnormal gain are based on expected output. Costs incurredExpected output = Rs. 45, 000900 units = Rs. 50 per unit

(Whether there is abnormal loss or gain does not affect the valuation of units of output. The figure of Rs. 50 per unit is exactly the same previously, when there were 40 units of abnormal loss.) Step 3 Calculate total cost of output and losses Rs Cost of output (920 Rs. 50) 46,000 Normal loss 0 Abnormal gain (20 Rs. 50) (1,000) 45,000 Step 4 Complete accounts PROCESS ACCOUNT Units Rs Units Rs Cost incurred 1,000 45,000 Normal loss 100 0Abnormal gain a/c 20 ( Rs. 50) 1,000 Output (finished 920 ( Rs. 50) 46,000

goods a/c) 1,020 46,000 1,020 46,000ABNORMAL GAIN Units Rs Units Rs Statement of profit or loss 20 1,000 Process a/c 20 1,000

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QUESTION Abnormal losses and gains Shiny LLC has two processes, Y and Z. There is an expected loss of 5% of input in process Y and 7% of input in process Z. Activity during a four-week period is as follows. Y Z Material input (kg) 20,000 28,000 Output (kg) 18,500 26,100 Required

Assess whether there is an abnormal gain or abnormal loss for each process. Y Z A Abnormal loss Abnormal loss B Abnormal gain Abnormal loss C Abnormal loss Abnormal gain D Abnormal gain Abnormal gain ANSWER The correct answer is C. Y Z Input (kg) 20,000 28,000 Normal loss (kg) 1,000 (5% of 20,000) 1,960 (7% of 28,000)Expected output 19,000 26,040 Actual output 18,500 26,100 Abnormal loss/gain 500 (loss) 60 (gain)

1.5.3 Example: Abnormal losses and gains (2) During a four-week period, period 3, costs of input to a process were Rs. 29,070. Input was 1,000 units, output was 850 units and normal loss is 10%. During the next period, period 4, costs of input were again Rs. 29,070. Input was again 1,000 units, but output was 950 units. There were no units of opening or closing inventory. Required

Prepare the process account and abnormal loss or gain account for each period.

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Solution

Step 1 Determine output and losses Period 3 Units Actual output 850 Normal loss (10% 1,000) 100 Abnormal loss 50 Input 1,000 Period 4 Units Actual output 950 Normal loss (10% 1,000) 100 Abnormal gain (50) Input 1,000

Step 2 Calculate cost per unit of output and losses For each period the cost per unit is based on expected output. Cost of inputExpected units of output = Rs. 29, 070900 = Rs. 32.30 per unit Step 3 Calculate total cost of output and losses

Period 3 Rs Cost of output (850 Rs. 32.30) 27,455 Normal loss 0 Abnormal loss (50 Rs. 32.30) 1,615 29,070 Period 4 Rs Cost of output (950 Rs. 32.30) 30,685 Normal loss 0 Abnormal gain (50 Rs. 32.30) 1,615 29,070

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Step 4 Complete accounts PROCESS ACCOUNT Units Rs Units Rs Period 3 Cost of input 1,000 29,070 Normal loss 100 0 Finished goods a/c 850 27,455 ( Rs. 32.30) Abnormal loss a/c 50 1,615 ( Rs. 32.30) 1,000 29,070 1,000 29,070 Period 4 Cost of input 1,000 29,070 Normal loss 100 0 Abnormal gain a/c ( Rs. 32.30) 50 1,615 Finished goods a/c 950 30,685 ( Rs. 32.30) 1,050 30,685 1,050 30,685 ABNORMAL LOSS OR GAIN ACCOUNT Rs Rs Period 3 Period 4 Abnormal loss in process a/c 1,615 Abnormal gain in process a/c 1,615 A nil balance on this account will be carried forward into period 5. If there is a closing balance in the abnormal loss or gain account when the profit for the period is calculated, this balance is taken to the statement of profit or loss. An abnormal gain will be a credit to the statement of profit or loss; an abnormal loss will be a debit to the statement of profit or loss.

QUESTION Process account 3,000 units of material are input to a process. Process costs are as follows. Material Rs. 11,700 Conversion costs Rs. 6,300 Output is 2,000 units. Normal loss is 20% of input. Required Prepare a process account and the appropriate abnormal loss/gain account.

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ANSWER

Step 1 Determine output and losses We are told that output is 2,000 units. Normal loss = 20% 3,000 = 600 units (ie an expected output of 2,400 units) Abnormal loss = (3,000 – 600) – 2,000 = 400 units Step 2 Calculate cost per unit of output and losses

Cost per unit = Rs 11, 700 + 6, 3002, 400 = Rs. 7.50 Step 3 Calculate total cost of output and losses Rs Output (2,000 Rs. 7.50) 15,000 Normal loss 0 Abnormal loss (400 Rs. 7.50) 3,000 18,000 Step 4 Complete accounts PROCESS ACCOUNT Units Rs Units Rs Material 3,000 11,700 Output 2,000 15,000 Conversion costs 6,300 Normal loss 600 Abnormal loss 400 3,000 3,000 18,000 3,000 18,000 ABNORMAL LOSS ACCOUNT Rs Rs Process a/c 3,000 Statement of profit or loss 3,000 QUESTION Finished output Charlton Co manufactures a product in a single process operation. Normal loss is 10% of input. Loss occurs at the end of the process. Data for June is as follows. Opening and closing inventories of work in progress Nil Cost of input materials (3,300 units) Rs. 59,100 Direct labour and production overhead Rs. 30,000 Output to finished goods 2,750 units Required

Calculate the full cost of finished output in June. A Rs. 74,250 B Rs. 81,000 C Rs. 82,500 D Rs. 89,100

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ANSWER

Step 1 Determine output and losses Units Actual output 2,750 Normal loss (10% 3,300) 330 Abnormal loss 220 3,300 Step 2 Calculate cost per unit of output and losses Cost of inputExpected units of output =

Rs. 89, 1003, 300 330 = Rs. 30 per unit Step 3 Calculate total cost of output and losses Rs Cost of output (2,750 Rs. 30) 82,500 (The correct answer is C) Normal loss 0 Abnormal loss (220 Rs. 30) 6,600 89,100 If you were reduced to making a calculated guess, you could have eliminated option D. This is simply the total input cost, with no attempt to apportion some of the cost to the abnormal loss. Option A is incorrect because it results from allocating a full unit cost to the normal loss: remember that normal loss does not carry any of the process cost. Option B is incorrect because it results from calculating a 10% normal loss based on output of 2,750 units (275 units normal loss), rather than on input of 3,300 units.

2 Losses with scrap value and disposal costs Scrap is 'Discarded material having some value.'

Loss or spoilage may have scrap value. The scrap value of normal loss is usually deducted from the cost of materials. The scrap value of abnormal loss (or abnormal gain) is usually set off against its cost, in an abnormal loss (abnormal gain) account.

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As the questions that follow will show, the three steps to remember are these. Step 1 Separate the scrap value of normal loss from the scrap value of

abnormal loss or gain. Step 2 In effect, subtract the scrap value of normal loss from the cost of the process, by crediting it to the process account (as a 'value' for normal loss). Step 3 Either subtract the value of abnormal loss scrap from the cost of abnormal loss, by crediting the abnormal loss account.

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QUESTION Losses and scrap 3,000 units of material are input to a process. Process costs are as follows. Material Rs. 11,700 Conversion costs Rs. 6,300 Output is 2,000 units. Normal loss is 20% of input. The units of loss could be sold for Rs. 1. Required

Prepare appropriate accounts. ANSWER

Step 1 Determine output and losses Input 3,000 units Normal loss (20% of 3,000) 600 units Expected output 2,400 units Actual output 2,000 units Abnormal loss 400 units Step 2 Calculate cost per unit of output and losses Rs Scrap value of normal loss 600 Scrap value of abnormal loss 400 Total scrap (1,000 units Rs. 1) 1,000

Cost per expected unit = 11, 700 600 + 6, 3002, 400Rs. = Rs. 7.25 Step 3 Calculate total cost of output and losses Rs Output (2,000 Rs. 7.25) 14,500 Normal loss (600 Rs. 1.00) 600 Abnormal loss (400 Rs. 7.25) 2,900 18,000

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Step 4 Complete accounts PROCESS ACCOUNT Units Rs Units Rs Material 3,000 11,700 Output 2,000 14,500 Conversion costs 6,300 Normal loss 600 600 Abnormal loss 400 2,900 3,000 18,000 3,000 18,000 ABNORMAL LOSS ACCOUNT Rs Rs Process a/c 2,900 Scrap a/c 400 Statement of profit or loss 2,500 2,900 2,900 SCRAP ACCOUNT Rs Rs Normal loss 600 Cash 1,000 Abnormal loss 400 1,000 1,000

QUESTION Two processes, losses and scrap JJ has a factory which operates two production processes, cutting and pasting. Normal loss in each process is 10%. Scrapped units out of the cutting process sell for Rs. 30 per unit, whereas scrapped units out of the pasting process sell for Rs. 50. Output from the cutting process is transferred to the pasting process: output from the pasting process is finished output ready for sale. Relevant information about costs for control period 7 are as follows. Cutting process Pasting process Units Rs Units Rs Input materials 18,000 540,000 Transferred to pasting process 16,000 Materials from cutting process 16,000 Added materials 14,000 700,000Labour and overheads 324,000 1,350,000Output to finished goods 28,000 Required Prepare accounts for the cutting process, the pasting process, abnormal loss, abnormal gain and scrap.

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ANSWER (a) Cutting process

Step 1 Determine output and losses The normal loss is 10% of 18,000 units = 1,800 units, and the actual loss is (18,000 – 16,000) = 2,000 units. This means that there is abnormal loss of 200 units. Actual output 16,000 units Abnormal loss 200 units Expected output (90% of 18,000) 16,200 units Step 2 Calculate cost per unit of output and losses (i) The total value of scrap is 2,000 units at Rs. 30 per unit = Rs. 60,000. We must split this between the scrap value of normal loss and the scrap value of abnormal loss. Rs Normal loss (1,800 Rs. 30) 54,000 Abnormal loss (200 Rs. 30) 6,000 Total scrap (2,000 units Rs. 30) 60,000 (ii) The scrap value of normal loss is first deducted from the materials cost in the process, in order to calculate the output cost per unit and then credited to the process account as a 'value' for normal loss. The cost per unit in the cutting process is calculated as follows. Cost per

expected Total cost unit of output Rs Rs Materials 540,000 Less normal loss scrap value* 54,000 486,000 ( 16,200) 30.00 Labour and overhead 324,000 ( 16,200) 20.00 Total 810,000 ( 16,200) 50.00 * It is usual to set this scrap value of normal loss against the cost of materials.

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Step 3 Calculate total cost of output and losses Rs Output (16,000 units Rs. 50) 800,000 Normal loss (1,800 units Rs. 30) 54,000 Abnormal loss (200 units Rs. 50) 10,000 864,000 Step 4 Complete accounts PROCESS 1 ACCOUNT Units Rs Units Rs Materials 18,000 540,000 Output to pasting process * 16,000 800,000Labour and overhead 324,000Normal loss (scrap a/c) ** 1,800 54,000 Abnormal loss a/c * 200 10,000 18,000 864,000 18,000 864,000* At Rs. 50 per unit ** At Rs. 30 per unit (b) Pasting process Step 1 Determine output and losses The normal loss is 10% of the units processed = 10% of (16,000 + 14,000) = 3,000 units. The actual loss is (30,000 – 28,000) = 2,000 units, so that there is abnormal gain of 1,000 units. These are deducted from actual output to determine expected output. Units Actual output 28,000 Abnormal gain (1,000)Expected output (90% of 30,000) 27,000 Step 2 Calculate cost per unit of output and losses (i) The total value of scrap is 2,000 units at Rs. 50 per unit = Rs. 100,000. We must split this between the scrap value of normal loss and the scrap value of abnormal gain. Abnormal gain's scrap value is 'negative'. Rs Normal loss scrap value 3,000 units Rs. 50 150,000 Abnormal gain scrap value 1,000 units Rs. 50 (50,000) Scrap value of actual loss 2,000 units Rs. 50 100,000 (ii) The scrap value of normal loss is first deducted from the cost of materials in the process, in order to calculate a cost per unit of output, and then credited to the process

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account as a 'value' for normal loss. The cost per unit in the pasting process is calculated as follows.

Total cost

Cost per expected

unit of output Rs Rs Materials: Transfer from cutting process 800,000 Added in pasting process 700,000 1,500,000 Less scrap value of normal loss 150,000 1,350,000 ( 27,000) 50 Labour and overhead 1,350,000 ( 27,000) 50 2,700,000 ( 27,000) 100

Step 3 Calculate total cost of output and losses Rs Output (28,000 units Rs. 100) 2,800,000 Normal loss (3,000 units Rs. 50) 150,000 2,950,000 Abnormal gain (1,000 units Rs. 100) (100,000) 2,850,000 Step 4 Complete accounts PASTING PROCESS ACCOUNT Units Rs Units Rs From cutting process 16,000 800,000 Finished output* 28,000 2,800,000Added materials 14,000 700,000 Labour and o/hd 1,350,000 Normal loss(scrap 30,000 2,850,000 a/c) 3,000 150,000Abnormal gain a/c 1,000* 10,000 31,000 295,000 31,000 2,950,000* At Rs. 100 per unit

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(c) and (d) Abnormal loss and abnormal gain accounts For each process, one or the other of these accounts will record three items. (i) The cost/value of the abnormal loss/gain (corresponding entry to that in the process account). (ii) The scrap value of the abnormal loss or gain, to set off against it. (iii) A balancing figure, which is written to the statement of profit or loss as an adjustment to the profit figure. ABNORMAL LOSS ACCOUNT Units Rs Rs Scrap a/c (scrap value of Cutting process 200 10,000 abnormal loss) 6,000 Statement of profit or loss (bal) 4,000 10,000 10,000 ABNORMAL GAIN ACCOUNT Rs Units Rs Pasting Scrap a/c (scrap value of process 1,000 100,000 abnormal gain units) 50,000 Statement of profit or loss (balance) 50,000 100,000 100,000(e) Scrap account This is credited with the cash value of actual units scrapped. The other entries in the account should all be identifiable as corresponding entries to those in the process accounts, and abnormal loss and abnormal gain accounts. SCRAP ACCOUNT Rs Rs Normal loss: Cash: Cutting process (1,800 Sale of cutting process scrap Rs. 30) 54,000 (2,000 Rs. 30) 60,000 Pasting process (3,000 Sale of pasting process scrap Rs. 50) 150,000 (2,000 Rs. 50) 100,000 Abnormal loss a/c 6,000 Abnormal gain a/c 50,000 210,000 210,000

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Abnormal losses and gains never affect the cost of good units of production. The scrap value of abnormal losses is not credited to the process account, and abnormal loss and gain units carry the same full cost as a good unit of production. 2.1 Losses with a disposal cost 2.1.1 Introduction You must also be able to deal with losses which have a disposal cost. The basic calculations required in such circumstances are as follows. (a) Increase the process costs by the cost of disposing of the units of normal loss and use the resulting cost per unit to value good output and abnormal loss/gain. (b) The normal loss is given no value in the process account. (c) Include the disposal costs of normal loss on the debit side of the process account. (d) Include the disposal costs of abnormal loss in the abnormal loss account and hence in the transfer of the cost of abnormal loss to the statement of profit or loss. 2.1.2 Example: Losses with a disposal cost Suppose that input to a process was 1,000 units at a cost of Rs. 4,500. Normal loss is 10% and there are no opening and closing inventories. Actual output was 860 units and loss units had to be disposed of at a cost of Rs. 0.90 per unit. Normal loss = 10% 1,000 = 100 units. Abnormal loss = 900 – 860 = 40 units Cost per unit = Rs. 45, 000 + 100 × Rs. 90900 = Rs. 50.10 The relevant accounts would be as follows. PROCESS ACCOUNT Units Rs Units Rs Cost of input 1,000 45,000 Output 860 43,860 Disposal cost of Normal loss 100 – normal loss 900 Abnormal loss 40 2,040 1,000 45,900 1,000 45,900 ABNORMAL LOSS ACCOUNT Rs Rs Process a/c 2,040 Statement of profit or loss 2,400 Disposal cost (40 Rs. 0.90) 360 2,400 2,400

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3 Valuing closing work in progress

3.1 Introduction When units are partly completed at the end of a period (and hence there is closing work in progress), it is necessary to calculate the equivalent units of production in order to determine the cost of a completed unit. In the examples we have looked at so far we have assumed that opening and closing inventories of work in progress have been nil. We must now look at more realistic examples and consider how to allocate the costs incurred in a period between completed output (that is, finished units) and partly completed closing inventory. Some examples will help to illustrate the problem, and the techniques used to share out (apportion) costs between finished output and closing inventories. Suppose that we have the following account for Process 2 for period 9. PROCESS ACCOUNT Units Rs Rs Materials 1,000 62,000 Finished goods 800 ?Labour and overhead 28,500 Closing WIP 200 ? 1,000 90,500 1,000 90,500How do we value the finished goods and closing work in process? With any form of process costing involving closing WIP, we have to apportion costs between output and closing WIP. To apportion costs 'fairly' we make use of the concept of equivalent units of production. 3.2 Equivalent units Equivalent units are notional whole units which represent incomplete work, and which are used to apportion costs between work in process and completed output.

We will assume that in the example above the degree of completion is as follows. (a) Direct materials. These are added in full at the start of processing, and so any closing WIP will have 100% of their direct material content. (This is not always the case in practice. Materials might be added gradually throughout the process, in which case closing inventory will only be a certain percentage complete as to material content. We will look at this later in the chapter.) (b) Direct labour and production overhead. These are usually assumed to be incurred at an even rate through the production process, so that when we refer to a unit that is 50% complete, we mean that it is half complete for labour and overhead, although it might be 100% complete for materials.

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Let us also assume that the closing WIP is 100% complete for materials and 25% complete for labour and overhead. How would we now put a value to the finished output and the closing WIP? In Step 1 of our framework, we have been told what output and losses are. However we also need to calculate equivalent units. STATEMENT OF EQUIVALENT UNITS Materials Labour and overhead Degree of Equivalent Degree of Equivalent Total units completion units completion units Finished output 800 100% 800 100% 800 Closing WIP 200 100% 200 25% 50 1,000 1,000 850 In Step 2 the important figure is average cost per equivalent unit. This can be calculated as follows. STATEMENT OF COSTS PER EQUIVALENT UNIT Labour and Materials overhead Costs incurred in the period Rs. 62,000 Rs. 28,500Equivalent units of work done 1,000 850Cost per equivalent unit (approx) Rs. 62.00 Rs. 33.5294To calculate total costs for Step 3, we prepare a statement of evaluation to show how the costs should be apportioned between finished output and closing WIP. STATEMENT OF EVALUATION

Materials Labour and overheads Cost per Cost per Equivalent equivalent Equiv equiv Total

Item units units Cost units units Cost cost Rs Rs Rs Rs Rs Finished output 800 62.00 49,600 800 33.5294 26,823 76,423 Closing WIP 200 62.00 12,400 50 33.5294 1,676 14,076 1,000 62,000 850 28,499 90,499 The process account (work in progress, or work in process account) would be shown as follows. PROCESS ACCOUNT Units Rs Units Rs Materials 1,000 62,000 Finished goods 800 76,423 Labour overhead 28,499 Closing WIP 200 14,076 1,000 90,499 1,000 90,499

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QUESTION Equivalent units for closing WIP Jegan LLC has the following information available on Process 9. PROCESS 9 ACCOUNT Rs Rs Finished Input 10,000 kg 591,500 Goods 8,000 kg 520,000 Closing WIP 2,000 kg 71,500 591,500 591,500 Required

Calculate how many equivalent units there were for Closing WIP. A 1,000 C 2,000 B 1,100 D 8,000 ANSWER The correct answer is B. This question requires you to work backwards. You can calculate the cost per unit using the Finished Goods figures. Cost per unit = Cost of finished goodsNumber of kg = 520,0008,000 = Rs. 65.00 If 2,000 kg (Closing WIP figure) were fully complete total cost would be 2,000 × Rs. 65.00 = Rs. 130,000 Actual cost of Closing WIP = Rs. 71,500 Degree of completion = 71,500130,000 = 55% Therefore, equivalent units = 55% of 2,000 = 1,100 kg

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QUESTION Equivalent units Iranga LLC operates a process costing system. The following details are available for Process 2. Materials input at beginning of process 12,000 kg, costing Rs. 18,000 Labour and overheads added Rs. 28,000 10,000kg were completed and transferred to the Finished Goods account. The remaining units were 60% complete with regard to labour and overheads. There were no losses in the period. Required

Calculate the value of Closing WIP in the process account. A Rs. 4,800 C Rs. 7,667 B Rs. 6,000 D Rs. 8,000 ANSWER The correct answer is B. STATEMENT OF EQUIVALENT UNITS Material Labour Units Degree of Units Degree of completion Units Equivalent completion units EquivalentFinished goods 10,000 100% 10,000 10,000 100% 10,000 Closing WIP 2,000 100% 2,000 2,000 60% 1,200 12,000 12,000 12,000 11,200 COSTS PER EQUIVALENT UNIT Material Labour Total cost Rs. 18,000 Rs. 28,000 Equivalent units 12,000 11,200 Cost per unit Rs. 1.50 Rs. 2.50 Total cost per unit = Rs. 4.00 Value of Closing WIP = (Rs. 1.50 × 2,000) + (Rs. 2.50 × 1,200) = Rs. 6,000

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3.3 Different rates of input In many industries, materials, labour and overhead may be added at different rates during the course of production. (a) Output from a previous process (for example the output from process 1 to process 2) may be introduced into the subsequent process all at once, so that closing inventory is 100% complete in respect of these materials. (b) Further materials may be added gradually during the process, so that closing inventory is only partially complete in respect of these added materials. (c) Labour and overhead may be 'added' at yet another different rate. When production overhead is absorbed on a labour-hour basis, however, we should expect the degree of completion on overhead to be the same as the degree of completion on labour. When this situation occurs, equivalent units, and a cost per equivalent unit, should be calculated separately for each type of material, and also for conversion costs. 3.4 Example: Equivalent units and different degrees of completion Suppose that Columbine Co is a manufacturer of processed goods, and that results in process 2 for April 20X3 were as follows. Opening inventory Nil Material input from process 1 4,000 units Costs of input: Rs Material from process 1 6,000 Added materials in process 2 1,080 Conversion costs 1,720 Output is transferred into the next process, process 3. Closing work in process amounted to 800 units, complete as to: Process 1 material 100% Added materials 50% Conversion costs 30% Required

Prepare the account for process 2 for April 20X3.

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Solution (a) STATEMENT OF EQUIVALENT UNITS (OF PRODUCTION IN THE PERIOD) Equivalent units of production Process 1 Added Labour and

Input Output Total material materials overhead Units Units Units % Units % Units % Completed 4,000 production 3,200 3,200 100 3,200 100 3,200 100 Closing inventory 800 800 100 400 50 240 30 4,000 4,000 4,000 3,600 3,440 (b) STATEMENT OF COST (PER EQUIVALENT UNIT) Equivalent production

Cost per Input Cost in units unit Rs Rs Process 1 material 6,000 4,000 1.50 Added materials 1,080 3,600 0.30 Labour and overhead 1,720 3,440 0.50 8,800 2.30 (c) STATEMENT OF EVALUATION (OF FINISHED WORK AND CLOSING INVENTORIES) Number of Cost per equivalent equivalent

Production Cost element units unit Total Cost Rs Rs Rs Completed production 3,200 2.30 7,360 Closing inventory: process 1 material 800 1.50 1,200 added material 400 0.30 120 labour and overhead 240 0.50 120 1,440 8,800 (d) PROCESS ACCOUNT Units Rs Units Rs Process 1 material 4,000 6,000 Process 3 a/c 3,200 7,360 Added material 1,080 Closing Conversion costs 1,720 inventory c/f 800 1,440 4,000 8,800 4,000 8,800

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4 Valuing opening work in progress: FIFO method

4.1 Introduction Account can be taken of opening work in progress using either the First in, First out (FIFO) method or the weighted average cost method (AVCO). Opening work in progress is partly complete at the beginning of a period and is valued at the cost incurred to date. In the example in section 4.4, closing work in progress of 800 units at the end of April 20X3 would be carried forward as opening inventory, value Rs. 1,440, at the beginning of May 20X3. It therefore follows that the work required to complete units of opening inventory is 100% minus the work in progress done in the previous period. For example, if 100 units of opening inventory are 70% complete at the beginning of June 20X2, the equivalent units of production would be as follows. Equivalent units in previous period (May 20X2) (70%) = 70 Equivalent units to complete work in current period (June 20X2) (30%) = 30 Total work done 100 The FIFO method of valuation deals with production on a first in, first out basis. The assumption is that the first units completed in any period are the units of opening inventory that were held at the beginning of the period. 4.2 Example: WIP and FIFO Suppose that information relating to process 1 of a two-stage production process is as follows, for August 20X2. Opening inventory 500 units: degree of completion 60% Cost to date Rs. 28,000 Costs incurred in August 20X2 Rs Direct materials (2,500 units introduced) 132,000 Direct labour 66,000 Production overhead 66,000 264,000 Closing inventory 300 units: degree of completion 80% There was no loss in the process. Required Prepare the process 1 account for August 20X2.

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Solution As the term implies, first in, first out means that in August 20X2 the first units completed were the units of opening inventory. Opening inventories: work done to date = 60% plus work done in August 20X2 = 40% The cost of the work done up to 1 August 20X2 is known to be Rs. 28,000, so that the cost of the units completed will be Rs. 28,000 plus the cost of completing the final 40% of the work on the units in August 20X2. Once the opening inventory has been completed, all other finished output in August 20X2 will be work started as well as finished in the month. Units Total output in August 20X2 * 2,700 Less opening inventory, completed first 500 Work started and finished in August 20X2 2,200 (* Opening inventory, plus units introduced, minus closing inventory = 500 + 2,500 300) What we are doing here is taking the total output of 2,700 units, and saying that we must divide it into two parts as follows. (a) The opening inventory, which was first in and so must be first out (b) The rest of the units, which were 100% worked in the period Dividing finished output into two parts in this way is a necessary feature of the FIFO valuation method. Continuing the example, closing inventory of 300 units will be started in August 20X2, but not yet completed. The total cost of output to process 2 during 20X2 will be as follows. Rs Opening inventory cost brought forward 28,000 (60%) plus cost incurred during August 20X2, to complete x (40%) 28,000 + x Fully worked 2,200 units y Total cost of output to process 2, FIFO basis 28,000 + x + y Equivalent units will again be used as the basis for apportioning costs incurred during August 20X2. Be sure that you understand the treatment of 'opening inventory units completed', and can relate the calculations to the principles of FIFO valuation.

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Step 1 Determine output and losses STATEMENT OF EQUIVALENT UNITS Total Equivalent units of

production units in August 20X2 Opening inventory units completed 500 (40%) 200 Fully worked units 2,200 (100%) 2,200 Output to process 2 2,700 2,400 Closing inventory 300 (80%) 240 3,000 2,640 Step 2 Calculate cost per unit of output and losses The cost per equivalent unit in August 20X2 can now be calculated. STATEMENT OF COST PER EQUIVALENT UNIT Cost incurred Equivalent units = Rs. 264,0002,640 Cost per equivalent unit = Rs. 100 Step 3 Calculate total costs of output, losses and WIP STATEMENT OF EVALUATION Equivalent units Valuation Rs Opening inventory, work done in August 20X2 200 20,000 Fully worked units 2,200 220,000 Closing inventory 240 24,000 2,640 264,000 The total value of the completed opening inventory will be Rs. 28,000 (brought forward) plus Rs. 20,000 added in August before completion = Rs. 48,000.

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Step 4 Complete accounts PROCESS 1 ACCOUNT Units Rs Units Rs Opening inventory 500 28,000 Output to process Direct materials 2,500 132,00 Opening inventory 500 48,000 Direct labour 66,000 Fully worked units 2,200 220,000 Production o'hd 66,000 2,700 268,000 Closing inventory 300 24,000 3,000 292,00 3,000 292,000We now know that the value of x is Rs. (48,000 – 28,000) = Rs. 20,000 and the value of y is Rs. 220,000. QUESTION FIFO and equivalent units Chatura LLC uses the FIFO method of process costing. At the end of a four-week period, the following information was available for process P. Opening WIP 2,000 units (60% complete) costing Rs. 3,000 to date Closing WIP 1,500 units (40% complete) Transferred to next process 7,000 units Required

Calculate how many units were started and completed during the period. A 5,000 units C 8,400 units B 7,000 units D 9,000 units ANSWER The correct answer is A. As we are dealing with the FIFO method, Opening WIP must be completed first. Total output 7,000 units Less Opening WIP (completed first) 2,000 units Units started and completed during the period 5,000 units

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QUESTION Closing WIP – FIFO The following information relates to process 3 of a three-stage production process for the month of January 20X9. Opening inventory 300 units complete as to: Rs materials from process 2 100% 44,000 added materials 90% 11,500 Labour 80% 5,400 production overhead 80% 8,100 69,000 In January 20X4, a further 1,800 units were transferred from process 2 at a valuation of Rs. 270,000. Added materials amounted to Rs. 66,000 and direct labour to Rs. 32,700. Production overhead is absorbed at the rate of 150% of direct labour cost. Closing inventory at 31 January 20X4 amounted to 450 units, complete as to: process 2 materials 100% added materials 60% labour and overhead 50% Required Prepare the process 3 account for January 20X4 using FIFO valuation principles. ANSWER

Step 1 Statement of equivalent units Total Process 2 Added Conversion units materials materials costs Opening inventory 300 0 (10%) 30 (20%) 60 Fully worked units * 1,350 1,350 1,350 1,350 Output to finished goods 1,650 1,350 1,380 1,410 Closing inventory 450 450 (60%) 270 (50%) 225 2,100 1,800 1,650 1,635 * Transfers from process 2, minus closing inventory.

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Step 2 Statement of costs per equivalent unit Cost per Total cost Equivalent

units equivalent unit Rs Rs Process 2 materials 270,000 1,800 150.00 Added materials 66,000 1,650 40.00 Direct labour 32,700 1,635 20.00 Production overhead (150% of Rs. 32,700) 49,050 1,635 30.00 240.00

Step 3 Statement of evaluation Process 2 Additional materials materials Labour Overhead Total Rs Rs Rs Rs Rs Opening inventory cost b/f 44,000 11,500 5,400 8,100 69,000 Added in Jan 20X4 – 1,200 1,200 1,800 4,200 44,000 12,700 6,600 9,900 73,200 Fully worked units 202,500 54,000 27,000 40,500 324,000 Output to finished Goods 246,500 66,700 33,600 50,400 397,200 Closing inventory 67,500 10,800 4,500 6,750 89,550 314,000 77,500 38,100 57,150 486,750

(270 × Rs. 40) (225 × Rs. 20) (225 × Rs. 30) (450×Rs. 150)

(30 × Rs.40) (60 × Rs.20) (60 × Rs.30)

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Step 4 Complete accounts PROCESS 3 ACCOUNT Units Rs Units Rs Opening inventory b/f 300 69,000 Finished goods a/c 1,650 397,200Process 2 a/c 1,800 270,000 Stores a/c 66,000 Wages a/c 32,700 Production o'hd a/c 49,050 Closing inventory c/f 450 89,550 2,100 486,750 2,100 486,750 QUESTION Equivalent units and FIFO Bayya LLC operates a FIFO process costing system. The following information is available for last month. Opening work in progress 2,000 units valued at Rs. 3,000 Input 60,000 units costing Rs. 30,000 Conversion costs Rs. 20,000 Units transferred to next process 52,000 units Closing work in progress 10,000 units Opening work in progress was 100% complete with regard to input materials and 70% complete as to conversion. Closing work in progress was complete with regard to input materials and 80% complete as to conversion. Required

Calculate the number of equivalent units with regard to conversion costs. A 44,000 C 52,000 B 50,600 D 58,600

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ANSWER The correct answer is D. Units Opening work in progress 30% of 2,000 units still to be completed 600 Closing work in progress 80% of 10,000 units completed 8,000 Units started and (Opening WIP + input – closing WIP) – completed opening WIP 50,000 58,600

5 Valuing opening work in progress: weighted average cost

method (AVCO)

5.1 Introduction An alternative to FIFO is the weighted average cost method of inventory valuation which calculates a weighted average cost of units produced from both opening inventory and units introduced in the current period. By this method no distinction is made between units of opening inventory and new units introduced to the process during the accounting period. The cost of opening inventory is added to costs incurred during the period, and completed units of opening inventory are each given a value of one full equivalent unit of production. 5.2 Example: Weighted average cost method Magpie produces an item which is manufactured in two consecutive processes. Information relating to process 2 during September 20X3 is as follows. Opening inventory 800 units Degree of completion: Rs process 1 materials 100% 47,000 added materials 40% 6,000 conversion costs 30% 10,000 63,000 During September 20X3, 3,000 units were transferred from process 1 at a valuation of Rs. 181,000. Added materials cost Rs. 96,000 and conversion costs were Rs. 118,000.

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Closing inventory at 30 September 20X3 amounted to 1,000 units which were 100% complete with respect to process 1 materials and 60% complete with respect to added materials. Conversion cost work was 40% complete. Magpie uses a weighted average cost system for the valuation of output and closing inventory. Required

Prepare the process 2 account for September 20X3. Solution

Step 1 Opening inventory units count as a full equivalent unit of production when the weighted average cost system is applied. Closing inventory equivalent units are assessed in the usual way. STATEMENT OF EQUIVALENT UNITS Equivalent units Total Process 1 Added Conversion units material material costs Opening inventory 800 (100%) 800 800 800 Fully worked units* 2,000 (100%) 2,000 2,000 2,000 Output to finished goods 2,800 2,800 2,800 2,800 Closing inventory 1,000 (100%) 1,000 (60%) 600 (40%) 400 3,800 3,800 3,400 3,200 (*3,000 units from process 1 minus closing inventory of 1,000 units)

Step 2 The cost of opening inventory is added to costs incurred in September 20X3, and a cost per equivalent unit is then calculated. STATEMENT OF COSTS PER EQUIVALENT UNIT Process 1 Added Conversion material materials costs Rs Rs Rs Opening inventory 47,000 6,000 10,000 Added in September 20X3 181,000 96,000 118,000 Total cost 228,000 102,000 128,000

Equivalent units 3,800 units 3,400 units 3,200 units Cost per equivalent unit Rs. 60 Rs. 30 Rs. 40

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Step 3 STATEMENT OF EVALUATION Process 1 Added Conversion Total material materials costs cost Rs Rs Rs Rs Output to finished goods (2,800 units) 168,000 84,000 112,000 364,000Closing inventory 60,000 18,000 16,000 94,000 458,000

Step 4 PROCESS 2 ACCOUNT Units Rs Units Rs Opening inventory b/f 800 63,000 Finished goods a/c 2,800 364,000 Process 1 a/c 3,000 181,000 Added materials 96,000 Conversion costs 118,000 Closing inventory c/f 1,000 94,000 3,800 458,000 3,800 458,000 5.3 Which method should be used? FIFO inventory valuation is more common than the weighted average method, and should be used unless an indication is given to the contrary. You may find that you are presented with limited information about the opening inventory, which forces you to use either the FIFO or the weighted average method. The rules are as follows. (a) If you are told the degree of completion of each element in opening inventory, but not the value of each cost element, then you must use the

FIFO method. (b) If you are not given the degree of completion of each cost element in opening inventory, but you are given the value of each cost element, then you must use the weighted average method.

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QUESTION Equivalent units During August, a factory commenced work on 20,000 units. At the start of the month there were no partly finished units but at the end of the month there were 2,000 units which were only 40% complete. Costs in the month were Rs. 3,722,400. Required (a) Calculate how many equivalent units of closing WIP there were in the month. A 20,000 C 18,000 B 2,000 D 800 (b) Calculate the total value of fully completed output which would show in the process account. A Rs. 3,960,000 C Rs. 3,722,400 B Rs. 3,564,000 D Rs. 3,350,160 ANSWER (a) The answer is D. Equivalent units of WIP = 40% 2,000 = 800 (b) The answer is B. Total finished output 18,000 units Total equivalent units = 18,000 100% 18,000 2,000 40% 800 18,800 Cost per equivalent unit = 3,722,400/18,800 = Rs. 198

Value of fully completed output: 18,000 198 = Rs. 3,564,000

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6 Joint products costing

Joint products are two or more products separated in a process, each of which has a significant value compared to the other. A by-product is an incidental product from a process, and has an insignificant value compared to the main product. The point at which joint products and by-products become separately identifiable is known as the split-off point or separation point. Costs incurred up to this point are called common costs or joint costs. The main methods of apportioning joint costs, each of which can produce significantly different results, are as follows. Physical measurement Relative sales value apportionment method; sales value at split-off point The relative sales value method is the most widely used method of apportioning joint costs because (ignoring the effect of further processing costs) it assumes that all products achieve the same profit margin. Process costing

Process costing is a costing method used where it is not possible to identify separate units of production or jobs, usually because of the continuous nature of the production processes involved. Process costing is centred on four key steps. The exact work done at each step will depend on whether there are normal losses, scrap, opening and closing work in progress (WIP) and so on.

Step 1 Determine output and losses Step 2 Calculate cost per unit of output, losses and WIP Step 3 Calculate total cost of output, losses and WIP Step 4 Complete accounts

Losses may occur in process. If a certain level of loss is expected, this is known as normal loss. If losses are greater than expected, the extra loss is abnormal loss. If losses are less than expected, the difference is known as abnormal gain.

The scrap value of normal loss is normally deducted from the cost of materials before a cost per equivalent unit is calculated. Abnormal losses and gains never affect the cost of good units of production. The scrap value of abnormal losses is not credited to the process account, and abnormal loss and gain units carry the same full cost as a good unit of production.

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When units are partly completed at the end of a period (and hence there is closing WIP), it is necessary to calculate the equivalent units of production in order to determine the cost of a completed unit. Account can be taken of opening WIP using either the First In, First Out (FIFO) method or the weighted average cost method. QUESTION Cost accounts Prema LLC has a factory which operates two production processes. Normal spoilage in each process is 10%, and scrapped units out of process 1 sell for Rs. 500 per unit whereas scrapped units out of process 2 sell for Rs. 3,000. Output from process 1 is transferred to process 2: output from process 2 is finished output ready for sale. Relevant information about costs for period 5 is as follows.

Process 1 Process 2 Units Rs '000 Units Rs '000 Input materials 2,000 8,100 Transferred to process 2 1,750 Materials from process 1 1,750 Added materials 1,250 1,900 Labour and overheads 10,000 22,000 Output to finished goods 2,800 Required

Prepare the following cost accounts. (a) Process 1 (b) Process 2 (c) Abnormal loss (d) Abnormal gain (e) Scrap ANSWER (a) Process 1

Step 1 Determine output and losses The normal loss is 10% of 2,000 units = 200 units, and the actual loss is (2,000 – 1,750) = 250 units. This means that there is abnormal loss of 50 units. Actual output 1,750 unitsAbnormal loss 50 unitsExpected output (90% of 2,000) 1,800 units

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Step 2 Calculate cost per unit of output and losses (i) The total value of scrap is 250 units at Rs. 500 per unit = Rs. 125,000. We must split this between the scrap value of normal loss and the scrap value of abnormal loss. Rs '000 Normal loss 100 Abnormal loss 25 Total scrap (250 units Rs. 500) 125 (ii) The scrap value of normal loss is first deducted from the materials cost in the process, in order to calculate the output cost per unit, and then credited to the process account as a 'value' for normal loss. The cost per unit in process 1 is calculated as follows. Cost per expected unit of Total cost output Rs '000 Rs '000 Materials 8,100 Less normal loss 100 scrap value* 8,000 ( 1,800) 4.44Labour and 10,000 ( 1,800) 5.56overhead Total 18,000 ( 1,800) 10.00* It is usual to set this scrap value of normal loss against the cost of materials.

Step 3 Calculate total cost of output and losses Rs '000 Output (1,750 units Rs. 10K) 17,500 Normal loss (200 units Rs. 500) 100 Abnormal loss (50 units Rs. 10K) 500 18,100

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Step 4 Complete accounts Now we can put the process 1 account together. PROCESS 1 ACCOUNT Units Rs '000 Units Rs '000 Materials 2,000 8,100 Output to process 2* 1,750 17,500Labour and Normal loss Overhead 10,000 (scrap a/c) 200 100 Abnormal loss a/c* 50 500 2,000 18,100 2,000 18,100* At Rs. 10,000 per unit. (b) Process 2

Step 1 Determine output and losses The normal loss is 10% of the units processed = 10% of (1,750 (from process 1) + 1,250) = 300 units. The actual loss is (3,000 – 2,800) = 200 units, so that there is abnormal gain of 100 units. These are deducted from actual output in arriving at the number of expected units (normal output) in the period. Expected units of output Units Actual output 2,800 Abnormal gain (100) Expected output (90% of 3,000) 2,700 Step 2 Calculate cost per unit of output and losses (i) The total value of scrap is 200 units at Rs. 3,000 per unit = Rs. 600,000. We must split this between the scrap value of normal loss and the scrap value of abnormal gain. Abnormal gain's scrap value is 'negative'. Rs '000 Normal loss scrap value 300 units Rs. 3K 900 Abnormal gain scrap value 100 units Rs. 3K (300) Scrap value of actual loss 200 units Rs. 3K 600

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(ii) The scrap value of normal loss is first deducted from the cost of materials in the process, in order to calculate a cost per unit of output, and then credited to the process account as a 'value' for normal loss. The cost per unit in process 2 is calculated as follows. Cost per expected unit Total cost of output Rs '000 Rs '000 Materials Transferred from 17,500 process 1 Added in process 2 1,900 19,400 Less scrap value of 900 normal loss 18,500 ( 2,700) 6.85 Labour and overhead 22,000 ( 2,700) 8.15 40,500 ( 2,700) 15.00

Step 3 Calculate total cost of output and losses Rs '000 Output (2,800 Rs. 15K) 42,000 Normal loss (300 units Rs. 3K) 900 42,900 Abnormal gain (100 units Rs. 15K) (1,500) 41,400 Step 4 Complete accounts PROCESS 2 ACCOUNT Units Rs '000 Units Rs '000 From 1,750 17,500 Finished 2,800 42,000 process 1 output Added 1,250 1,900 Materials Labour and Normal loss 300 900 Overhead 22,000 (scrap a/c) 3,000 41,400 Abnormal 100 1,500 gain a/c 3,100 42,900 3,100 42,900

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(c) and (d) Abnormal loss and abnormal gain accounts For each process, one or the other of these accounts will record three items. (i) The cost/value of the abnormal loss/gain. This is the corresponding entry to the entry in the process account. (ii) The scrap value of the abnormal loss or gain, to set off against it. (iii) A balancing figure, which is written to profit or loss as an adjustment to the profit figure. ABNORMAL LOSS ACCOUNT Rs '000 Rs '000 Process 1 500 Scrap a/c (scrap value of abnormal loss) 25 Profit and Loss (balance) 475 500 500 ABNORMAL GAIN ACCOUNT Rs '000 Rs '000 Scrap a/c (scrap value of abnormal gain units) 300 Process 2 1,500

Profit and Loss (balance) 1,200 1,500 1,500 (e) Scrap account This is credited with the cash value of actual units scrapped. The other entries in the account should all be identifiable as corresponding entries to those in the process accounts, and abnormal loss and abnormal gain accounts. SCRAP ACCOUNT Rs '000 Rs '000 Normal loss Cash: sale of Process 1 (200 Rs. 500) 100 process 1 scrap (250 Rs. 500) 125 Process 2 (300 Rs. 3K) 900 Cash: sale of process 2 scrap (200 Abnormal loss a/c 25 Rs. 3K) 600 Abnormal gain a/c 300 1,025 1,025

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6.1 Joint products and by-products Joint products are two or more products which are output from the same processing operation, but which are indistinguishable from each other up to their point of separation. A by-product is a supplementary or secondary product (arising as the result of a process) whose value is small relative to that of the principal product. (a) Joint products have a substantial sales value. Often they require further processing before they are ready for sale. Joint products arise, for example, in the oil refining industry where diesel fuel, petrol, paraffin and lubricants are all produced from the same process. (b) The distinguishing feature of a by-product is its relatively low sales value in comparison to the main product. In the timber industry, for example, by-products include sawdust, small offcuts and bark.

What exactly separates a joint product from a by-product? (a) A joint product is regarded as an important saleable item, and so it should be separately costed. The profitability of each joint product should be assessed in the cost accounts. (b) A by-product is not important as a saleable item, and whatever revenue it earns is a 'bonus' for the organisation. Because of their relative insignificance, by-products are not separately costed. 6.2 Problems in accounting for joint products Costs incurred prior to this point of separation are common or joint costs, and these need to be allocated (apportioned) in some manner to each of the joint products. In the following sketched example, there are two different split-off points. Inputraw materials

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Problems in accounting for joint products are basically of two different sorts. (a) How common costs should be apportioned between products, in order to put a value to closing stocks and to the cost of sale (and profit) for each product (b) Whether it is more profitable to sell a joint product at one stage of processing, or to process the product further and sell it at a later stage 6.3 Dealing with common costs The problem of costing for joint products concerns common costs; that is, those common processing costs shared between the units of eventual output up to their 'split-off point'. Some method needs to be devised for sharing the common costs between the individual joint products for the following reasons. (a) To put a value to closing stocks of each joint product (b) To record the costs and therefore the profit from each joint product (c) Perhaps to assist in pricing decisions Here are some examples of the common costs problem. (a) How to spread the common costs of oil refining between the joint products made (petrol, naphtha, kerosene and so on) (b) How to spread the common costs of running the telephone network between telephone calls in peak and cheap rate times, or between local and long-distance calls Various methods that might be used to establish a basis for apportioning or allocating common costs to each product are as follows. Physical measurement Relative sales value apportionment method; sales value at split-off point 6.4 Dealing with common costs: physical measurement With physical measurement, the common cost is apportioned to the joint products on the basis of the proportion that the output of each product bears by weight or volume to the total output. An example of this would be the case where two products, product 1 and product 2, incur common costs to the point of separation of Rs. 3,000,000 and the output of each product is 600 tons and 1,200 tons respectively. Product 1 sells for Rs. 4,000 per ton and product 2 for Rs. 2,000 per ton. The division of the common costs (Rs. 3,000) between product 1 and product 2 could be based on the tonnage of output.

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Product 1 Product 2 Total Output 600 tons + 1,200 tons 1,800 tons Proportion of common cost 6001,800 + 1,2001,800 Rs '000 Rs '000 Rs '000 Apportioned cost 1,000 2,000 3,000 Sales 2,400 2,400 4,800 Profit 1,400 400 1,800 Profit/sales ratio 58.3% 16.7% 37.5%Physical measurement has the following limitations. (a) Where the products separate during the processes into different states, for example where one product is a gas and another is a liquid, this method is unsuitable. (b) This method does not take into account the relative income-earning potentials of the individual products, with the result that one product might appear very profitable and another appear to be incurring losses. 6.5 Dealing with common costs: sales value at split-off point With relative sales value apportionment of common costs, the cost is allocated according to the product's ability to produce income. This method is most widely used because the assumption that some profit margin should be attained for all products under normal marketing conditions is satisfied. The common cost is apportioned to each product in the proportion that the sales (market) value of that product bears to the sales value of the total output from the particular processes concerned. Using the previous example where the sales price per unit is Rs. 4,000 for product 1 and Rs. 2,000 for product 2. (a) Common costs of processes to split-off point Rs. 3.0m (b) Sales value of product 1 at Rs. 4,000 per ton Rs. 2.4m (c) Sales value of product 2 at Rs. 2,000 per ton Rs. 2.4m

Product 1 Product 2 Total Sales Rs. 2.4m Rs. 2.4m Rs. 4.8m Proportion of common cost apportioned

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Rs '000 Rs '000 Rs '000 Apportioned cost 1,500 1,500 3,000 Sales 2,400 2,400 4,800 Profit 900 900 1,800 Profit/sales ratio 37.5% 37.5% 37.5%A comparison of the gross profit margin resulting from the application of the above methods for allocating common costs will illustrate the greater acceptability of the relative sales value apportionment method. Physical measurement gives a higher profit margin to product 1, not necessarily because product 1 is highly profitable, but because it has been given a smaller share of common costs. 6.6 Joint products in process accounts This example illustrates how joint products are incorporated into process accounts. 6.7 Example: Joint products and process accounts Three joint products are manufactured in a common process, which consists of two consecutive stages. Output from process 1 is transferred to process 2, and output from process 2 consists of the three joint products, Hans, Nils and Bumpsydaisies. All joint products are sold as soon as they are produced. Data for period 2 of 20X6 are as follows. Process 1 Process 2 Opening and closing stock None None Direct material (30,000 units at Rs. 2,000 per unit) Rs. 60m – Conversion costs Rs. 76.5m Rs. 226.2m Normal loss 10% of input 10% of input Scrap value of normal loss Rs. 500 per unit Rs. 2,000 per unit Output 26,000 units 10,000 units of Han 7,000 units of Nil 6,000 units of Bumpsydaisy Selling prices are Rs. 18,000 per unit of Han, Rs. 20,000 per unit of Nil and Rs. 30,000 per unit of Bumpsydaisy.

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Required (a) Prepare the process 1 account. (b) Prepare the process 2 account using the sales value method of apportionment. (c) Prepare a profit statement for the joint products. Solution (a) Process 1 equivalent units

Total Equivalent units units Output to process 2 26,000 26,000 Normal loss 3,000 0 Abnormal loss (balance) 1,000 1,000 30,000 27,000 Costs of process 1 Rs '000 Direct materials 60,000 Conversion costs 76,500 136,500 Less scrap value of normal loss (3,000 Rs. 500) 1,500 135,000 Cost per equivalent unit = 135,000,00027,000 = Rs. 5,000 PROCESS 1 ACCOUNT Rs Mn Rs Mn Direct materials 60.0 Output to process 2 130.0 (26,000 Rs. 5K) Conversion costs 76.5 Normal loss (scrap value) 1.5 Abnormal loss (1,000 5.0 Rs. 5K) 136.5 136.5 (b) Process 2 equivalent units Total Equivalent units units Units of Hans produced 10,000 10,000 Units of Nils produced 7,000 7,000 Units of Bumpsydaisies produced 6,000 6,000 Normal loss (10% of 26,000) 2,600 0 Abnormal loss (balance) 400 400 26,000 23,400

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Costs of process 2 Rs Mn Material costs: from process 1 130.0 Conversion costs 226.2 356.2 Less scrap value of normal loss (2,600 Rs. 2K) 5.2 351.0 Cost per equivalent unit 351,000,00023,400 = Rs. 15,000 Cost of good output (10,000 + 7,000 + 6,000) = 23,000 units Rs. 15,000 = Rs. 345m The sales value of joint products, and the apportionment of the output costs of Rs. 345m, is as follows. Sales value

Costs (process 2) Rs Mn % Rs Mn Hans (10,000 Rs. 18K) 180 36 124.2 Nils (7,000 Rs. 20K) 140 28 96.6 Bumpsydaisy (6,000 Rs. 30K) 180 36 124.2 500 100 345.0 PROCESS 2 ACCOUNT Rs Mn Rs Mn Process 1 materials 130.0 Finished goods accounts Conversion costs 226.2 Hans 124.2 Nils 96.6 Bumpsydaisies 124.2 Normal loss (scrap value) 5.2 Abnormal loss a/c 6.0 356.2 356.2 (c) PROFIT STATEMENT

Hans Nils Bumpsydaisies Total Rs Mn Rs Mn Rs Mn Rs Mn Sales 180.0 140.0 180.0 500 Costs 124.2 96.6 124.2 345 Profit 55.8 43.4 55.8 155 Profit/ sales ratio 31% 31% 31% 31%

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QUESTION Unit basis of apportionment

Prepare the process 2 account and a profit statement for the joint products in the above example using the unit basis of apportionment. ANSWER PROCESS 2 ACCOUNT Rs Mn Rs Mn Process 1 materials 130.0 Finished goods accounts Conversion costs 226.2 Hans (10,000 Rs. 15K) 150.0 Nils (7,000 Rs. 15K) 105.0 Bumpsydaisies (6,000 Rs. 15K) 90.0 Normal loss (scrap value) 5.2 Abnormal loss a/c 6.0 356.2 356.2 PROFIT STATEMENT Hans Nils Bumpsydaisies Total Rs Mn Rs Mn Rs Mn Rs Mn Sales 180 140 180 500 Costs 150 105 90 345 Profit 30 35 90 155 Profit/sales ratio 16.7% 25% 50% 31%In the previous question, when using ‘sales value’ apportionment of common costs, the cost is allocated according to each product's income generation. The cost of Rs 345,000 in this case was apportioned to each product in proportion to its share of sales value, so that each product has the same profit margin (and this is the overall profit margin of the combined operation – 31%). Using the unit basis of apportionment, the common cost has been apportioned on the basis of the proportion of output. This method does not take into account the relative income-earning potential of each product. Physical measurement gives a higher profit margin to Bumpsydaisy, not necessarily because it is more profitable, but because it has been given a smaller share of common costs because fewer units were produced from the common process. The reverse is the case for Hans and Nils. Physical measurement gives a lower profit margin to them, not necessarily because they are less profitable, but because they have been given a larger share of costs.

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7 By-products costing

The most common method of accounting for by-products is to deduct the net realisable value of the by-product from the cost of the main products. A by-product has some commercial value and any income generated from it may be treated as follows. (a) Income (minus any post-separation further processing or selling costs) from the sale of the by-product may be added to sales of the main product, thereby increasing sales turnover for the period. (b) The sales of the by-product may be treated as a separate, incidental

source of income against which are set only post-separation costs (if any) of the by-product. The revenue would be recorded in the profit and loss account as 'other income'. (c) The sales income of the by-product may be deducted from the cost of production or cost of sales of the main product. (d) The net realisable value of the by-product may be deducted from the cost of production of the main product. The net realisable value is the final saleable value of the by-product minus any post-separation costs. Any closing inventory valuation of the main product or joint products would therefore be reduced. The choice of method (a), (b), (c) or (d) will be influenced by the circumstances of production and ease of calculation, as much as by conceptual correctness. The method you are most likely to come across in examinations is method (d). An example will help to clarify the distinction between the different methods.

7.1 Example: Methods of accounting for by-products During November 20X3, Splatter LLC recorded the following results. Opening stock main product P, nil by-product Z, nil Cost of production Rs. 120m Sales of the main product amounted to 90% of output during the period, and 10% of production was held as closing inventory at 30 November. Sales revenue from the main product during November 20X2 was Rs. 150m A by-product Z is produced, and output had a net sales value of Rs. 1m. Of this output, Rs. 700,000 was sold during the month and Rs. 300,000 was still in inventory at 30 November.

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Required

Calculate the profit for November using the four methods of accounting for by-products. Solution The four methods of accounting for by-products are shown below. (a) Income from by-product added to sales of the main product Rs Mn Rs Mn Sales of main product (Rs. 150m + Rs. 0.7m) 150.7 Opening stock 0 Cost of production 120 120 Less closing inventory (10%) 12 Cost of sales 108.0 Profit, main product 42.7 The closing inventory of the by-product has no recorded value in the cost accounts. (b) By-product income treated as a separate source of income Rs Mn Rs Mn Sales, main product 150 Opening stock 0 Cost of production 120 120 Closing inventory (10%) 12 Cost of sales, main product 108 Profit, main product 42 Other income 0.7 Total profit 42.7 The closing inventory of the by-product again has no value in the cost accounts. (c) Sales income of the by-product deducted from the cost of production in

the period Rs Mn Rs Mn Sales, main product 150.00 Opening stock 0 Cost of production (120m 0.7m) 119.30 119.30 Less closing inventory (10%) 11.93 Cost of sales 107.37 Profit, main product 42.63

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Although the profit is different from the figure in (a) and (b), the by-product closing inventory again has no value. (d) Net realisable value of the by-product deducted from the cost of production in the period Rs Mn Rs Mn Sales, main product 150.0 Opening stock 0 Cost of production (120m 1m) 119.0 119.0 Less closing inventory (10%) 11.9 Cost of sales 107.1 Profit, main product 42.9 As with the other three methods, closing inventory of the by-product has no value in the books of accounting, but the value of the closing inventory (Rs. 300,000) has been used to reduce the cost of production, and in this respect it has been allowed for in deriving the cost of sales and the profit for the period.

QUESTION Profits RN LLC manufactures two joint products, J and K, in a common process. A by-product X is also produced. Data for the month of December 20X2 were as follows. Opening stocks nil Costs of processing direct materials Rs. 25.5m direct labour Rs. 10m Production overheads are absorbed at the rate of 300% of direct labour costs. Production Sales Units Units Output and sales consisted of: product J 8,000 7,000 product K 8,000 6,000 by-product X 1,000 1,000 The sales value per unit of J, K and X is Rs. 4,000, Rs. 6,000 and Rs. 500 respectively. The saleable value of the by-product is deducted from process costs before apportioning costs to each joint product. Costs of the common processing are apportioned between product J and product K on the basis of sales value of production. Required

Calculate the individual profits for December 20X2.

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ANSWER The sales value of production was Rs. 80m. Rs Mn Product J (8,000 Rs. 4K) 32 (40%)Product K (8,000 Rs. 6K) 48 (60%) 80 The costs of production were as follows. Rs Mn Direct materials 25.5 Direct labour 10.0 Overhead (300% of Rs. 10m) 30.0 65.5 Less sales value of by-product (1,000 Rs. 500) 0.5 Net production costs 65.0 The profit statement would appear as follows (nil opening stocks). Product J Product K Total Rs Mn Rs Mn Rs Mn Production costs (40%) 26.00 (60%) 39.00 65 Less closing (1,000 units) 3.25 (2,000 9.75 13 Stock units) Cost of sales 22.75 29.25 52 Sales (7,000 units) 28.00 (6,000 36.00 64 units) Profit 5.25 6.75 12

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Process costing is a costing method used where it is not possible to identify separate units of production or jobs, usually because of the continuous nature of the production processes involved. Process costing is centred around four key steps. The exact work done at each step will depend on whether there are normal losses, scrap, opening and closing work in progress. Step 1 Determine output and losses Step 2 Calculate cost per unit of output, losses and WIP Step 3 Calculate total cost of output, losses and WIP Step 4 Complete accounts Losses may occur in process. If a certain level of loss is expected, this is known as

normal loss. If losses are greater than expected, the extra loss is abnormal loss. If losses are less than expected, the difference is known as abnormal gain. The scrap value of normal loss is usually deducted from the cost of materials. The scrap value of abnormal loss (or abnormal gain) is usually set off against its cost, in an abnormal loss (abnormal gain) account. Abnormal losses and gains never affect the cost of good units of production. The scrap value of abnormal loss is not credited to the process account, and abnormal loss and gain units carry the same full cost as a good unit of production. When units are partly completed at the end of a period (and hence there is closing work in progress), it is necessary to calculate the equivalent units of production in order to determine the cost of a completed unit. Account can be taken of opening work in progress using either the First in, First out (FIFO) method or the weighted average cost method (AVCO). Joint products are two or more products separated in a process, each of which has a significant value compared to the other. A by-product is an incidental product from a process, and has an insignificant value compared to the main product. The point at which joint products and by-products become separately identifiable is known as the split-off point or separation point. Costs incurred up to this point are called common costs or joint costs. The main methods of apportioning joint costs, each of which can produce significantly different results are as follows.

Physical measurement Relative sales value apportionment method; sales value at split-off point

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The relative sales value method is the most widely used method of apportioning joint costs because (ignoring the effect of further processing costs) it assumes that all products achieve the same profit margin. The most common method of accounting for by-products is to deduct the net

realisable value of the by-product from the cost of the main products.

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1 Define process costing. 2 Process costing is centred around four key steps.

Step 1 ……………………………………………………………………………………….. Step 2 ……………………………………………………………………………………….. Step 3 ……………………………………………………………………………………….. Step 4 …………………………………………………………………………………………...

3 Abnormal gains result when actual loss is less than normal or expected loss. True False 4 Normal loss (no scrap value) Same value as good output (positive cost) Abnormal loss ? No value Abnormal gain Same value as good output (negative cost) 5 How is revenue from scrap treated? A As an addition to sales revenue C As a bonus to employees B As a reduction in costs of processing D Any of the above 6 Define the term 'equivalent unit'. 7 State the first step in the four step approach to process costing questions when there is closing WIP at the end of a process, and the reason for it. 8 State the weighted average cost method of inventory valuation. 9 Unless given an indication to the contrary, the weighted average cost method of inventory valuation should be used to value opening WIP. True False 10 Joint cost allocations are essential for the purposes of determining relative product profitability.

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11 When deciding, purely on financial grounds, whether or not to process a joint product further, the information required is: (i) The value of the joint process costs (ii) The method of apportioning the joint costs between the joint products (iii) The sales value of the joint product at the separation point (iv) The final sales value of the joint product (v) The further processing cost of the joint product Which of the above statements are correct? A (i), (ii) and (iii) only B (iii), (iv) and (v) only C (iv) and (v) only D (i), (ii), (iv) and (v) only 12 Choose the correct words from those highlighted. A joint product should be processed further if post-separation/pre-separation costs are greater than/less than the increase in revenue/additional fixed

costs. 13 Fill in the blanks. The accounting treatment of a by-product usually consists of deducting the ……………………………. of the by-product from the …………………………………… of the main product.

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1 Process costing is a costing method used where it is not possible to identify separate units of production or jobs, usually because of the continuous nature of the production processes involved. 2 Step 1. Determine output and losses Step 2. Calculate cost per unit of output, losses and WIP Step 3. Calculate total cost of output, losses and WIP

Step 4. Complete accounts 3 True 4 Normal loss (no scrap value) Same value as good output (positive cost) Abnormal loss No value Abnormal gain Same value as good output (negative cost) 5 The answer is B. 6 An equivalent unit is a notional whole unit which represents incomplete work, and which is used to apportion costs between work in process and completed output. 7 Step 1 It is necessary to calculate the equivalent units of production (by drawing up a statement of equivalent units). Equivalent units of production are notional whole units which represent incomplete work and which are used to apportion costs between work in progress and completed output. 8 A method where no distinction is made between units of opening inventory and new units introduced to the process during the current period. 9 False. FIFO inventory valuation is more common than the weighted average method and should be used unless an indication is given to the contrary. 10 False 11 The answer is B. Any costs incurred up to the point of separation are irrelevant. 12 post-separation, less than, increase in revenue 13 net realisable value, cost of production

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Knowledge Component A Cost accounting 1.9 Marginal and absorption costing

1.9.1 Compute inventory value and profit under absorption costing and marginal costing 1.9.2 Prepare reconciliation for the differences in profit calculated under absorption costing and marginal costing systems

INTRODUCTION This chapter defines marginal costing and compares it with absorption costing. Whereas absorption costing recognises fixed costs (usually fixed production costs) as part of the cost of a unit of output and hence as product costs, marginal costing treats all fixed costs as period costs. Two such different costing methods obviously each have their supporters and so we will be looking at the arguments both in favour of and against each method. Each costing method, because of the different inventory valuation used, produces a different profit figure; we will be looking at this particular point in detail.

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CHAPTER CONTENTS

LEARNING OUTCOME1 Choosing a costing method 1.9.12 Absorption costing inventory valuation / Profit statement under absorption costing 1.9.1

3 Marginal costing inventory valuation / Profit statement under marginacosting 1.9.24 Profit reconciliation 5 Marginal costing versus absorption costing 1.9.21.9.1

1 Choosing a costing method

1.1 Introduction In marginal costing, fixed production costs are treated as period costs and are written off as they are incurred. In absorption costing, fixed production costs are absorbed into the cost of units and are carried forward in inventory to be charged against sales for the next period. Inventory values using absorption costing are therefore greater than those calculated using marginal costing. Marginal costing as a cost accounting system is significantly different from absorption costing. It is an alternative method of accounting for costs and profit, which rejects the principles of absorbing fixed overheads into unit costs. Marginal costing Absorption costing Opening & closing inventory are valued at marginal production cost. Opening & closing inventory are valued at full production cost. Fixed production costs are period costs. Fixed production costs are absorbed into unit costs. Cost of sales does not include a share of fixed overheads. Cost of sales does include a share of fixed overheads (see note below). Note. The share of fixed overheads included in cost of sales are from the previous period (in opening inventory values). Some of the fixed overheads from the current period will be excluded by being carried forward in closing inventory values.

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In marginal costing, it is necessary to identify the following. Variable costs Fixed costs Contribution In absorption costing (sometimes known as full costing), it is not necessary to distinguish variable costs from fixed costs.

2 Absorption costing inventory valuation/Profit statement under absorption costing

The objective of absorption costing is to include in the total cost of a product an appropriate share of the organisation's total overhead. 'An appropriate share' is generally taken to mean an amount which reflects the amount of time and effort that has gone into producing a unit or completing a job. An organisation with one production department that produces identical units will divide the total overheads among the total units produced. Absorption costing is a method for sharing overheads between different products on a fair basis. 2.1 Is absorption costing necessary? Suppose that a company makes and sells 100 units of a product each week. The prime cost per unit is Rs. 600 and the unit sales price is Rs. 1,000. Production overhead costs Rs. 20,000 per week and administration, selling and distribution overhead costs Rs. 15,000 per week. The weekly profit could be calculated as follows. Rs '000 Rs '000 Sales (100 units Rs. 1,000) 100 Prime costs (100 Rs. 600) 60 Production overheads 20 Administration, selling and distribution costs 15 95 Profit 5 In absorption costing, overhead costs will be added to each unit of product manufactured and sold. Rs per unit Prime cost per unit 600 Production overhead (Rs. 20,000 per week for 100 units) 200 Full factory cost 800 The weekly profit would be calculated as follows. Rs '000 Sales 100 Less factory cost of sales 80 Gross profit 20 Less administration, selling and distribution costs 15 Net profit 5

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Sometimes, but not always, the overhead costs of administration, selling and distribution are also added to unit costs, to obtain a full cost of sales. Rs per unit Prime cost per unit 600 Factory overhead cost per unit 200 Administration, selling and distribution costs per unit 150 Full cost of sales 950 The weekly profit would be calculated as follows. Rs Sales 1,000 Less full cost of sales 950 Profit 50 It may already be apparent that the weekly profit is Rs. 50, no matter how the figures have been presented. So, how does absorption costing serve any useful purpose in accounting? The theoretical justification for using absorption costing is that all production overheads are incurred in the production of the organisation's output and so each unit of the product receives some benefit from these costs. Each unit of output should therefore be charged with some of the overhead costs. 2.2 Practical reasons for using absorption costing The main reasons for using absorption costing are for inventory valuations, pricing decisions, and establishing the profitability of different products. (a) Inventory valuations. Inventory in hand must be valued for two reasons. (i) For the closing inventory figure in the statement of financial position (ii) For the cost of sales figure in the statement of profit or loss The valuation of inventory will affect profitability during a period because of the way in which the cost of sales is calculated. The cost of goods produced + the value of opening inventories – the value of closing inventories = the cost of goods sold. In our example, closing inventories might be valued at prime cost (Rs. 6), but in absorption costing, they would be valued at a fully absorbed factory cost, Rs. 8 per unit. (They would not be valued at Rs. 9.50, the full cost of sales, because the only costs incurred in producing goods for finished inventory are factory costs.) (b) Pricing decisions. Many companies attempt to fix selling prices by calculating the full cost of production or sales of each product, and then adding a margin for profit. In our example, the company might have fixed a

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gross profit margin at 25% on factory cost, or 20% of the sales price, in order to establish the unit sales price of Rs. 10. 'Full cost-plus pricing' can be particularly useful for companies which do jobbing or contract work, where each job or contract is different, so that a standard unit sales price cannot be fixed. Without using absorption costing, a full cost is difficult to ascertain. (c) Establishing the profitability of different products. This argument in favour of absorption costing is more contentious, but is worthy of mention here. If a company sells more than one product, it will be difficult to judge how profitable each individual product is, unless overhead costs are shared on a fair basis and charged to the cost of sales of each product. 2.3 International Accounting Standard 2 (IAS 2) Absorption costing is recommended in financial accounting by IAS 2 Inventories, which deals with financial accounting systems. The cost accountant is (in theory) free to value inventories by whatever method seems best, but where companies integrate their financial accounting and cost accounting systems into a single system of accounting records, the valuation of closing inventories will be determined by IAS 2. IAS 2 states that costs of all inventories should comprise those costs which have been incurred in the normal course of business in bringing the inventories to their 'present location and condition'. These costs incurred will include all related production overheads, even though these overheads may accrue on a time basis. In other words, in financial accounting, closing inventories should be valued at full factory cost, and it may therefore be convenient and appropriate to value inventories by the same method in the cost accounting system.

3 Marginal costing inventory valuation/Profit statement under marginal costing

3.1 Introduction

Marginal cost is the variable cost of one unit of a product or service. Marginal costing is an alternative method of costing to absorption costing. In marginal costing, only variable costs are charged as a cost of sale and a contribution is calculated (sales revenue minus variable cost of sales). Closing inventories of work in progress or finished goods are valued at marginal (variable) production cost. Fixed costs are treated as a period cost, and are charged in full to the profit and loss account of the accounting period in which they are incurred.

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The marginal production cost per unit of an item usually consists of the following. Direct materials Variable production overheads Direct labour Direct labour costs might be excluded from marginal costs when the work force is a given number of employees on a fixed wage or salary. Even so, it is not uncommon for direct labour to be treated as a variable cost, even when employees are paid a basic wage for a fixed working week. If in doubt, you should treat direct labour as a variable cost unless given clear indications to the contrary. Direct labour is often a step cost, with sufficiently short steps to make labour costs act in a variable fashion. The marginal cost of sales usually consists of the marginal cost of production adjusted for inventory movements plus the variable selling costs, which would include items such as sales commission, and possibly some variable distribution costs. 3.2 Contribution

Contribution is an important measure in marginal costing, and it is calculated as the difference between sales value and marginal or variable cost of sales. Contribution is of fundamental importance in marginal costing, and the term 'contribution' is really short for 'contribution towards covering fixed overheads and making a profit'. 3.3 The principles of marginal costing The principles of marginal costing are as follows. (a) Period fixed costs are the same, for any volume of sales and production (provided that the level of activity is within the 'relevant range'). Therefore, by selling an extra item of product or service the following will happen. (i) Revenue will increase by the sales value of the item sold. (ii) Costs will increase by the variable cost per unit. (iii) Profit will increase by the amount of contribution earned from the extra item. (b) Similarly, if the volume of sales falls by one item, the profit will fall by the amount of contribution earned from the item.

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(c) Profit measurement should therefore be based on an analysis of total contribution. Since fixed costs relate to a period of time, and do not change with increases or decreases in sales volume, it is misleading to charge units of sale with a share of fixed costs. Absorption costing is therefore misleading, and it is more appropriate to deduct fixed costs from total contribution for the period to derive a profit figure. (d) When a unit of product is made, the extra costs incurred in its manufacture are the variable production costs. Fixed costs are unaffected, and no extra fixed costs are incurred when output is increased. It is therefore argued that the valuation of closing inventories should be at variable production cost (direct materials, direct labour, direct expenses (if any) and variable production overhead) because these are the only costs properly attributable to the product.

3.3.1 Example: Marginal costing principles Rain LLC makes a product, the Splash, which has a variable production cost of Rs. 600 per unit and a sales price of Rs. 1,000 per unit. At the beginning of September 20X0, there were no opening inventories and production during the month was 20,000 units. Fixed costs for the month were Rs. 4.5 million (production, administration, sales and distribution). There were no variable marketing costs. Required

Calculate the contribution and profit for September 20X0, using marginal costing principles, if sales were as follows. (a) 10,000 Splashes (b) 15,000 Splashes (c) 20,000 Splashes Solution The stages in the profit calculation are as follows. To identify the variable cost of sales, and then the contribution. Deduct fixed costs from the total contribution to derive the profit. Value all closing inventories at marginal production cost (Rs. 6 per unit).

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10,000 Splashes 15,000 Splashes 20,000 Splashes Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Sales (at Rs. 1,000) 10,000 15,000 20,000Opening inventory 0 0 0 Variable production cost 12,000 12,000 12,000 Less value of closing inventory (at marginal cost) 6,000 3,000 – Variable cost of sales 6,000 9,000 12,000Contribution 4,000 6,000 8,000Less fixed costs 4,500 4,500 4,500Profit/(loss) (500) 1,500 3,500Profit (loss) per unit Rs.(50) Rs. 100 Rs. 175Contribution per unit Rs. 400 Rs. 400 Rs. 400The conclusions which may be drawn from this example are as follows. (a) The profit per unit varies at differing levels of sales, because the average fixed overhead cost per unit changes with the volume of output and sales. (b) The contribution per unit is constant at all levels of output and sales. Total contribution, which is the contribution per unit multiplied by the number of units sold, increases in direct proportion to the volume of sales. (c) Since the contribution per unit does not change, the most effective way of calculating the expected profit at any level of output and sales would be as follows. (i) First calculate the total contribution. (ii) Then deduct fixed costs as a period charge in order to find the profit. (d) In our example the expected profit from the sale of 17,000 Splashes would be as follows. Rs '000 Total contribution (17,000 Rs. 400) 6,800 Less fixed costs 4,500 Profit 2,300 (i) If total contribution exceeds fixed costs, a profit is made (ii) If total contribution exactly equals fixed costs, no profit or loss is made (iii) If total contribution is less than fixed costs, there will be a loss

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QUESTION Marginal costing principles Mill Stream LLC makes two products, the Mill and the Stream. Information relating to each of these products for April 20X1 is as follows. Mill Stream Opening inventory nil nil Production (units) 15,000 6,000 Sales (units) 10,000 5,000 Sales price per unit Rs. 200 Rs. 300 Unit costs Rs Rs Direct materials 80 140 Direct labour 40 20 Variable production overhead 20 10 Variable sales overhead 20 30 Fixed costs for the month Rs Production costs 400,000 Administration costs 150,000 Sales and distribution costs 250,000

Required (a) Calculate the profit in April 20X1 using marginal costing principles and the method in Section 2.1(d) above. (b) Calculate the profit if sales had been 15,000 units of Mill and 6,000 units of Stream. ANSWER (a) Rs Contribution from Mills (unit contribution = Rs. 200 – Rs. 160 = Rs. 40 10,000) 400,000 Contribution from Streams (unit contribution = Rs. 300 – Rs. 200 = Rs. 100 5,000) 500,000 Total contribution 900,000 Fixed costs for the period 800,000 Profit 100,000 (b) At a higher volume of sales, profit would be as follows. Rs Contribution from sales of 15,000 Mills ( Rs. 40) 600,000 Contribution from sales of 6,000 Streams ( Rs. 100) 600,000 Total contribution 1,200,000 Less fixed costs 800,000 Profit 400,000

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3.4 Profit or contribution information The main advantage of contribution information (rather than profit information) is that it allows an easy calculation of profit if sales increase or decrease from a certain level. By comparing total contribution with fixed overheads, it is possible to determine whether profits or losses will be made at certain sales levels. Profit information, on the other hand, does not lend itself to easy manipulation but note how easy it was to calculate profits using contribution information in the question earlier. Contribution information is more useful for decision making than profit information.

4 Profit reconciliation

4.1 Introduction

Reported profit figures using marginal costing or absorption costing will differ if there is any change in the level of inventories in the period. If production is equal to sales, there will be no difference in calculated profits using the costing methods. The difference in profits reported under the two costing systems is due to the different inventory valuation methods used.

If inventory levels increase between the beginning and end of a period, absorption costing will report the higher profit. This is because some of the fixed production overhead incurred during the period will be carried forward in closing inventory (which reduces cost of sales) to be set against sales revenue in the following period, instead of being written off in full against profit in the period concerned. If inventory levels decrease, absorption costing will report the lower profit: as well as the fixed overhead incurred, fixed production overhead (which had been carried forward in opening inventory) is released and is also included in cost of sales. QUESTION Absorption costing profit When opening inventories were 8,500 litres and closing inventories 6,750 litres, a firm had a profit of Rs. 62,100 using marginal costing. Required

Calculate the profit using absorption costing assuming that the fixed overhead absorption rate was Rs. 3 per litre. A Rs. 41,850 B Rs. 56,850 C Rs. 67,350 D Rs. 82,350

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ANSWER Difference in profit = (8,500 – 6,750) Rs. 3 = Rs. 5,250 Absorption costing profit = Rs. 62,100 – Rs. 5,250 = Rs. 56,850 The correct answer is B. Since inventory levels reduced, the absorption costing profit will be lower than the marginal costing profit. You can therefore eliminate options C and D. QUESTION Absorption versus marginal costing profits Last month a manufacturing company's profit was Rs. 2,000,000 calculated using absorption costing principles. If marginal costing principles had been used, a loss of Rs. 3,000,000 would have occurred. The company's fixed production cost is Rs. 2,000 per unit. Sales last month were 10,000 units. Required

Calculate last month's production (in units). A 7,500 B 9,500 C 10,500 D 12,500 ANSWER The correct answer is D. Any difference between marginal and absorption costing profit is due to changes in inventory. Rs '000 Absorption costing profit 2,000 Marginal costing loss (3,000) Difference 5,000 Change in inventory = Difference in profit/fixed product cost per unit = Rs. 5,000,000/Rs. 2,000 = 2,500 units Marginal costing loss is lower than absorption costing profit, therefore inventory has gone up: that is, production was greater than sales by 2,500 units. Production = 10,000 units (sales) + 2,500 units = 12,500 units

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4.2 Example: Reconciling profits The profits reported under absorption costing and marginal costing for January – March in the Big Woof question above can be reconciled as follows. Rs '000 Marginal costing profit 266,400Adjust for fixed overhead included in inventory: Inventory increase of 40,000 units Rs. 12.50 500 Absorption costing profit 266,9004.3 Reconciling profits – a shortcut A quick way to establish the difference in profits, without going through the whole process of drawing up the statements of profit or loss, is as follows. Difference in profits = change in inventory level × overhead absorption rate per unit If inventory levels have gone up (that is, closing inventory > opening inventory) then absorption costing profit will be greater than marginal costing profit. If inventory levels have gone down (that is, closing inventory < opening inventory) then absorption costing profit will be less than marginal costing profit. In the Big Woof example above Change in inventory = 40,000 units (an increase) Overhead absorption rate = Rs. 12.50 per unit We would expect absorption costing profit to be greater than marginal costing profit by 40,000 Rs. 12.50 = Rs. 500,000. If you check back to the answer, you will find that this is the case.

5 Marginal costing versus absorption costing

Absorption costing is most used for routine profit reporting and must be used for financial accounting purposes. Marginal costing provides better management information for planning and decision making. There are a number of arguments both for and against each of the costing systems.

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Figure 11.1 summarises the arguments in favour of both marginal and absorption costing.

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5.1 Example: Marginal and absorption costing compared The following example will be used to lead you through the various steps in calculating marginal and absorption costing profits, and will highlight the differences between the two techniques.

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Woof LLC manufactures a single product, the Bark, with these details: Per unit Rs Selling price 1,800 Direct materials 400 Direct labour 160 Variable overheads 100 Annual fixed production overheads are budgeted to be Rs. 16 million and Big Woof expects to produce 1,280,000 units of the Bark each year. Overheads are absorbed on a per unit basis. Actual overheads are Rs. 16 million for the year. Budgeted fixed selling costs are Rs. 3.2 million per quarter. Actual sales and production units for the first quarter of 20X8 are given below. January – March Sales 240,000 Production 280,000 There is no opening inventory at the beginning of January. Required

Prepare statements of profit or loss for the quarter, using (a) Marginal costing (b) Absorption costing

Solution

Step 1 Calculate the overhead absorption rate per unit Remember that overhead absorption rate is based only on budgeted figures. Overhead absorption rate = units Budgeted overheadsfixedBudgeted Also be careful with your calculations. You are dealing with a three-month period but the figures in the question are for a whole year. You will have to convert these to quarterly figures. Budgeted overheads (quarterly) = Rs. 16 million4 = Rs. 4 million Budgeted production (quarterly) = 4million1.28 = 320,000 units Overhead absorption rate per unit = Rs. 4, 000, 000320, 000 = Rs. 12.50 per unit

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Step 2 Calculate total cost per unit Total cost per unit (absorption costing) = Variable cost + fixed production cost = (400 + 160 + 100) + 12.50 = Rs. 672.50 Total cost per unit (marginal costing) = (400 + 160 + 100) = Variable cost per unit = Rs. 660 Step 3 Calculate closing inventory in units Closing inventory = Opening inventory + production – sales Closing inventory = 0 + 280,000 – 240,000 = 40,000 units Step 4 Calculate under/over-absorption of overheads This is based on the difference between actual production and budgeted production. Actual production = 280,000 units Budgeted production = 320,000 units (see step 1 above) Under-production = 40,000 units As Big Woof produced 40,000 fewer units than expected, there will be an under-absorption of overheads of 40,000 Rs. 12.50 (see step 1 above) = Rs. 500,000. This will be added to production costs in the statement of profit or loss.

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Step 5 Produce statements of profit or loss Marginal costing Absorption costing Rs '000 Rs '000 Rs '000 Rs '000 Sales (240,000 Rs. 1,800) 432,000 432,000 Less Cost of Sales Opening inventory 0 0 Add Production cost 280,000 Rs. 66 184,800 280,000 Rs. 67.25 188,300 Less Closing inventory 40,000 Rs. 660 (26,400) 40,000 Rs. 672.50 (26,900) (158,400) 161,400 Add under-absorbed overhead 500 (161,900)Contribution 273,600 Gross profit 270,100 Less Fixed production o/h 4,000 Nil Fixed selling o/h 3,200 3,200 (7,200) (3,200)Net profit 266,400 266,900 5.2 No changes in inventory You will notice from the above calculations that there are differences between marginal and absorption costing profits. Before we go on to reconcile the profits, how would the profits for the two different techniques differ if there were no changes between opening and closing inventory (that is, if production = sales)?

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For the first quarter we will now assume that sales were 280,000 units. Marginal costing Absorption costing Rs '000 Rs '000 Rs '000 Rs '000 Sales (280,000 Rs. 1,800) 504,000 504,000 Less Cost of Sales Opening inventory 0 Add Production cost 280,000 Rs. 660 184,800 280,000 Rs. 672,50 188,300 Less Closing inventory NIL NIL (184,800) 188,300 Add under-absorbed o/h 500 (188,800) Contribution 319,200 Gross profit 315,200 Less Fixed production o/h 4,000 Fixed selling o/h 3,200 3,200 (7,200) (3,200) Net profit 312,000 312,000 You will notice that there are now no differences between the two profits. The difference in profits was due to changes in inventory levels during the period. QUESTION AC versus MC The overhead absorption rate for product X is Rs. 1,000 per machine hour. Each unit of product X requires five machine hours. Inventory of product X on 1.1.X1 was 150 units and on 31.12.X1 it was 100 units. Required

Calculate the difference in profit between results reported using absorption costing and results reported using marginal costing. A The absorption costing profit would be Rs. 250,000 less B The absorption costing profit would be Rs. 250,000 greater C The absorption costing profit would be Rs. 500,000 less D The absorption costing profit would be Rs. 500,000 greater

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ANSWER Difference in profit = change in inventory levels fixed overhead absorption per unit = (150 – 100) Rs. 1,000 5 = Rs. 250,000 lower profit, because inventory levels decreased. The correct answer is therefore option A. The key is the change in the volume of inventory. Inventory levels have decreased therefore absorption costing will report a lower profit. This eliminates options B and D. Option C is incorrect because it is based on the closing inventory only (100 units Rs. 1,000 5 hours).

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Marginal cost is the variable cost of one unit of product or service. Contribution is an important measure in marginal costing, and it is calculated as the difference between sales value and marginal or variable cost of sales. In marginal costing, fixed production costs are treated as period costs and are written off as they are incurred. In absorption costing, fixed production costs are absorbed into the cost of units and are carried forward in inventory to be charged against sales for the next period. Inventory values using absorption costing are therefore greater than those calculated using marginal costing. Reported profit figures using marginal costing or absorption costing will

differ if there is any change in the level of inventories in the period. If production is equal to sales, there will be no difference in calculated profits using these costing methods. Absorption costing is most often used for routine profit reporting and must be used for financial accounting purposes. Marginal costing provides better management information for planning and decision making. There are a number of arguments both for and against each of the costing systems. The objective of absorption costing is to include in the total cost of a product an appropriate share of the organisation's total overhead. An appropriate share is generally taken to mean an amount which reflects the amount of time and effort that has gone into producing a unit or completing a job. The main reasons for using absorption costing are for inventory valuations,

pricing decisions and establishing the profitability of different products.

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1 Define the term 'marginal costing'. 2 State what a period cost is in marginal costing. 3 Sales value – marginal cost of sales = …………………. 4 Marginal costing and absorption costing are different techniques for assessing profit in a period. If there are changes in inventory during a period, marginal costing and absorption costing give different results for profit obtained.

Identify which of the following statements are true. I If inventory levels increase, marginal costing will report the higher profit. II If inventory levels decrease, marginal costing will report the lower profit. III If inventory levels decrease, marginal costing will report the higher profit. IV If the opening and closing inventory volumes are the same, marginal costing and absorption costing will give the same profit figure. A All of the above C I and IV B I, II and IV D III and IV 5 Identify which of the following are arguments in favour of marginal costing. (a) Closing inventory is valued in accordance with IAS 2. (b) It is simple to operate. (c) There is no under or over-absorption of overheads. (d) Fixed costs are the same regardless of activity levels. (e) The information from this costing method may be used for decision making.

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1 Marginal costing is an alternative method of costing to absorption costing. In marginal costing, only variable costs are charged as a cost of sale and a contribution is calculated (sales revenue – variable cost of sales). 2 A fixed cost 3 Contribution 4 The answer is D. 5 (b), (c), (d), (e)

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Knowledge Component B Planning & controlling 2.1 Introduction to standard costing and variance analysis

2.1.1 Explain the importance of standard costing 2.1.2 Compute and interpret variances related to sales and costs 2.1.3 Prepare a statement that reconciles budgeted contribution with the actual contribution calculated using marginal costing

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INTRODUCTION Just as there are standards for most things in our daily lives (cleanliness in hamburger restaurants, educational achievement of nine-year-olds, number of trains running on time), there are standards for the costs of products and services. Moreover, just as the standards in our daily lives are not always met, the standards for the costs of products and services are not always met. In this chapter we will be looking at standards for costs, what they are used for and how they are set. We will also see how standard costing forms the basis of a process called variance analysis, a vital management control tool. The actual results achieved by an organisation during a reporting period (week, month, quarter, year) will, more than likely, be different from the expected results (the expected results being the standard costs and revenues which we looked at in the previous chapter). Such differences may occur between individual items, such as the cost of labour and the volume of sales, and between the total expected contribution and the total actual contribution. Management will have spent considerable time and trouble setting standards. Actual results have differed from the standards. The wise manager will consider the differences that have occurred and use the results of these considerations to assist in attempts to attain the standards. The wise manager will use variance analysis as a method of control.

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CHAPTER CONTENTS

LEARNING OUTCOME1 What is standard costing? 2.1.12 Setting standards 2.1.13 Budgets and standards compared 2.1.14 Criticisms of standard costing 2.1.15 Variances 6 Direct material cost variances 7 Direct labour cost variances 8 Variable production overhead variances 9 The reasons for cost variances 10 Sales variances 11 Operating statement reconciling budget contribution to actual contribution 12 Deriving actual data from standard cost details and variances 13 Accounting for variances in the integrated accounting system 14 Control action

2.1.22.1.22.1.22.1.22.1.22.1.22.1.32.1.32.1.32.1.3

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1 What is standard costing?

1.1 Introduction A standard cost is a predetermined estimated unit cost, used for inventory valuation and control. The building blocks of standard costing are standard costs; before we look at standard costing in any detail, you really need to know what a standard cost is. 1.2 Standard cost card A standard cost card shows full details of the standard cost of each product. The standard cost card of product 1234 is set out below in Figure 14.1. STANDARD COST CARD – PRODUCT 1234 Rs '000 Rs '000 Direct materials Material X – 3 kg at Rs. 400 per kg 1,200 Material Y – 9 litres at Rs. 200 per litre 1,800 3,000 Direct labour Grade A – 6 hours at Rs. 150 per hour 900 Grade B – 8 hours at Rs. 200 per hour 1,600 2,500 Standard direct cost 5,500 Variable production overhead – 14 hours at Rs. 50 per hour 700 Standard variable cost of production 6,200 Fixed production overhead – 14 hours at Rs. 450 per hour 6,300 Standard full production cost 12,500 Administration and marketing overhead 1,500 Standard cost of sale 14,000 Standard profit 2,000 Standard sales price 16,000 Figure 14.1: Standard cost card Notice how the total standard cost is built up from standards for each cost element: standard quantities of materials at standard prices, standard quantities of labour time at standard rates and so on. It is therefore determined by management's estimates of the following. The expected prices of materials, labour and expenses Efficiency levels in the use of materials and labour Budgeted overhead costs and budgeted volumes of activity We will see how management arrives at these estimates in Section 2. But why should management want to prepare standard costs? Obviously to assist with standard costing, but what is the point of standard costing?

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1.3 The uses of standard costing Standard costing has a variety of uses but its two principal ones are as follows. (a) To value inventories and cost production for cost accounting purposes. (b) To act as a control device by establishing standards (planned costs), highlighting (via variance analysis which we will cover in the next chapter) activities that are not conforming to plan and thus alerting management to areas which may be out of control and in need of corrective action. QUESTION Standard cost card Bloggs makes one product, the joe. Two types of labour are involved in the preparation of a joe, skilled and semi-skilled. Skilled labour is paid Rs. 1,000 per hour and semi-skilled Rs. 500 per hour. Twice as many skilled labour hours as semi-skilled labour hours are needed to produce a joe, four semi-skilled labour hours being needed. A joe is made up of three different direct materials. Seven kilograms of direct material A, four litres of direct material B and three metres of direct material C are needed. Direct material A costs Rs. 100 per kilogram, direct material B costs Rs. 200 per litre and direct material C costs Rs. 300 per metre. Variable production overheads are incurred at Bloggs Co at the rate of Rs. 250 per direct labour (skilled) hour. A system of absorption costing is in operation at Bloggs Co. The basis of absorption is direct labour (skilled) hours. For the forthcoming accounting period, budgeted fixed production overheads are Rs. 250 million and budgeted production of the joe is 5,000 units. Administration, selling and distribution overheads are added to products at the rate of Rs. 1,000 per unit, and a mark-up of 25% is made on the joe. Required Prepare a standard cost card for the joe using the above information. ANSWER STANDARD COST CARD – PRODUCT JOE Direct materials Rs '000 Rs '000 A – 7 kg Rs. 100 700 B – 4 litres Rs. 200 800 C – 3 m Rs. 300 900 2,400 Direct labour Skilled – 8 Rs. 1,000 8,000 Semi-skilled – 4 Rs. 500 2,000 10,000 Standard direct cost 12,400

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Direct materials Rs '000 Rs '000 Variable production overhead – 8 Rs. 250 2,000 Standard variable cost of production 14,400 Fixed production overhead – 8 Rs. 625 (W) 5,000 Standard full production cost 19,400 Administration, selling and distribution overhead 1,000 Standard cost of sale 20,400 Standard profit (25% 20,400) 5,100 Standard sales price 25,500 WORKING Overhead absorption rate = Rs. 25,000,0005,000 ×8 = Rs. 625 per skilled labour hour

QUESTION Marginal costing system

Prepare a standard cost card for product joe under a marginal system. ANSWER STANDARD COST CARD – PRODUCT JOE Rs '000 Direct materials 2,400 Direct labour 10,000 Standard direct cost 12,400 Variable production overhead 2,000 Standard variable production cost 14,400 Standard sales price 25,500 Standard contribution 11,100

Although the use of standard costs to simplify the keeping of cost accounting records should not be overlooked, we will be concentrating on the control and variance analysis aspect of standard costing. Standard costing is a control technique which compares standard costs and revenues with actual results to obtain variances which are used to improve performance.

Notice that the above definition highlights the control aspects of standard costing. 1.4 Standard costing as a control technique Differences between actual and standard costs are called variances. Standard costing therefore involves the following. The establishment of predetermined estimates of the costs of products or services

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The collection of actual costs The comparison of the actual costs with the predetermined estimates The predetermined costs are known as standard costs and the difference between standard and actual cost is known as a variance. The process by which the total difference between standard and actual results is analysed is known as variance analysis. Although standard costing can be used in a variety of costing situations (batch and mass production, process manufacture, jobbing manufacture (where there is standardisation of parts) and service industries (if a realistic cost unit can be established)), the greatest benefit from its use can be gained if there is a degree of repetition in the production process. It is therefore most suited to mass production and repetitive assembly work.

2 Setting standards

2.1 Introduction Standard costs may be used in both absorption costing and in marginal costing systems. We shall, however, confine our description to standard costs in absorption costing systems. As we noted earlier, the standard cost of a product (or service) is made up of a number of different standards, one for each cost element, each of which has to be set by management. We have divided this section into two: the first part looks at setting the monetary part of each standard, whereas the second part looks at setting the resources requirement part of each standard. 2.2 Types of performance standard

Performance standards are used to set efficiency targets. There are four types: ideal, attainable, current and basic. The setting of standards raises the problem of how demanding the standard should be. Should the standard represent a perfect performance or an easily attainable performance? The type of performance standard used can have behavioural implications. There are four types of standard. Type of standard

Description

Ideal These are based on perfect operating conditions: no wastage, no spoilage, no inefficiencies, no idle time, no breakdowns. Variances from ideal standards are useful for pinpointing areas where a close examination may result in large savings in order to maximise

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Type of standard

Description

efficiency and minimise waste. However, ideal standards are likely to have an unfavourable motivational impact, because reported variances will always be adverse. Employees will often feel that the goals are unattainable and not work so hard. Attainable These are based on the hope that a standard amount of work will be carried out efficiently, machines properly operated or materials properly used. Some allowance is made for wastage and

inefficiencies. If well-set they provide a useful psychological incentive by giving employees a realistic, but challenging, target of efficiency. The consent and co-operation of employees involved in improving the standard are required. Current These are based on current working conditions (current wastage, current inefficiencies). The disadvantage of current standards is that they do not attempt to improve on current levels of efficiency. Basic These are kept unaltered over a long period of time, and may be out of date. They are used to show changes in efficiency or performance over a long period of time. Basic standards are perhaps the least useful and least common type of standard in use. Ideal standards, attainable standards and current standards each have their supporters and it is by no means clear which of them is preferable. QUESTION Performance standards

Identify which of the following statements is not true. A Variances from ideal standards are useful for pinpointing areas where a close examination might result in large cost savings. B Basic standards may provide an incentive to greater efficiency even though the standard cannot be achieved. C Ideal standards cannot be achieved and so there will always be adverse variances. If the standards are used for budgeting, an allowance will have to be included for these 'inefficiencies'. D Current standards or attainable standards are a better basis for budgeting, because they represent the level of productivity which management will wish to plan for.

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ANSWER The correct answer is B. Statement B is describing ideal standards, not basic standards. 2.3 Direct material prices Direct material prices will be estimated by the purchasing department from their knowledge of the following. Purchase contracts already agreed Pricing discussions with regular suppliers The forecast movement of prices in the market The availability of bulk purchase discounts Price inflation can cause difficulties in setting realistic standard prices. Suppose that a material costs Rs. 10 per kilogram at the moment; during the course of the next twelve months it is expected to go up in price by 20% to Rs. 12 per kilogram. What standard price should be selected? The current price of Rs. 10 per kilogram The average expected price for the year, say Rs. 11 per kilogram Either would be possible, but neither would be entirely satisfactory. (a) If the current price were used in the standard, the reported price variance will become adverse as soon as prices go up, which might be very early in the year. If prices go up gradually rather than in one big jump, it would be difficult to select an appropriate time for revising the standard. (b) If an estimated mid-year price were used, price variances should be favourable in the first half of the year and adverse in the second half of the year, again assuming that prices go up gradually throughout the year. Management could only really check that in any month, the price variance did not become excessively adverse (or favourable) and that the price variance switched from being favourable to adverse around month six or seven and not sooner. 2.4 Direct labour rates Direct labour rates per hour will be set by discussion with the personnel department and by reference to the payroll and to any agreements on pay rises with trade union representatives of the employees. (a) A separate hourly rate or weekly wage will be set for each different labour grade/type of employee.

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(b) An average hourly rate will be applied for each grade (even though individual rates of pay may vary according to age and experience). Similar problems to those described for material prices can be met when setting labour standards and dealing with inflation. 2.5 Overhead absorption rates When standard costs are fully absorbed costs, the absorption rate of fixed production overheads will be predetermined, usually each year when the budget is prepared, and based, in the usual manner, on budgeted fixed production overhead expenditure and budgeted production. For selling and distribution costs, standard costs might be absorbed as a percentage of the standard selling price. Standard costs under marginal costing will, of course, not include any element of absorbed overheads. 2.6 Standard resource requirements To estimate the materials required to make each product (material usage) and also the labour hours required (labour efficiency), technical specifications must be prepared for each product by production experts (either in the production department or the work study department). (a) The 'standard product specification' for materials must list the quantities required per unit of each material in the product. These standard input quantities must be made known to the operators in the production department, so that control action by management to deal with excess

material wastage will be understood by them. (b) The 'standard operation sheet' for labour will specify the expected hours required by each grade of labour in each department to make one unit of product. These standard times must be carefully set (for example, by work study) and must be understood by the labour force. Where necessary, standard procedures or operating methods should be stated.

3 Budgets and standards compared A budget is a quantified monetary plan for a future period, which managers will try to achieve. Its major function lies in communicating plans and co-ordinating activities within an organisation. On the other hand, a standard is a carefully predetermined quantity target which can be achieved in certain conditions.

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Budgets and standards are similar in the following ways. (a) They both involve looking to the future and forecasting what is likely to happen given a certain set of circumstances. (b) They are both used for control purposes. A budget aids control by setting financial targets or limits for a forthcoming period. Actual achievements or expenditures are then compared with the budgets and action is taken to correct any variances where necessary. A standard also achieves control by comparison of actual results against a predetermined target. As well as being similar, budgets and standards are interrelated. For example, a standard unit production cost can act as the basis for a production cost budget. The unit cost is multiplied by the budgeted activity level to arrive at the budgeted expenditure on production costs. There are, however, important differences between budgets and standards. Budgets Standards Gives planned total aggregate costs for a function or cost centre Shows the unit resource usage for a single task, for example the standard labour hours for a single unit of production Can be prepared for all functions, even where output cannot be measured Limited to situations where repetitive actions are performed, and output can be measured Expressed in money terms Need not be expressed in money terms. For example, a standard rate of output does not need a financial value put on it

4 Criticisms of standard costing

Standard costing is most appropriate in a stable, standardised and repetitive environment and one of the main objectives of standard costing is to ensure that processes conform to standards, that they do not vary and that variances are eliminated. This may seem restrictive and inhibiting in the business environment of the early twenty-first century. 4.1 Standard costing in the modern business environment Critics of standard costing have argued that traditional variance analysis has limited applicability in the modern business environment. The modern business environment is characterised by a need to respond to customer demands for immediate availability of products, shortening product life cycles and higher quality standards and continuous improvement.

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4.2 Standard costing and new technology Standard costing has traditionally been associated with labour-intensive operations, but can it be applied to capital-intensive production too? (a) In an environment which includes advanced manufacturing technology (AMT), the cost of labour is a small proportion of total costs and so labour rates and efficiency variances will have little control value. (b) Fixed costs represent a significant proportion of total costs, but there is some doubt over the relevance of the information provided by fixed

overhead volume variances. (c) Material usage variances should be virtually non-existent, given the accuracy afforded by machines as opposed to human operators. (d) It is quite possible that, with AMT, variable overheads are incurred in relation to machine time rather than labour time, and standard costs should reflect this where appropriate. In an AMT environment, machine efficiency variances will be of value, however, and standards will still be needed for costing, pricing and budgeting purposes. 4.3 Other problems with using standard costing in today's

environment (a) Variance analysis concentrates on only a narrow range of costs, and does not give sufficient attention to issues such as quality and customer satisfaction. (b) Standard costing places too much emphasis on direct labour costs. Direct labour is only a small proportion of costs in the modern manufacturing environment and so this emphasis is not appropriate. (c) Many of the variances in a standard costing system focus on the control of short-term variable costs. In most modern manufacturing environments, the majority of costs, including direct labour costs, tend to be fixed in the short run. (d) The use of standard costing relies on the existence of repetitive operations and relatively homogeneous output. Nowadays, many organisations are continually forced to respond to customers' changing requirements, with the result that output and operations are not so repetitive. (e) Standard costing systems were developed when the business environment was more stable and less prone to change. The current business environment is more dynamic and it is not possible to assume stable conditions.

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(f) Standard costing systems assume that performance to standard is acceptable. Today's business environment is more focused on continuous improvement. (g) Most standard costing systems produce control statements weekly or monthly. The modern manager needs much more prompt control information in order to function efficiently in a dynamic business environment. This long list of criticisms of standard costing may lead you to believe that such systems have little use in today's business environment. Standard costing systems can be adapted to remain useful, however.

4.4 The role in modern business of standards and variances (a) Planning. Even in an environment where the focus is on continual improvement, budgets will still need to be quantified. For example, the planned level of prevention and appraisal costs needs to be determined. Standards, such as 'returns of a particular product should not exceed one per cent of deliveries during a budget period', can be set. (b) Control. Cost and mix changes from plan will still be relevant in many processing situations. (c) Decision making. Existing standards can be used as the starting point in the construction of a cost for a new product. (d) Improvement and change. Variance trends can be monitored over time. 5 Variances

A variance is the difference between a planned, budgeted or standard cost and the actual cost incurred. The same comparisons may be made for revenues. The process by which the total difference between standard and actual results is analysed is known as variance analysis. When actual results are better than expected results, we have a favourable variance (F). If, on the other hand, actual results are worse than expected, we have an adverse variance (A). Variances can be divided into two main groups. Variable cost variances Sales variances In the remainder of this chapter we will consider, in detail, the material, labour and variable cost variances.

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6 Direct material cost variances

6.1 Introduction The direct material total variance can be subdivided into the direct material price variance and the direct material usage variance. The direct material total variance is the difference between what the output actually cost and what it should have cost, in terms of material. The direct material price variance. This is the difference between the standard cost and the actual cost for the actual quantity of material used or purchased. In other words, it is the difference between what the material did cost and what it should have cost. The direct material usage variance. This is the difference between the standard quantity of materials that should have been used for the number of units actually produced, and the actual quantity of materials used, valued at the standard cost per unit of material. In other words, it is the difference between how much material should have been used and how much material was used, valued at standard cost.

6.2 Example: Direct material variances Product X has a standard direct material cost as follows. 10 kilograms of material Y at Rs. 10 per kilogram = Rs. 100 per unit of X. During period 4, 1,000 units of X were manufactured, using 11,700 kilograms of material Y which cost Rs. 98,600. Required

Calculate the following variances. (a) The direct material total variance (b) The direct material price variance (c) The direct material usage variance Solution (a) The direct material total variance This is the difference between what 1,000 units should have cost and what they did cost. Rs 1,000 units should have cost ( Rs. 100) 100,000 but did cost 98,600 Direct material total variance 1,400 (F)

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The variance is favourable: the units cost less than they should have cost. Now we can break down the direct material total variance into its two constituent parts: the direct material price variance and the direct material usage variance. (b) The direct material price variance This is the difference between what 11,700 kg should have cost and what 11,700 kg did cost. Rs 11,700 kg of Y should have cost ( Rs. 10) 117,000 but did cost 98,600 Material Y price variance 18,400 (F) The variance is favourable because the material cost less than it should have. (c) The direct material usage variance This is the difference between how many kilograms of Y should have been used to produce 1,000 units of X and how many kilograms were used, valued at the standard cost per kilogram. 1,000 units should have used ( 10 kg) 10,000 kg but did use 11,700 kg Usage variance in kg 1,700 kg (A) standard cost per kilogram × Rs. 10 Usage variance in Rs Rs. 17,000 (A) The variance is adverse because more material than should have been used was used. (d) Summary Rs Price variance 18,400 (F) Usage variance 17,000 (A) Total variance 1,400 (F)

6.3 Materials variances and opening and closing inventory Direct material price variances are usually extracted at the time of the receipt of the materials rather than at the time of usage. Suppose that a company uses raw material P in production, and that this raw material has a standard price of Rs. 3 per metre. During one month 6,000 metres are bought for Rs. 18,600, and 5,000 metres are used in production. At the end of the month, inventory will have been increased by 1,000 metres. In variance analysis, the problem is to decide the material price variance. Should it be

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calculated on the basis of materials purchased (6,000 metres) or on the basis of materials used (5,000 metres)? The answer to this problem depends on how closing inventories of the raw materials will be valued. (a) If they are valued at standard cost, (1,000 units at Rs. 3 per unit) the price variance is calculated on material purchases in the period. (b) If they are valued at actual cost (FIFO) (1,000 units at Rs. 3.10 per unit) the price variance is calculated on materials used in production in the period. The price variance is usually calculated on purchases in the period. The variance on the full 6,000 metres will be written off to the costing profit and loss account, even though only 5,000 metres are included in the cost of production. There are two main advantages in extracting the material price variance at the time of receipt. (a) If variances are extracted at the time of receipt they will be brought to the

attention of managers earlier than if they are extracted as the material is used. If it is necessary to correct any variances then management action can be more timely. (b) Since variances are extracted at the time of receipt, all inventories will be valued at standard price. This is administratively easier and it means that all issues from inventory can be made at standard price. If inventories are held at actual cost it is necessary to calculate a separate price variance on each batch as it is issued. Since issues are usually made in a number of small batches this can be a time-consuming task, especially with a manual system. The price variance would be calculated as follows. Rs 6,000 metres of material P purchased should cost ( Rs. 3) 18,000 but did cost 18,600 Price variance 600 (A)

7 Direct labour cost variances

7.1 Introduction The direct labour total variance can be subdivided into the direct labour rate variance and the direct labour efficiency variance. The direct labour total variance is the difference between what the output should have cost and what it did cost, in terms of labour. The direct labour rate variance. This is similar to the direct material price variance. It is the difference between the standard cost and the actual cost for the actual number of hours paid for.

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In other words, it is the difference between what the labour did cost and what it should have cost. The direct labour efficiency variance is similar to the direct material usage variance. It is the difference between the hours that should have been worked for the number of units actually produced, and the actual number of hours worked, valued at the standard rate per hour. In other words, it is the difference between how many hours should have been worked and how many hours were worked, valued at the standard rate per hour.

The calculation of direct labour variances is very similar to the calculation of direct material variances. 7.2 Example: Direct labour variances The standard direct labour cost of product X is as follows. 2 hours of grade Z labour at Rs. 500 per hour = Rs. 1,000 per unit of product X. During period 4, 1,000 units of product X were made, and the direct labour cost of grade Z labour was Rs. 890,000 for 2,300 hours of work. Required

Calculate the following variances. (a) The direct labour total variance (b) The direct labour rate variance (c) The direct labour efficiency (productivity) variance Solution (a) The direct labour total variance This is the difference between what 1,000 units should have cost and what they did cost. Rs '000 1,000 units should have cost ( Rs. 1,000) 1,000 but did cost 890 Direct labour total variance 110 (F) = Rs. 110,000 (F). The variance is favourable because the units cost less than they should have done. Again, we can analyse this total variance into its two constituent parts. (b) The direct labour rate variance This is the difference between what 2,300 hours should have cost and what 2,300 hours did cost.

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Rs '000 2,300 hours of work should have cost ( Rs. 5 per hr) 1,150 but did cost 890 Direct labour rate variance 260 (F) = Rs. 260,000 (F). The variance is favourable because the labour cost less than it should have cost. (c) The direct labour efficiency variance 1,000 units of X should have taken ( 2 hrs) 2,000 hrs but did take 2,300 hrs Efficiency variance in hours 300 hrs (A) standard rate per hour × Rs. 500 Efficiency variance in Rs Rs. 150,000 (A) The variance is adverse because more hours were worked than should have been worked. (d) Summary Rs '000 Rate variance 260 (F) Efficiency variance 150 (A) Total variance 110 (F) = Rs. 110,000 (F).

7.3 Idle time variance Idle time occurs when no actual work is done but the workforce still has to be paid for the time at work. The idle time variance is: (hours paid – hours worked) standard direct labour rate per hour A company may operate a costing system in which any idle time is recorded. Idle time may be caused by machine breakdowns or not having work to give to employees, perhaps because of bottlenecks in production or a shortage of orders from customers. Time paid for without any work being done is unproductive and therefore inefficient. In variance analysis, idle time is usually an adverse efficiency variance. If, however, idle time is built into the cost budget, it could be a favourable variance. The direct labour idle time variance 'occurs when the hours paid exceed the hours worked and there is an extra cost caused by this idle time'. (CIMA Official Terminology)

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When idle time is recorded separately, it is helpful to provide control information that identifies the cost of idle time separately and, in variance analysis, there will be an idle time variance as a separate part of the total labour efficiency variance. The remaining efficiency variance will then relate only to the productivity of the labour force during the hours spent actively working. 7.4 Example: Labour Variances During period 5, 1,500 units of product X were made and the cost of grade Z labour was Rs1,750,000 for 3,080 hours. During the period, however, there was a shortage of customer orders and 100 hours were recorded as idle time. Required Calculate the following variances. (a) The direct labour total variance (b) The direct labour rate variance (c) The idle time variance (d) The direct labour efficiency variance Solution (a) The direct labour total variance Rs’000 1,500 units of product X should have cost ( Rs1,000) 1,500 but did cost 1,750 Direct labour total variance 250 (A) Actual cost is greater than standard cost. The variance is therefore adverse. (b) The direct labour rate variance The rate variance is a comparison of what the hours paid should have cost and what they did cost. Rs’000 3,080 hours of grade Z labour should have cost ( Rs500) 1,540 but did cost 1,750 Direct labour rate variance 210 (A) Actual cost is greater than standard cost. The variance is therefore adverse. (c) The idle time variance The idle time variance is the hours of idle time, valued at the standard rate per hour. Idle time variance = 100 hours (A) Rs500 = Rs50,000 (A) It is an adverse variance because it was not built into the cost budget.

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(d) The direct labour efficiency variance The efficiency variance considers the hours actively worked (the difference between hours paid for and idle time hours). In our example, there were (3,080 – 100) = 2,980 hours when the labour force was not idle. The variance is calculated by taking the amount of output produced (1,500 units of product X) and comparing the time it should have taken to make them, with the actual time spent actively making them (2,980 hours). Once again, the variance in hours is valued at the standard rate per labour hour. 1,500 units of product X should take ( 2 hours) 3,000 hours but did take (3,080 – 100) 2,980 hours Direct labour efficiency variance in hours 20 hours (F) standard rate per hour × Rs500 Direct labour efficiency variance in Rs Rs10,000 (F) (e) Summary Rs’000 Direct labour rate variance 210 (A) Idle time variance 50 (A) Direct labour efficiency variance 10 (F) Direct labour total variance 250 (A) (f) Remember that, if idle time is recorded, the actual hours used in the efficiency variance calculation are the hours worked and not the hours paid for. (g) If there is a budgeted level of idle time and the actual level is less than the budgeted level, the idle time variance will be favourable. (h) Some organisations might experience 'expected' or 'normal' idle time at less busy periods, perhaps because demand is seasonal or irregular (but they wish to maintain and pay a constant number of workers). In such circumstances, the standard labour rate may include an allowance for the cost of the expected idle time. Only the impact of unexpected/abnormal idle time would be included in the idle time variance. 8 Variable production overhead variances The variable production overhead total variance can be subdivided into the variable production overhead expenditure variance and the variable production overhead efficiency variance (based on actual hours).

8.1 Example: Variable production overhead variances Suppose that the variable production overhead cost of product X is as follows. 2 hours at Rs. 150 = Rs. 300 per unit

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During period 6, 1,000 units of product X were made. The labour force worked 2,020 hours, of which 60 hours were recorded as idle time. The variable overhead cost was Rs. 307,500. Required

Calculate the following variances. (a) The variable overhead total variance (b) The variable production overhead expenditure variance (c) The variable production overhead efficiency variance Since this example relates to variable production costs, the total variance is based on actual units of production. (If the overhead had been a variable selling cost, the variance would be based on sales volumes.) Rs '000 1,000 units of product X should cost ( Rs. 300) 300 but did cost 307.5 Variable production overhead total variance 7.5 (A) = Rs. 7,500 (A). In many variance reporting systems, the variance analysis goes no further, and expenditure and efficiency variances are not calculated. However, the adverse variance of Rs. 7,500 may be explained as the sum of two factors. (a) The hourly rate of spending on variable production overheads was higher than it should have been; that is, there is an expenditure variance. (b) The labour force worked inefficiently, and took longer to make the output than it should have done. This means that spending on variable production overhead was higher than it should have been; in other words, there is an efficiency (productivity) variance. The variable production overhead efficiency variance is exactly the same, in hours, as the direct labour efficiency variance, and occurs for the same reasons. It is usually assumed that variable overheads are incurred during active working hours, but are not incurred during idle time (for example, the machines are not running, therefore power is not being consumed, and no indirect materials are being used). This means in our example that, although the labour force was paid for 2,020 hours, they were actively working for only 1,960 of those hours and so variable production overhead spending occurred during 1,960 hours. The variable production overhead expenditure variance is the difference between the amount of variable production overhead that should have been incurred in the actual hours actively worked, and the actual amount of variable production overhead incurred.

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(a) Rs '000 1,960 hours of variable production overhead should cost ( Rs. 150) 294 but did cost 307.5 Variable production overhead expenditure variance 13.5 (A) = Rs. 13,500 (A). The variable production overhead efficiency variance. If you already know the direct labour efficiency variance, the variable production overhead efficiency variance is exactly the same in hours, but priced at the variable production overhead rate per hour. (b) In our example, the efficiency variance would be as follows. 1,000 units of product X should take ( 2 hrs) 2,000 hrs but did take (active hours) 1,960 hrs Variable production overhead efficiency variance in hours 40 hrs (F) standard rate per hour × Rs. 150 Variable production overhead efficiency variance in Rs Rs. 6,000 (F)(c) Summary Rs '000 Variable production overhead expenditure variance 13.5 (A) Variable production overhead efficiency variance 6.0 (F) Variable production overhead total variance 7.5 (A) = Rs. 7,500 (A). Usage variance 1,320,000 (F)

9 The reasons for cost variances There are many possible reasons for cost variances arising, as you will see from the following list of possible causes. 9.1 General causes of variances There are four general causes of variances, (a) Inappropriate standard. Incorrect or out-of-date standards could have been used, which will not reflect current conditions. For example, a material price standard may have been wrong if an old price was used or the wrong type of material was priced. (b) Inaccurate recording of actual costs. For example, if time sheets are filled in incorrectly, this may lead to variances. (c) Random events. Examples include unusual adverse weather conditions or a flu epidemic. These may cause additional unforeseen costs.

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(d) Operating inefficiency. If the variance is not caused by inappropriate standards, inaccurate recording or random events, then it must be due to operating efficiency. The operating efficiency may be due to controllable or uncontrollable factors. Variance Favourable Adverse (a) Material price Unforeseen discounts received More care taken in purchasing Change in material standard Price increase Careless purchasing Change in material standard (b) Material usage Material used of higher quality than standard More effective use made of material Errors in allocating material to jobs

Defective material Excessive waste Theft Stricter quality control Errors in allocating material to jobs (c) Labour rate Use of apprentices or other workers at a rate of pay lower than standard Wage rate increase Use of higher-grade labour (d) Labour efficiency Output produced more quickly than expected because of work motivation, better quality of equipment or materials, or better methods. Errors in allocating time to jobs

Lost time in excess of standard allowed Output lower than standard set because of deliberate restriction, lack of training, or sub-standard material used Errors in allocating time to jobs (e) Overhead expenditure Savings in costs incurred More economical use of services Increase in cost of services used Excessive use of services Change in services used 10 Sales variances

10.1 Selling price variance The selling price variance is a measure of the effect on expected contribution of a different selling price to standard selling price. It is calculated as the difference between what the sales revenue should have been for the actual quantity sold, and what it was.

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10.2 Example: Selling price variance Suppose that the standard selling price of product X is Rs. 1,500. Actual sales in 20X3 were 2,000 units at Rs. 1,530 per unit. The selling price variance is calculated as follows. Rs '000 Sales revenue from 2,000 units should have been ( Rs. 1,500) 3,000 but was ( Rs. 1,530) 3,060 Selling price variance 60 (F) = Rs. 60,000 (F). The variance calculated is favourable because the price was higher than expected. 10.3 Sales volume contribution variance The sales volume contribution variance is the difference between the actual units sold and the budgeted (planned) quantity, valued at the standard contribution per unit. In other words, it measures the increase or decrease in standard contribution as a result of the sales volume being higher or lower than budgeted (planned). 10.4 Example: Sales volume contribution variance Suppose that a company budgets to sell 8,000 units of product J for Rs. 1,200 per unit. The standard full cost per unit is Rs. 700. Actual sales were 7,700 units, at Rs. 1,250 per unit. The sales volume contribution variance is calculated as follows. Budgeted sales volume 8,000 units Actual sales volume 7,700 units Sales volume variance in units 300 units (A) standard contribution per unit (Rs. (1,200 – 700)) × Rs. 500 Sales volume contribution variance Rs. 15,000 (A) The variance calculated above is adverse because actual sales were less than budgeted (planned). QUESTION Selling price and volume variance Jasper Co has the following budget and actual figures for 20X4. Budget ActualSales units 600 620Selling price per unit Rs. 3,000 Rs. 2,900Standard full cost of production = Rs. 2,800 per unit.

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Required Calculate the selling price variance and the sales volume contribution variance. ANSWER Rs '000 Sales revenue for 620 units should have been ( Rs. 3,000) 1,860 but was ( Rs. 2,900) 1,798 Selling price variance = Rs. 62,000 (A) 62 (A) Budgeted sales volume 600 units Actual sales volume 620 units Sales volume contribution variance in units 20 units (F) standard contribution per unit (Rs. (3,000 – 2,800)) × Rs. 200 Sales volume contribution variance Rs. 4,000 (F)

10.5 The significance of sales variances The possible interdependence between sales price and sales volume variances should be obvious to you. A reduction in the sales price might stimulate bigger sales demand, so that an adverse sales price variance might be counterbalanced by a favourable sales volume variance. Similarly, a price rise would give a favourable price variance, but possibly at the cost of a fall in demand and an adverse sales volume variance. It is therefore important in analysing an unfavourable sales variance that the overall consequence should be considered: that is, has there been a counterbalancing favourable variance as a direct result of the unfavourable one? 11 Operating statement reconciling budget contribution to

actual contribution

11.1 Introduction

Operating statements show how the combination of variances reconcile budgeted contribution and actual contribution. So far, we have considered how variances are calculated without considering how they combine to reconcile the difference between budgeted contribution and actual contribution during a period. This reconciliation is usually presented as a

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report to senior management at the end of each control period. The report is called an operating statement or statement of variances. An operating statement is a regular report for management of actual costs and revenues, usually showing variances from budgeted contribution to actual contribution. Here is a proforma for an operating statement which reconciles budget contribution to actual contribution. Rs Rs Budget contribution X Sales volume contribution variance X Standard contribution from actual sales X

(F) (A) Variances Rs Rs Sales price Material price Material usage Labour rate Labour efficiency Variable overhead expenditure Variable overhead efficiency X X X Actual contribution X Actual fixed costs can then be deducted to derive actual profit. An extensive example will now be introduced, both to revise the variance calculations already described, and also to show how to combine them into an operating statement. 11.2 Example 1: Variances and operating statements Sydney Co manufactures one product, and the entire product is sold as soon as it is produced. There are no opening or closing inventories and work in progress is negligible. The company operates a standard costing system and analysis of variances is made every month. The standard cost card for a product is as follows. Standard cost card Direct materials 0.5 kg at Rs 40 per kilo 20Direct wages 2 hours at Rs 80 per hour 160Variable overheads 2 hours at Rs 3 per hour 6Standard variable cost 186Standard contribution 134Standing selling price 320

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Budgeted output for the month of June 20X7 was 5,100 units. Actual results for June 20X7 were as follows. Production of 4,850 units was sold for Rs 1,503,500. Materials consumed in production amounted to 2,300 kg at a total cost of Rs 98,000. Labour hours paid for amounted to 8,500 hours at a cost of Rs 678,000. Actual operating hours amounted to 8,000 hours. Actual variable overheads amounted to Rs 26,000. Actual contribution was Rs 701,500 Required Calculate all variances and provide an operating statement reconciling budget contribution to actual contribution. Solution Rs(a) 2,300 kg of material should cost ( Rs 40) 92,000 but did cost 98,000 Material price variance in Rs 6,000 (A) (b) 4,850 units should use ( 0.5 kg) 2,425 kg but did use 2,300 kg Material usage variance in kg 125 kg (F) standard price per kg × Rs 40 Material usage variance in Rs 5,000 (F) (c) Rs

8,500 hours of labour should cost ( Rs 80) 680,000 but did cost 678,000 Labour rate variance in Rs 2,000 (F) (d) 4,850 units should take ( 2 hrs) 9,700 hrs but did take (active hours) 8,000 hrsLabour efficiency variance in hours 1,700 hrs (F) standard rate per hour × Rs 80Labour efficiency variance in Rs 136,000 (F) (e) Idle time variance 500 hours (A) Rs 80 in Rs 40,000 (A)

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(f) Rs8,000 hours incurring variable overhead expenditure should cost ( Rs 3) 24,000 but did cost 26,000 Variable overhead expenditure variance in Rs 2,000 (A) (g) Variable overhead efficiency variance in hours is the same as the labour efficiency variance: 1,700 hours (F) Rs 3 per hour 5,100 (F) (h) Rs Revenue from 4,850 units should be ( Rs 320) 1,552,000 but was 1,503,500 Sales price variance in Rs 48,500 (A) (i) Budgeted sales volume 5,100 units Actual sales volume 4,850 units Sales volume contribution variance in units 250 units (A) standard contribution per unit Rs 13.40 Sales volume contribution variance in Rs 33,500 (A

Sydney Operating Statement June 20X7 Rs Budgeted contribution (Rs 134 5,100) 683,400 Sales volume variance 33,500 (A) Budgeted contribution from actual sales

649,900 Sales price variance 48,500 (A) Actual sales minus the standard variable cost of sales

601,400

Cost variances (F) (A) Rs Rs Material price 6,000 Material usage 5,000 Labour rate 2,000 Labour efficiency 136,000 Labour idle time 40,000 Variable overhead expenditure 2,000 Variable overhead efficiency 5,100 148,100 48,000 100,100 (F) Actual contribution 701,500

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QUESTION Variances Goatee, a manufacturing firm It makes a single product, GOAT, using a single raw material KID. Standard costs relating to GOAT have been calculated as follows. Standard cost schedule – GOAT Per unit Rs Direct material, KID, 100 kg at Rs. 500 per kg 50,000 Direct labour, 10 hours at Rs. 800 per hour 8,000 Variable production overhead, 10 hours at Rs. 200 per hour 2,000 60,000 The standard selling price of a GOAT is Rs. 90,000 and Goatee LLC budget to produce 1,020 units a month. During December 20X0, 1,000 units of GOAT were produced. Relevant details of this production are as follows. Direct material KID 90,000 kg costing Rs. 72,000,000 were bought and used. Direct labour 8,200 hours were worked during the month and total wages were Rs. 6,300,000. Variable production overhead The actual cost for the month was Rs. 2,500,000. Inventories of the direct material KID are valued at the standard price of Rs. 500 per kg. Each GOAT was actually sold for Rs. 97,500. The actual contribution was Rs 16,700,000. Required Calculate the following for the month of December 20X0. (a) Variable production cost variance (b) Direct labour cost variance, analysed into rate and efficiency variances (c) Direct material cost variance, analysed into price and usage variances (d) Variable production overhead variance, analysed into expenditure and efficiency variances (e) Selling price variance (f) Sales volume contribution variance Then, determine the operating statement for GOAT for the month of December 20X0.

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ANSWER (a) This is simply a 'total' variance. Rs '000 1,000 units should have cost ( Rs. 60,000) 60,000 but did cost (see working) 80,800 Variable production cost variance 20,800 (A) = Rs. 20,800,000 (A). (b) Direct labour cost variances Rs '000 8,200 hours should cost ( Rs. 800) 6,560 but did cost 6,300 Direct labour rate variance = Rs. 260,000 (F). 260 (F) Rs '000 1,000 units should take ( 10 hours) 10,000 hrs but did take 8,200 hrs Direct labour efficiency variance in hrs 1,800 hrs (F)

standard rate per hour × Rs. 800 Direct labour efficiency variance in Rs Rs. 1,440(F)

Summary Rs '000 Rate 260 (F)Efficiency 1,440 (F)Total 1,700 (F) = Rs. 1,700,000 (F). (c) Direct material cost variances Rs '000 90,000 kg should cost ( Rs. 500) 45,000 but did cost 72,000 Direct material price variance 27,000 (A) = Rs. 27,000,000 (A). Rs '000 1,000 units should use ( 100 kg) 100,000 kg but did use 90,000 kg Direct material usage variance in kg 10,000 kg (F) standard cost per kg × Rs. 500 Direct material usage variance in Rs Rs. 5,000 (F)

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Summary Rs '000 Price 27,000 (A) Usage 5,000 (F) Total 22,000 (A) = Rs. 22,000,000 (A). (d) Variable production overhead variances Rs '000 8,200 hours incurring o/h should cost ( Rs. 200) 1,640 but did cost 2,500 Variable production overhead expenditure variance 860 (A) = Rs. 860,000 (A). Rs '000 Efficiency variance in hrs (from (b)) 1,800 hrs (F)

standard rate per hour × Rs. 200 Variable production overhead efficiency variance 360 (F) Summary Rs '000 Expenditure 860 (A) Efficiency 360 (F) Total 500 (A) (e) Selling price variance Rs '000 Revenue from 1,000 units should have been ( Rs. 90,000) 90,000 but was ( Rs. 97,500) 97,500 Selling price variance 7,500 (F) (f) Sales volume contribution variance Rs '000 Budgeted sales 1,020 units Actual sales 1,000 units Sales volume variance in units 20 units (A) standard contribution margin (Rs. (90,000 – 60,000)) × Rs. 30,000 Sales volume contribution variance in Rs Rs. 600 (A) WORKINGS Rs '000 Direct material 72,000 Total wages 6,300 Variable production overhead 2,500 80,800

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Goat Operating Statement for the month December 20X0

Rs '000

Budgeted contribution (Rs 1,020 30,000) 30,600 Sales volume variance (600) (A)Budgeted contribution from actual sales 30,000 Sales price variance 7,500 (F) Actual sales minus the standard variable cost of sales 37,500 Cost variances (F) (A) R '000s R '000s Material price 27,000 Material usage 5,000 Labour rate 260 Labour efficiency 1,440 Variable overhead expenditure 860 Variable overhead efficiency 360 7,060 27,860 20,800(A) Actual contribution 16,700 QUESTION Reconciling contributions A company uses standard marginal costing. Last month the standard contribution on actual sales was Rs. 10,000 and the following variances arose. Rs Total variable costs variance 2,000 (A) Sales price variance 500 (F) Sales volume contribution variance 1,000 (A) Required

Calculate the actual contribution for last month. A Rs. 7,000 B Rs. 7,500 C Rs. 8,000 D Rs. 8,500

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ANSWER The correct answer is D. Rs Standard contribution on actual sales 10,000 Add: favourable sales price variance 500 Less: adverse total variable costs variance (2,000) Actual contribution 8,500

QUESTION Calculating actual contribution from variances A company uses standard marginal costing. Last month, when all sales were at the standard selling price, the standard contribution from actual sales was Rs. 50,000 and the following variances arose: Rs Total variable costs variance 3,500 (A) Total fixed costs variance 1,000 (F) Sales volume contribution variance 2,000 (F) Required

Calculate the actual contribution for last month. A Rs. 46,500 B Rs. 47,500 C Rs. 48,500 D Rs. 49,500 ANSWER The correct answer is A. Rs Standard contribution on actual sales 50,000 Less: Adverse total variable costs variance (3,500) Actual contribution 46,500

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12 Deriving actual data from standard cost details and variances

Variances can be used to derive actual data from standard cost details. Rather than being given actual data and asked to calculate the variances, you may be given the variances and required to calculate the actual data on which they were based. See if you can do these two questions. QUESTION Rate of pay XYZ uses standard costing. The following data relates to labour grade ll. Actual hours worked 10,400 hoursStandard allowance for actual production 8,320 hoursStandard rate per hour Rs. 500Rate variance (adverse) Rs. 41,600Required Calculate the actual rate of pay per hour. A Rs. 495 B Rs. 496 C Rs. 504 D Rs. 505 ANSWER The correct answer is C. Rate variance per hour worked = Rs. 41,60010,400 = Rs. 4 (A) Actual rate per hour = Rs. (500 + 4) = Rs. 504. You should have been able to eliminate options A and B because they are both below the standard rate per hour. If the rate variance is adverse then the actual rate must be above standard. Option D is incorrect because it results from basing the calculations on standard hours rather than actual hours. QUESTION Quantity of material The standard material content of one unit of product A is 10 kg of material X which should cost Rs. 100 per kilogram. In June 20X4, 5,750 units of product A were produced and there was an adverse material usage variance of Rs. 1,500.

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Required

Calculate the quantity of material X used in June 20X4. ANSWER Let the quantity of material X used = Y 5,750 units should have used ( 10 kg) 57,500 kg but did use Y kgUsage variance in kg (Y – 57,500) kg standard price per kg × Rs. 100Usage variance in Rs Rs. 15,000 (A) 10(Y – 57,500) = 1,500 Y – 57,500 = 150 Y = 57,650 kg

13 Accounting for variances in the integrated accounting system In an integrated accounting system, both financial and cost accounting records are maintained in one system of accounting records which meet financial accounting and cost accounting purposes. Essentially, these two systems of accounting are integrated. Therefore, an integrated accounting system provides all information regarding cost of each product, job or operation and variances will also be highlighted for effective control purpose. In this system, costs of manufacture are recorded at standard cost. Therefore, if materials, labour and overheads are accounted for at standard cost, at the volumes manufactured, then the difference with the actual cost paid, will be the price and volume variance. The variance is accounted for separately in variance control accounts, so overhead variances remain transparent and cost and financial accounts can be produced from the same source accounting data. A debit will be required for adverse cost variances to capture an increase from standard to the actual cost paid. For example, Dr material cost account (at standard cost) Dr material price variance control a/c Dr material volume variance control a/c Cr cash/receivables

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A credit will be required for favourable cost variances to capture a decrease from standard to the actual cost paid. For example, Dr material cost account (at standard cost) Cr material price variance control a/c Cr material volume variance control a/c Cr cash/receivables The double entry above records the actual cost of labour and overheads split between valued at standard, price variance and usage variance. This means, for reporting, the standard value and variance control accounts can be combined to show actual cost. These accounts can also be kept separate to for variance analysis using the operating statement.

14 Control action

A variance should only be investigated if the expected value of benefits from investigation and any control action exceed the costs of investigation. If the cause of a variance is controllable, action can be taken to bring the system back under control in future. If the variance is uncontrollable, but not simply due to chance, it will be necessary to review forecasts of expected results, and perhaps to revise the budget. If a variance is assessed as significant then control action may be necessary. Since a variance compares historical actual costs with standard costs, it is a statement of what has gone wrong (or right) in the past. By taking control action, managers can do nothing about the past, but they can use their analysis of past results to identify where the 'system' is out of control. If the cause of the variance is controllable, action can be taken to bring the system back under control in future. If the variance is uncontrollable, on the other hand, but not simply due to chance, it will be necessary to revise forecasts of expected results, and perhaps to revise the budget. It may be possible for control action to restore actual results back on course to achieve the original budget. For example, if there is an adverse labour efficiency variance in month 1 of 1,100 hours, control action by the production department might succeed in increasing efficiency above standard by 100 hours per month for the next 11 months. It is also possible that control action might succeed in restoring better order to a situation, but the improvements might not be sufficient to enable the company to achieve its original budget. For example, for three months there has been an adverse labour efficiency in a production department, so that the cost per unit of

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output was Rs. 800 instead of a standard cost of Rs. 500. Control action might succeed in improving efficiency, so that unit costs are reduced to Rs. 700, Rs. 600 or even Rs. 500; but the earlier excess spending means that the contribution in the master budget will not be achieved. Depending on the situation and the control action taken, the action may take immediate effect, or it may take several weeks or months to implement. The effect of control action might be short-lived, lasting for only one control period; but it is more likely to be implemented with the aim of long-term improvement. 14.1 Possible control action The control action which may be taken will depend on the reason why the variance occurred. Some reasons for variances are outlined in the paragraphs which follow. 14.2 Measurement errors In practice it may be extremely difficult to establish that 1,000 units of product A used 32,000 kg of raw material X. Scales may have been misread; pilfering or wastage of materials may have gone unrecorded; items may have been wrongly classified (as material X3, say, when material X8 was used in reality); employees may have made adjustments to records to make their own performance look better. An investigation may show that control action is required to improve the accuracy of the recording system so that measurement errors do not occur. 14.3 Out-of-date standards Price standards are likely to become out of date when changes to the costs of material, power, labour and so on occur, or in periods of high inflation. In such circumstances an investigation of variances is likely to highlight a general change in market prices rather than efficiencies or inefficiencies in acquiring resources. Standards may also be out of date where operations are subject to technological development or if learning curve effects have not been taken into account. Investigation of this type of variance will provide information about the inaccuracy of the standard and highlight the need to frequently review and update standards.

14.4 Efficient or inefficient operations Spoilage and better quality material or more highly skilled labour than standard are all likely to affect the efficiency of operations and hence cause variances. Investigation of variances in this category should highlight the cause of the

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inefficiency or efficiency and will lead to control action to eliminate the inefficiency being repeated – or action to compound the benefits of the efficiency. For example, stricter supervision may be required to reduce wastage levels. 14.5 Random or chance fluctuations A standard is an average figure. It represents the midpoint of a range of possible values and therefore actual results are likely to deviate unpredictably within the predictable range. As long as the variance falls within this range, it will be classified as a random or chance fluctuation and control action will not be necessary. QUESTION Report on variances As the management accountant of the ABC Production LLC you have prepared the following variance report for the general manager. VARIANCE REPORT: SEPTEMBER 20X5 Variance Variance Total (Adverse) (Favourable) variance Rs Rs Rs Material (2,000) Usage 5,500 Price 3,500 Labour (1,500) Utilisation 3,000 Rate 1,500 Overhead (500) Price 4,500 Efficiency 2,000 Capacity 3,000 Actual costs for September 20X5 were as follows. Rs Materials 100,000 Labour 80,000 Overheads 75,000 Total 255,000 The general manager tells you that he is quite satisfied with this result, because the total adverse variance of Rs. 4,000 is only 1.57% of total costs. Required

Prepare a brief report to the General Manager giving your own interpretation of the month's results.

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ANSWER REPORT ON RESULTS FOR SEPTEMBER 20X5 1 TERMS OF REFERENCE This report provides a management accounting interpretation of the company's results for September 20X5. The report was prepared by A N Employee, Management Accountant and submitted to A Boss, General Manager, on XX October 20X5. 2 METHOD Using the management accounting department's variance report for September 20X5 and actual cost data for the month, the company's results were analysed. 3 FINDINGS Total variance The total variance may only be 1.57% of total costs but this total disguises a number of significant adverse and favourable variances which need investigating. Materials variances The fact that there is a favourable price variance and an adverse usage variance could indicate interdependence. The purchasing department may have bought cheap materials but these cheaper materials may have been more difficult to work with, so that more material was required per unit produced. The possibility of such an interdependence should be investigated. Whether or not there is an interdependence, both variances do require investigation, since they represent 5.5% (usage) and 3.5% (price) of the actual material cost for the month. Labour variances Again there could be an interdependence between the adverse utilisation variance and the favourable rate variance: less skilled (and lower paid) employees, perhaps, having worked less efficiently than standard. Discussions with factory management should reveal whether this is so. Both variances do need investigation since they again represent a high percentage (compared with 1.57%) of the actual labour cost for the month (3.75% for the utilisation variance and 1.875% for the rate variance). Overhead variances An investigation into the fixed and variable components of the overhead would facilitate control information. The cause of the favourable price variance, which represents 6% of the total overhead costs for the month, should be encouraged.

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The adverse overhead variances in total represent 6.67% of actual overhead cost during the month and must therefore be investigated. The capacity variance signifies that actual hours of work were less than budgeted hours of work. The company is obviously working below its planned capacity level. Efforts should therefore be made to increase production so as to eradicate this variance. 4 Conclusion It is not the total of the monthly variances which should be considered, but the individual variances: a number of them represent significant deviations from planned results. Investigations into their causes should be performed and control action taken to ensure that either performance is back under control in future (if the cause of the variance can be controlled) or the forecasts of expected results are revised, if the variance is uncontrollable. QUESTION Control problems

Outline ideas for answering the following questions. (a) Explain the problems concerning control of operations that a manufacturing company can be expected to experience in using a standard costing system during periods of rapid inflation. (b) State a method by which the company could try to overcome the problems to which you have referred in answer to (a) above, indicating the shortcoming of the method. ANSWER (a) (i) Inflation should be budgeted for in standard prices. But how can the rate of inflation and the timing of inflationary increases be accurately estimated? Who decides how much inflationary 'allowance' should be added to the standards? (ii) How can actual expenditure be judged against a realistic 'standard' price level. Ideally, there would be an external price index (for example, one published by the government's Department of Census and Statistics) but even external price indices are not reliable guides to the prices an organisation ought to be paying. (iii) The existence of inflation tends to eliminate the practical value of price variances as a pointer to controlling spending. (iv) Inflation affects operations more directly. Usually costs go up before an organisation can put up the prices of its own products to customers. Inflation therefore tends to put pressure on a company's cash flows.

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(v) To provide useful and accurately valued variances, the standard costs ought to be revised frequently. This would be an administrative burden on the organisation. (vi) If the organisation uses standard costs for pricing or inventory valuation, frequent revisions of the standard would be necessary to keep prices ahead of costs or inventories sensibly valued. (b) To overcome the problems, we could suggest the following. (i) Frequent revision of the standard costs. Problem – the administrative burden. (ii) Incorporating estimates of the rate of inflation and the timing of inflation into standard costs. Problem – accurate forecasting.

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A standard cost is a predetermined estimated unit cost, used for inventory valuation and control. A standard cost card shows full details of the standard cost of each product. Differences between actual and standard cost are called variances. Performance standards are used to set efficiency targets. There are four types: ideal, attainable, current and basic. A budget is a quantified monetary plan for a future period, which managers

will try to achieve. Its major function lies in communicating plans and co-ordinating activities within an organisation.

On the other hand, a standard is a carefully predetermined quantity target which can be achieved in certain conditions. Standard costing is most appropriate in a stable, standardised and repetitive environment and one of the main objectives of standard costing is to ensure that

processes conform to standards, that they do not vary and that variances are eliminated. This may seem restricted and inhibiting in the business environment of the early twenty-first century.

A variance is the difference between a planned, budgeted or standard cost and the actual cost incurred. The same comparisons can be made for revenues. The process by which the total difference between standard and actual results is analysed is known as the variance analysis. The direct material total variance can be subdivided into the direct material

price variance and the direct material usage variance. Direct material price variances are usually extracted at the time of receipt of the materials, rather than at the time of usage. The direct labour total variance can be subdivided into the direct labour rate variance and the direct labour efficiency variance. The variable production overhead total variance can be subdivided into the variable production overhead expenditure variance and the variable production overhead efficiency variance (based on actual hours). The selling price variance is a measure of the effect on expected profit of a different selling price to standard selling price. It is calculated as the difference between what the sales revenue should have been for the actual quantity sold and what it was. The sales volume contribution variance is the difference between the actual units sold and the budgeted (planned) quantity, valued at the standard contribution per unit. In other words, it measures the increase or decrease in standard contribution as a result of the sales volume being higher or lower than budgeted (planned).

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Operating statements show how the combination of variances reconcile budgeted contribution and actual contribution. Variances can be used to derive actual data from standard cost details. A variance should only be investigated if the expected value of benefits from investigation and any control action exceed the costs of investigation. If the cause of a variance is controllable, action can be taken to bring the system back under control in future. If the variance is uncontrollable, but not simply due to chance, it will be necessary to review forecasts of expected results, and perhaps to revise the budget.

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1 A standard cost is ………………………………………………….. . 2 State two main uses of standard costing. 3 A control technique which compares standard costs and revenues with actual results, to obtain variances which are used to stimulate improved performance, is known as: A Standard costing B Variance analysis C Budgetary control D Budgeting 4 Standard costs may only be used in absorption costing. True False 5 State two types of performance standard. 6 Fill in the gaps using the following words: standards/budgets/aggregate total/budgets/single task/standards (a) Budgets are prepared for ……………………. costs; standards are for a ………….. . (b) ………… can be prepared for all functions; ………… are only suitable for repetitive actions where output can be measured. (c) …………. are expressed in money terms; …………… need not be expressed in money terms. 7 Subdivide the following variances. (a) Direct materials cost variance (b) Direct labour cost variance (c) Variable production overhead variance

8 List two advantages in calculating the material price variance at the time of receipt of materials.

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9 Adverse material usage variances might occur for the following reasons. I Defective material II Excessive waste III Theft IV Unforeseen discounts received A I B I and II C I, II and III D I, II, III and IV 10 List the factors which should be taken into account when deciding whether or not a variance should be investigated. 11 Define the term 'sales volume contribution variance'. 12 A regular report for management of actual cost and revenue, and usually comparing actual results with budgeted (planned) results (and showing variances) is known as A Bank statement B Variance statement C Budget statement D Operating statement 13 List the first three lines in an operating statement

The following information is applicable for questions 14 to 17. Wood Co manufactures tables. Standard cost card per table Rs per table Actual cost Rs Direct materials (2 m2 @ Rs 350 per m2) 700 Direct labour (12 hours @ Rs 200 per hour) 2,400 During June, 450 tables were produced, which used 950 m2 of materials, at a total cost of Rs 342,000, and 5,000 labour hours at a total cost of Rs 1,134,000. 14 What is material price variance? 15 What is material usage variance? 16 What is labour rate variance? 17 What is labour efficiency variance?

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1 A planned unit cost. 2 (a) To value inventories and cost production for cost accounting purposes. (b) To act as a control device by establishing standards and highlighting activities that are not conforming to plan, and bringing these to the attention of management. 3 The answer is A. 4 False. They may be used in a marginal costing system as well. 5 (a) Attainable (b) Ideal 6 (a) Aggregate total Single task (b) Budgets Standards (c) Budgets Standards 7 P r ic e ( a ) U s a g e R a t e ( b ) E f fi c ie n c y E x p en d it u r e ( c ) E f fi c ie n c y

8 (a) The earlier variances are extracted, the sooner they will be brought to the attention of managers. (b) All inventories will be valued at standard price which requires less administration effort. 9 The answer is C. 10 Materiality Interdependence between variances

Controllability Costs of investigation Type of standard being used

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11 It is a measure of the increase or decrease in standard contribution as a result of the sales volume being higher or lower than budgeted (planned). 12 The answer is D. 13 Budgeted contribution Sales volume contribution variance Standard contribution from actual sales (Make sure that you learn this. After these lines, include the variances.) 14 Materials price 950 m2 should cost ( Rs 350 per m2) = Rs 332,500 did cost Rs 342,000 9,500 (A) 15 Materials usage 450 tables should use ( 2m2) = 900 m2 did use 950 m2 50 m2 (A) @ Rs 350 per m2 standard cost Rs 17,500 (A) 16 Labour rate 5,000 labour hours should cost ( Rs 200 per hr) Rs 1,000,000 did cost Rs 1,134,000 Rs 134,000 (A) 17 Labour efficiency 450 tables should take ( 12 hrs) 5,400 hours did take 5,000 hours 400 hours (F) @ standard cost per hour (Rs 200 per hr) Rs 80,000 (F)

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Knowledge Component B Planning and controlling 2.2 Budgeting; preparation and control 2.2.1 Explain how and why organisations prepare budgets 2.2.2 Prepare functional budgets 2.2.3 Prepare cash budgets and explain the solutions for budgeted cash deficits and surpluses in the short and long run 2.2.4 Explain the master budget 2.2.5 Calculate projected sales volumes, revenue and costs using forecasting techniques 2.2.6 Explain feedback and feed forward controls and their behavioural implications 2.2.7 Identify disadvantages of budgeting including budget slack 2.2.8 Explain budgeting at different levels of planning of the organisation 2.2.9 Prepare and interpret a flexible budget and budget variance

INTRODUCTION The chapter begins by explaining the reasons why an organisation might prepare a budget and goes on to detail the steps in the preparation of a budget. The method of preparing and the relationship between the various functional budgets is then set out. The chapter also considers the construction of cash budgets and budgeted statements of profit or loss and statements of financial position; these three budgets make up what is known as a master budget. We will also outline the managerial processes of planning, control and decision making. The actual results achieved by an organisation will, more than likely, be different from the expected results. These differences are variances which you will have covered in your earlier studies. We will revise the basic variances. The next step would be to identify which warrant investigation and then to investigate the reasons behind them. We suggest reasons for different types of variances and highlight the way in which they interrelate; the cause of a variance on one cost can often have an impact on another cost variance. The last part of this chapter looks at Fixed and flexible costs, feed forward and feedback control plus the disadvantages of budget slack.

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CHAPTER CONTENTS

LEARNING OUTCOME1 Definitions and purposes of budgeting 2.2.12 A framework for budgeting 2.2.13 Steps in the preparation of a budget – including the principal budget factor 2.2.1

4 Functional budgets, cash budgets and master budgets 2.2.2/2.2.3/2.2.45 The regression and moving average method 2.2.56 Strategic, tactical and operational planning 2.2.4/2.2.87 Fixed vs flexible budgets 2.2.5/2.2.98 Feedback and feedforward control 2.2.7

1 Definitions and purposes of budgeting Budgeting is a quantifiable action plan for a specified time period. 1.1 Reasons for preparing budgets Here are some of the reasons why budgets are used. Function Detail

Compel planning Budgeting forces management to look ahead, to set out detailed plans for achieving the targets for each department, operation and (ideally) each manager and to anticipate problems.

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Function Detail

Communicate ideas and plans A formal system is necessary to ensure that each person affected by the plans is aware of what he or she is supposed to be doing. Communication might be one-way, with managers giving orders to subordinates, or there might be two-way communication. Co-ordinate activities The activities of different departments need to be co-ordinated to ensure everyone in an organisation is working towards the same goals. This means, for example, that the purchasing department should base its budget on production requirements; and that the production budget should, in turn, be based on sales expectations. Provide a framework for responsibility accounting

Budgets require that managers are made responsible for the achievement of budget targets for the operations under their personal control. Establish a system of control

Control over actual performance is provided by the comparisons of actual results against the budget plan. Departures from budget can then be investigated and the reasons for the departures can be divided into controllable and uncontrollable factors. Provide a means of performance evaluation

Budgets provide targets which can be compared with actual outcomes in order to assess employee performance. Motivate employees to improve their performance

The interest and commitment of employees can be retained if there is a system that lets them know how well or badly they are performing. The identification of controllable reasons for departures from budget with managers responsible provides an incentive for improving future performance. Here's a definition of the purpose of budgets. Budgets have a range of purposes including the communication of organisation objectives in financial terms. They are also used in planning, authorising expenditure, controlling operations and evaluating performance.

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1.2 Different things to different people A budget, since it has different purposes, might mean different things to different people. A budget might be a forecast, a means of allocating resources, a yardstick or a target. What it might mean

Detail

Forecast It helps managers to plan for the future. Given uncertainty about the future, however, it is quite likely that a budget will become outdated as events occur and so the budget will cease to be a realistic forecast. New forecasts might be prepared that differ from the budget. (A forecast is what is likely to happen; a budget is what an organisation wants to happen. These are not necessarily the same thing.)

Means of allocating resources

It can be used to decide how many resources are needed (cash, labour and so on) and how many should be given to each area of the organisation's activities. As we saw when we looked at limiting factor analysis, resource allocation is particularly important when some resources are in short supply. Budgets often set ceilings or limits on how much administrative departments and other service departments are allowed to spend in the period. Public expenditure budgets, for example, set spending limits for each government department. Yardstick By comparing it with actual performance, the budget provides a means of indicating where and when control action may be necessary (and possibly where some managers or employees are open to censure for achieving poor results). Target A budget might be a means of motivating the workforce to greater personal accomplishment, another aspect of control. A budget is a 'quantitative expression of a plan for a defined period of time. It may include planned sales volumes and revenues; resource quantities, costs and expenses; assets, liabilities and cash flows.'

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2 A framework for budgeting

2.1 Budget committee The budget committee is the co-ordinating body in the preparation and administration of budgets. The budget committee is usually headed up by the managing director (as chairman) and is assisted by a budget officer who is usually an accountant. Every part of the organisation should be represented on the committee, so there should be a representative from sales, production, marketing and so on. Functions of the budget committee include the following. Co-ordination and allocation of responsibility for the preparation of budgets Issuing of the budget manual Timetabling Provision of information to assist in the preparation of budgets Communication of final budgets to the appropriate managers Monitoring the budgeting process by comparing actual and budgeted results 2.2 The budget period A budget period is a period for which a budget is prepared, and used, which may then be sub-divided into control periods.

Except for capital expenditure budgets, the budget period is usually the accounting year (sub-divided into 12 or 13 control periods). 2.3 Responsibility for budgets The manager responsible for preparing each budget should, ideally, be the manager responsible for carrying out the budget. For example, the preparation of particular budgets might be allocated as follows. (a) The sales manager should draft the sales budget and the selling overhead cost centre budgets. (b) The purchasing manager should draft the material purchases budget. (c) The production manager should draft the direct production cost budgets.

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QUESTION Budget committee

Identify which of the following the budget committee is not responsible for? A Preparing functional budgets B Timetabling the budgeting operation C Allocating responsibility for the budget preparation D Monitoring the budgeting process ANSWER The correct answer is A. It is the manager responsible for implementing the budget who must prepare the functional budget, not the budget committee. If you don't know the answer, remember not to fall for the common pitfall of thinking, 'Well, we haven't had a D for a while, so I'll guess that'. It is good practice to guess if you don't know the answer (never leave out an assessment question) but first eliminate some of the options if you can. Since the committee is a co-ordinating body we can definitely say that they are responsible for B and D. Similarly, a co-ordinating body is more likely to allocate responsibility than to actually undertake the budget preparation, so eliminate C and select A as the correct answer.

2.4 The budget manual The budget manual is a collection of instructions governing the responsibilities of persons and the procedures, forms and records relating to the preparation and use of budgetary data. The budget manual (traditionally a printed manual but now likely to be held electronically) includes detailed explanation of the process that will be followed top produce the budget. This information usually includes a timetable showing key budgetary events, specimen forms, and any relevant assumptions the budget is based upon. A budget manual may contain the following. (a) An explanation of the objectives of the budgetary process (i) The purpose of budgetary planning and controlling (ii) The objectives of the various stages of the budgetary process (iii) The importance of budgets in the long-term planning of the business

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(b) Organisational structures (i) An organisation chart (ii) A list of individuals holding budget responsibilities (c) An outline of the principal budgets and the relationship between them (d) Administrative details of budget preparation (i) Membership and terms of reference of the budget committee (ii) The sequence in which budgets are to be prepared (iii) A timetable (e) Procedural matters (i) Specimen forms and instructions for their completion (ii) Specimen reports (iii) Account codes (or a chart of accounts) (iv) The name of the budget officer to whom enquiries must be sent 3 Steps in the preparation of a budget – including the

principal budget factor

The first task in the budgetary process is to identify the principal budget factor. This is also known as the key budget factor or limiting budget factor. The principal budget factor is the factor which limits the activities of an organisation. The procedures for preparing a budget will differ from organisation to organisation but the steps described below will be indicative of the steps followed by many organisations. The preparation of a budget may take weeks or months and the budget committee may meet several times before the master budget (budgeted statement of profit or loss, budgeted statement of financial position and budgeted cash flow) is finally agreed. Functional budgets (sales budgets, production budgets, direct labour budgets and so on), which are amalgamated into the master budget, may need to be amended many times over as a consequence of discussions between departments, changes in market conditions and so on during the course of budget preparation. 3.1 Identifying the principal budget factor The principal budget factor is the factor that limits the capacity of the entity or activities being budgeted. It is sometimes referred to as the limiting factor. This factor is key in the budget-setting process, as it sets the maximum level of activity or production. The principal budget factor is often sales demand, but could be an item used in the production process or the capacity of a key production facility or function.

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The principal budget factor is usually sales demand. A company is usually restricted from making and selling more of its products because there would be no sales demand for the increased output at a price which would be acceptable/profitable to the company. The principal budget factor may also be machine capacity, distribution and selling resources, the availability of key raw materials or the availability of cash. Once this factor is defined, then the remainder of the budgets can be prepared. For example, if sales are the principal budget factor then production managers can only prepare their budgets after the sales budget is complete. 3.2 The order of budget preparation Assuming that the principal budget factor has been identified as being sales, the stages involved in the preparation of a budget can be summarised as follows. (a) The sales budget is prepared in units of product and sales value. The

finished goods inventory budget can be prepared at the same time. This budget decides the planned increase or decrease in finished goods inventory levels. (b) With the information from the sales and inventory budgets, the production budget can be prepared. This is, in effect, the sales budget in units plus (or minus) the increase (or decrease) in finished goods inventory. The production budget will be stated in terms of units. (c) This leads on logically to budgeting the resources for production. This involves preparing a materials usage budget, machine usage budget and a labour budget. (d) In addition to the materials usage budget, a materials inventory budget will be prepared, to decide the planned increase or decrease in the level of inventory held. Once the raw materials usage requirements and the raw materials inventory budget are known, the purchasing department can prepare a raw materials purchases budget in quantities and value for each type of material purchased. (e) During the preparation of the sales and production budgets, the managers of the cost centres of the organisation will prepare their draft budgets for the department overhead costs. Such overheads will include maintenance, stores, administration, selling and research and development. (f) From the above information a budgeted statement of profit or loss can be produced.

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(g) In addition, several other budgets must be prepared in order to arrive at the budgeted statement of financial position. These are the capital expenditure budget (for non-current assets), the working capital budget (for budgeted increases or decreases in the level of receivables and accounts payable as well as inventories), and a cash budget. Make sure that you understand the meaning of principal budget factor.

4 Functional budgets, cash budgets and master budgets

Functional/departmental budgets include budgets for sales, production, purchases and labour. A departmental/functional budgets are budgets for other areas of the organisation like distribution and administration. Having seen the theory of budget preparation, let us look at functional (or

departmental) budget preparation, which is best explained by means of an example. 4.1 Example: preparing a materials purchases budget ECO Co manufactures two products, S and T, which use the same raw materials, D and E. One unit of S uses 3 litres of D and 4 kilograms of E. One unit of T uses 5 litres of D and 2 kilograms of E. A litre of D is expected to cost Rs. 300 and a kilogram of E Rs. 700. Budgeted sales for 20X2 are 8,000 units of S and 6,000 units of T; finished goods in inventory at 1 January 20X2 are 1,500 units of S and 300 units of T, and the company plans to hold inventories of 600 units of each product at 31 December 20X2. Inventories of raw material are 6,000 litres of D and 2,800 kilograms of E at 1 January and the company plans to hold 5,000 litres and 3,500 kilograms respectively at 31 December 20X2. The warehouse and stores managers have suggested that a provision should be made for damages and deterioration of items held in store, as follows. Product S: loss of 50 units Material D: loss of 500 litres Product T: loss of 100 units Material E: loss of 200 kilograms Required

Prepare a material purchases budget for the year 20X2.

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Solution To calculate material purchases requirements it is first necessary to calculate the material usage requirements. That, in turn, depends on calculating the budgeted production volumes. Product S Product T Units Units Production required To meet sales demand 8,000 6,000 To provide for inventory loss 50 100 For closing inventory 600 600 8,650 6,700 Less: inventory already in hand 1,500 300 Budgeted production volume 7,150 6,400 Material D Material E Litres Kg Usage requirements To produce 7,150 units of S 21,450 28,600 To produce 6,400 units of T 32,000 12,800 To provide for inventory loss 500 200 For closing inventory 5,000 3,500 58,950 45,100 Less: inventory already in hand 6,000 2,800 Budgeted material purchases 52,950 42,300 Unit cost Rs. 300 Rs. 700 Cost of material purchases Rs. 15,885,000 Rs. 29,610,000 Total cost of material purchases Rs. 45,495,000 The basics of the preparation of each functional budget are similar to those above. Work carefully through the following question, which covers the preparation of a number of different types of functional budget.

QUESTION Functional budgets XYZ company produces three products X, Y and Z. For the coming accounting period budgets are to be prepared based on the following information. Budgeted sales Product X 2,000 at Rs. 10,000 each Product Y 4,000 at Rs. 13,000 each Product Z 3,000 at Rs. 15,000 each

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Budgeted usage of raw material RM11 RM22 RM33 Product X 5 2 – Product Y 3 2 2 Product Z 2 1 3 Cost per unit of material Rs. 500 Rs. 300 Rs. 400 Finished inventories budget Product X Product Y Product Z Opening 500 800 700 Closing 600 1,000 800 Raw materials inventory budget RM11 RM22 RM33 Opening 21,000 10,000 16,000 Closing 18,000 9,000 12,000 Product X Product Y Product Z Expected hours per unit 4 6 8 Expected hourly rate (labour) Rs. 900 Rs. 900 Rs. 900 Required

Record the budgetary information in the spaces below. (a) Sales budget Product X Product Y Product Z Total Sales quantity Sales value Rs. Rs. Rs. Rs. (b) Production budget Product X Product Y Product Z Units Units Units Budgeted production (c) Material usage budget RM11 RM22 RM33 Units Units Units Budgeted material usage (d) Material purchases budget RM11 RM22 RM33 Budgeted material purchases Rs. Rs. Rs. (e) Labour budget Budgeted total wages Rs.

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ANSWER (a) Sales budget Product X Product Y Product Z Total Sales quantity 2,000 4,000 3,000 Sales price Rs. 10,000 Rs. 13,000 Rs. 15,000 Sales value (Rs Mn) Rs. 20 Rs. 52 Rs. 45 Rs.

117 (b) Production budget Product X Product Y Product Z Units Units Units Sales quantity 2,000 4,000 3,000 Closing inventories 600 1,000 800 2,600 5,000 3,800 Less opening inventories 500 800 700 Budgeted production 2,100 4,200 3,100 (c) Material usage budget Production RM11 RM22 RM33 Units Units Units Units Product X 2,100 10,500 4,200 – Product Y 4,200 12,600 8,400 8,400 Product Z 3,100 6,200 3,100 9,300 Budgeted material usage 29,300 15,700 17,700 (d) Material purchases budget RM11 RM22 RM33 Units Units Units Budgeted material usage 29,300 15,700 17,700 Closing inventories 18,000 9,000 12,000 47,300 24,700 29,700 Less opening inventories 21,000 10,000 16,000 Budgeted material purchases 26,300 14,700 13,700 Standard cost per unit Rs. 500 Rs. 300 Rs. 400 Budgeted material purchases (Rs Mn) Rs. 13.15 Rs. 4.41 Rs. 5.48

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(e) Labour budget Product

Production

Hours required per unit

Total hours

Rate per

hour

Cost Units Rs Rs Mn X 2,100 4 8,400 900 7.56 Y 4,200 6 25,200 900 22.68 Z 3,100 8 24,800 900 22.32 Budgeted total wages 52.56 You may get an exam question which asks you to work out one budgeted figure from another. For example, you may be given the sales budget and asked to work out the production budget. Make sure that you learn this formula. Units made = units sold + units in closing inventory – units in opening inventory. The business must produce enough to cover its sales volume and to leave enough in closing inventory, but it gets a 'head start' from opening inventory. This is why opening inventory is deducted. You can apply this principle to other areas of budgeting. For example:

QUESTION Units of production The following information is available for B Co. Budgeted annual sales 100,000 units Opening inventory 25,000 units Closing inventory 27,500 units Required

Calculate the number of units of production for the year. A 72,500 C 100,000 B 97,500 D 102,500 ANSWER The answer is D, 102,500. Units made = units sold + closing inventory units – opening inventory units = 100,000 + 27,500 – 25,000 = 102,500

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4.2 Cash budgets A cash budget is a statement in which estimated future cash receipts and payments are tabulated in such a way as to show the forecast cash balance of a business at defined intervals. A cash budget shows estimated cash inflows and outflows for revenue and capital items.

4.2.1 Preparing cash budgets For example, in December 20X2 an accounts department might wish to estimate the cash position of the business during the three following months, January to March 20X3. A cash budget might be drawn up in the following format. Jan Feb Mar Rs '000 Rs '000 Rs '000 Estimated cash receipts From accounts payable 14,000 16,500 17,000 From cash sales 3,000 4,000 4,500 Proceeds on disposal of non-current assets 2,200 Total cash receipts 17,000 22,700 21,500 Estimated cash payments To suppliers of goods 8,000 7,800 10,500 To employees (wages) 3,000 3,500 3,500 Purchase of non-current assets 16,000 Rent and rates 1,000 Other overheads 1,200 1,200 1,200 Repayment of loan 2,500 14,700 28,500 16,200 Net surplus/(deficit) for month 2,300 (5,800) 5,300 Opening cash balance 1,200 3,500 (2,300) Closing cash balance 3,500 (2,300) 3,000 In this example (where the figures are purely for illustration) the accounts department has calculated that the cash balance at the beginning of the budget period, 1 January, will be Rs. 1,200. Estimates have been made of the cash which is likely to be received by the business (from cash and credit sales, and from a planned disposal of non-current assets in February). Similar estimates have been made of cash due to be paid out by the business (payments to suppliers and employees, payments for rent, rates and other overheads, payment for a planned purchase of non-current assets in February and a loan repayment due in January).

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From these estimates it is a simple step to calculate the excess of cash receipts over cash payments in each month. In some months, cash payments may exceed cash receipts and there will be a deficit for the month; this occurs during February in the above example, because of the large investment in non-current assets in that month. The last part of the cash budget above shows how the business's estimated cash balance can then be rolled along from month to month. Starting with the opening balance of Rs. 1,200 at 1 January, a cash surplus of Rs. 2,300 is generated in January. This leads to a closing January balance of Rs. 3,500 which becomes the opening balance for February. The deficit of Rs. 5,800 in February throws the business's cash position into overdraft and the overdrawn balance of Rs. 2,300 becomes the opening balance for March. Finally, the healthy cash surplus of Rs. 5,300 in March leaves the business with a favourable cash position of Rs. 3,000 at the end of the budget period. 4.2.2 The usefulness of cash budgets The usefulness of cash budgets is that they enable management to make any forward-planning decisions that may be needed, such as advising their bank of estimated overdraft requirements or strengthening their credit control procedures to ensure that customers pay more quickly. The cash budget is one of the most important planning tools that an organisation can use. It shows the cash effect of all plans made within the budgetary process and hence its preparation can lead to a modification of budgets if it shows that there are insufficient cash resources to finance the planned operations. It can also give management an indication of potential problems that could arise and allows them the opportunity to take action to avoid such problems. A cash budget can show four positions. Management will need to take appropriate action depending on the potential position. 4.2.3 Potential cash positions

Cash position Appropriate management action Short-term surplus Pay suppliers early to obtain discount Attempt to increase sales by increasing receivables and inventories Make short-term investments Short-term shortfall Increase accounts payable Reduce receivables Arrange an overdraft

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Cash position Appropriate management action Long-term surplus Make long-term investments Expand Diversify Replace/update non-current assets Long-term shortfall Raise long-term finance (such as by issue of share capital) Consider shutdown/disinvestment opportunities

QUESTION Cash budget Tick the boxes to identify which of the following should be included in a cash budget. Include Do not include Funds from the receipt of a bank loan Revaluation of a non-current asset Receipt of dividends from outside the business Depreciation of distribution vehicles Bad debts written off Share dividend paid

ANSWER Any item that is a cash flow will be included. Non-cash items are excluded from a cash budget. Include Do not include Funds from the receipt of a bank loan Revaluation of a non-current asset Receipt of dividends from outside the business Depreciation of distribution vehicles Bad debts written off Share dividend paid

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4.2.4 Example: cash budgets again Arjuna Hinni has worked for some years as a sales representative, but has recently been made redundant. He intends to start up in business on his own account, using Rs. 15,000,000 which he currently has invested with a building society. Arjuna maintains a bank account showing a small credit balance, and he plans to approach his bank for the necessary additional finance. Arjuna asks you for advice and provides the following additional information. (a) Arrangements have been made to purchase non-current assets costing Rs. 8,000,000. These will be paid for at the end of September and are expected to have a five-year life, at the end of which they will possess a nil residual value. (b) Inventories costing Rs. 5,000,000 will be acquired on 28 September and subsequent monthly purchases will be at a level sufficient to replace forecast sales for the month. (c) Forecast monthly sales are Rs. 3,000,000 for October, Rs. 6,000,000 for November and December, and Rs. 10,500,000 from January 20X9 onwards. (d) Selling price is fixed at the cost of inventory plus 50%. (e) Two months' credit will be allowed to customers, but only one month's credit will be received from suppliers of inventory. (f) Running expenses, including rent but excluding depreciation of non-current assets, are estimated at Rs. 1,600,000 per month. (g) Hinni intends to make monthly cash drawings of Rs. 1,000,000. Required

Prepare a cash budget for the six months to 31 March 20X9. Solution The opening cash balance at 1 October will consist of Arjuna's initial Rs. 15,000,000 less the Rs. 8,000,000 expended on non-current assets purchased in September. In other words, the opening balance is Rs. 7,000,000. Cash receipts from credit customers arise two months after the relevant sales. Payments to suppliers are a little more tricky. We are told that cost of sales is 100/150 sales. Thus, for October, cost of sales is 100/150 Rs. 3,000,000 = Rs. 2,000,000. These goods will be purchased in October but not paid for until November. Similar calculations can be made for later months. The initial inventory of Rs. 5,000,000 is purchased in September and consequently paid for in October. Depreciation is not a cash flow and so is not included in a cash budget. The cash budget can now be constructed.

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CASH BUDGET FOR THE SIX MONTHS ENDING 31 MARCH 20X9 Oct Nov Dec Jan Feb Mar Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Payments Suppliers 5,000 2,000 4,000 4,000 7,000 7,000 Running expenses 1,600 1,600 1,600 1,600 1,600 1,600 Drawings 1,000 1,000 1,000 1,000 1,000 1,000 7,600 4,600 6,600 6,600 9,600 9,600 Receipts Receivables – – 3,000 6,000 6,000 10,500 Surplus/(shortfall) (7,600) (4,600) (3,600) (600) (3,600) 900 Opening balance 7,000 (600) (5,200) (8,800) (9,400) (13,000)Closing balance (600) (5,200) (8,800) (9,400) (13,000) (12,100)QUESTION Cash budget again

You are presented with the budgeted data shown in Annex A for the period November 20X1 to June 20X2 by your firm. It has been extracted from the other functional budgets that have been prepared. You are also told the following. (a) Sales are 40% cash, 60% credit. Credit sales are paid two months after the month of sale. (b) Purchases are paid the month following purchase. (c) 75% of wages are paid in the current month and 25% the following month. (d) Overheads are paid the month after they are incurred. (e) Dividends are paid three months after they are declared. (f) Capital expenditure is paid two months after it is incurred. (g) The opening cash balance at 1 January 20X2 is Rs. 15,000,000. Annex A Nov X1 Dec X1 Jan X2 Feb X2 Mar X2 Apr X2 May X2 June X2 Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Rs '000Sales 80,000 100,000 110,000 130,000 140,000 150,000 160,000 180,000Purchases 40,000 60,000 80,000 90,000 110,000 130,000 140,000 150,000Wages 10,000 12,000 16,000 20,000 24,000 28,000 32,000 36,000Overheads 10,000 10,000 15,000 15,000 15,000 20,000 20,000 20,000Dividends 20,000 40,000Capital expend. 30,000 40,000 Required

Calculate the net cash balance carried forward at the end of June 20X2.

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ANSWER The net cash balance carried forward at the end of June 20X2 is Rs. . WORKINGS January February March April May June Rs Mn Rs Mn Rs Mn Rs Mn Rs Mn Rs Mn Receipts Sales revenue Cash 44 52 56 60 64 72 Credit 48 60 66 78 84 90 92 112 122 138 148 162 Payments Purchases 60 80 90 110 130 140 Wages 75% 12 15 18 21 24 27 25% 3 4 5 6 7 8 Overheads 10 15 15 15 20 20 Dividends 20 Capital expenditure 30 40 85 114 178 152 181 235 Net cash flow 7 (2) (56) (14) (33) (73) b/f 15 22 20 (36) (50) (83) c/f 22 20 (36) (50) (83) (156) QUESTION ABC Co The following information is available for ABC Co. May June Rs '000 Rs '000 Budgeted sales 30,000 40,000 Gross profit as a percentage of sales 30% 30% Closing trade payables as a percentage of cost of sales 50% 50% Opening inventory nil nil Closing inventory nil nil Required Calculate how much money should be budgeted for supplier payments in June. A Rs. 10,500,000 B Rs. 14,000,000 C Rs. 24,500,000 D Rs. 30,000,000

(156,000,000)

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ANSWER The answer is C. May June Rs '000 Rs '000 Sales 30,000 40,000 Gross profit (@ 30%) 9,000 12,000 Cost of sales (sales – GP) 21,000 28,000 Closing trade payables (@ 50%) 10,500 14,000 Rs '000 June opening payables 10,500 Increase in amounts owing (COS) 28,000 June closing payables (14,000) Amount paid in June 24,500 4.2.5 Example: using cash budgets Suppose that a bank overdraft with a ceiling of Rs. 50,000,000 has been arranged to accommodate the increased inventory levels and wage bill for overtime required to support the rising sales shown in Annex A in the question above. Required Advise on possible courses of action, given the cash budget prepared in answering the question. Solution The overdraft arrangements are quite inadequate to service the cash needs of the business over the six-month period. If the figures are realistic then action should be taken now to avoid difficulties in the near future. The following are possible courses of action. (a) Activities could be curtailed. (b) Other sources of cash could be explored, for example a long-term loan to finance the capital expenditure and a factoring arrangement to provide cash due from customers more quickly. (c) Efforts to increase the speed of debt collection could be made. (d) Payments to suppliers could be delayed. (e) The dividend payments could be postponed (the figures indicate that this is a small company, possibly owner-managed).

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(f) Staff might be persuaded to work at a lower rate in return for, say, an annual bonus or a profit-sharing agreement. (g) Extra staff might be taken on to reduce the amount of overtime paid. (h) The stockholding policy should be reviewed: it may be possible to meet demand from current production and minimise cash tied up in inventories. 4.3 Master budgets

The master budget provides a consolidation of all the subsidiary budgets and normally consists of a budgeted statement of profit or loss, budgeted statement of financial position, and a cash budget. As well as wishing to forecast its cash position, a business might want to estimate its profitability and its financial position for a coming period. This would involve the preparation of a budgeted statement of profit or loss and statement of financial position, both of which form a part of the master budget. Note that your KE2 syllabus states that you only need to understand the master budget. In other words, you will not be required to prepare a master budget. We have produced the example below just to aid your understanding.

4.3.1 Example: preparing a budgeted statement of profit or loss and statement of financial position

Required Using the information in Section 5.4, you are required to prepare Arjuna Hinni's budgeted statement of profit or loss for the six months ending on 31 March 20X9 and a budgeted statement of financial position as at that date. Solution The statement of profit or loss is straightforward. The first figure is sales, which can be computed very easily from the information in Section 5.4(c). It is sufficient to add up the monthly sales figures given there; for the statement of profit or loss there is no need to worry about any closing receivables. Similarly, cost of sales is calculated directly from the information on gross margin contained in Section 5.4(d).as

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FORECAST TRADING AND STATEMENT OF PROFIT OR LOSS FOR THE SIX MONTHS ENDING 31 MARCH 20X9 Rs Mn Rs Mn Sales (3 million + (2 6 million) + (3 10.5 million) 46.5 Cost of sales (2/3 Rs. 46.5 million) 31 Gross profit 15.5 Expenses Running expenses (6 Rs. 1.6 million) 9.6 Depreciation (Rs. 8 million 20% 6/12) 0.8 10.4 Net profit 5.1 Items will be shown in the statement of financial position as follows. (a) Inventory will comprise the initial purchases of Rs. 5,000,000. (b) Receivables will comprise sales made in February and March (not paid until April and May respectively). (c) Accounts payable will comprise purchases made in March (not paid for until April). (d) The bank overdraft is the closing cash figure computed in the cash budget. STATEMENT OF FINANCIAL POSITION FORECAST AT 31 MARCH 20X9 Rs Mn Rs Mn Non-current assets Rs. (8 million – 0.8 million) 7.2 Current assets Inventories 5 Receivables (2 Rs. 10.5 million) 21 26 Current liabilities Bank overdraft 12.1 Trade suppliers (March purchases) 7 19.1 Net current assets 6.9 14.1 Proprietor's interest Capital introduced 15 Profit for the period 5.1 Less drawings (6) Deficit retained (0.9) 14.1 We have now prepared all of the elements of Arjuna Hinni's master budget: the budgeted statement of profit or loss and statement of financial position, and the budgeted cash flow from Section 5.4.

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5 The regression and moving average method

5.1 Least squares method of linear regression analysis 5.1.1 Introduction

Linear regression analysis (the least squares method) is one technique for estimating a line of best fit. Once an equation for a line of best fit has been determined, forecasts can be made. FORMULA TO LEARN The least squares method of linear regression analysis involves using the following formulae for a and b in Y = a + bX. b =

2X2Xn YXXYn

a = nXbnY where n is the number of pairs of data

The line of best fit that is derived represents the regression of Y upon X. A different line of best fit could be obtained by interchanging X and Y in the formulae. This would then represent the regression of X upon Y (X = a + bY) and it would have a slightly different slope. For examination purposes, always use the regression of Y upon X, where X is the independent variable, and Y is the dependent variable whose value we wish to forecast for given values of X. In a time series, X will represent time. 5.1.2 Example: the least squares method (a) Calculate an equation to determine the expected level of costs, for any given volume of output, using the least squares method. You may assume the variables X (output) and Y (total cost). Time period 1 2 3 4 5 Output ('000 units) 20 16 24 22 18 Total cost (Rs. 000) 82 70 90 85 73 (b) Prepare a budget for total costs, if output is 22,000 units. (c) Calculate the correlation coefficient and state whether there is a high degree of correlation between output and costs.

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Solution (a) WORKINGS X Y XY X2 Y2 20 82 1,640 400 6,724 16 70 1,120 256 4,900 24 90 2,160 576 8,100 22 85 1,870 484 7,225 18 73 1,314 324 5,329

X = 100 Y = 400 XY = 8,104 X2 = 2,040 Y2 = 32,278 n = 5 (There are five pairs of data for x and y values) b = 22 X)(Xn YXXYn = 21002,0405 400)(1008,104)(5

= 10,00010,200 40,00040,520 = 200520 = 2.6

a = nXbnY = 5400 – 2.6

5100 = 28 Y = 28 + 2.6X where Y = total cost, in thousands of Rs.; X = output, in thousands of units. Note that the fixed costs are Rs. 28,000 (when X = 0 costs are Rs. 28,000) and the variable cost per unit is Rs. 2.60. (b) If the output is 22,000 units, we would expect costs to be 28 + 2.6 22 = 85.2 = Rs. 85,200. (c) r = 240032,2785200 520

= 1,390200520

= 527.3520 = +0.99

5.1.3 Regression lines and time series The same technique can be applied to calculate a regression line (a trend line) for a time series. This is particularly useful for purposes of forecasting. As with correlation, years can be numbered from 0 upwards.

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QUESTION Trend line

Calculate the trend line of sales and forecast sales in 20Y2 and 20Y3 using the data in the question entitled 'Correlation'. ANSWER Using workings from the question entitled 'Correlation': b =

210305 78101345

= 100150 780670 = –2.2

a = nXbnY = 5 102.2578 = 20 Y = 20 – 2.2X where X = 0 in 20X7, X = 1 in 20X8 and so on. Using the trend line, predicted sales in 20Y2 (year 5) would be: 20 – (2.2 5) = 9 ie 9,000 units and predicated sales in 20Y3 (year 6) would be: 20 – (2.2 6) = 6.8 ie 6,800 units.

QUESTION Regression analysis Regression analysis was used to find the equation Y = 300 – 4.7X, where X is time (in quarters) and Y is sales level in thousands of units. Required Given that X = 0 represents 20X0 quarter 1, calculate the forecast sales levels for 20X5 quarter 4. ANSWER X = 0 corresponds to 20X0 quarter 1 Therefore X = 23 corresponds to 20X5 quarter 4 Forecast sales = 300 – (4.7 × 23) = 191.9 = 191,900 units

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QUESTION Forecasting Over a 36-month period, sales have been found to have an underlying regression line of Y = 14.224 + 7.898X where Y is the number of items sold and X represents the month. Required

Calculate the forecast number of items to be sold in month 37. ANSWER Y = 14.224 + 7.898X = 14.224 + (7.898 × 37) = 306.45 = 306 units

5.1.4 The reliability of regression analysis forecasts As with all forecasting techniques, the results from regression analysis will not be wholly reliable. There are a number of factors which affect the reliability of forecasts made using regression analysis. (a) It assumes a linear relationship exists between the two variables (since linear regression analysis produces an equation in the linear format) whereas a non-linear relationship might exist. (b) It assumes that the value of one variable, Y, can be predicted or estimated from the value of one other variable, X. In reality the value of Y might depend on several other variables, not just X. (c) When it is used for forecasting, it assumes that what has happened in the past will provide a reliable guide to the future. (d) When calculating a line of best fit, there will be a range of values for X. In the example in section 4.2, the line Y = 28 + 2.6X was predicted from data with output values ranging from X = 16 to X = 24. Depending on the degree of correlation between X and Y, we might safely use the estimated line of best fit to predict values for Y in the future, provided that the value of X remains within the range 16 to 24. We would be on less safe ground if we used the formula to predict a value for Y when X = 10, or 30, or any other value outside the range 16 to 24, because we would have to assume that the trend line applies outside the range of X values used to establish the line in the first place.

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(i) Interpolation means using a line of best fit to predict a value within the two extreme points of the observed range. (ii) Extrapolation means using a line of best fit to predict a value outside the two extreme points. When linear regression analysis is used for forecasting a time series (when the X values represent time) it assumes that the trend line can be extrapolated into the future. This might not necessarily be a good assumption to make. (e) As with any forecasting process, the amount of data available is very important. Even if correlation is high, if we have fewer than about ten pairs of values, we must regard any forecast as being somewhat unreliable. (It is likely to provide more reliable forecasts than the scattergraph method, however, since it uses all of the available data.) (f) The reliability of a forecast will depend on the reliability of the data collected to determine the regression analysis equation. If the data is not collected accurately or if data used is false, forecasts are unlikely to be acceptable. A check on the reliability of the estimated line Y= 28 + 2.6X can be made, however, by calculating the coefficient of correlation. From the answer to the example in section 4.2, we know that r = 0.99. This is a high positive correlation, and r2 = 0.9801, indicating that 98.01% of the variation in cost can be explained by the variation in volume. This would suggest that a fairly large degree of reliance can probably be placed on estimates. If there is a perfect linear relationship between X and Y (r = 1) then we can predict Y from any given value of X with great confidence. If correlation is high (for example r = 0.9) the actual values will all lie quite close to the regression line and so predictions should not be far out. If correlation is below about 0.7, predictions will only give a very rough guide as to the likely value of Y.

5.1.5 Advantages of regression analysis (a) It gives a definitive line of best fit, taking account of all of the data. (b) Linear regression makes efficient use of data and good results can be obtained with relatively small data sets. (c) The significance/reliability of the relationship between variables can be statistically tested (but you don't need to know the details of this for KE2.) (d) Many processes are linear, so are well described by regression analysis. Even many non-linear relationships can be well-approximated by a linear model over a short range.

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5.2 Moving Average Method One method of finding the trend is by the use of moving averages. Remember that when finding the moving average of an even number of results, a second moving average has to be calculated, so that trend values can relate to specific actual figures. Look at these monthly sales figures. Year 6 Sales Rs '000 August 0.02 September 0.04 October 0.04 November 3.20 December 14.60 It looks as though the business is expanding rapidly – and so it is, in a way. But when you know that the business is a Thai Pongal card manufacturer, then you see immediately that the January sales will no doubt slump right back down again. It is obvious that the business will do better during the Thai Pongal season than at any other time – that is the seasonal variation with which the statistician has to contend. Using the monthly figures, how can he or she tell whether or not the business is doing well overall – whether there is a rising sales trend over time other than the short-term rise over the festival period? One possibility is to compare figures with the equivalent figures of a year ago. However, many things can happen over a period of twelve months to make such a comparison misleading – for example, new products might now be manufactured and prices will probably have changed. In fact, there are a number of ways of overcoming this problem of distinguishing trend from seasonal variations. One such method is called moving averages. This method attempts to remove seasonal (or cyclical) variations from a time

series by a process of averaging, so as to leave a set of figures representing the trend. 5.2.1 Finding the trend by moving averages A moving average is an average of the results of a fixed number of periods. Since it is an average of several time periods, it is related to the mid-point of the overall period.

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5.2.2 Example: moving averages Year Sales Units 20X0 390 20X1 380 20X2 460 20X3 450 20X4 470 20X5 440 20X6 500 Required

Calculate a moving average of the annual sales over a period of three years. Solution (a) Average sales in the three year period 20X0 – 20X2 were

390+380+4603 = 1,2303 = 410 This average relates to the middle year of the period, 20X1. (b) Similarly, average sales in the three year period 20X1 – 20X3 were

380+460+4503 = 1,2903 = 430 This average relates to the middle year of the period, 20X2. (c) The average sales can also be found for the periods 20X2 – 20X4, 20X3 – 20X5 and 20X4 – 20X6, to give the following. Moving total of Moving average of Year Sales 3 years' sales 3 year's sales ( 3) 20X0 390 20X1 380 1,230 410 20X2 460 1,290 430 20X3 450 1,380 460 20X4 470 1,360 453 20X5 440 1,410 470 20X6 500 Note the following points. (i) The moving average series has five figures, relating to the years from 20X1 to 20X5. The original series had seven figures for the years from 20X0 to 20X6. (ii) There is an upward trend in sales, which is more noticeable from the series of moving averages than from the original series of actual sales each year.

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5.2.3 Moving averages of an even number of results In the previous example, moving averages were taken of the results in an odd number of time periods, and the average then related to the mid-point of the overall period. If a moving average were taken of results in an even number of time periods, the basic technique would be the same, but the mid-point of the overall period would not relate to a single period. For example, suppose an average were taken of the following four results. Spring 120 Summer 90 Autumn 180 average 115 Winter 70 The average would relate to the mid-point of the period, between summer and autumn. The trend line average figures need to relate to a particular time period; otherwise, seasonal variations cannot be calculated. To overcome this difficulty, we take a moving average of the moving average. An example will illustrate this technique. 5.2.4 Example: moving averages over an even number of periods

Calculate a moving average trend line of the following results of Linden Co. Year Quarter Volume of sales '000 units 20X5 1 600 2 840 3 420 4 720 20X6 1 640 2 860 3 420 4 740 20X7 1 670 2 900 3 430 4 760 Solution A moving average of four will be used, since the volume of sales would appear to depend on the season of the year, and each year has four quarterly results. The moving average of four does not relate to any specific period of time; therefore a second moving average of two will be calculated on the first moving average trend line.

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Moving Moving Mid-point of total of 4 average of 4 2 moving Actual volume quarters' quarters' averages Year Quarter of sales sales sales Trend line '000 units '000 units '000 units '000 units (A) (B) (B 4) (C) 20X5 1 600 2 840 3 420 2,580 645.0 650.00 4 720 2,620 655.0 657.50 20X6 1 640 2,640 660.0 660.00 2 860 2,640 660.0 662.50 3 420 2,660 665.0 668.75 4 740 2,690 672.5 677.50 20X7 1 670 2,730 682.5 683.75 2 900 2,740 685.0 687.50 3 430 2,760 690.0 4 760 By taking a mid point (a moving average of two) of the original moving averages, we can relate the results to specific quarters (from the third quarter of 20X5 to the second quarter of 20X7). QUESTION Trends in sales

Identify the trend in sales of Linden Co in the solution above. ANSWER The trend in sales is upward.

5.2.5 Moving averages on graphs One way of displaying the trend clearly is to show it by plotting the moving average on a graph.

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5.2.6 Example: moving averages on graphs Actual sales of Slap-It-On suntan lotion for 20X5 and 20X6 were as follows. Sales Rs'000 Rs'000 20X5 20X6 January 100 110 February 120 130 March 200 220 April 200 210 May 240 230 June 250 240 July 210 250 August 210 300 September 200 150 October 110 110 November 90 80 December 50 40 1,980 2,070 Required

Calculate the trend in the suntan lotion sales and display it on a graph. (Hint. Calculate an annual moving total.) Solution Moving average 20X6 Sales Moving total (trend) Rs '000 Rs '000 Rs '000 January 110 1,990 165.83 February 130 2,000 166.67 March 220 2,020 168.33 April 210 2,030 169.17 May 230 2,020 168.33 June 240 2,010 167.50 July 250 2,050 170.83 August 300 2,140 178.33 September 150 2,090 174.17 October 110 2,090 174.17 November 80 2,080 173.33 December 40 2,070 172.50 There is one very important point not immediately obvious from the above table, and that is to do with the time periods covered by the moving total and moving average. (a) The moving total, as we have seen, is the total for the previous twelve months. The figure of Rs. 1,990, for instance, represents total sales from February 20X5 to January 20X6.

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(b) The moving average is the average monthly sales over the previous twelve months. The figure of Rs. 165.83, for instance, represents average monthly sales for each month during the period February 20X5 to January 20X6. When plotting a moving average on a graph, it is therefore important to remember that the points should be located at the mid-point of the period to which they apply. For example, the figure of Rs. 165.83 (moving average at end of January 20X6) relates to the 12 months ending January 20X6 and so it must be plotted in the middle of that period (31 July 20X5). The moving data on suntan lotion sales could be drawn on a graph as follows.

Rs

300

250

200

150

100

50

0

Monthly sales

Annual moving average

20X5 20X6

Time

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Figure 18.8: Plotting moving averages Points to note about this graph are as follows. (a) The annual moving average can only be plotted from July 20X5 to May 20X6 as we have no data prior to January 20X5 or after December 20X6. (b) The moving average has the effect of smoothing out the seasonal fluctuations in the ordinary sales graph (which is the reason why moving averages are used in the first place).

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5.3 Finding the seasonal variations Seasonal variations are the difference between actual and trend figures (additive model). An average of the seasonal variations for each time period within the cycle must be determined and then adjusted so that the total of the seasonal variations sums to zero. Once a trend has been established, we can find the seasonal variations. The actual and trend sales for Linden Co (as calculated in Section 8.5) are set out below. The difference between the actual results for any one quarter and the trend figure for that quarter will be the seasonal variation for that quarter. 5.4 Additive model Year Quarter Actual Trend Seasonal

variation 20X5 1 600 2 840 3 420 650.00 –230.00 4 720 657.50 62.50 20X6 1 640 660.00 –20.00 2 860 662.50 197.50 3 420 668.75 –248.75 4 740 677.50 62.50 20X7 1 670 683.75 –13.75 2 900 687.50 212.50 3 430 4 760 The variation between the actual result for any one particular quarter and the trend line average is not the same from year to year, but an average of these variations can be taken.

Q1 Q2 Q3 Q4 20X5 230.00 62.50 20X6 20.00 197.50 248.75 62.50 20X7 13.75 212.50 Total 33.75 410.00 478.75 125.00 Average (÷ 2) 16.875 205.00 239.375 62.50

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QUESTION Additive model The results of an additive time series model analysing production are shown below. Weekly production '000 units Week 1 –4 Week 2 +5 Week 3 +9 Week 4 –6 Required

Identify which of the following statements is/are true in relation to the data shown in the table above. I Production is on average 9,000 units above the trend in week 3. II Production is on average 4% below the trend in week 1. III Production is on average 5% above the trend in week 2. IV Production in week 4 is typically 6% below the trend. A I only B I and II only C I and III only D II and IV only ANSWER The answer is A. With an additive model, the weekly component represents the average value of actual production minus the trend for that week, so a component of +9 means production is 9,000 units above the trend. This is the only correct statement. If you selected option B, C or D, you have confused the additive variation of –4, +5 and –6 (actually –4,000 units, +5,000 units and –6,000 units respectively) with the multiplicative variation of –4%, +5% and –6% respectively. Multiplicative variations are covered later in this chapter.

5.5 A weakness in moving average analysis The moving average calculations described so far in this chapter are based on an additive model which means that we add the values for a number of periods and take the average of those values.

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An additive model has the important drawback that when there is a steeply rising or a steeply declining trend, the moving average trend will either get ahead of, or fall behind, the real trend.

5.6 Examples: moving averages Suppose that we were to take a three-period moving average of the following sales figures. Actual Three-year Moving sales moving total average Rs '000 Rs '000 Rs '000 20X1 1,000 20X2 1,200 3,700 1,233 20X3 1,500 4,800 1,600 20X4 2,100 6,600 2,200 20X5 3,000 9,300 3,100 20X6 4,200 12,900 4,300 20X7 5,700 18,000 6,000 20X8 8,100 In this example, sales are on a steeply rising trend; this means that the moving average value for each year consistently overstates sales, because it is partly influenced by the value of sales in the next year. The moving average value for 20X7, for example, is Rs. 6,000, which is Rs. 300 above actual sales for 20X7. This is because the moving average is partly based on the higher sales value in 20X8. The consequences are as follows. (a) The trend sales is not a good representation of actual sales. (b) The trend will probably be unsuitable for forecasting. 5.7 Seasonal variations using the multiplicative model The method of estimating the seasonal variations in the above example was to use the differences between the trend and actual data. This model assumes that the components of the series are independent of each other, so that an increasing trend does not affect the seasonal variations and make them increase as well, for example. The alternative is to use the multiplicative model, whereby each actual figure is expressed as a proportion of the trend. It may be easier to understand this model if we state this as an equation. The example below uses the equation to calculate the seasonal variation. The proportional (multiplicative) model summarises a time series as Y = T S R (or Y = T*S*R).

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The trend component will be the same whichever model is used but the values of the seasonal and random components will vary according to the model being applied. In our examples, we assume that the random component is small and so can be ignored for our purposes. The multiplicative model will be Y = T × S. Refer back to our example, Linden Ltd, taking the first two years of data only. We can use the equation here to work out the seasonal variations. The trend is calculated in exactly the same way as before. So if Y = T × S then S = Y/T and we can calculate S = Y/T for the multiplicative model.

Actual Trend Seasonal percentage Year Quarter (Y) (T) (Y/T) 20X5 1 600 2 840 3 420 650.00 0.646 4 720 657.50 1.095 20X6 1 640 660.00 0.970 2 860 662.50 1.298 3 420 4 740 Suppose that seasonal variations for the next four quarters are 0.628, 1.092, 0.980 and 1.309 respectively. The summary of the seasonal variations expressed in proportional terms is, therefore, as follows.

Year Q1 Q2 Q3 Q4 % % % % 20X5 0.646 1.095 20X6 0.970 1.298 0.628 1.092 20X7 0.980 1.309 Total 1.950 2.607 1.274 2.187 Average 0.975 1.3035 0.637 1.0935 The averages should sum (in this case) to 4.0, 1.0 for each of the four quarters. They actually sum to 4.009 so 0.00225 has to be deducted from each one.

Q1 Q2 Q3 Q4 Average 0.97500 1.30350 0.63700 1.09350 Adjustment –0.00225 –0.00225 –0.00225 –0.00225 Final estimate 0.97275 1.30125 0.63475 1.09125 Rounded 0.97 1.30 0.64 1.09 Note that the proportional model is better than the additive model when the trend is increasing or decreasing over time. In such circumstances, seasonal variations are likely to be increasing or decreasing, too. The additive model simply adds absolute and unchanging seasonal variations to the trend figures, whereas the proportional model, by multiplying increasing or decreasing trend values by a constant seasonal variation factor, takes account of changing seasonal variations.

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5.8 Deseasonalisation Deseasonalised data are often used by economic commentators. Economic statistics, such as unemployment figures, are often 'seasonally adjusted' or 'deseasonalised' so as to ensure that the overall trend (rising, falling or stationary) is clear. All this means is that seasonal variations (derived from previous data) have been taken out, to leave a figure which might be taken as indicating the trend. 5.9 Example: deseasonalisation Actual sales figures for four quarters, together with appropriate seasonal adjustment factors derived from previous data, are as follows.

Actual Seasonal Quarter sales adjustments Rs '000 Rs '000 1 150 +3 2 160 +4 3 164 –2 4 170 –5

Required

Calculate the deseasonalised data. Solution We are reversing the normal process of applying seasonal variations to trend figures, so we subtract positive seasonal variations (and add negative ones). Actual Deseasonalised

Quarter sales sales Rs '000 Rs '000 1 150 147 2 160 156 3 164 166 4 170 175

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6 Strategic, tactical and operational planning

6.1 Planning Information for management is likely to be used for planning, control and decision making. An organisation should never be surprised by developments which occur gradually over an extended period of time because the organisation should have implemented a planning process. Planning involves the following. Establishing objectives Selecting appropriate strategies to achieve those objectives Planning, therefore, forces management to think ahead systematically in both the short term and the long term. 6.2 Objectives of organisations An objective is the aim or goal of an organisation (or an individual). Note that, in practice, the terms objective, goal and aim are often used interchangeably. A strategy is a possible course of action that might enable an organisation (or an individual) to achieve its objectives. The two main types of organisation that you are likely to come across in practice are as follows. Profit making Non-profit seeking The main objective of profit-making organisations is to maximise profits. A secondary objective of profit-making organisations might be to increase output of its goods/services. The main objective of non-profit seeking organisations is usually to provide goods and services. A secondary objective of non-profit seeking organisations might be to minimise the costs involved in providing the goods/services. In conclusion, the objectives of an organisation might include one or more of the following. Maximise profits Maximise revenue Maximise shareholder value Increase market share Minimise costs Remember that the type of organisation concerned will have an impact on its objectives.

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6.3 Strategy and organisational structure There are two schools of thought on the link between strategy and organisational structure. Structure follows strategy Strategy follows structure Let's consider the first idea that structure follows strategy. What this means is that organisations develop a structure in order to implement a strategy. Or do they? The second school of thought suggests that strategy follows structure. This side of the argument suggests that the strategy of an organisation is determined or influenced by the structure of the organisation. The structure of the organisation therefore limits the number of strategies available. We could explore these ideas in much more detail, but for the purposes of your management accounting studies, you really just need to be aware that there is a link between strategy and the structure of an organisation. 6.4 Long-term strategic planning Long-term strategic planning, also known as corporate planning, involves selecting appropriate strategies so as to prepare a long-term plan to attain the objectives.

The time span covered by a long-term plan depends on the organisation, the industry in which it operates and the particular environment involved. Typical periods are 2, 5, 7 or 10 years although longer periods are frequently encountered. Long-term strategic planning is a detailed, lengthy process, essentially incorporating three stages and ending with a corporate plan. Figure 2.2 provides an overview of the process and shows the link between short-term and long-term planning.

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6.5 Short-term tactical planning The long-term corporate plan serves as the long-term framework for the organisation as a whole; for operational purposes it is necessary to convert the corporate plan into a series of short-term plans, usually covering one year, which relate to sections, functions or departments. The annual process of short-term planning should be seen as stages in the progressive fulfilment of the corporate plan: each short-term plan steers the organisation towards its long-term objectives. It is, therefore, vital that, to obtain the maximum advantage from short-term planning, some sort of long-term plan exists. The planning process

THE

ASSESSMENT

STAGE

THE

OBJECTIVE

STAGE

THE

EVALUATION

STAGE

THE

CORPORATE

PLAN

Assess the

external

environment

Assess the

organisationAssess the

future

Assess

expectations

Evaluate

corporate

objectives

Consider

alternative

ways of achieving

objectives

Agree a

corporate

plan

Production

planning

Resource

planning

Product

planning

Research and

development

planning

Detailed operational plans which implement the corporate plan on a monthly,

quarterly or annual basis. Operational plans include short-term budgets,

standards and objectives.

LONG-

TERM

STRATEGY

PLANNING

SHORT-

TERM

PLANNING

Figure 2.2: The planning process

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6.6 Control Remember that we said that information for management is likely to be used for planning, control and decision making. We have just looked at planning. Now we'll look at control. There are two stages in the control process. (a) The performance of the organisation, as set out in the detailed operational plans, is compared with the actual performance of the organisation on a regular and continuous basis. Any deviations from the plans can then be identified and corrective action taken. (b) The corporate plan is reviewed in the light of the comparisons made and any changes in the parameters on which the plan was based (such as new competitors, government instructions and so on) to assess whether the objectives of the plan can be achieved. The plan is modified as necessary before any serious damage to the organisation's future success occurs. Effective control is therefore not practical without planning, and planning without control is pointless. An established organisation should have a system of management reporting that produces control information in a specified format at regular intervals. Smaller organisations may rely on informal information flows or ad hoc reports, produced as required.

6.7 Decision making Management is decision taking. Managers of all levels within an organisation take decisions. Decision making always involves a choice between alternatives and it is the role of the management accountant to provide information so that management can reach an informed decision. It is, therefore, vital that the management accountant understands the decision-making process so that he/she can supply the appropriate type of information.

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6.7.1 Decision-making process

Make the choice/decision.

State the expected outcome

and check that the expected

outcome is in keeping with

the overall goals or objectives.

Identify goals,

objectives or problems.

Identify alternative solutions/

opportunities which might

contribute towards achieving

them.

Collect and analyse relevant

data about each alternative.

Implement the decision.

Obtain data about actual results.

Compare actual results with

the expected outcome.

Evaluate achievements.

PLANNING

CONTROL

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7 Figure 2.3: The decision-making process

6.8 Anthony's view of management activity Anthony divides management activities into strategic planning, management control and operational control. R N Anthony, a leading writer on organisational control, has suggested that the activities of planning, control and decision making should not be separated since all managers make planning and controlling decisions. He has identified three types of management activity.

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(a) Strategic planning: 'the process of deciding on objectives of the organisation, on changes in these objectives, on the resources used to attain these objectives, and on the policies that are to govern the acquisition, use and disposition of these resources.' (b) Tactical (or management) control: 'the process by which managers assure that resources are obtained and used effectively and efficiently in the accomplishment of the organisation's objectives.' (c) Operational control: 'the process of assuring that specific tasks are carried out effectively and efficiently.' 6.8.1 Strategic planning

Strategic plans are those which set or change the objectives, or strategic targets of an organisation. They would include such matters as the selection of products and markets, the required levels of company profitability, the purchase and disposal of subsidiary companies or major non-current assets and so on. 6.8.2 Tactical/management control Whilst strategic planning is concerned with setting objectives and strategic targets, management control is concerned with decisions about the efficient and effective use of an organisation's resources to achieve these objectives or targets. (a) Resources, often referred to as the '4 Ms' (manpower, materials, machines and money). (b) Efficiency in the use of resources means that optimum output is achieved from the input resources used. It relates to the combinations of manpower, land and capital (for example how much production work should be automated) and to the productivity of labour, or material usage. (c) Effectiveness in the use of resources means that the outputs obtained are in line with the intended objectives or targets. 6.8.3 Operational control The third, and lowest, tier in Anthony's hierarchy of decision making consists of operational control decisions. As we have seen, operational control is the task of ensuring that specific tasks are carried out effectively and efficiently. Just as 'management control' plans are set within the guidelines of strategic plans, so too are 'operational control' plans set within the guidelines of both strategic planning and management control. Consider the following.

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(a) Senior management may decide that the company should increase sales by 5% per annum for at least five years – a strategic plan. (b) The sales director and senior sales managers will make plans to increase sales by 5% in the next year, with some provisional planning for future years. This involves planning direct sales resources, advertising, sales promotion and so on. Sales quotas are assigned to each sales territory – a tactical plan (management control). (c) The manager of a sales territory specifies the weekly sales targets for each sales representative. This is operational planning: individuals are given tasks which they are expected to achieve. Although we have used an example of selling tasks to describe operational control, it is important to remember that this level of planning occurs in all aspects of an organisation's activities, even when the activities cannot be scheduled nor properly estimated because they are non-standard activities (such as repair work, answering customer complaints). The scheduling of unexpected or ad hoc work must be done at short notice, which is a feature of much operational planning. In the repairs department, for example, routine preventive maintenance can be scheduled, but breakdowns occur unexpectedly and repair work must be scheduled and controlled 'on the spot' by a repairs department supervisor.

6.9 Management control systems A management control system is a system which measures and corrects the performance of activities of subordinates in order to make sure that the objectives of an organisation are being met and the plans devised to attain them are being carried out. The management function of control is the measurement and correction of the activities of subordinates in order to make sure that the goals of the organisation, or planning targets, are achieved. The basic elements of a management control system are as follows. Planning: deciding what to do and identifying the desired results Recording the plan, which should incorporate standards of efficiency or targets Carrying out the plan and measuring actual results achieved Comparing actual results against the plans Evaluating the comparison, and deciding whether further action is necessary Where corrective action is necessary, this should be implemented

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6.10 Types of information Information within an organisation can be analysed into the three levels assumed in Anthony's hierarchy: strategic, tactical and operational. 6.10.1 Strategic information

Strategic information is used by senior managers to plan the objectives of their organisation, and to assess whether the objectives are being met in practice. Such information includes overall profitability, the profitability of different segments of the business, capital equipment needs and so on. Strategic information, therefore, has the following features. It is derived from both internal and external sources. It is summarised at a high level. It is relevant to the long term. It deals with the whole organisation (although it might go into some detail). It is often prepared on an ad hoc basis. It is both quantitative and qualitative. It cannot provide complete certainty, given that the future cannot be predicted. 6.10.2 Tactical information

Tactical information is used by middle management to decide how the resources of the business should be employed, and to monitor how they are being and have been employed. Such information includes productivity measurements (output per man hour or per machine hour), budgetary control or variance analysis reports, and cash flow forecasts and so on. Tactical information therefore has the following features. It is primarily generated internally. It is summarised at a lower level. It is relevant to the short and medium term. It describes or analyses activities or departments. It is prepared routinely and regularly. It is based on quantitative measures. 6.10.3 Operational information

Operational information is used by 'front-line' managers such as foremen or head clerks to ensure that specific tasks are planned and carried out properly within a factory or office and so on. In the payroll office, for example, information at this level will relate to day-rate labour and will include the hours worked each

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week by each employee, the rate of pay per hour, details of the deductions; and, for the purpose of wages analysis, details of the time each person spent on individual jobs during the week. In this example, the information is required weekly, but more urgent operational information, such as the amount of raw materials being input to a production process, may be required daily, hourly or, in the case of automated production, second-by-second. Operational information has the following features. It is derived almost entirely from internal sources. It is highly detailed, being the processing of raw data. It relates to the immediate term, and is prepared constantly, or very frequently. It is task-specific and largely quantitative.

7 Fixed vs flexible budgets

7.1 Fixed budgets

Fixed budgets remain unchanged regardless of the level of activity; flexible budgets are designed to flex with the level of activity. Comparison of a fixed budget with the actual results for a different level of activity is of little use for control purposes. Flexible budgets should be used to show what cost and revenues should have been for the actual level of activity. A fixed budget is a budget which is designed to remain unchanged regardless of the volume of output or sales achieved.

The master budget prepared before the beginning of the budget period is known as the fixed budget. The term 'fixed' has the following meaning. (a) The budget is prepared on the basis of an estimated volume of production and an estimated volume of sales, but no plans are made for the event that actual volumes of production and sales may differ from budgeted volumes. (b) When actual volumes of production and sales during a control period (month or four weeks or quarter) are achieved, a fixed budget is not adjusted (in retrospect) to the new levels of activity. The major purpose of a fixed budget is at the planning stage, when it seeks to define the broad objectives of the organisation.

7.2 Flexible budgets A flexible budget is a budget which, by recognising different cost behaviour patterns, is designed to change as volumes of output change.

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Flexible budgets may be used in one of two ways. (a) At the planning stage. For example, suppose that a company expects to sell 10,000 units of output during the next year. A master budget (the fixed budget) would be prepared on the basis of these expected volumes. However, if the company thinks that output and sales might be as low as 8,000 units or as high as 12,000 units, it may prepare contingency flexible budgets, at volumes of, say 8,000, 9,000, 11,000 and 12,000 units. There are a number of advantages of planning with flexible budgets. (i) It is possible to find out, well in advance, the costs of lay-off pay, idle time and so on if output falls short of budget. (ii) Management can decide whether it would be possible to find alternative uses for spare capacity if output falls short of budget (could employees be asked to overhaul their own machines, for example, instead of paying for an outside contractor?). (iii) An estimate of the costs of overtime, subcontracting work or extra machine hire if sales volume exceeds the fixed budget estimate can be made. From this, it can be established whether there is a limiting factor which would prevent high volumes of output and sales being achieved. (b) Retrospectively. At the end of each month (control period) or year, flexible budgets can be used to compare actual results achieved with what results should have been under the circumstances. Flexible budgets are an essential factor in budgetary control and overcome the practical problems involved in monitoring the budgetary control system. (i) Management needs to be informed about how good or bad actual performance has been. To provide a measure of performance, there must be a yardstick (budget or standard) against which actual performance can be measured. (ii) Every business is dynamic, and actual volumes of output cannot be expected to conform exactly to the fixed budget. Comparing actual costs directly with the fixed budget costs is meaningless (unless the actual level of activity turns out to be exactly as planned). (iii) For useful control information, it is necessary to compare actual

results at the actual level of activity achieved, against the results that should have been expected at this level of activity, which are shown by the flexible budget.

QUESTION Flexible budgets

Discuss briefly whether flexible budgets are particularly useful to the car industry during a recession.

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ANSWER During a recession the car industry often has to put workers on a three- or four-day week due to lack of demand for its products. Budgets, therefore, have to be reassessed to match the reduced production time available.

7.3 Preparing flexible budgets (including high-low method) Flexible budgeting uses the principles of marginal costing. In estimating future costs it is often necessary to begin by looking at cost behaviour in the past. For costs which are wholly fixed or wholly variable no problem arises. But you may be presented with a cost which appears to have behaved in the past as a mixed cost (partly fixed and partly variable). The high-low method may be used for estimating the level of such a cost in a future period. This method was introduced in Chapter 3 and will be re-visited in Chapter 18. 7.4 High-low method (a) To estimate the fixed and variable elements of semi-variable costs, records of costs in previous periods are reviewed and the costs of the following two

periods are selected. (i) The period with the highest volume of output (ii) The period with the lowest volume of output (Note. The periods with the highest/lowest output may not be the periods with the highest/lowest cost.) (b) The difference between the total cost of the high output and the total cost of the low output will be the variable cost of the difference in output levels (since the same fixed cost is included in each total cost). (c) The variable cost per unit may be calculated from this (difference in total costs difference in output levels), and the fixed cost may then also be determined (total cost at either output level – variable cost for output level chosen).

7.5 Example: the high-low method The costs of operating the maintenance department of a television manufacturer for the last four months have been as follows. Month Cost Production volume Rs Units 1 1,100,000 7,000 2 1,150,000 8,000 3 1,110,000 7,700 4 970,000 6,000

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Required

Calculate the costs that should be expected in month five when output is expected to be 7,500 units. Ignore inflation. Solution (a) Units Rs High output 8,000 total cost 1,150,000 Low output 6,000 total cost 970,000 Variable cost of 2,000 180,000 Variable cost per unit Rs. 180,000/2,000 = Rs. 90 (b) Substituting in either the high or low-volume cost: High Low Rs Rs Total cost 1,150,000 970,000 Variable costs (8,000 × Rs. 90) 720,000 (6,000 × Rs. 90) 540,000 Fixed costs 430,000 430,000 (c) Estimated costs of 7,500 units of output: Rs Fixed costs 430,000 Variable costs (7,500 × Rs. 9) 675,000 Total costs 1,105,000 QUESTION High-low

Calculate the cost of electricity in July, if 2,750 units of electricity are consumed, using the high-low method and the following information. Month Cost Electricity consumed Rs '000 Units January 204 2,600 February 212 2,800 March 200 2,500 April 220 3,000 May 184 2,100 June 188 2,200

ANSWER Units Rs '000 High units 3,000 total cost = 220 Low units 2,100 total cost = 184 900 36 Variable cost per unit = 90036,000Rs. = Rs. 40

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Substituting: Rs '000 Total cost of 3,000 units 220 Variable costs (3,000 × Rs. 40) 120 Fixed cost 100 Total cost in July = Rs.(100,000 + (2,750 40)) = Rs. 210,000 We can now look at a full example of preparing a flexible budget.

7.6 Example: preparing a flexible budget (a) Prepare a budget for 20X6 for the direct labour costs and overhead expenses of a production department at the activity levels of 80%, 90% and 100%, using the information listed below. (i) The direct labour hourly rate is expected to be Rs. 37.50. (ii) 100% activity represents 60,000 direct labour hours. (iii) Variable costs Indirect labour Rs. 7.50 per direct labour hour Consumable supplies Rs. 37.5 per direct labour hour Canteen and other welfare services 6% of direct and indirect labour costs (iv) Semi-variable costs are expected to relate to the direct labour hours in the same manner as for the last five years. Direct Semi- labour variable Year hours costs Rs '000 20X1 64,000 2,080 20X2 59,000 1,980 20X3 53,000 1,860 20X4 49,000 1,780 20X5 (estimate) 40,000 1,600 (v) Fixed overhead per labour hour at 100% activity Rs '000 Depreciation 30 Maintenance 20 Insurance 10 Rates 25 Management salaries 40 (vi) Inflation is to be ignored. (b) Calculate the budget cost allowance (ie expected expenditure) for 20X6 assuming that 57,000 direct labour hours are worked.

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Solution (a) 80% level 90% level 100% level 48,000 hrs 54,000 hrs 60,000 hrs Rs Rs Rs Direct labour 1.8m 2.025m 2.25m Other variable costs Indirect labour 360,000 405,000 450,000 Consumable supplies 1.8m 2.03m 2.25m Canteen etc 1.3m 1.46m 1.62m Total variable costs (Rs. 109.58 per hour, W1) 5.26m 5.92m 6.57m Semi-variable costs (W2) 1.76m 1.88m 2m Fixed costs Depreciation (60,000 Rs. 30) 1.8m 1.8m 1.8m Maintenance (60,000 Rs. 20) 1.2m 1.2m 1.2m Insurance (60,000 Rs. 10) 0.6m 0.6m 0.6m Rates (60,000 Rs. 25) 1.5m 1.5m 1.5m Management salaries (60,000 Rs. 40) 2.4m 2.4m 2.4m Budgeted costs 14.52m 15.3m 16.07m WORKING W1 Total variable cost = direct labour + indirect labour + canteen + consumables = Rs. 45 + Rs. 27 + Rs. 37.5 = Rs. 109.58 W2 Using the high/low method: Rs Mn Total cost of 64,000 hours 2,080 Total cost of 40,000 hours 1,600 Variable cost of 24,000 hours 480 Variable cost per hour (Rs. 480,000/24,000) Rs. 20 Rs Mn Total cost of 64,000 hours 2,080 Variable cost of 64,000 hours ( Rs. 20) 1,280 Fixed costs 800 Semi-variable costs are calculated as follows. Rs Mn 60,000 hours (60,000 Rs. 20) + Rs. 800,000 = 2,000 54,000 hours (54,000 Rs. 20) + Rs. 800,000 = 1,880 48,000 hours (48,000 Rs. 20) + Rs. 800,000 = 1,760

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(b) The budget cost allowance for 57,000 direct labour hours of work would be as follows. Rs Mn Variable costs (57,000 Rs. 109.58) 6,246 Semi-variable costs (Rs. 8,000,000 + (57,000 Rs. 20)) 1,940 Fixed costs 7,500 15,686 Note that in each case the fixed costs remain the same when the level of activity changes and are not flexed. 7.7 The measure of activity in flexible budgets The preparation of a flexible budget requires an estimate of the way in which costs (and revenues) vary with the level of activity. Sales revenue will clearly vary with sales volume, and direct material costs (and often direct labour costs) will vary with production volume. In some instances, however, it may be appropriate to budget for overhead costs as mixed costs (part-fixed, part-variable) which vary with an 'activity' which is neither production nor sales volume. Taking production overheads in a processing department as an illustration, the total overhead costs will be partly fixed and partly variable. The variable portion may vary with the direct labour hours worked in the department, or with the number of machine hours of operation. The better measure of activity, labour hours or machine hours, may only be decided after a close analysis of historical results. Note: In an exam do not fall into the trap of flexing fixed costs. Do not forget that they remain unchanged regardless of the level of activity. Even if fixed overheads are initially expressed on a 'per unit' basis in a question, remember that once you have calculated the total fixed cost for a given activity level, it will remain unchanged when activity levels alter. The measure of activity used to estimate variable costs should satisfy certain criteria. Criteria Detail

Independent of variable factors other than its own volume For example, if labour hours are the measure of activity, the level of activity should be measured in labour hours, and not the labour cost of those hours (the latter being prone to the effect of a price change).

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Criteria Detail

Stable In this respect, a standard unit of output provides a better measure than actual units. For example, if total costs are assumed to vary with direct labour hours, it would be more appropriate to choose 'standard hours produced' as a measure of activity than 'actual hours worked' because the actual hours may have been worked efficiently or inefficiently, and the variations in performance would probably affect the actual costs incurred. 7.8 Flexible budgets and budgetary control A prerequisite of flexible budgeting is a knowledge of cost behaviour. The differences between the components of the fixed budget and the actual results are known as budget variances. Budgetary control is the practice of establishing budgets which identify areas of responsibility for individual managers (for example, production managers, purchasing managers and so on) and of regularly comparing actual results against expected results. The differences between actual results and expected results are called variances and these are used to provide a guideline for control action by individual managers.

Individual managers are held responsible for investigating differences between budgeted and actual results, and are then expected to take corrective action or amend the plan in the light of actual events. The wrong approach to budgetary control is to compare actual results against a fixed budget. Consider the following example. Tree manufactures a single product, the bough. Budgeted results and actual results for June are shown below.

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Budget Actual results Variance Production and sales of the bough (units) 2,000 3,000 Rs Rs Rs Sales revenue (a) 20,000 30,000 10,000 (F) Direct materials 6,000 8,500 2,500 (A) Direct labour 4,000 4,500 500 (A) Maintenance 1,000 1,400 400 (A) Depreciation 2,000 2,200 200 (A) Rent and rates 1,500 1,600 100 (A) Other costs 3,600 5,000 1,400 (A) Total costs (b) 18,100 23,200 5,100 Profit (a)–(b) 1,900 6,800 4,900 (F) Note. (F) denotes a favourable variance and (A) an adverse or unfavourable variance. Adverse variances are sometimes denoted as (U) for 'unfavourable'. (a) In this example, the variances are meaningless for purposes of control. Costs

were higher than budget because the volume of output was also higher; variable costs would be expected to increase above the budgeted costs. There is no information to show whether control action is needed for any aspect of costs or revenue. (b) For control purposes, it is necessary to know the following. (i) Were actual costs higher than they should have been to produce and sell 3,000 boughs? (ii) Was actual revenue satisfactory from the sale of 3,000 boughs? (iii) Has the volume of units made and sold varied from the budget favourably or adversely? Correct approach to budgetary control (a) Identify fixed and variable costs. (b) Produce a flexible budget using marginal costing techniques. In the previous example of Tree, let us suppose that we have the following information regarding cost behaviour. (a) Direct materials and maintenance costs are variable. (b) Although basic wages are a fixed cost, direct labour is regarded as variable in order to measure efficiency/productivity. (c) Rent and rates and depreciation are fixed costs. (d) Other costs consist of fixed costs of Rs. 1,600 plus a variable cost of Rs. 1 per unit made and sold.

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Now that the cost behaviour patterns are known, a budget cost allowance can be calculated for each item of expenditure. This allowance is shown in a flexible budget as the expected expenditure on each item for the relevant level of activity. The budget cost allowances are calculated as follows. (a) Variable cost allowances = original budgets (3,000 units/2,000 units) eg material cost allowance = Rs. 6,000 3/2 = Rs. 9,000 (b) Fixed cost allowances = as original budget (c) Semi-fixed cost allowances = original budgeted fixed costs + (3,000 units variable cost per unit) eg other cost allowances = Rs. 1,600 + (3,000 Rs. 1) = Rs. 4,600 The budgetary control analysis should be as follows. Fixed Flexible Actual Budget budget budget results variance (a) (b) (c) (b)–(c) Production & sales (units) 2,000 3,000 3,000 Rs Rs Rs Rs Sales revenue 20,000 30,000 30,000 0 Variable costs Direct materials 6,000 9,000 8,500 500 (F) Direct labour 4,000 6,000 4,500 1,500 (F) Maintenance 1,000 1,500 1,400 100 (F) Semi-variable costs Other costs 3,600 4,600 5,000 400 (A) Fixed costs Depreciation 2,000 2,000 2,200 200 (A) Rent and rates 1,500 1,500 1,600 100 (A) Total costs 18,100 24,600 23,200 1,400 (F) Profit 1,900 5,400 6,800 1,400 (F) We can analyse the above as follows. (a) In selling 3,000 units, the expected profit should have been the flexible budget profit of Rs. 5,400, not the fixed budget profit of Rs. 1,900. Instead, actual profit was Rs. 6,800 ie Rs. 1,400 more than we should have expected. One of the reasons for the improvement is that, given actual output and

sales of 3,000 units, costs were lower than expected (and sales revenue exactly as expected).

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Rs Direct materials cost variance 500 (F) Direct labour cost variance 1,500 (F) Maintenance cost variance 100 (F) Other costs variance 400 (A) Fixed cost variances Depreciation 200 (A) Rent and rates 100 (A) 1,400 (F) Profit was therefore increased by Rs. 1,400 because costs were lower than anticipated. (b) Another reason for the improvement in profit above the fixed budget profit is the sales volume. Tree sold 3,000 boughs instead of 2,000 boughs, with the following result. Rs Rs Sales revenue increased by 10,000 Variable costs increased by: direct materials 3,000 direct labour 2,000 Maintenance 500 variable element of other costs 1,000 Fixed costs are unchanged 6,500 Profit increased by 3,500 Profit was therefore increased by Rs. 3,500 because sales volumes increased. If management believes any variance is significant enough to warrant investigation, they will investigate to see whether any corrective action is necessary or whether the plan needs amending in the light of actual events.

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QUESTION Budgetary control The budgeted and actual results of Crunch for September were as shown here. The company uses a marginal costing system. There were no opening or closing inventories. Fixed budget Actual Sales and production 1,000 units 700 units Rs '000 Rs '000 Rs '000 Rs '000 Sales 20,000 14,200 Variable cost of sales Direct materials 8,000 5,200 Direct labour 4,000 3,100 Variable overhead 2,000 1,500 14,000 9,800 Contribution 6,000 4,400 Fixed costs 5,000 5,400 Profit/(loss) 1,000 (1,000) Required

Prepare a budget that will be useful for management control purposes. ANSWER We need to prepare a flexible budget for 700 units.

Budget Flexed budget

Actual Variances 1,000 units Per unit 700 units 700 units Rs '000 Rs '000 Rs '000 Rs '000 Rs '000 Sales 20,000 (20) 14,000 14,200 200 (F)

Variable costs Direct material 8,000 (8) 5,600 5,200 400 (F)Direct labour 4,000 (4) 2,800 3,100 300 (A)Variable production overhead 2,000 (2) 1,400 1,500 100 (A) 14,000 (14) 9,800 9,800 Contribution 6,000 4,200 4,400 200 (F)Fixed costs 5,000 (N/A) 5,000 5,400 400 (A)Profit/(loss) 1,000 (800) (1,000) 200 (A)Note that the differences between actual results (what revenues and costs were for 700 units) and the flexed budget (what revenues and costs should be for 700 units) have been noted in the right-hand column as variances.

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By flexing the budget in the exercise above we removed the effect on sales revenue of the difference between budgeted sales volume and actual sales volume. But there is still a variance of Rs. 200 (F). This means that the actual selling price must have been different to the budgeted selling price, resulting in a Rs. 200 (F) selling price variance. 7.9 Factors to consider when preparing flexible budgets The mechanics of flexible budgeting are, in theory, fairly straightforward. In practice, however, there are a number of points that must be considered before figures are flexed. (a) The separation of costs into their fixed and variable elements is not always straightforward. (b) Fixed costs may behave in a step-line fashion as activity levels increase/decrease. (c) Account must be taken of the assumptions upon which the original fixed budget was based. Such assumptions might include the constraint posed by limiting factors, the rate of inflation, judgements about future uncertainty, the demand for the organisation's products and so on. 7.10 Fixed and flexible budgets: a summary 7.10.1 Fixed and flexible budget differences A fixed budget will not change to take into account variations in production, sales or expenses actually experienced. A flexible budget can do this by adjusting expected total costs for the level of production achieved. The original budget based on a given volume is 'flexed' to the actual volume by analysing budgeted costs over budgeted volume and multiplying by actual units produced. 7.10.2 When fixed and flexible budgets are appropriate Both sorts of budget are used essentially for cost control, although they also provide management with a yardstick to measure achievement and may thus encourage the attainment of objectives. Fixed budgets are useful at the planning stage as they provide a common ground for the preparation of all the many types of budget. At the end of the period, actual results may be compared with the fixed budget and analysed for control. However, this analysis may be distorted by uncorrected errors underlying the estimates on which the fixed budget was constructed. A flexible budget may be needed at the planning stage to complement the master budget; output may be budgeted at a number of different possible levels for instance. During the period the flexible budget may then be updated to the actual level of activity and the results compared.

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As a result, flexible budgets assist management control by providing more dynamic and comparable information. Relying only on a fixed budget would give rise to massive variances; since forecast volume is very unlikely to be matched, the variances will contain large volume differences. Flexible budgets are more likely to pinpoint actual problem areas on which control may be exercised. 8 Feedback and feedforward control

The term 'feedback' is used to describe both the process of reporting back control information to management and the control information itself. Feedforward control is based on comparing original targets or actual results with a forecast of future results. 8.1 Feedback The term feedback is used to describe both the process of reporting back control information to management and the control information itself. In a business organisation, it is information produced from within the organisation (management control reports) with the purpose of helping management and other employees with control decisions.

(a) Single loop feedback, normally expressed as feedback, is the feedback of relatively small variations between actual and plan in order that corrective action can bring performance in line with planned results. This implies that the existing plans will not change. This type of feedback is associated with budgetary control and standard costing. (b) Double loop feedback, also known as higher-level feedback, ensures that plans, budgets, organisational structures and the control systems themselves are revised to meet changes in conditions. (c) Feedback will most often be negative: targets were missed and this was not what was required. It may, however, be positive: targets were missed, but other targets were hit which were better than those we were aiming at. Negative feedback would result in control action to get back onto target. Positive feedback means that the target should be moved.

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8.2 The feedback loop in the control cycle

Plan, target

or budget

Feedback of

information

Compare

actual results

with plan

Control

action

INPUT

RESOURCES

OPERATIONS

Measure

outputs

OUTPUTS

(eg actual output

revenues, costs)

Figure 6.1 Feedback loop in the control cycle The elements in the control cycle, illustrated in the diagram, are as follows. Step 1 Plans and targets are set for the future. These could be long-, medium- or short-term plans. Examples include budgets, profit targets and standard costs. Step 2 Plans are put into operation. As a consequence, materials and labour are used, and other expenses are incurred. Step 3 Actual results are recorded and analysed. Step 4 Information about actual results is fed back to the management concerned, often in the form of accounting reports. This reported information is feedback. Step 5 The feedback is used by management to compare actual results with the plan or targets (what should be or should have been achieved). Step 6 By comparing actual and planned results, management can then do one of three things, depending on how they see the situation. Management's potential reactions to divergences from planned performance (a) They can take controlling action. By identifying what has gone wrong, and then finding out why, corrective measures can be taken. (b) They can decide to do nothing. This could be the decision when actual results are going better than planned, or when poor results were caused by something which is unlikely to happen again in the future. (c) They can alter the plan or target if actual results are different from the plan or target, and there is nothing that management can do (or nothing, perhaps, that they want to do) to correct the situation.

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It may be helpful at this stage to relate the control system to a practical example, such as monthly sales. Step 1 A sales budget or plan is prepared for the year. Step 2 Management organises the business's resources to achieve the budget targets. Step 3 At the end of each month, actual results are reported back to

management. Step 4 Managers compare actual results against the plan. Step 5 Where necessary, they take corrective action to adjust the

workings of the system, probably by amending the inputs to the system; for example, salespeople might be asked to work longer hours or new price discounts might be implemented. This monthly sales example demonstrates how variance analysis is a form of feedback control. Variances can give negative or positive feedback. An adverse cost variance would be negative feedback and a favourable sales variance may well be seen as positive feedback. 8.3 Feedforward control Feedforward control is the 'forecasting of differences between actual and planned outcomes, and the implementation of action, before the event, to avoid such differences'.

Most control systems make use of a comparison between results of the current period (historical costs) and the planned results. Past events are therefore used as a means of controlling or adjusting future activity. A major criticism of this approach to control activity is that it is backward looking. Consider, however, a cash budget. This is used to identify likely peaks and troughs in cash balances, and if it seems probable that, say, a higher overdraft facility will be needed later in the year, control action will be taken in advance of the actual need, to make sure that the facility will be available. This is an example of feedforward control, that is, control based on comparing original targets or actual results with a forecast of future results. The 'information revolution', which has arisen from computer technology, management information systems theory and the growing use of quantitative techniques, has widened the scope for the use of this control technique. Forecasting models can be constructed which enable regular revised forecasts to be prepared about what is now likely to happen in view of changes in key variables (such as sales demand, wage rates and so on).

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If regular forecasts are prepared, managers will have both the current forecast and the original plan to guide their action. The original plan may or may not be achievable in view of the changing circumstances. The current forecast indicates what is expected to happen in view of these circumstances. Examples of control comparisons

Step 1 Current forecast versus plan. What action must be taken to get back to the plan, given the differences between the current forecast and the plan? Is any control action worthwhile? Step 2 If control action is planned, the current forecast will need to be amended to take account of the effects of the control action and a

revised forecast prepared. Step 3 The next comparison should then be revised forecast versus plan to determine whether the plan is now expected to be achieved. Step 4 A comparison between the original current forecast and the revised

forecast will show what the expected effect of the control action will be. Step 5 At the end of a control period, actual results will be analysed and two comparisons may be made.

Actual results versus the revised forecast. Why did differences between the two occur? Actual results so far in the year versus the plan. How close are actual results to the plan?

Step 6 At the same time, a new current forecast should be prepared, and the cycle of comparisons and control action may begin again. It is in this way that costs are constantly controlled and monitored. Another example of a system of feedforward control is target costing. This is when a business sets a target rate of return for its products or services. The results are forecast periodically and if it looks as if the target will not be met, action is taken to bring it back in line with target. 9 Disadvantages of budgeting There are various disadvantages of budgeting: • Time consuming & costly – a detailed budget process can take time and would involve the management team. • If management have not been involved, then they may accept the budget set. • The feeling that a budget is a punitive device – it can be viewed as a negative control by senior management.

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• The feeling of team spirit may disappear. • The acceptance of organisational goals and objectives could be limited. • Unachievable budgets could result if consideration is not given to local operating and political environments. • They can support 'empire building' by subordinates. • Managers may set 'easy' budgets to ensure that they are achievable. • Dissatisfaction, defensiveness and low morale amongst employees. It is hard for people to be motivated to achieve what may be perceived as unachievable targets. • Budgets being set with ‘budget slack’. Budget slack – this is where figures have been used that have a ‘built-in’ contingency – ‘just in case’. The impact of budget slack is that the budgets are not realistic. If all the management involved in the budget process have included and element of ‘budget slack’ then the impact of this means that budget set does not reflect what should be happening.

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Budgeting is a quantifiable plan of action for a specified time period. A budget might be a forecast, a means of allocating resources, a yardstick or a

target. The budget committee is the co-ordinating body in the preparation and administration of budgets. The manager responsible for preparing each budget should ideally be the manager responsible for carrying out the budget. The budget manual is a collection of instructions governing the responsibilities of persons and the procedures, forms and records relating to the preparation and use of budgetary data. The first task in the budgetary process is to identify the principal budget factor. This is also known as the key budget factor or limiting budget factor. The principal budget factor is the factor which limits the activities of an organisation. Functional/departmental budgets include budgets for sales, production, purchases and labour. A cash budget is a statement in which estimated future cash receipts and payments are tabulated in such a way as to show the forecast cash balance of a business at defined intervals. The usefulness of cash budgets is that they enable management to make any

forward planning decisions that may be needed, such as advising their bank of estimated overdraft requirements or strengthening their credit control procedures to ensure that customers pay more quickly. The master budget provides a consolidation of all the subsidiary budgets and normally consists of a budgeted income statement, budgeted statement of financial position and a cash budget. Linear regression analysis (the least squares method) is one technique for estimating a line of best fit. Once an equation for a line of best fit has been determined, forecasts can be made. As with all forecasting techniques, the results from regression analysis will not be wholly reliable. There are a number of factors which affect the reliability of forecasts made using regression analysis. One method of finding the trend is by the use of moving averages. Remember that when finding the moving average of an even number of results, a second moving average has to be calculated, so that trend values can relate to specific actual figures. Information for management is likely to be used for planning, control and

decision making.

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An objective is the aim or goal of an organisation (or an individual). Note that, in practice, the terms objective, goal and aim are often used interchangeably. A strategy is a possible course of action that might enable an organisation (or an individual) to achieve its objectives.

Anthony divides management activities into strategic planning, management control and operational control.

A management control system is a system which measures and corrects the performance of activities of subordinates in order to make sure that the objectives of an organisation are being met and the plans devised to attain them are being carried out. Information within an organisation can be analysed into the three levels assumed in Anthony's hierarchy: strategic, tactical and operational. Fixed budgets remain unchanged regardless of the level of activity; flexible

budgets are designed to flex with the level of activity. Comparison of a fixed budget with the actual results for a different level of activity is of little use for control purposes. Flexible budgets should be used to show what cost and revenues should have been for the actual level of activity. A prerequisite of flexible budgeting is a knowledge of cost behaviour. The differences between the components of the fixed budget and the actual results are known as budget variances. The term 'feedback' is used to describe both the process of reporting back control information to management and the control information itself. Feedforward control is based on comparing original targets or actual results with a forecast of future results. Budgeting is based on the current year's results plus an extra amount for estimated growth or inflation next year. It encourages slack and wasteful spending to creep into budgets. Seasonal variations are the difference between actual and trend figures (additive

model). An average of the seasonal variation for each time period within the cycle must be determined and then adjusted so that the total of the seasonal variations sums to zero. Deseasonalised data is often used by economic commentators.

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1 Budgets have a number of purposes. Fill in the key words which are missing from the statements below. (a) To ……………… the activities of different departments towards a single plan. (b) To ……………… targets to managers responsible for achieving them. (c) To establish a system of ……………………. by comparing budgeted and actual results. (d) To compel …………………. . 2 Which of the following is unlikely to be contained with a budget manual? A Organisational structures B Objectives of the budgetary process C Selling overhead budget D Administrative details of budget preparation 3 The factor which limits the activities of an organisation is known as: I The key budget factor III The principal budget factor II The limiting budget factor IV The main budget factor A I, II and IV C II and III B I and III D I, II and III 4 If the principal budget factor is sales demand, in which order would the following budgets be prepared? Material usage Material purchase Production Sales Cash

1st 2nd 3rd 4th 5th

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5 Match the following cash positions with the appropriate management action. Short-term surplus Increase payables Long-term surplus Replace/update non-current assets Short-term shortfall Issue share capital Long-term shortfall Increase receivables and inventory 6 Depreciation has an effect on net profit and is therefore included in a cash budget. True False 7 Which of the following are included in the master budget? I Budgeted income statement II Budgeted statement of financial position III Budgeted cash flow IV Functional budgets A I, II and III B II and III C II, III and IV D IV only 8 State the location of the moving averages when they are plotted against time. 9 In terms of management accounting, information is most likely to be used for: (1) ………………………. (2) ………………………. (3) ………………………. 10 A strategy is the aim or goal of an organisation. True False 11 State the main objective of the following organisations: A Profit-making B Non-profit seeking 12 List the three types of management activity identified by R N Anthony. (1) ………………………. (2) ………………………. (3) ……………………….

?

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13 Fill in the blanks. The material price variance is the difference between ……………………………… and ……………………………… The material usage variance is the difference between ……………………………… and ……………………………… 14 The sales volume variance is valued at the standard selling price per unit. True False 15 Match the following causes of variances to the appropriate variance.

Variances Causes (a) Favourable labour efficiency (b) Adverse sales volume (c) Adverse material price (d) Adverse selling price (e) Adverse fixed production overhead volume (f) Idle time

(1) Inexperienced staff in the purchasing department (2) Materials of higher quality than standard (3) Unexpected slump in demand (4) Production difficulties (5) Strike (6) Poor machine maintenance 16 Match the three pairs of interrelated variances. (a) Adverse selling price (e) Adverse materials price (b) Favourable labour rate (f) Favourable materials usage (c) Adverse materials usage (g) Adverse sales volume (d) Favourable sales volume (h) Idle time 17 The following information is available for Biscuit Co. Jan Feb Rs Rs Budgeted sales 60,000 80,000 Gross profit as a percentage of sales 40% 40% Closing trade payables as a percentage of cost of sales 50% 50% Opening inventory nil nil Closing inventory nil nil Note that all cost of sales are paid for on credit.

Identify the amount to be budgeted for supplier payments in February. A Rs. 10,500 C Rs. 24,500 B Rs. 14,000 D Rs. 42,000

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18 Jay Co produces a product called the Bee. There has been a surge in Bee sales as a result of an advertising campaign and so Jay Co is paying its staff overtime to build up the inventory levels. Labour hours per unit 3 Basic wage rate per hour Rs. 20 Overtime premium 25% Normal number of labour hours per month 340,000 hours Jay Co expects sales of 100,000 units in September and wants to have closing inventory at the end of September of 20,000 units. There will be no opening inventory on 1st September. Calculate the budgeted labour cost.

19 Fill in the blanks. When preparing a production budget, the quantity to be produced is equal to sales ………… opening inventory ………. closing inventory. 20 Incremental budgeting is widely used and is a particularly efficient form of budgeting.

True False 21 State the need for the sum of the seasonal variations to be zero. 22 State the important weakness of the additive model. 23 Define the term 'deseasonalised data'.

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1 (a) Co-ordinate (c) Control (b) Communicate (d) Planning 2 The answer is C. 3 The answer is D. 4 1st Sales 2nd Production 3rd Material usage 4th Material purchase 5th Cash 5 Short term surplus Increase payables Long-term surplus Replace/update non-current assets Short-term shortfall Issue share capital Long-term shortfall Increase receivables and inventory 6 False. Only cash flow items are included in cash budgets. Depreciation is not a cash flow and so is not included in a cash budget. 7 The answer is A. 8 Points should be plotted at the midpoint of the period to which they apply. 9 (1) Planning (2) Control (3) Decision making 10 False. This is the definition of an objective. A strategy is a possible course of action that might enable an organisation to achieve its objectives. 11 A Profit-making = maximise profits B Non-profit seeking = provide goods and services 12 (1) Strategic planning (2) Management control (3) Operational control

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13 The material price variance is the difference between what the material did cost and what it should have cost. The material usage variance is the difference between the standard cost of the material that should have been used and the standard cost of the material that was used. 14 False. It is valued at the standard profit margin per unit. 15 (a) (2) (d) (3) (b) (3) or (4) or (5) (e) (4) or (5) or (6) (c) (1) (f) (5) or (6) 16 (a) and (d) (b) and (c) (e) and (f) 17 The answer is D. Jan Feb Rs Rs Sales 60,000 80,000 Gross profit (@ 40%) 24,000 32,000 Cost of sales (sales – GP) 36,000 48,000 Closing trade payables (@ 50%) 18,000 24,000 Rs Feb opening payables 18,000 Increase in amounts owing (COS) 48,000 Feb closing payables (24,000) Amount paid in Feb 42,000 18 Rs. 7,300,000 Jay Co needs to produce 100,000 + 20,000 = 120,000 units in September. Labour hours required = 120,000 units × 3 hours = 360,000 hours Only 340,000 hours are usually worked so there will need to be overtime of 360,000 – 340,000 = 20,000 hours. Rs 360,000 hours at basic rate (× Rs. 20) 7,200,000 20,000 hours at premium (× Rs. 20 × 25%) 100,000 Budgeted labour cost 7,300,000 19 When preparing a production budget, the quantity to be produced is equal to sales

minus opening inventory plus closing inventory.

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20 True 21 Average seasonal variations are adjusted to sum to zero because variations around the basic trend line should cancel each other out and add up to zero. 22 An additive model has the important drawback that, when there is a steeply rising or a steeply declining trend, the moving average trend will either get ahead of or fall behind the real trend. 23 Deseasonalised data is data from which the seasonal variations have been removed, leaving a figure which might be taken as indicating the trend.

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A ABC method of stores control, 571 Abnormal gain, 199 Abnormal loss, 199 Absorption base, 111 Absorption costing, 257 Absorption costing and marginal costing compared, 257 Absorption of overheads, 110 Accounting rate of return (ARR)

method, 462 Additive model, 365 Administration overhead, 29 Allocation, 95 AND law, 498 Annuity, 469 Annuity factors, 470 Annuity tables, 469 Arithmetic mean of combined data, 508 Arithmetic mean of grouped data, 507 Arithmetic mean of ungrouped data, 505 Arithmetic mean, 505 Array, 513 Attainable standards, 285 AVCO, 595 Average inventory, 580 Avoidable costs, 44, 443 B Basic standard, 285 Batch, 173 Bill of materials, 163 Bin cards, 574 Blanket absorption rates, 114 Blanket overhead absorption rate, 114 Bonus schemes, 85 Breakeven chart, 426 Breakeven charts, 433 Breakeven point, 409 Budget, 333, 334 Budget committee, 335 Budget cost allowance, 381, 386 Budget manual, 336 Budget period, 335 Budget preparation, 335

Budget variance, 386 Budgetary control, 384 Budgeted income statement, 351 Budgeted statement of financial position, 351 Budgeting, 332 Budgets and standards compared, 287 Bulk discounts, 584 By-product, 238 C C/S ratio, 411, 412 Capital investment appraisal – net present value method, 473 Capital investment appraisal – payback method, 459, 462, 483 Cash budget, 344 Cash v profit, 475 Coefficient of determination, 65, 70 Coefficient of rank correlation, 66 Coefficient of variation, 521 Complementary outcomes, 495 Conditional events, 502 Conditional probability, 502 Conservatism, 540, 541 Contingency tables, 503 Continuous stocktaking, 572 Contract, 176 Contract accounts, 177 Contract costing, 176 Contribution, 260 Contribution breakeven chart, 410, 429 Contribution tables, 550 Control, 17, 372 Controllable cost, 45 Corporate planning, 14, 370 Correlation, 53, 60 Correlation and causation, 65 Correlation coefficient, 60 Correlation in a time series, 63 Cost accounting, 6 Cost accounts, 6 Cost behaviour, 34 Cost behaviour and decision making, 34 Cost behaviour and levels of activity, 34

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Cost behaviour assumptions, 43 Cost behaviour patterns, 35 Cost behaviour principles, 35 Cost of capital, 467, 473 Cost per service unit, 180 Cost plus pricing, 131, 166 Cost-volume-profit analysis (CVP),

408 Cumulative present value factors, 470 Cumulative weighted average pricing, 595 Current standards, 285 Curvilinear variable costs, 39 D Data, 8 Day-rate system, 78 Decision support information, 483 Decision-making, 18, 372 Delivery note, 567 Departmental absorption rates, 114 Departmental/functional budgets, 339 Dependent events, 502 Deseasonalisation, 368 Deteriorating inventory, 573 Direct expenses, 28 Direct labour efficiency variance,

294 Direct labour idle time variance,

296 Direct labour rate variance, 294 Direct labour total variance, 293 Direct material, 28 Direct material price variance, 291 Direct material total variance, 291 Direct material usage variance,

291 Direct wages, 28 Discounted cash flow (DCF), 473 Discounting, 466 Discounting formula, 467 Distribution overhead, 30 Double loop feedback, 390 E Economic Order Quantity (EOQ), 581 Effectiveness, 19, 374

Efficiency, 19, 374 EOQ (Economic Order Quantity), 581 Equivalent units, 215 Expected idle time, 297 Expenses, 27 F Feedback, 390, 391 Feedforward control, 392 FIFO, 591 FIFO (first in, first out) method, 221 Financial accounts, 4 Financial information, 12 Finished goods inventory budget, 338 First in, first out, 591 Fixed budget, 377 Fixed costs, 34, 35 Flexible budget, 377, 378 Focus groups, 541 Forecast, 334 Free inventory, 575 Full cost-plus pricing, 132 Function costing, 178 Functional budgets, 339 Functional costs, 27 G General rule of multiplication, 502 Goods received note (GRN), 567 GRN, 567 Group bonus scheme, 87 Grouped data, 518 Guaranteed minimum wage, 81 H High day-rate system, 83 Higher-level feedback, 390 High-low method, 43, 46, 51, 60, 357, 379 Holding costs, 577 I Ideal standard, 284 Idle time, 79 Idle time ratio, 80 Idle time variance, 296 Incentive schemes, 85 Incremental budgeting, 393

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Incremental costs, 44, 443 Independent events, 499 Indirect cost, 27 Indirect expenses, 29 Indirect materials, 29 Indirect wages, 29 Individual bonus schemes, 86 Information, 8 Internal rate of return (IRR) method – graphical approach, 477 International Accounting Standard 2 (IAS 2), 109, 259 Inventory codes, 576 Inventory control, 564, 578 Inventory control levels, 576, 578 Inventory control systems, 569 Inventory costs, 576 Inventory count, 572 Inventory discrepancies, 572 Inventory valuation, 589 IRR, 479, 482 IRR method of discounted cash

flow, 477 Issue of materials, 568 J Job, 160 Job cost cards, 162 Job cost information, 162 Job cost sheets, 162 Job costing, 160 Job costing and computerisation, 167 Job costing for internal services, 170 Joint costs, 238 Joint products, 238 Joint products and common costs, 232 K Key budget factor, 337 Key factor, 441 L Labour, 27 Labour budget, 338 Last in, first out, 593 Laws of probability, 494 Least squares method of linear regression analysis, 55, 353

LIFO, 593 Limiting factor, 441 Limiting budget factor, 337 Long-term strategic planning, 14,

370 M Machine usage budget, 338 Machinery user costs, 446 Management accounting, 7 Management accounts, 4 Management control, 19, 374 Management control system, 20, 375 Margin of safety, 415 Marginal costing, 256, 259, 379 Marginal costing and absorption costing compared, 257 Marginal costing operating statement, 310 Marginal costing principles, 128, 261 Marginal cost-plus pricing, 135 Market research, 540 Mark-up pricing, 135 Master budget, 351 Materials, 27 Materials codes, 576 Materials inventory budget, 338 Materials requisition note, 568 Materials returned note, 569 Materials returns, 568 Materials transfer note, 568 Materials transfers, 568 Materials usage budget, 338 Materials variances and opening and closing inventory, 292 Maximax basis, 547 Maximax criterion, 548 Maximin decision rule, 547 Maximum level, 579 Median, 513 Median of an ungrouped frequency distribution, 515 Minimax regret rule, 549 Minimum level, 578 Mixed costs, 39 Modal value, 511 Mode, 511 Mode from a histogram, 511 Motivation and budgets, 333

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Moving averages, 358 Multiplicative model, 366 Multi-product P/V charts, 436 Mutually exclusive outcomes, 497 Mutually exclusive projects, 464 N Negative correlation, 55 Negative feedback, 390 Net present value (NPV) method, 473 Non-controllable costs, 45 Non-financial information, 12 Non-linear variable costs, 39 Normal distribution, 525 Normal distribution tables, 527 Normal idle time, 297 Normal loss, 199 NPV, 473 O Objectives, 13, 369 Obsolete inventory, 573 Operating statements, 304 Operational control, 20, 374 OR law, 496 Order cycling method of stores control, 570 Ordering costs, 577 Ordering materials, 565 Over-absorption, 116 Overhead absorption, 110, 112, 122, 232 Overhead absorption rate, 114, 115 Overhead apportionment, 96 Overhead recovery, 110, 122 Overheads, 27, 94 Overtime, 28, 79, 88 Overtime premium, 78 P P/V graph, 430 P/V ratio, 410, 412 Pareto (80/20) distribution, 571 Partial correlation, 54 Payback period, 459 Pay-off tables, 545 Perfect correlation, 54 Performance standard, 284 Period costs, 33

Periodic stocktaking, 572 Perpetual inventory, 573 Perpetuity, 471 Piecework schemes, 81 Planning, 13, 17 Positive correlation, 55 Positive feedback, 390 Predetermined overhead absorption rate, 110 Present value of a perpetuity, 471 Present value of an annuity, 470 Present value tables, 468 Present values, 467 Principal budget factor, 337 Principles of discounted cash flow, 466 Probabilities, 542 Probability, 492 Probability distribution, 522 Probability of achieving the desired result, 494 Process costing, 196, 197 Process costing and closing work in progress, 215 Process costing and opening work in progress, 221 weighted average cost method, 228 Process costing framework, 198 Procurement costs, 577 Production, 29 Production budget, 338 Profit/volume (P/V) graph, 430 Profit/volume ratio, 410, 412 Project appraisal – payback method, 460 Proportional (multiplicative)

model, 366 Purchase order, 566 Purchase requisition, 565 Q Qualitative data, 541 Qualitative research, 541 Quantitative data, 541 R Rank correlation coefficient, 66 Raw materials purchases budget, 338 Receiving materials, 565

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Rectification costs, 165 Regression lines and time series, 57, 354 Regret, 549 Relevant cost, 44, 442, 446 Remuneration methods, 78 Reorder level, 578 Resource allocation, 334 Responsibility accounting, 333 Return on capital employed

(ROCE) method, 462 Return on investment (ROI)

method, 462 Risk, 538 Risk averse, 539 Risk neutral, 539 Risk preference, 539 Risk seeker, 539 Role of market research, 540 S Salaried labour, 84 Sales budget, 338 Sales variances – significance, 303 Sales variances, 301 Sales volume profit variance, 302 Scattergraph, 53 Scrap, 206 Seasonal variations, 364 Selling overhead, 29 Selling price variance, 301 Semi-fixed costs, 39 Semi-variable costs, 39 Separate absorption rates, 114 Service cost analysis, 181 Service cost analysis in service industry situations, 185 Service costing, 178 unit cost measures, 180 Shift premium, 79 Short-term tactical planning, 14, 371 Sigma , 507 Simple addition law, 496 Simple multiplication law, 498 Simple probability, 494 Single loop feedback, 390 Slow-moving inventories, 573

Split off point, 232 Standard cost, 281 Standard costing, 280, 283 Standard costing and new technology, 289 Standard Criticisms, 288 Standard deviation, 517 Standard deviation (for grouped data), 518 Standard deviation (for ungrouped data), 518 Standard operation sheet, 287 Standard product specification, 287 Standard resource requirements, 287 Step costs, 36 Step down method of reapportionment, 102 Stockout costs, 577 Storage of raw materials, 573 Stores ledger accounts, 574 Stores requisition, 568 Strategic information, 15, 376 Strategic planning, 19, 374 Strategy and organisational structure, 13, 370 Sunk cost, 444 T Tactical information, 16, 376 Target profit, 417, 418 Throughput accounting (TA), 441 Tied ranks, 67 Time work, 78 Transfers and returns of materials, 568 Two-bin system of stores control, 571 U Uncertain events, 538 Uncontrollable cost, 45 Under-/over-absorbed overhead account, 120, 149 Under-absorption, 116 Ungrouped data, 518 User costs, 446

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V Variable costing, 128 Variable costs, 35, 37 Variable overhead total variance, 298 Variable production overhead

efficiency variance, 299 Variable production overhead

expenditure variance, 299 Variable production overhead variances, 298 Variance, 290, 301, 517 Variance for grouped data, 517 Variance for ungrouped data, 517 Variances, 290, 384, 385, 388

Variances in a standard marginal costing system, 309 Venn diagrams, 495 W Wages control account, 147 Wages department, 80 Weighted average price, 595 Worst/most likely/best outcome estimates, 544 Z Z score, 530

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First edition 2019 ISBN 9781 5097 3120 6 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Published by BPP Learning Media Ltd BPP House, Aldine Place 142-144 Uxbridge Road London W12 8AA www.bpp.com/learningmedia The copyright in this publication is owned by BPP Learning Media Ltd. The publishers are grateful to the IASB for permission to reproduce extracts from the International Financial Reporting Standards including all International Accounting Standards, SIC and IFRIC Interpretations (the Standards). The Standards together with their accompanying documents are issued by: The International Accounting Standards Board (IASB) 30 Cannon Street, London, EC4M 6XH, United Kingdom. Email: info@ifrs.org Web: www.ifrs.org Disclaimer: The IASB, the International Financial Reporting Standards (IFRS) Foundation, the authors and the publishers do not accept responsibility for any loss caused by acting or refraining from acting in reliance on the material in this publication, whether such loss is caused by negligence or otherwise to the maximum extent permitted by law. Copyright © IFRS Foundation All rights reserved. Reproduction and use rights are strictly limited. No part of this publication may be translated, reprinted or reproduced or utilised in any form either in whole or in part or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage and retrieval system, without prior permission in writing from the IFRS Foundation. Contact the IFRS Foundation for further details. The IFRS Foundation logo, the IASB logo, the IFRS for SMEs logo, the "Hexagon Device", "IFRS Foundation", "eIFRS", "IAS", "IASB", "IFRS for SMEs", "IASs", "IFRS", "IFRSs", "International Accounting Standards" and "International Financial Reporting Standards", "IFRIC" "SIC" and "IFRS Taxonomy" are Trade Marks of the IFRS Foundation. Further details of the Trade Marks including details of countries where the Trade Marks are registered or applied for are available from the Licensor on request.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright holder. The contents of this book are intended as a guide and not professional advice and every effort has been made to ensure that the contents of this book are correct at the time of going to press by CA Sri Lanka, BPP Learning Media, the Editor and the Author. Every effort has been made to contact the copyright holders of any material reproduced within this publication. If any have been inadvertently overlooked, CA Sri Lanka and BPP Learning Media will be pleased to make the appropriate credits in any subsequent reprints or editions. We are grateful to CA Sri Lanka for permission to reproduce the Learning Outcomes and past examination questions, the copyright of which is owned by CA Sri Lanka, and to the Association of Chartered Certified Accountants and Chartered Institute of Management Accountants for use of past examination questions in which they hold the copyright. © BPP Learning Media Ltd 2019

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Introduction iii

Contents

Page Introduction iv Chapter features vi Learning outcomes vii Action verbs checklist xiv Business Level II – Management Accounting Part A Cost Accounting Chapter 1 Introduction to Management Accounting 3 Chapter 2 Cost Classification 25 Chapter 3 Accounting for Labour Costs 79 Chapter 4 Accounting for Overhead Costs 97 Chapter 5 Pricing 129 Chapter 6 Integrated Accounting 145 Chapter 7 Job, Batch, Contract and Service Costing 163 Chapter 8 Process Costing 199 Chapter 9 Marginal & Absorption Costing 259 Part B Planning and Controlling Chapter 10 Standard Costing and Variance Analysis 283 Chapter 11 Budgeting; Preparation and Control 329 Part C Decision Making Chapter 12 Short-Term Decision Making 405 Chapter 13 Long-Term Decision Making 459 Part D Risk and Uncertainty Chapter 14 Risk and Uncertainty 493 Part E Working Capital Management Chapter 15 Inventory Control 565 Index

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Business Level II – Management Accounting iv

Introduction

Business Level II – Management Accounting The Business II Level course module for Management Accounting aims to provide a firm understanding of fundamentals of cost and management accounting and a blended learning by coupling business mathematics relevant to the subject. Accordingly, Management Accounting covers a number of mathematical fundamentals and their application to cost and management accounting.

Syllabus structure

Main syllabus areas Weightings A. Cost Accounting 35% B. Planning and Controlling 20% C. Decision Making 25% D. Risk and Uncertainty 10% E. Working Capital Management 10% One of the key elements in examination success is practice. It is important that not only you fully understand the topics by reading carefully the information contained in this Study Text, but it is also vital that you practise the techniques and apply the principles that you have learned. In order to do this, you should: Work through all the examples provided within the chapters and review the solutions, ensuring that you understand them; Complete the progress test for each chapter. In addition, you should use the Practice and Revision Kit. These questions will provide you with excellent examination practice when you are in the revision phase of your studies.

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Introduction v

Pillar structure The Chartered Accountant Curriculum is structured around four progressively ascending levels of competency, namely, Business I, Business II, Corporate and Strategic Levels. Business Level II provides the fundamentals of accounting and harnesses the skills and professional values needed to mould a Certified Business Accountant. The Curriculum is also subdivided into specific subject areas or knowledge pillars and learning material is delivered to meet the knowledge requirements. These Knowledge Pillars focus on imparting the technical knowledge required of a competent CA and comprise of five pillars that focus on the following subject areas: Knowledge Pillar 1: Audit, Assurance and Ethics (AA&E) Knowledge Pillar 2: Financial Accounting and Reporting (FA&R) Knowledge Pillar 3: Performance Measurement and Risk (PM&R) Knowledge Pillar 4: Taxation and Law (T&L) Knowledge Pillar 5: Business Management and Strategy (BM&S)

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Business Level II – Management Accounting vi

Chapter features

Each chapter contains a number of helpful features to guide you through each topic. Topic list This tells you what you will be studying in the chapter. The topic items form the numbered headings within the chapter. Chapter introduction

The introduction puts the chapter topic into perspective and explains why it is important, both within your studies and within your practical working life. Learning Outcomes

The learning outcomes issued for the module by CA Sri Lanka are listed at the beginning of the chapter, with reference to the chapter section within which coverage will be found. Key terms

These are definitions of important concepts that you really need to know and understand before the exam. Examples These are illustrations of particular techniques or concepts with a worked solution or explanation provided immediately afterwards. Case study

Often based on real world scenarios and contemporary issues, these examples or illustrations are designed to enrich your understanding of a topic and add practical emphasis. Questions

These are questions that enable you to practise a technique or test your understanding. You will find the answer underneath the question. Formula to learn

These are the formula that you are required to learn for the exam. Section introduction

This summarises the key points to remember from each section. Chapter roundup This provides a recap of the key areas covered in the chapter. Progress Test Progress tests at the end of each chapter are designed to test your memory. Bold text Throughout the Study Text you will see that some of the text is in bold type. This is to add emphasis and to help you to grasp the key elements within a sentence or paragraph.

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Introduction

vii

Lear

ning

out

com

es

CA Sri Lanka'

s Learning out

comes for the

Module are se

t out on the fol

lowing pages.

They are cros

s-referenced t

o the chapter

in the Study T

ext where the

y are covere

d. Sy

llabu

s Ar

ea

Kno

wle

dge

Com

pone

nt

Lear

ning

Out

com

es

Spec

ific

Kno

wle

dge

Chap

ter

A. C

ost

Acco

unti

ng

1.1

Intr

oduc

tion

to

Cost

and

M

anag

emen

t Ac

coun

ting

1.1.1 Explain

the difference

between

the role of a m

anagement acc

ountant

and the financ

ial accountant

Definit

ions of manag

ement accoun

ting and

cost accountin

g, nature of m

anagement

accounting inf

ormation

1

1.1.2 Explain

the role of ma

nagement

accountant to

support plan

ning, contro

lling and decis

ion making

Objective and

scope of man

agement

accounting, po

licies and plan

s to achieve

desired object

ives of manag

ement, levels

of plannin

g and controll

ing (operation

al, manag

ement and co

rporate level)

1

1.

2 Co

st

Clas

sific

atio

n 1.2.1 Id

entify key com

ponents of

production co

st Compo

nents classifie

d under produ

ction and ser

vice cost

2

1.2.2 Explain

different cost

classifi

cations and id

entify differen

t cost ca

tegories

2

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Cost cl

assifications:

• by nature (

material, labo

ur, other cost

) • for

profit measure

ment and stoc

k valuati

on (direct cos

t, indirect cos

t, manufa

cturing cost an

d non-manufa

cturing cost, p

roduct cost,

periodic cost)

• by b

ehaviour, for

decision maki

ng and

controlling (v

ariable cost, fi

xed cost,

semi-variable

cost, relevan

t cost, irrelev

ant cost, contr

ollable cost, n

on-contro

llable cost)

1.2.3 Calculat

e appropriate c

ost estima

tions having i

dentified the

cost behavi

our Cost es

timation using

high-low meth

od, scatter

diagram and

regression me

thod, compu

te and interpr

et correlation

coeffici

ent, rank corre

lation 2

1.

3 La

bour

Cos

ts

1.3.1 Comput

e labour costs

using differe

nt remunerat

ion methods

Time-based pa

y (concept of o

vertime, idle

time), perform

ance-based pa

y, guaranteed

remun

eration, bonus

schemes

3

1.3.2 Comput

e labour cost f

or a produc

tion organisat

ion Direct

and indirect la

bour costs

3

1.

4 O

verh

ead

Cost

s 1.4.1 P

repare an ove

rhead cost

statement

Definition and

components u

nder overhead

cost, ov

erhead allocat

ion and

apportionmen

t, reapportionm

ent under

reciprocal serv

icing (repeate

d distribution

method

, elimination m

ethod)

4

1.4.2 Comput

e the full cost o

f produc

ts, services an

d activities

under absorp

tion costing a

nd margin

al costing

Treatment of d

irect and indir

ect costs in

ascertaining th

e full cost of a p

roduct

Overhead abso

rption (single

O.A.R, depart

mental O.A.R)

Over/u

nder absorptio

n of overhead

s 4

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1.

5 Pr

icin

g 1.5.1 A

pply cost infor

mation in

pricing decisio

ns Margin

al cost plus pr

icing and full c

ost pricing

to achieve sp

ecified targets

(eg, return

on investment

, margin, mark

-up) 5

1.

6 In

tegr

ated

Ac

coun

ting

1.6.1 E

xplain the inte

gration of cost

accoun

ts with the fin

ancial accoun

ting system

Explain the ad

vantages and

disadvantage

s of integ

rated account

ing 6

1.6.2 P

repare accoun

ts for inventor

y, labour

, overheads, w

ork-in-progre

ss, finishe

d goods flowi

ng up to incom

e statem

ent Invento

ry control a/c

s (material, wo

rk in progre

ss, finished go

ods), wages co

ntrol a/c, pr

oduction and n

on-production

overhe

ad control a/c

, accounting fo

r overhe

ad under abso

rption/over

absorption, co

st of sales con

trol a/c, incom

e statem

ent

6

1.

7 Sp

ecifi

c O

rder

Co

stin

g 1.7.1 C

ompute and a

ccount for the

costs o

f a specific ord

er using job

costing and ba

tch costing

Specific order

costing (job c

osting and ba

tch costing

) Charac

teristics of job

costing and b

atch costing

Job cos

t card Accoun

ting for jobs

7

1.7.2 Comput

e and account

for the

costs of a spec

ific order usin

g contrac

t costing

Contract costi

ng (characteri

stics, prepar

ation contract

accounts and

recognising p

rofits) 7

1.7.3 Comput

e the cost of a s

pecific order u

sing service co

sting Service

costing with

composite cos

t units Charac

teristics of a s

ervice vs prod

uct 7

1.

8 Pr

oces

s Co

stin

g1.8.1 Id

entify stages o

f a process and

accoun

t for process c

osts Losses

and gains, cos

t entries in pro

cess accoun

ts 8

1.8.2 Interpret

and apply the

concept

of equivalent

units of produ

ct costing Equiva

lent unit conc

ept for WIP, F

IFO method

and weighted

average meth

od for WIP

8

1.8.3 Comput

e the cost of jo

int produc

ts and by-pro

ducts Joint an

d by-product c

osting 8

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1.

9 M

argi

nal a

nd

Abso

rpti

on C

osti

ng1.9.1 C

ompute inven

tory value and

profit u

nder absorptio

n costing and

margin

al costing

Inventory valu

ation and pro

fit statement

under margin

al and absorp

tion costing

Arguments 'fo

r' and 'against

' each method;

marginal and

absorption co

sting 9

1.9.2 Prepare

reconciliation

for the

differences in

profit calcula

ted under

absorption co

sting and mar

ginal costing

system

Profit reconcil

iations

9

B. P

lann

ing

and

Cont

rolli

ng

2.1

Intr

oduc

tion

to

Stan

dard

Cos

ting

an

d Va

rian

ce

Anal

ysis

2.1.1 Explain

the importance

of standa

rd costing

Definitions an

d purposes of

standard

costing

Different type

s of standards

(ideal,

attainable and

current)

Preparation o

f the standard

cost card

10

2.1.2 Comput

e and interpre

t varianc

es related to s

ales and costs

Calculate and

interpret basi

c variances;

Cost variances

: material (tot

al, price and

usage) / labou

r (total, rate, e

fficiency and

idle time) / va

riable overhea

d (total,

expenditure an

d efficiency) v

ariances

Note: Material

variances with

raw material

stocks need to

be computed

Sales variance

s: sales price v

ariance/ sales

volume

contribution v

ariance

10

2.1.3 Prepare

a statement th

at reconc

iles budgeted c

ontribution

with the actua

l contribution

calcula

ted using mar

ginal costing

The use of var

iances to reco

ncile the

budgeted and

actual contrib

ution that has

been ca

lculated using

marginal costi

ng Accoun

ting for varian

ces in the inte

grated accoun

ting system

10

2.2

Budg

etin

g;

Prep

arat

ion

and

Cont

rol

2.2.1 Explain

how and why

organisations

prepare budg

ets Definit

ions and purp

oses of budge

ting, budget

preparation p

rocess (budge

t period,

budget centre

, budget comm

ittee, budget

manual, princ

ipal budget fa

ctor) 11

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2.2.2 P

repare functio

nal budgets

Functional bud

gets (sales, pro

duction,

material usag

e/purchases,

labour, overh

ead budget

s) 11

2.2.3 P

repare cash b

udgets and

explain the sol

utions for bud

geted cash de

ficits and surpl

uses in the

short and long

run Cash b

udget. Tools f

or short term

and long term

cash deficits

and surpluses

11

2.2.4 Explain

the master bu

dget Linkag

e between bu

dgeted incom

e statem

ent, balance s

heet and cash

flow statem

ent in the mas

ter budget

11

2.2.5 Calculat

e projected sa

les volume

s, revenue and

costs using

forecasting tec

hniques

Time series fo

recasting (reg

ression metho

d and mo

ving average m

ethod), adjust

ing for

seasonality (a

dditive and m

ultiplicative

methods)

11

2.2.6 Explain

feedback and

feed forwar

d controls and

their behavi

oural implicatio

ns Feed fo

rward vs feed

back control

11

2.2.7 Identify d

isadvantages o

f budget

ing including

budget slack

Disadvantage

s of budgeting

including

budget slack

11

2.2.8 Explain

budgeting at d

ifferent

levels of plann

ing of the orga

nisation Strateg

ic, tactical and

operational p

lanning

11

2.2.9 Prepare

and interpret

a flexible

budget and bu

dget variance

Fixed v

s flexible budg

et Budget

ary control sta

tement

11

C. D

ecis

ion

Mak

ing

3.1

Cost

-Vol

ume-

Prof

it A

naly

sis

3.1.1 Comput

e the contribut

ion from

products, serv

ices and activ

ities Concep

t of contributio

n and C:S ratio

12

3.1.2 Comput

e breakeven p

oint and

identify volum

e required for

a given

profit target

Single produc

t: breake

ven analysis /

target profit /

margin

of safety / bre

akeven charts

(traditional,

contribution, p

rofit-volume)

12

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3.

2 Si

ngle

Lim

itin

g Fa

ctor

Dec

isio

ns

3.2.1 Identify t

he optimum

production/sa

les mix for a s

ingle limitin

g factor scena

rio Limitin

g factor analy

sis (contributio

n per limitin

g factor) for a

multi-produc

t company

with one scarc

e resource

12

3.

3 Re

leva

nt

Cost

ing

3.3.1 Identify t

he relevant co

st for short-t

erm decision m

aking Releva

nt (opportunit

y cost, avoida

ble cost,

incremental c

ost) vs non-re

levant costs

(sunk cost, com

mitted cost, n

on-cash flow

cost, common

cost, notional c

osts) 12

3.3.2 Apply re

levant costing

to prepar

e a cost sheet

for decision

making

Relevant cost

of material, la

bour, variable

OH, fix

ed OH 12

3.

4 Lo

ng-T

erm

D

ecis

ion

Mak

ing

3.4.1 Explain

the purpose of

investm

ent appraisal

Objectives of i

nvestment app

raisals,

investment app

raisal process,

time value of

money

13

3.4.2 Comput

e the financia

l feasibility

using differen

t investment a

ppraisal

techniques

Investment app

raisal techniq

ues: Non-di

scounted cash

flow techniqu

es (accoun

ting rate of ret

urn , payback p

eriod) Time va

lue of money –

discounted cash

flow, perpetu

ity Discou

nted cash flow

techniques (d

iscounted

payback perio

d, NPV, IRR)

Working capita

l in investmen

t appraisals

NPV vs IRR

Non-financial f

actors in inve

stment

appraisals

13

D. R

isk

and

Unc

erta

inty

4.

1 In

trod

ucti

on

to R

isk

and

Unc

erta

inty

4.1.1 Explain

the concept of

risk and

uncertainty

Risk and unce

rtainty

14

4.

2 Ba

sic

Dec

isio

n-M

akin

g To

ols

Und

er R

isk

4.2.1 Calculat

e summary me

asures of

central tenden

cy and dispers

ion for

both grouped

and ungroupe

d data Arithm

etic mean, me

dian, mode, ra

nge, varianc

e, standard dev

iation and coe

fficient

of variation for

both ungroup

ed and

grouped data

14

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4.2.2 Demons

trate the use o

f probab

ility in decisio

n making

Probability (co

mplementary

law, addition

law and multi

plication law)

Normal distrib

ution 14

4.2.3 Analyse

outcomes usin

g the basic d

ecision tools u

nder risk

Maxi-max, max

i-min, mini-max

regret

criteria

Expected valu

e and pay off t

able Limitat

ions of expect

ed values

14

E. W

orki

ng

Capi

tal

Man

agem

ent

5.1

Mat

eria

l M

anag

emen

t 5.1.1 Il

lustrate the in

ventory contr

ol proces

s Invento

ry control ove

rview; orderin

g, purcha

sing, receiving

, storing and i

ssuing,

storing metho

ds; centralised

vs decent

ralised storing

, periodic vs pe

rpetual

stock taking

15

5.1.2 Calculat

e inventory re

lated costs fo

r a manufactur

ing organis

ation Purcha

sing cost, orde

ring cost, hold

ing cost,

stock-out cost

15

5.1.3 Calculat

e inventory co

ntrol levels a

nd EOQ

Inventory cont

rol levels (re-o

rder level,

maximum sto

ck level, minim

um stock leve

l) Econom

ic order quant

ity 15

5.1.4 Calculat

e the cost of iss

ued stocks

and closing in

ventory using

FIFO, L

IFO and weigh

ted average co

st method

s Issuing

and valuation

: FIFO method,

LIFO method

, weighted ave

rage cost meth

ods 15

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Business Level II – Management Accounting xiv

Action verbs checklist

Knowledge Process Verb List Verb Definitions

Define Describe exactly the nature, scope or meaning Draw Produce (a picture or diagram) Identify Recognise, establish or select after consideration List Write the connected items one below the other Relate To establish logical or causal connections

Tier – 1 Remember Recall important information

State Express something definitely or clearly Calculate/Compute Make a mathematical computation Discuss Examine in detail by argument showing different aspects, for the purpose of arriving at a conclusion Explain Make a clear description in detail revealing relevant facts Interpret Present in understandable terms or to translate Recognise To show validity or otherwise, using knowledge or contextual experience Record Enter relevant entries in detail

Tier – 2 Comprehension Explain important information

Summarise Give a brief statement of the main points (in facts or figures)

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Introduction xv

Knowledge Process Verb List Verb Definitions

Apply Put to practical use Assess Determine the value, nature, ability or quality Demonstrate Prove, especially with examples Graph Represent by means of a graph Prepare Make ready for a particular purpose Prioritise Arrange or do in order of importance Reconcile Make consistent with another

Tier – 3 Application Use knowledge in a setting other than the one in which it was learned/solve close-ended problems

Solve To find a solution through calculations and/or explanations Analyse Examine in detail in order to determine the solution or outcome Compare Examine for the purpose of discovering similarities Contrast Examine in order to show unlikeness or differences Differentiate Constitute a difference that distinguishes something

Tier – 4 Analysis Draw relations among ideas and to compare and contrast/solve open-ended problems Outline Make a summary of significant features

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Business Level II – Management Accounting xvi

Knowledge Process Verb List Verb Definitions

Advise Offer suggestions about the best course of action in a manner suited to the recipient Convince To persuade others to believe something using evidence and/or argument Criticise Form and express a judgment Evaluate To determine the significance by careful appraisal Recommend A suggestion or proposal as to the best course of action Resolve Settle or find a solution to a problem or contentious matter

Tier – 5 Evaluate Formation of judgments and decisions about the value of methods, ideas, people or products

Validate Check or prove the accuracy Compile Produce by assembling information collected from various sources Design Devise the form or structure according to a plan Develop To disclose, discover, perfect or unfold a plan or idea

Tier – 6 Synthesis Solve unfamiliar problems by combining different aspects to form a unique or novel solution Propose To form or declare a plan or intention for consideration or adoption

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Knowledge Component C Decision making 3.1 Cost-volume-profit analysis

3.2 Single limiting factor

decisions 3.3 Relevant costing

3.1.1 Compute the contribution from products, services and activities 3.1.2 Compute breakeven point and identify volume required for a given profit target 3.2.1 Identify the optimum production/sales mix for a single limiting factor scenario 3.3.1 Identify the relevant cost for short-term decision making 3.3.2 Apply relevant costing to prepare a cost sheet for decision making

INTRODUCTION In this chapter we cover breakeven analysis, which examines the relationships between costs, volumes produced and sold and profits. You should remember that one of the major assumptions underpinning breakeven analysis is that it can only be applied to one product or to a constant (fixed proportions) mix of products. We shall cover single product breakeven analysis but as most organisations produce and sell a range of products we are also going to look at what is known as multi-product breakeven analysis. We will see how to perform calculations such as the contribution to sales (C/S) ratio and the margin of safety, applied to multi-product situations.

C H

A P

T E

R

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CHAPTER CONTENTS

LEARNING OUTCOME1 Concept of contribution, C/S ratio and single product breakeven 3.1.1/3.1.22 Single product breakeven point, target profit and margin of safety 3.1.2/3.2.1

3 Breakeven charts 3.1.24 Contribution per limiting factor and optimum production mix decision with single limiting factor 3.2.15 Relevant vs non-relevant, including opportunity, avoidable, incremental, sunk, committed and common costs 3.3.1, 3.3.26 Relevant cost of material, labour, variable overheads and fixed overheads 3.3.1, 3.3.2

1 Concept of contribution, C/S ratio and single product

breakeven

Breakeven analysis or cost-volume-profit (CVP) analysis is the study of the interrelationships between costs, volume and profit at various levels of activity. The breakeven point occurs when there is neither a profit nor a loss and so fixed costs equal contribution. Despite the advantages of breakeven analysis, the technique has some serious limitations. 1.1 Contribution Cost-volume-profit analysis (CVP) is the 'study of the effects on future profit of changes in fixed cost, variable cost, sales price, quantity and mix'.

Contribution is fundamental to CVP analysis. As you know, contribution per unit is the difference between selling price per unit and variable costs per unit. The total contribution from the sales volume for a period can be compared with the fixed costs for the period. Any excess of contribution is profit; any deficit of contribution is a loss.

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1.2 Breakeven point The breakeven point is the 'level of activity at which there is neither profit nor loss'. The management of an organisation usually wishes to know the profit likely to be made if the aimed-for production and sales for the year are achieved. Management may also be interested to know the activity level at which there is neither profit nor loss. This is known as the breakeven point. The breakeven point (BEP) can be calculated arithmetically.

FORMULA TO LEARN Breakeven point = number of units of sale required to break even = total fixed costs/contribution per unit = contribution required to break even/contribution per unit

1.3 Example: breakeven point Expected sales 10,000 units at Rs. 8,000 = Rs. 80m Variable cost Rs. 5,000 per unit Fixed costs Rs. 21m Required

Compute the breakeven point. Solution The contribution per unit is (8K 5K) = Rs. 3,000 Contribution required to break even = fixed costs = Rs. 21m Breakeven point (BEP) = 21m ÷ 3,000 = 7,000 units In revenue, BEP = (7,000 Rs. 8,000) = Rs. 56m

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Sales above Rs. 56m will result in profit of Rs. 3,000 per unit of additional sales and sales below Rs. 56m will mean a loss of Rs. 3,000 per unit for each unit by which sales fall short of 7,000 units. In other words, profit will improve or worsen by the amount of contribution per unit. 7,000 units 7,001 units Rs '000 Rs '000 Revenue 56,000 56,008 Less variable costs 35,000 35,005 Contribution 21,000 21,003 Less fixed costs 21,000 21,000 Profit 0 (= break even) 3 1.4 Limitations of breakeven analysis Important limitations of breakeven analysis include the following. It can only apply to a single product or a single mix of a group of products. A breakeven chart may be time consuming to prepare. It assumes fixed costs are constant at all levels of output. It assumes that variable costs are the same per unit at all levels of output. It assumes that sales prices are constant at all levels of output. It assumes production and sales are the same (inventory levels are ignored). It ignores the uncertainty in the estimates of fixed costs and variable cost per unit. 1.5 Contribution/sales (C/S) ratio and breakeven arithmetic The contribution/sales (C/S) ratio, or profit/volume (P/V) ratio, is a measure of how much contribution is earned from each Rs. 1 of sales. At the breakeven point, there is no profit or loss and so sales revenue = total costs or total contribution = fixed costs. The target profit is achieved when sales revenue equals variable costs plus fixed costs plus profit. Therefore the total contribution required for a target profit = fixed costs + required profit.

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1.6 C/S ratio and breakeven point An alternative way of calculating the breakeven point to give an answer in terms of sales revenue and using the C/S ratio is as follows. FORMULA TO LEARN Breakeven point = sales revenue required to break even = Contribution required to break evenC/S ratio = Fixed costsC/S ratio

1.7 Example: C/S ratio In the example in Section 2.1 the C/S ratio is 38 = 37.5% Break even is where sales revenue equals 21m37.5% = Rs. 56m. At a price of Rs. 8,000 per unit, this represents 7,000 units of sales. The C/S ratio is a measure of how much contribution is earned from each Rs. 1 of sales. The C/S ratio of 37.5% in the above example means that for every Rs. 1 of sales, a contribution of Rs. 0.375 is earned. Thus, in order to earn a total contribution of Rs. 21m and if contribution increases by Rs. 0.375 per Rs. 1 of sales, sales must be: 10.375 Rs. 21m = Rs. 56m The C/S (contribution/sales) ratio is sometimes called the profit/volume or P/V ratio. QUESTION C/S ratio The C/S ratio of product W is 20%. IB, the manufacturer of product W, wishes to make a contribution of Rs. 50m towards fixed costs. Required If the selling price is Rs. 10,000 per unit, calculate the number of units of W that must be sold.

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ANSWER The number of units that must be sold is 25,000. WORKING Required contributionC/S ratio = Rs. 50m20%

1.8 Contribution/sales (C/S) ratio for multiple products The breakeven point in terms of sales revenue can be calculated as fixed costs/average C/S ratio. Any change in the proportions of products in the mix will change the contribution per mix and the average C/S ratio and hence the breakeven point. 1.9 Calculating the ratio An alternative way of calculating the breakeven point is to use the average contribution to sales (C/S) ratio for the standard mix. As you should already know, the C/S ratio is sometimes called the profit/volume ratio or P/V ratio. We can calculate the breakeven point of PL (see Section 4.1) as follows.

Step 1 Calculate revenue per mix = (5 7,000) + (1 15,000) = Rs. 50,000 Step 2 Calculate contribution per mix = Rs. 30,800 Step 3 Calculate average C/S ratio = (30,800/50,000) 100% = 61.6% Step 4 Calculate breakeven point (total) = fixed costs ÷ C/S ratio = Rs. 36m/0.616 = Rs. 58.442m (rounded)

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Step 5 Calculate revenue ratio of mix = (5 7,000) : (1 15,000) = 35:15, or 7:3 Step 6 Calculate breakeven sales M = Rs. 58.442m 7/10 = Rs. 40.909m (rounded) N = Rs. 58,442m 3/10 = Rs. 17.533m (rounded)

QUESTION C/S ratio for multiple products

Required

Calculate the breakeven sales revenue of products beta, gamma and delta (see Question above) using the approach shown above. ANSWER

Step 1 Calculate revenue per mix = (3 135K) + (4 165K) + (5 220K) = Rs. 2,165K Step 2 Calculate contribution per mix = Rs. 977.90K (from Question: breakeven point for multiple products) Step 3 Calculate average C/S ratio = (977.90/2,165) 100% = 45.17% Step 4 Calculate breakeven point (total) = fixed costs C/S ratio = 950m/0.4517 = Rs. 2,103.166m (rounded) Step 5 Calculate revenue ratio of mix = 405:660:1,100 or 81:132:220 Step 6 Calculate breakeven sales Breakeven sales of beta = 81/433 Rs. 2,103.166 = Rs. 393.433m Breakeven sales of gamma = 132/433 Rs. 2,103.166 = Rs. 641.150m Breakeven sales of delta = 220/433 Rs. 2,103.166 = Rs.1,068.583m

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Alternatively, you might be provided with the individual C/S ratios of a number of products. For example, if an organisation sells two products (A and B) in the ratio 2:5 and if the C/S ratio of A is 10% whereas that of B is 50%, the average C/S ratio is calculated as follows. Average C/S ratio = (2×10%)+(5×50%)2+5 = 38.6%

QUESTION Average C/S ratio TIM produces and sells two products, the MK and the KL. The organisation expects to sell 1 MK for every 2 KLs and have monthly sales revenue of Rs. 150m. The MK has a C/S ratio of 20% whereas the KL has a C/S ratio of 40%. Budgeted monthly fixed costs are Rs. 30m. Required

Calculate the budgeted breakeven sales revenue. ANSWER Average C/S ratio = (20% × 1) + (40% × 2)3 = 331/3% Sales revenue at the breakeven point = fixed costsC / S ratio = 30m/0.333 = Rs. 90m

The C/S ratio is a measure of how much contribution is earned from each Rs. 1 of sales of the standard mix. The C/S ratio of 331/3% in the question above means that for every Rs. 1 of sales of the standard mix of products, a contribution of Rs. 0.3333 is earned. To earn a total contribution of, say, Rs. 20m, sales revenue from the standard mix must therefore be: 1/0.3333 Rs. 20m = Rs. 60m QUESTION Using the C/S ratio Refer back to the information in the paragraph following Question: C/S ratio for multiple products. Suppose the organisation in question has fixed costs of Rs. 100m and wishes to earn total contribution of Rs. 200m. Required Calculate the level of revenue that must be achieved.

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ANSWER Sales revenue must be 1/0.386 Rs. 200m = Rs. 518.135m

1.10 Points to bear in mind Any change in the proportions of products in the mix will change the contribution per mix and the average C/S ratio and hence the breakeven point. (a) If the mix shifts towards products with lower contribution margins, the breakeven point (in units) will increase and profits will fall unless there is a corresponding increase in total revenue. (b) A shift towards products with higher contribution margins without a corresponding decrease in revenues will cause an increase in profits and a lower breakeven point. (c) If sales are at the specified level but not in the specified mix, there will be either a profit or a loss depending on whether the mix shifts towards products with higher or lower contribution margins. 2 Single product breakeven point, target profit and

margin of safety

The margin of safety is the difference in units between the budgeted sales volume and the breakeven sales volume. It is sometimes expressed as a percentage of the budgeted sales volume. Alternatively, the margin of safety can be expressed as the difference between the budgeted sales revenue and breakeven sales revenue, expressed as a percentage of the budgeted sales revenue. As well as being interested in the breakeven point, management may also be interested in the amount by which actual sales can fall below anticipated sales without a loss being incurred. This is the margin of safety. The margin of safety 'indicates the percentage by which forecast revenue exceeds or falls short of that required to break even'.

FORMULA TO LEARN

Margin of safety = Projected sales breakeven point 100Projected sales

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2.1 Example: Margin of safety MM LLC makes and sells a product which has a variable cost of Rs. 30,000 and which sells for Rs. 40,000. Budgeted fixed costs are Rs. 70m and budgeted sales are 8,000 units. Required

Calculate the breakeven point and the margin of safety. Solution (a) Breakeven point = Total fixed costsContribution per unit =

70m(40K 30K) = 7,000 units (b) Margin of safety = 8,000 7,000 units = 1,000 units which may be expressed as 1,000 units 100%8,000 units = 12½% of budget (c) The margin of safety indicates to management that actual sales can fall short of budget by 1,000 units or 12½% before the breakeven point is reached and no profit at all is made. = Rs. 250m

Number of units = Rs. 250m Rs. 10,000 = 25,000 2.2 Margin of safety for multiple products The margin of safety for a multi-product organisation is equal to the budgeted sales in the standard mix less the breakeven sales in the standard mix. It may be expressed as a percentage of the budgeted sales. 2.3 Calculation of margin of safety It should not surprise you to learn that the calculation of the margin of safety for multiple products is exactly the same as for single products, but we use the standard mix. The easiest way to see how it's done is to look at an example, which we do in this section. 2.3.1 Example: Margin of safety for multiple products BA produces and sells two products. The W sells for Rs. 8,000 per unit and has a total variable cost of Rs. 3,800 per unit, while the R sells for Rs. 14,000 per unit and has a total variable cost of Rs. 4,200. For every five units of W sold, six units of R are sold. BA's fixed costs are Rs. 43.89m per period.

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Budgeted sales revenue for next period is Rs. 74.4m, in the standard mix. Required

Calculate the margin of safety in terms of sales revenue and also as a percentage of budgeted sales revenue. Solution To calculate the margin of safety we must first determine the breakeven point. Step 1 Calculate contribution per unit W R Rs '000 per unit Rs '000 per unit Selling price 8.00 14.00 Variable cost 3.80 4.20 Contribution 4.20 9.80 Step 2 Calculate contribution per mix = (4.20K 5) + (9.80K 6) = Rs. 79.80K Step 3 Calculate the breakeven point in terms of the number of mixes = fixed costs/contribution per mix = 43,890K/79.80K = 550 mixes Step 4 Calculate the breakeven point in terms of the number of units of the

products = (550 5) 2,750 units of W and (550 6) 3,300 units of R Step 5 Calculate the breakeven point in terms of revenue = (2,750 8K) + (3,300 14K) = Rs. 22m of W and Rs. 46.2m of R = Rs. 68.2m in total Step 6 Calculate the margin of safety = budgeted sales – breakeven sales = Rs. 74.4m – Rs. 68.2m = Rs. 6.2m sales in total, in the standard mix Or, as a percentage = ((Rs. 74.4m – Rs. 68.2m)/Rs. 74.4m) 100% = 8.3% of budgeted sales

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2.4 Target profits A similar formula may be applied where a company wishes to achieve a certain profit during a period. To achieve this profit, sales must cover all costs and leave the required profit. FORMULA TO LEARN The target profit is achieved when S = V + F + P where S = sales revenue V = variable costs F = fixed costs P = required profit Subtracting V from each side of the equation, we get S V = F + P, so total contribution required = F + P

2.4.1 Example: Target profits RB Co makes and sells a single product, for which variable costs are as follows. Rs '000 Direct materials 10 Direct labour 8 Variable production overhead 6 24 The sales price is Rs. 30,000 per unit, and fixed costs per annum are Rs. 68m. The company wishes to make a profit of Rs. 16m per annum. Required

Calculate the sales required to achieve this profit. Solution Required contribution = fixed costs + profit = Rs. 68m + Rs. 16m = Rs. 84m Required sales can be calculated in one of two ways. (a) Required contributionContribution per unit =

84m(30K 24K) = 14,000 units, or Rs. 420m in revenue

(b) Required contributionC/S ratio = 84m20%* = Rs. 420m of revenue, or 14,000 units. * C/S ratio = 30K 24K30K = Rs. 6KRs. 30K = 0.2 = 20%.

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QUESTION Target profits SLB LLC wishes to sell 14,000 units of its product, which has a variable cost of Rs. 15,000 to make and sell. Fixed costs are Rs. 47m and the required profit is Rs. 23m. Required

Calculate the required sales price per unit. ANSWER The required sales price per unit is Rs. 20,000. WORKING Required contribution = fixed costs + profit = Rs. 47m + Rs. 23m = Rs. 70m Required sales = 14,000 units Rs '000 Required contribution per unit sold 5 Variable cost per unit 15 Required sales price per unit 20

2.5 Variations on breakeven and profit target calculations You may come across variations on breakeven and profit target calculations in which you will be expected to consider the effect of altering the selling price, variable cost per unit or fixed cost. 2.5.1 Example: Change in selling price ST Cakes LLC bakes and sells a single type of cake. The variable cost of production is Rs. 150 and the current sales price is Rs. 250. Fixed costs are Rs. 2.6m per month, and the annual profit for the company at current sales volume is Rs. 36m. The volume of sales demand is constant throughout the year. The sales manager wishes to raise the sales price to Rs. 290 per cake, but considers that a price rise will result in some loss of sales. Required

Calculate the minimum volume of sales required each month to raise the price to Rs. 290.

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Solution The minimum volume of demand which would justify a price of Rs. 290m is one which would leave total profit at least the same as before, ie Rs. 3m per month. Required profit should be converted into required contribution, as follows. Rs Mn Monthly fixed costs 2.6 Monthly profit, minimum required 3.0 Current monthly contribution 5.6 Contribution per unit (250 150) = 100 Current monthly sales = 56,000 cakes The minimum volume of sales required after the price rise will be an amount which earns a contribution of Rs. 5.6m per month, no worse than at the moment. The contribution per cake at a sales price of Rs. 290 would be Rs. 140. Required sales = Required contributionContribution per unit = 5.6m140 = 40,000 cakes per month. 2.5.2 Example: Change in production costs CB LLC makes a product which has a variable production cost of Rs. 8,000 and a variable sales cost of Rs. 2,000 per unit. Fixed costs are Rs. 40m per annum, the sales price per unit is Rs. 18,000 and the current volume of output and sales is 6,000 units. The company is considering whether to hire an improved machine for production. Annual hire costs would be Rs. 10m and it is expected that the variable cost of production would fall to Rs. 6,000 per unit. Required (a) Calculate the number of units that must be produced and sold to achieve the same profit as is currently earned, if the machine is hired. (b) Calculate the annual profit with the machine if output and sales remain at 6,000 units per annum. Solution The current unit contribution is (18K (8K + 2K)) = Rs. 8,000 (a) Rs Mn Current contribution (6,000 Rs. 8K) 48 Less current fixed costs 40 Current profit 8

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With the new machine fixed costs will go up by Rs. 10m to Rs. 50m per annum. The variable cost per unit will fall to (6K + 2K) = Rs. 8,000 and the contribution per unit will be Rs. 10,000. Rs Mn Required profit (as currently earned) 8 Fixed costs 50 Required contribution 58 Contribution per unit = Rs. 10,000 Sales required to earn Rs. 8m profit = 5,800 units (b) If sales are 6,000 units Rs Mn Rs Mn Sales (6,000 Rs. 18K) 108 Variable costs: production (6,000 Rs. 6K) 36 sales (6,000 Rs. 2K) 12 48 Contribution (6,000 Rs. 10K) 60 Less fixed costs 50 Profit 10 Alternative calculation Rs Mn Profit at 5,800 units of sale (see (a)) 8 Contribution from sale of extra 200 units ( Rs. 10K) 2 Profit at 6,000 units of sale 10

2.6 More applications of breakeven arithmetic It may be clear by now that, given no change in fixed costs, total profit is maximised when the total contribution is at its maximum. Total contribution in turn depends on the unit contribution and on the sales volume. An increase in the sales price will increase unit contribution, but sales volume is likely to fall because fewer customers will be prepared to pay the higher price. A decrease in sales price will reduce the unit contribution, but sales volume may increase because the goods on offer are now cheaper. The optimum combination of sales price and sales volume is arguably the one which maximises total contribution. 2.6.1 Example: Profit maximisation C LLC has developed a new product which is about to be launched on to the market. The variable cost of selling the product is Rs. 12,000 per unit. The marketing department has estimated that at a sales price of Rs. 20,000, annual demand would be 10,000 units.

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However, if the sales price is set above Rs. 20,000, sales demand would fall by 500 units for each Rs. 500 increase above Rs. 20,000. Similarly, if the price is set below Rs. 20,000 demand would increase by 500 units for each Rs. 500 stepped reduction in price below Rs. 20,000. Required

Calculate the price which would maximise C Co's profit in the next year. Solution At a price of Rs. 20,000 per unit, the unit contribution would be (20K 12K) = Rs. 8,000. Each Rs. 500 increase (or decrease) in price would raise (or lower) the unit contribution by Rs. 500. The total contribution is calculated at each sales price by multiplying the unit contribution by the expected sales volume.

Unit price Unit contribution Sales volume Total

contribution Rs '000 Rs '000 Units Rs '000 20.00 8.00 10,000 80,000 (a) Reduce price 19.50 7.50 10,500 78,750 19.00 7.00 11,000 77,000 (b) Increase price 20.50 8.50 9,500 80,750 21.00 9.00 9,000 81,000 21.50 9.50 8,500 80,750 22.00 10.00 8,000 80,000 22.50 10.50 7,500 78,750 The total contribution would be maximised, and therefore profit maximised, at a sales price of Rs. 21,000 per unit, and sales demand of 9,000 units. QUESTION Breakeven point BB LLC manufactures a product which has a selling price of Rs. 20,000 and a variable cost of Rs. 10,000 per unit. The company incurs annual fixed costs of Rs. 29m. Annual sales demand is 9,000 units. New production methods are under consideration, which would cause a Rs. 1m increase in fixed costs and a reduction in variable cost to Rs. 9,000 per unit. The new production methods would result in a superior product and would enable sales to be increased to 9,750 units per annum at a price of Rs. 21,000 each. Required

Calculate the breakeven output level if the change in production methods were to take place.

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ANSWER Current Revised Difference Rs '000 Rs '000 Selling price 20 21 Variable costs 10 9 Contribution per unit 10 12 Fixed costs Rs. 29m Rs. 30m Breakeven point (units) 2,900 2,500 400 lowerBreakeven point (BEP) = Total fixed costsContribution per unit Current BEP = 29m10K = 2,900 units Revised BEP = 30m12K = 2,500 units

QUESTION Breakeven point percentages CH LLC produces a single product and the following information is available. Rs '000 Selling price per unit 28 Variable cost per unit 13 Fixed overheads 105,000 The breakeven point was calculated using these figures but management have decided that the variable cost and selling price will rise by 1.9% and 5% respectively. Required

Calculate the breakeven point when the new cost and price are taken into account. ANSWER Now Revised Rs '000 Rs '000 Selling price 28 29.40 Variable cost 13 13.25 Contribution 15 16.15 Breakeven volume 105m/15K = 7,000 105m/16.15K = 6,500 Decrease in breakeven volume = (7,000 – 6,500)/7,000 = 7.14%

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2.7 Target profits for multiple products The number of mixes of products required to be sold to achieve a target profit is calculated as (fixed costs + required profit)/contribution per mix. 2.8 The formula for target profits At breakeven point there is no profit – that is: Contribution = fixed costs Suppose an organisation wishes to achieve a certain level of profit during a period. To achieve this profit, contribution must cover fixed costs and leave the required profit. So total contribution required = fixed costs + required profit Once we know the total contribution required we can calculate the sales revenue of each product needed to achieve a target profit. The method is similar to the method used to calculate the breakeven point. FORMULA TO LEARN The number of mixes of products required to be sold to achieve a target profit is calculated as (fixed costs + required profit)/contribution per mix. 2.8.1 Example: Target profits for multiple products An organisation makes and sells three products, F, G and H. The products are sold in the proportions F:G:H = 2:1:3. The organisation's fixed costs are Rs. 80m per month and details of the products are as follows.

Product Selling price Variable cost Rs '000 per unit Rs '000 per unit F 22 16 G 15 12 H 19 13

Required The organisation wishes to earn a profit of Rs. 52m next month. Calculate the required sales value of each product in order to achieve this target profit.

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Solution

Step 1 Calculate contribution per unit F G H Rs '000 per unit Rs '000 per unit Rs '000 per unit Selling price 22 15 19 Variable cost 16 12 13 Contribution 6 3 6 Step 2 Calculate contribution per mix = (6K 2) + (3K 1) + (6K 3) = Rs. 33K Step 3 Calculate the required number of mixes = (fixed costs + required profit)/contribution per mix = (80m + 52m)/33K = 4,000 mixes Step 4 Calculate the required sales in terms of the number of units of the products and sales revenue of each product

Sales Selling revenue

Product price required Units Rs '000 per unit Rs MnF 4,000 2 8,000 22 176 G 4,000 1 4,000 15 60 H 4,000 3 12,000 19 228 Total 464 The sales revenue of Rs. 464m will generate a profit of Rs. 52m if the products are sold in the mix 2:1:3. Alternatively, the C/S ratio could be used to determine the required sales revenue for a profit of Rs. 52m. The method is again similar to that demonstrated earlier when calculating the breakeven point. 2.8.2 Example: Using the C/S ratio to determine the required sales We'll use the data from the example above. Step 1 Calculate revenue per mix = (2 22K) + (1 15K) + (3 19K) = Rs. 116K Step 2 Calculate contribution per mix = Rs. 33K (from Solution above)

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Step 3 Calculate average C/S ratio = (33K/116K) 100% = 28.45% Step 4 Calculate required total revenue = required contribution C/S ratio = (80m + 52m) 0.2845 = Rs. 463.972m Step 5 Calculate revenue ratio of mix = (2 22K) : (1 15K) : (3 19K) = 44:15:57 Step 6 Calculate required sales Required sales of F = 44/116 Rs. 463.972m = Rs. 175.989m Required sales of G = 15/116 Rs. 463.972m = Rs. 59.996m Required sales of H = 57/116 Rs. 463.972m = Rs. 227.986m Which, allowing for rounding, is the same answer as calculated in the first example.

3 Breakeven charts

The breakeven point can also be determined graphically using a breakeven chart. A contribution breakeven chart depicts variable costs, so that contribution can be read directly from this chart. The profit/volume (P/V) graph is a variation of the breakeven chart and illustrates the relationship of profit to sales volume. 3.1 Breakeven charts A breakeven chart is a chart that indicates approximate profit or loss at different levels of sales volume within a limited range. A breakeven chart has the following axes. A horizontal axis showing the sales/output (in value or units) A vertical axis showing R for sales revenues and costs

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3.1.1 Lines on a breakeven chart The following lines are drawn on the breakeven chart. (a) The sales line (i) Starts at the origin (ii) Ends at the point signifying expected sales (b) The fixed costs line (i) Runs parallel to the horizontal axis (ii) Meets the vertical axis at a point which represents total fixed costs (c) The total costs line (i) Starts where the fixed costs line meets the vertical axis (ii) Ends at the point which represents anticipated sales on the horizontal axis and total costs of anticipated sales on the vertical axis The breakeven point is the intersection of the sales line and the total costs line. The distance between the breakeven point and the expected (or budgeted) sales, in units, indicates the margin of safety. 3.1.2 Example: A breakeven chart The budgeted annual output of a factory is 120,000 units. The fixed overheads amount to Rs. 40m and the variable costs are Rs. 500 per unit. The sales price is Rs. 1,000 per unit. Required Construct a breakeven chart showing the current breakeven point and profit earned up to the present maximum capacity. Solution We begin by calculating the profit at the budgeted annual output. Rs Mn Sales (120,000 units) 120 Variable costs 60 Contribution 60 Fixed costs 40 Profit 20 The breakeven chart is shown on the following page.

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The chart is drawn as follows. (a) The vertical axis represents money (costs and revenue) and the horizontal axis represents the level of activity (production and sales). (b) The fixed costs are represented by a straight line parallel to the horizontal axis (in our example, at Rs. 40m). (c) The variable costs are added 'on top of' fixed costs, to give total costs. It is assumed that fixed costs are the same in total and variable costs are the same per unit at all levels of output. The line of costs is therefore a straight line and only two points need to be plotted and joined up. Perhaps the two most convenient points to plot are total costs at zero output, and total costs at the budgeted output and sales. (i) At zero output, costs are equal to the amount of fixed costs only, Rs. 40m, since there are no variable costs. (ii) At the budgeted output of 120,000 units, costs are Rs. 100m. Rs Mn Fixed costs 40 Variable costs (120,000 Rs. 500) 60 Total costs 100 (d) The sales line is also drawn by plotting two points and joining them up. (i) At zero sales, revenue is nil. (ii) At the budgeted output and sales of 120,000 units, revenue is Rs. 120m.

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Figure 9.1

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3.1.3 Interpreting the breakeven chart

The breakeven point is where total costs are matched exactly by total revenue. From the chart, this can be seen to occur at output and sales of 80,000 units, when revenue and costs are both Rs. 80m. This breakeven point can be proved mathematically as: Required contribution (= fixed costs)Contribution per unit = Rs. 40m500 = 80,000 units The margin of safety can be seen on the chart as the difference between the budgeted level of activity and the breakeven level. 3.1.4 The value of breakeven charts Breakeven charts are used as follows. To plan the production of a company's products To market a company's products To give a visual display of breakeven arithmetic 3.2 The contribution breakeven chart The main problem with the traditional breakeven chart is that it is not possible to read contribution directly from the chart. The contribution breakeven chart remedies this by drawing the variable cost line instead of the fixed cost line. A contribution breakeven chart for the example above would include the variable cost line passing through the origin and the total variable cost of Rs. 60m for 120,000 units. The contribution breakeven chart is shown below.

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Contribution breakeven chart

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Figure 9.2 If you look back at the breakeven chart above you will see that the breakeven point is the same, but that the budgeted contribution can now be read more easily from the chart. 3.3 The profit/volume (P/V) graph 3.3.1 Construction of a P/V graph A P/V graph is constructed as follows (look at the chart in the example that follows as you read the explanation). (a) 'P' is on the y axis and actually comprises not only 'profit' but contribution to profit (in monetary value), extending above and below the x axis with a zero point at the intersection of the two axes, and the negative section below the x axis representing fixed costs. This means that at zero production, the firm is incurring a loss equal to the fixed costs. (b) 'V' is on the x axis and comprises either volume of sales or value of sales (revenue).

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(c) The profit/volume line is a straight line drawn with its starting point (at zero production) at the intercept on the y axis representing the level of fixed costs, and with a gradient of contribution/unit (or the C/S ratio if sales value is used rather than units). The P/V line will cut the x axis at the breakeven point of sales volume. Any point on the P/V line above the x axis represents the profit to the firm (as measured on the vertical axis) for that particular level of sales. 3.3.2 Example: P/V graph Let us draw a P/V graph for our example above. At sales of 120,000 units, total contribution will be 120K (1K – 0.5K) = Rs. 60m and total profit will be Rs. 20m.

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Figure 9.3 3.3.3 The advantage of the P/V graph (a) If the budgeted selling price of the product in our example is increased to Rs. 1,200, with the result that demand drops to 105,000 units despite additional fixed costs of Rs. 10m being spent on advertising, we could add a line representing this situation to our P/V chart. (b) At sales of 105,000 units, contribution will be 105K (1,200 – 500) = Rs. 73.5m and total profit will be Rs. 23.5m (fixed costs being Rs. 50m).

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(c) The diagram shows that if the selling price is increased, the breakeven point occurs at a lower level of sales volume (71,429 units instead of 80,000 units), although this is not a particularly large decrease when viewed in the context of the projected sales volume. It is also possible to see that for sales above 50,000 units, the profit achieved will be higher (and the loss achieved lower) if the price is Rs. 1,200. For sales volumes below 50,000 units the first option will yield lower losses. (d) The P/V graph is the clearest way of presenting such information; two conventional breakeven charts on one set of axes would be very confusing. (e) Changes in the variable cost per unit or in fixed costs at certain activity levels can also be incorporated easily into a P/V graph. The profit or loss at each point where the cost structure changes should be calculated and plotted on the graph so that the P/V line becomes a series of straight lines. (f) For example, suppose that in our example, at sales levels in excess of 120,000 units the variable cost per unit increases to Rs. 600 (perhaps because of overtime premiums that are incurred when production exceeds a certain level). At sales of 130,000 units, contribution would therefore be 130K (1,000 – 600) = Rs. 52m and total profit would be Rs. 12m. P/V graph (2)

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30

20

10PROFIT

BREAKEVEN

10

20

30

40

50

LOSS

Breakeven point 2

Breakeven point 1

105 120

Sales volume

Rs Mn (units)

x

x

x

x

Figure 9.4

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40

20

Breakeven point

Fixedcosts

BREAKEVEN

LOSS

PROFIT

Profit/loss

Rs MnP/V graph (3)

Sales volume(units)

10

10

20

30

120,000 130,000

Figure 9.5 3.4 Breakeven charts Breakeven charts for multiple products can be drawn if a constant product sales mix is assumed. The P/V chart can show information about each product individually. 3.4.1 Breakeven charts A very serious limitation of breakeven charts is that they can show the costs, revenues, profits and margins of safety for a single product only, or at best for a single 'sales mix' of products. Breakeven charts for multiple products can be drawn if a constant product sales mix is assumed. For example, suppose that FA sells three products, X, Y and Z, which have variable unit costs of Rs. 3,000, Rs. 4,000 and Rs. 5,000 respectively. The sales price of X is Rs. 8,000, the price of Y is Rs. 6,000 and the price of Z is Rs. 6,000. Fixed costs per annum are Rs. 10m. A breakeven chart cannot be drawn, because we do not know the proportions of X, Y and Z in the sales mix. There are a number of ways in which we can overcome this problem, however.

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3.4.2 Approach 1: output in Rupees sales and a constant product mix Assume that budgeted sales are 2,000 units of X, 4,000 units of Y and 3,000 units of Z. A breakeven chart would make the assumption that output and sales of X, Y and Z are in the proportions 2,000:4,000:3,000 at all levels of activity; in other words, that the sales mix is 'fixed' in these proportions. We begin by carrying out some calculations. Budgeted costs Costs Revenue Rs Mn Rs Mn Variable costs of X (2,000 3K) 6 X (2,000 8K) 16 Variable costs of Y (4,000 4K) 16 Y (4,000 6K) 24 Variable costs of Z (3,000 5K) 15 Z (3,000 6K) 18 Total variable costs 37 Budgeted revenue 58 Fixed costs 10 Total budgeted costs 47 The breakeven chart can now be drawn.

10

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000

20

30

40

50

60

70

80

90

100Costsand

revenueRs Mn

Sales units

Breakeven point

Total costs

Fixed costs

Revenue

Profit(Rs. 11m at budget)

Figure 9.6 The breakeven point is approximately Rs. 27.5m of sales revenue. This may either be read from the chart or computed mathematically. (a) The budgeted C/S ratio for all three products together is contribution/sales = (58m – 37m)/58m = 36.21%. (b) The required contribution to break even is Rs. 10m, the amount of fixed costs. The breakeven point is 10m/36.21% = Rs. 27.5m (approx) in sales revenue. The margin of safety is approximately (58m – 27.5m) = Rs. 30.5m.

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3.4.3 Approach 2: products in sequence The products could be plotted in a particular sequence (say X first, then Y, then Z). Using the data from Approach 1, we can calculate cumulative costs and revenues as follows. Product Cumulative units Cumulative costs Cumulative revenue revenue Rs Mn Rs Mn Nil 10 Nil X (2,000 units) 2,000 16 16 Y (4,000 units) 6,000 32 40 Z (3,000 units) 9,000 47 58

costsandrevenues

60

50

40

30

20

10

Sales units (2,000 X then 4,000 Y then 3,000 Z)

Breakeven point

Revenue

Totalcosts

Fixedcosts

Rs Mn

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000

Figure 9.7 In this case the breakeven point occurs at 2,000 units of sales (2,000 units of product X). The margin of safety is roughly 4,000 units of Y and 3,000 units of Z. 3.4.4 Approach 3: output in terms of % of forecast sales and a constant

product mix

Rs Mn

Costs

and

revenue

60

50

40

30

20

10

010 20 30 40 50 60 70 80 90 100

% of forecast sales

Costs

Revenue

Breakeven point

Figure 9.8

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The breakeven point can be read from the graph as approximately 48% of forecast sales (Rs. 30m of revenue). Alternatively, with contribution of (58m – 37m) = Rs. 21m, 1% of forecast sales is associated with Rs. 21m/100 = Rs. 210K contribution. Breakeven point (%) = fixed costs/contribution per 1% = 10m/210K = 47.62% Margin of safety = (100 – 47.62) = 52.38% 3.5 Multi-product P/V charts The same information could be shown on a P/V chart, as follows.

Multi-product P/V chartProfit/loss

(Rs Mn)

PROFIT

BREAKEVEN

LOSS

10

5

0

5

10

Breakeven point(Rs. 27.5m)

20 40 5860 Revenue(Rs Mn)

Budgetedprofit

Figure 9.9 An addition to the chart would show further information about the contribution earned by each product individually, so that their performance and profitability can be compared. Contribution Sales C/S ratio Rs Mn Rs Mn % Product X 10 16 62.50 Product Y 8 24 33.33 Product Z 3 18 16.67 Total 21 58 36.21 By convention, the products are shown individually on a P/V chart from left to right, in order of the size of their C/S ratio. In this example, product X will be plotted first, then product Y and finally product Z. A dotted line is used to show the cumulative profit/loss and the cumulative sales as each product's sales and contribution in turn are added to the sales mix.

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Product Cumulative sales Cumulative profit Rs Mn Rs Mn X 16 –* X and Y 40 8 X, Y and Z 58 11 (* Rs. 10m contribution – Rs. 10m fixed costs) You will see on the graph which follows that these three pairs of data are used to plot the dotted line, to indicate the contribution from each product. The solid line which joins the two ends of this dotted line indicates the average profit which will be earned from sales of the three products in this mix. Multi-product P/V chartProfit/loss

(Rs Mn)

PROFIT

BREAKEVEN

LOSS

11

8

4

0

4

8

12

10 20 30 40 50 5860 Revenue(Rs Mn)

Budgetedprofit

Z

Y

XBreakeven

point

Figure 9.10 The diagram highlights the following points. (a) Since X is the most profitable in terms of C/S ratio, it might be worth considering an increase in the sales of X, even if there is a consequent fall in the sales of Z. (b) Alternatively, the pricing structure of the products should be reviewed and a decision made as to whether the price of product Z should be raised so as to increase its C/S ratio (although an increase is likely to result in some fall in sales volume).

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The multi-product P/V chart therefore helps to identify the following. (a) The overall company breakeven point (b) Which products should be expanded in output and which, if any, should be discontinued (c) What effect changes in selling price and sales volume will have on the company's breakeven point and profit QUESTION Multi-product P/V chart A company sells three products, X, Y and Z. Cost and sales data for one period are as follows. X Y Z Sales volume 2,000 units 2,000 units 5,000 units Sales price per unit Rs. 3,000 Rs. 4,000 Rs. 2,000 Variable cost per unit Rs. 2,250 Rs. 3,500 Rs. 1,250 Total fixed costs Rs. 3.25m Required

Draw a multi-product P/V chart based on the above information on the axes below. Rs’000

Figure 9.11

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ANSWER X Y Z Total Contribution per unit Rs. 750 Rs. 500 Rs. 750 Rs '000Budgeted contribution (total) Rs. 1,500K Rs. 1,000K Rs. 3,750K 6,250Fixed costs 3,250Budgeted profit 3,000

Cumulative Cumulative Product sales profit Rs '000 Rs '000 Z 10,000 (Rs. 3,750K – Rs. 3,250K) 500 Z and X 16,000 2,000 Z, X and Y 24,000 3,000

Rs’000

(Rs’000)

Figure 9.12

QUESTION Breakeven point and sales value constraints Chaturi produces four products. Relevant data is shown below for period 2. Product M Product A Product R Product P C/S ratio 5% 10% 15% 20% Maximum sales value Rs. 200m Rs. 120m Rs. 200m Rs. 180mMinimum sales value Rs. 50m Rs. 50m Rs. 20m Rs. 10mThe fixed costs for period 2 are budgeted at Rs. 60m.

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Required

Identify the missing figure in the sentence below. The lowest breakeven sales value, subject to meeting the minimum sales value constraints, is Rs.........….. ANSWER The correct answer is Rs. 390m. Breakeven point occurs when contribution = fixed costs Minimum breakeven point occurs when contribution is Rs. 60m. Contribution achieved from minimum sales value Rs Mn M 5% 50 2.5 A 10% 50 5.0 R 15% 20 3.0 P 20% 10 2.0 12.5Product P has the highest C/S ratio and so should be produced first (as it earns more contribution per Rs of revenue than the others). Contribution from sales of P between minimum and maximum points = Rs. 170m 20% = Rs. 34m Required contribution from product R (which has the next highest C/S ratio) = 60 – 12.5 – 34 = Rs. 13.5m Revenue from product R of Rs. 13.5m/0.15 = Rs. 90m will produce Rs. 13.5m of contribution. Lowest breakeven sales = Rs. 130m (minimum sales) + Rs. 170m (from P) + Rs. 90m (from R) = Rs. 390m

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4 Contribution per limiting factor and optimum production mix decision with single limiting factor

A limiting factor is anything that is in scarce supply and therefore limits the activities that a business can carry out. In a limiting factor situation, contribution will be maximised by earning the biggest possible contribution per unit of limiting factor. Throughput accounting is a product management system which aims to maximise throughput, and therefore cash generation from sales, rather than profit. We have briefly covered this topic in chapter 11, section 8. We are now looking at this subject in relation to short-term decision making. 4.1 Limiting factor analysis A limiting factor or key factor is 'anything which limits the activity of an entity. An entity seeks to optimise the benefit it obtains from the limiting factor. Examples are a shortage of supply of a resource or a restriction on sales demand at a particular price'.

A limiting factor could be sales if there is a limit to sales demand, but any one of the organisation's resources (labour, materials and so on) may be insufficient to meet the level of production demanded. It is assumed in limiting factor analysis that management wishes to maximise profit and that profit will be maximised when contribution is maximised (given no change in fixed costs expenditure incurred). Contribution per unit of scarce resource can therefore be used to prioritise production in cases where there are insufficient quantities of one material. QUESTION Limiting factor analysis A company manufactures three products, details of which are as follows. Product J Product K Product L Rs '000 per unit Rs '000 per unit Rs '000 per unit Selling price 140 122 134 Direct materials (Rs. 2K/kg) 22 14 26 Other variable cost 84 72 51 Fixed cost 20 26 40

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Required

Calculate the ranking of the products in terms of the most profitable use of the material in a period when direct material is restricted in supply. ANSWER 1st K, 2nd L, 3rd J Product J Product K Product L Rs '000 per unit Rs '000 per unit Rs '000 per unit Selling price 140 122 134 Variable cost 106 86 77 Contribution 34 36 57 Kg of material 11 7 13 Contribution per kg Rs '000 3.09 5.14 4.38 Ranking 3 1 2

5 Relevant vs non-relevant, including opportunity, avoidable, incremental, sunk, committed and common costs

5.1 Relevant costs

Relevant costs are future cash flows arising as a direct consequence of a decision. Relevant costs are future costs Relevant costs are cash flows Relevant costs are incremental costs Decision making should be based on relevant costs. (a) Relevant costs are future costs. A decision is about the future and it cannot alter what has been done already. Costs that have been incurred in the past are totally non relevant to any decision that is being made 'now'. Such costs are past costs or sunk costs. Costs that have been incurred include not only costs that have already been paid, but also costs that have been committed. A committed cost is a future cash flow that will be incurred anyway, regardless of the decision taken now. (b) Relevant costs are cash flows. Only cash flow information is required. This means that costs or charges which do not reflect additional cash spending (such as depreciation and notional costs) should be ignored for the purpose of decision making.

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(c) Relevant costs are incremental costs. For example, if an employee is expected to have no other work to do during the next week, but will be paid his basic wage (of, say, Rs. 100 per week) for attending work and doing nothing, his manager might decide to give him a job which earns the organisation Rs. 40. The net gain is Rs. 40 and the Rs. 100 is irrelevant to the decision because, although it is a future cash flow, it will be incurred anyway whether the employee is given work or not. Decision making is based only on relevant costs which are future, incremental cashflows. The following aspects fulfil the definition of a relevant cost, so should be included, when decision making. 5.2 Avoidable costs Avoidable costs are costs which would not be incurred if the activity to which they relate did not exist.

One of the situations in which it is necessary to identify the avoidable costs is in deciding whether or not to discontinue a product. The only costs which would be saved are the avoidable costs which are usually the variable costs and sometimes some specific costs. Costs which would be incurred whether or not the product is discontinued are known as unavoidable costs. 5.3 Specific fixed costs Specific fixed costs are additional costs which may be required to increase production.

For example. a new machine may be required to increase production capacity. The cost of this machine is relevant to the decision to increase production as it represents an additional incremental, future, cash outflow. 5.4 Differential costs and opportunity costs Relevant costs are also differential costs and opportunity costs. Differential costs are the difference in total cost between alternatives. An opportunity cost is the value of the benefit sacrificed when one course of action is chosen in preference to an alternative. For example, if decision option A costs Rs. 300 and decision option B costs Rs. 360, the differential cost is Rs. 60.

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5.3.1 Example: Differential costs and opportunity costs Suppose, for example, that there are three options, A, B and C; only one of them can be chosen. The net profit from each would be Rs. 80m, Rs. 100m and Rs. 70m respectively. Since only one option can be selected, option B would be chosen because it offers the biggest benefit. Rs Mn Profit from option B 100 Less opportunity cost (ie the benefit from the most profitable alternative, A) 80 Differential benefit of option B 20 The decision to choose option B would not be taken simply because it offers a profit of Rs. 100m, but because it offers a differential profit of Rs. 20m in excess of the next-best alternative. 5.5 Non-relevant costs Non-relevant costs are costs which would not be incurred if the activity to which they relate did not exist.

One of the situations in which it is necessary to identify the irrelevant costs is in deciding whether or not to discontinue a product. The only costs which would be saved are the relevant costs which are usually the variable costs and sometimes some specific costs. Costs which would be incurred whether or not the product is discontinued are known as non-relevant costs The following types of non-relevant costs are excluded from decision making. A sunk cost is a cost that has been irreversibly incurred in the past or committed. A sunk cost cannot be changed so fails the required future, cash flow requirement in the relevant cost definition. An example of a sunk cost are research costs already incurred before the decision to proceed with production is made A committed cost is a future cash outflow that will be incurred anyway, whatever decision is taken. Committed costs may exist because of legal contracts already entered into by the organisation, which it cannot avoid paying in the future. A non-cashflow cost, such as depreciation or other non-cash accounting cost adjustments, fails the required cash flow definition of a relevant cost, so are excluded from decision making.

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A notional cost is a cost used in product evaluation, decision-making and performance measurement to reflect the use of resources which carry no actual cashflow. An example is the notional rent of a machine, which is actually owned, in order to understand the full cost of production which reflects all assets and resources required to manufacture a product. A general fixed overhead or one which is estimated (absorbed) into production fail the incremental requirement of a relevant cost. A fixed overhead is excluded from decision making as the cost does not change as a result of the decision. An example is a machine maintenance overhead which must always be incurred. 5.6 Sunk costs A sunk cost is a past cost which is not directly relevant in decision making. The principle underlying decision accounting is that management decisions can only affect the future. In decision making, managers therefore require information about future costs and revenues which would be affected by the decision under review. They must not be misled by events, costs and revenues in the past, about which they can do nothing. Sunk costs, which have been charged already as a cost of sales in a previous accounting period or will be charged in a future accounting period although the expenditure has already been incurred, are irrelevant to decision making. 5.6.1 Example: Sunk costs An example of a sunk cost is development costs which have already been incurred. Suppose that a company has spent Rs. 250,000 in developing a new service for customers, but the marketing department's most recent findings are that the service might not gain customer acceptance and could be a commercial failure. The decision whether or not to abandon the development of the new service would have to be taken, but the Rs. 250,000 spent so far should be ignored by the decision makers because it is a sunk cost. 5.7 Common costs We previously visited this topic when looking at process costing in Chapter 8, section 6. The problem of costing for joint products concerns common costs; that is, those common processing costs shared between the units of eventual output up to their

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'split-off point'. Some method needs to be devised for sharing the common costs between the individual joint products for the following reasons. (a) To put a value to closing stocks of each joint product (b) To record the costs and therefore the profit from each joint product (c) Perhaps to assist in pricing decisions Here are some examples of the common costs problem. (a) How to spread the common costs of oil refining between the joint products made (petrol, naphtha, kerosene and so on) (b) How to spread the common costs of running the telephone network between telephone calls in peak and cheap rate times, or between local and long-distance calls Various methods that might be used to establish a basis for apportioning or allocating common costs to each product are as follows. Physical measurement Relative sales value apportionment method; sales value at split-off point 5.8 Dealing with common costs: physical measurement With physical measurement, the common cost is apportioned to the joint products on the basis of the proportion that the output of each product bears by weight or volume to the total output. An example of this would be the case where two products, product 1 and product 2, incur common costs to the point of separation of Rs. 3,000,000 and the output of each product is 600 tons and 1,200 tons respectively. Product 1 sells for Rs. 4,000 per ton and product 2 for Rs. 2,000 per ton. The division of the common costs (Rs. 3,000) between product 1 and product 2 could be based on the tonnage of output. Product 1 Product 2 Total Output 600 tons + 1,200 tons 1,800 tons Proportion of common cost 6001,800 + 1,2001,800 Rs '000 Rs '000 Rs '000 Apportioned cost 1,000 2,000 3,000 Sales 2,400 2,400 4,800 Profit 1,400 400 1,800 Profit/sales ratio 58.3% 16.7% 37.5%

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Physical measurement has the following limitations. (a) Where the products separate during the processes into different states, for example where one product is a gas and another is a liquid, this method is unsuitable. (b) This method does not take into account the relative income-earning potentials of the individual products, with the result that one product might appear very profitable and another appear to be incurring losses. 6 Relevant cost of material, labour, variable overheads and

fixed overheads

Relevant costs are future cash flows arising as a direct consequence of a decision. Relevant costs are future costs Relevant costs are cash flows Relevant costs are incremental costs In this section we provide a fairly gentle introduction to the sort of thought processes that you will have to go through when you encounter a decision-making question. First some general points about machinery, labour and, particularly, materials, that often catch people out. 6.1 Machinery user costs Once a machine has been bought its cost is a sunk cost. Depreciation is not a relevant cost, because it is not a cash flow. However, using machinery may involve some incremental costs. These costs might be referred to as user costs and they include hire charges and any fall in resale value of owned assets through use. 6.1.1 Example: Machine user costs Bronty Co is considering whether to undertake some contract work for a customer. The machinery required for the contract would be as follows. (a) A special cutting machine will have to be hired for three months for the work (the length of the contract). Hire charges for this machine are Rs. 75,000 per month, with a minimum hire charge of Rs. 300,000. (b) All other machinery required in the production for the contract has already been purchased by the organisation on hire purchase terms. The monthly hire purchase payments for this machinery are Rs. 500,000. This consists of Rs. 450,000 for capital repayment and Rs. 50,000 as an interest charge. The last hire purchase payment is to be made in two months' time. The cash price

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of this machinery was Rs. 9m two years ago. It is being depreciated on a straight-line basis at the rate of Rs. 200,000 per month. However, it still has a useful life which will enable it to be operated for another 36 months. The machinery is highly specialised and is unlikely to be required for other, more profitable jobs over the period during which the contract work would be carried out. Although there is no immediate market for selling this machine, it is expected that a customer might be found in the future. It is further estimated that the machine would lose Rs. 200,000 in its eventual sale value if it is used for the contract work. What is the relevant cost of machinery for the contract? Solution (a) The cutting machine will incur an incremental cost of Rs. 300,000, the minimum hire charge. (b) The historical cost of the other machinery is irrelevant as a past cost; depreciation is irrelevant as a non-cash cost; and future hire purchase repayments are irrelevant because they are committed costs. The only relevant cost is the loss of resale value of the machinery, estimated at Rs. 200,000 through use. This 'user cost' will not arise until the machinery is eventually resold and the Rs. 200,000 should be discounted to allow for the time value of money. However, discounting is ignored here, and will be discussed in a later chapter. (c) Summary of relevant costs Rs '000 Incremental hire costs 300 User cost of other machinery 200 500 6.2 Materials The relevant cost of raw materials is generally their current replacement cost, unless the materials have already been purchased and would not be replaced once used. If materials have already been purchased but will not be replaced, then the relevant cost of using them is either (a) their current resale value or (b) the value they would obtain if they were put to an alternative use, if this is greater than their current resale value. The higher of (a) or (b) is then the opportunity cost of the materials. If the materials have no resale value and no other possible use, then the relevant cost of using them for the opportunity under consideration would be nil.

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The flowchart below shows how the relevant costs of materials can be identified, provided that the materials are not in short supply, and so have no internal opportunity cost.

Are the materials already

in stock, or contracted

to buy in a purchase

agreement?NoYes

No

Relevant cost =

future/current

purchase cost of

materialsDo the materials have

an alternative use, or

would they be scrapped

if not used?Other use

available

Are the materials

regularly used, and

replaced with fresh

supplies when stocks

run out?Yes

Scrapped

if not used

Relevant cost

= future/current

purchase cost of

materials

Relevant cost

= scrap value/

disposal value

Relevant cost

= higher of value in

other use or scrap

value/disposal value Figure 8.1 QUESTION Relevant cost of materials Dayani LLC has been approached by a customer who would like a special job to be done for them, and who is willing to pay Rs. 22m for it. The job would require the following materials.

Material

Total units

required

Units already in inventory

Book value of units in

inventory Realisable

value Replacement

cost Rs '000/unit Rs '000/unit Rs '000/unit A 1,000 0 – – 6 B 1,000 600 2 2.5 5 C 1,000 700 3 2.5 4 D 200 200 4 6.0 9 (a) Material B is used regularly by O'Reilly Co, and if units of B are required for this job, they would need to be replaced to meet other production demand. (b) Materials C and D are in inventory as the result of previous over buying, and they have a restricted use. No other use could be found for material C, but the units of material D could be used in another job as substitute for 300 units of material E, which currently costs Rs. 5K per unit (of which the company has no units in inventory at the moment).

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Required

Calculate the relevant costs of material, in deciding whether or not to accept the contract. ANSWER (a) Material A is not owned and would have to be bought in full at the replacement cost of Rs. 6,000 per unit. (b) Material B is used regularly by the company. There is existing inventory (600 units) but if these are used on the contract under review a further 600 units would be bought to replace them. Relevant costs are therefore 1,000 units at the replacement cost of Rs. 5,000 per unit. (c) Material C. 1,000 units are needed and 700 are already in inventory. If used for the contract, a further 300 units must be bought at Rs. 4,000 each. The existing inventory of 700 will not be replaced. If they are used for the contract, they could not be sold at Rs. 2,500 each. The realisable value of these 700 units is an opportunity cost of sales revenue forgone. (d) Material D. These are already in inventory and will not be replaced. There is an opportunity cost of using D in the contract because there are alternative opportunities either to sell the existing inventory for Rs. 6,000 per unit (Rs. 1.2m in total) or avoid other purchases (of material E), which would cost 300 Rs. 5,000 = Rs. 1.5m. Since substitution for E is more beneficial, Rs. 1.5m is the opportunity cost. (e) Summary of relevant costs Rs '000 Material A (1,000 Rs. 6K) 6,000 Material B (1,000 Rs. 5K) 5,000 Material C (300 Rs. 4K) + (700 Rs. 2.5K) 2,950 Material D 1,500 Total 15,450

6.3 Labour Often the labour force will be paid irrespective of the decision made and the costs are therefore not incremental. There are certain scenarios, where the labour cost will be incremental to a decision, and so relevant to the costing analysis.

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(1) There is spare labour capacity and employees and wages are guaranteed. The relevant cost of utilising spare labour capacity is zero, as there is no future incremental cash flow, as employees are already been paid. (2) If a project requires overtime then this will be incremental to a decision to proceed, and so will be relevant to the costing analysis and should be included. (3) If the company is operating at full labour capacity then, the relevant cost will be additional cashflows of hiring more staff. (4) If the company is operating at full labour capacity but it is not possible to hire more employees, then the existing labour force must be put to an alternative use, in which case the relevant costs are the variable costs of the labour and associated variable overheads plus the contribution forgone from not being able to put it to its alternative use. These scenarios are summarised in the following diagram which explains how the relevant cost of labour is determined in each case.

Current labour force

Sparecapacity

Fullcapacity

Additionalwork can beundertaken

Additionalwork cannot be

undertaken

Relevant cost is ...

Nil Currentrate of pay

Variablecost & lost

contribution

Cannot hiremore staff

Hire morestaff

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QUESTION Relevant cost of labour A plc is deciding whether to undertake a new contract. 15 hours of labour are required for the contract. Labour is currently at full capacity producing X. Cost card for X Rs /unit Direct materials (10 kg @ Rs 20) 200 Direct labour (5 hrs @ Rs 60) 300 500 Selling price 750 Contribution 250 What is the cost of using 15 hours of labour for the contract?

ANSWER The correct answer is: Rs 1,650. Labour is currently working at full capacity therefore, if 15 hours are used in the contract 15 hrs = 3 units of X will not be made5 hrs . The relevant cost calculation is as follows. Undertake contract Rs Direct labour (15 hrs @ Rs 60) 900 Lost contribution 3X (3 Rs 250) 750 Relevant cost 1,650

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6.4 Variable and fixed overheads Variable overheads will be incremental to a decision, the relevant cost is simply the additional cash flows incurred. For example, if a project requires 100 additional machine hours are a variable overhead rate of Rs 10 per machine hour, then the relevant cost is 50 hrs 10 Rs per hour = Rs 500. As explained earlier, a general fixed overhead or one which is estimated (absorbed) into production fail the incremental requirement of a relevant cost. A fixed overhead is excluded from decision making as the cost does not change as a result of the decision. An example is the fixed costs of running the staff canteen as further projects will not affect this cost. A specific fixed cost will only be a relevant cost, if new fixed costs are introduced specifically for the project. This additional incremental cash flow will then be included in the relevant cost analysis.

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Breakeven analysis or cost-volume-profit (CVP) analysis is the study of the interrelationships between costs, volume and profit at various levels of activity. The breakeven point occurs when there is neither a profit nor a loss and so fixed costs equal contribution. Despite the advantages of breakeven analysis, the technique has some serious

limitations. The margin of safety is the difference in units between the budgeted sales volume and the breakeven sales volume. It is sometimes expressed as a percentage of the budgeted sales volume. Alternatively, the margin of safety can be expressed as the difference between the budgeted sales revenue and breakeven sales revenue, expressed as a percentage of the budgeted sales revenue. The contribution/sales (C/S) ratio, or profit/volume (P/V) ratio, is a measure of how much contribution is earned from each Rs. 1 of sales. At the breakeven point, there is no profit or loss and so sales revenue = total

costs or total contribution = fixed costs. The target profit is achieved when sales revenue equals variable costs plus fixed costs plus profit. Therefore the total contribution required for a target profit =

fixed costs + required profit. The breakeven point can also be determined graphically using a breakeven chart. A contribution breakeven chart depicts variable costs, so that contribution can be read directly from this chart. The profit/volume (P/V) graph is a variation of the breakeven chart and illustrates the relationship of profit to sales volume. The breakeven point in terms of sales revenue can be calculated as fixed costs/average C/S ratio. Any change in the proportions of products in the mix will change the

contribution per mix and the average C/S ratio and hence the breakeven point. The margin of safety for a multi-product organisation is equal to the budgeted sales in the standard mix less the breakeven sales in the standard mix. It may be expressed as a percentage of the budgeted sales. The number of mixes of products required to be sold to achieve a target profit is calculated as (fixed costs + required profit)/contribution per mix. Breakeven charts for multiple products can be drawn if a constant product sales mix is assumed. The P/V chart can show information about each product individually.

CHA

PTER

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UN

DU

P

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A limiting factor is anything that is in scarce supply and therefore limits the activities that a business can carry out. In a limiting factor situation, contribution will be maximised by earning the biggest possible contribution per unit of limiting factor. An opportunity cost is the value of the benefit sacrificed when one course of action is chosen in preference to an alternative. A sunk cost is a past cost which is not directly relevant in decision making. Relevant costs are future cash flows arising as a direct consequence of a decision. Relevant costs are future costs Relevant costs are cash flows Relevant costs are incremental costs In a make or buy decision with no limiting factors, the relevant costs are the differential costs between the two options. In general terms, a contract will probably be accepted if it increases

contribution and profit, and rejected if it reduces profit. The relevant costs/revenues in decisions relating to the operating of internal

service departments or the use of external services are the differential costs between the two options. Throughput accounting is a product management system which aims to maximise throughput, and therefore cash generation from sales, rather than profit. Relevant costs are also differential costs and opportunity costs. Differential costs are the difference in total cost between alternatives. An opportunity cost is the value of the benefit sacrificed when one course of action is chosen in preference to an alternative.

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1 Fill in the blanks. Breakeven point = Contribution per mix = Contribution per mix 2 C/S ratio = P/V ratio 100.

True False 3 Fill in the blanks. Margin of safety (as %) =

........................ sales ........................ sales........................ sales 100% 4 Mark the following on the breakeven chart below.

Profit Variable costs Sales revenue Fixed costs Total costs Breakeven point Margin of safety

Units

Rs Mn

5 Mark the following on the P/V chart below.

Breakeven point Contribution Fixed costs Profit

Sales volume

or revenue

Profit

Rs Mn

0

Loss

Rs Mn

PRO

GR

ESS

TES

T

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6 Which of the following is not a major assumption of breakeven analysis? A It can only apply to one product or a constant mix. B Fixed costs are the same in total and unit variable costs are the same at all levels of output. C Sales prices vary in line with levels of activity. D Production level is equal to sales level 7 Fill in the blanks in the statements below, using the words in the box. Some words

may be used twice. (a) The theory of constraints is an approach to production management which aims to maximise (1)........................................ less (2)......................................... It focuses on factors such as (3)........................................ which act as (4)........................................ (b) Throughput contribution = (5)........................................ minus (6) ........................................ (c) TA ratio = (7) ........................................ per factory hour (8) ........................................ per factory hour bottlenecks throughput contribution material costs constraints sales revenue conversion cost

8 Fill in the relevant costs in the four boxes in the diagram below.

Are the materials already

in stock, or contracted

to buy in a purchase

agreement?

No

Relevant cost =

No

Yes

Yes

Are the materials

regularly used, and

replaced with fresh

supplies when stocks

run out?

Relevant cost

=

Do the materials have

an alternative use, or

would they be scrapped

if not used?Other use

available

Relevant cost

=Relevant cost

=

Scrapped

if not used

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1 Breakeven point = Total fixed costsContribution per unit = Contribution required to breakevenContribution per unit 2 False. The C/S ratio is another name for the P/V ratio. 3 Margin of safety (as %) =

Budgeted sales breakeven salesBudgeted sales 100% 4

Marginof safety

Total costs

Breakeven pointSale

s re

venue

Profit

Variable costs

Fixed costs

Units

Fixed costs

Rs Mn

5

The gradient of the straight line is

the contribution per unit (if the

horizontal axis is measured in

sales units) or the C/S ratio (if the

horizontal axis is measured in

sales value).

Profit

Rs Mn

Breakeven point

B’even

Fixed

costs

Loss

Rs Mn

Profit

Sales volume

or revenue

Contribution

6 The answer is C. Sales prices are constant at all levels of activity. 7 1 sales revenue 2 material costs 3 bottlenecks 4 constraints 5 sales revenue 6 material costs 7 throughput contribution 8 conversion cost

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8 Are the materials already

in stock, or contracted

to buy in a purchase

agreement?

No

No

Yes

Relevant cost =

future/current

purchase cost of

materials

Are the materials

regularly used, and

replaced with fresh

supplies when stocks

run out?

Yes

Relevant cost

= future/current

purchase cost of

materials

Do the materials have

an alternative use, or

would they be scrapped

if not used?

Scrapped

if not used

Other use

available

Relevant cost

= scrap value/

disposal value

Relevant cost

= higher of value in

other use or scrap

value/disposal value

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Knowledge Component C Decision making 3.4 Long-term decision making 3.4.1 Explain the purpose of investment appraisal 3.4.2 Compute the financial feasibility using different investment appraisal techniques

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INTRODUCTION Decision making for the long term is similar in many respects to short-term decision making, and relevant costs must be used to assess whether a proposed investment should go ahead or not (assuming that the decision will be made on financial considerations only). In addition, however, the financial assessment of long-term investments should also take into consideration the time value of money. Investments should be expected to earn a return, and the size of the return should be expected to increase with time. Cash flow considerations may also be important, and a business may not want to invest in a project where it may take a long time to earn the investment returns. This chapter explains how long-term decisions should take into consideration the time value of money, and possibly also the cash payback period. It introduces the technique of discounted cash flow, which is extremely important in financial management.

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CHAPTER CONTENTS

LEARNING OUTCOME1 Introduction to capital investment appraisal 2 Capital investment appraisal – payback method 3 Capital investment appraisal – ARR method 3.4.1 /3.4.23.4.23.4.14 The principles of discounted cash flow 3.4.15 Annuities and perpetuities 3.4.26 Working capital and profits 3.4.27 Net present value (NPV) method 3.4.28 Capital investment appraisal – internal rate of return (IRR) method 3.4.2

9 NPV v IRR 3.4.210 Non-financial factors 3.4.2 1 Introduction to capital investment appraisal

Why do we need to do investment appraisals? When capital investment is made by an organisation it is normally for a substantial amount, relative the size of the organisation. Therefore, an appraisal should be completed to enable the business to make a decision as to whether invest in a particular project. The organisation needs to ensure that it is using the resources available to the business in order to obtain the maximum benefits from them. So, we will now look at the different methods that senior management might use to enable the decision to invest or not to be made.

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2 Capital investment appraisal – payback method The payback period is the time that is required for the cash inflows from a capital investment project to equal the cash outflows. 2.1 What is the payback period? The payback period is the time that is required for the total of the cash inflows of a capital investment project to equal the total of the cash outflows. Before the payback period can be calculated, management must have details of the following. The initial cash outflow for the project under consideration Estimates of any future cash inflows or savings 2.2 Example: Payback method Ruby LLC is considering a new project which will require an initial investment of Rs. 60 million. The estimated profits before depreciation are as follows.

Year

Estimated net cash inflows Rs '000 1 20,000 2 30,000 3 40,000 4 50,000 5 60,000 The payback period is calculated by considering the cumulative estimated profits before depreciation.

Estimated net Cumulative net Year cash inflows cash inflows Rs '000 Rs '000 1 20,000 20,000 2 30,000 50,000 3 40,000 90,000 4 50,000 140,000 5 60,000 200,000 The investment of Rs. 60 million is paid back in year 3. If the cash flows accrue evenly throughout the year, we can calculate the payback period as follows. At the end of year 2, Rs. 50 million of the cash invested has been paid back, leaving Rs. 10 million outstanding. The net cash inflow in year 3 is Rs. 40 million. The point at which the Rs. 60 million investment has been paid back is:

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2 years + (Rs. 10 million/Rs. 40 million 12 months) = 2 years and 3 months If, on the other hand, the cash flows are received at the end of the year then the payback period would be 3 years. 2.3 Using the payback period to appraise capital investment

projects There are two ways in which the payback period can be used to appraise projects. (a) If two or more mutually exclusive projects are under consideration, the usual decision is to accept the project with the shortest payback period. (b) If the management of a company have a payback period limit, then only projects with payback periods which are less than this limit would be considered for investment. 2.4 Example: Project appraisal – payback method Suppose Ruby LLC has a payback period limit of two years, and is considering investing in one of the following projects, both of which require an initial investment of Rs. 4 million. Cash flows accrue evenly throughout the year.

Project A Project B Year Cash inflow Year Cash inflow Rs '000 Rs '000 1 100,000 1 200,000 2 200,000 2 180,000 3 100,000 3 120,000 4 150,000 4 100,000 5 150,000 5 100,000

Required

Calculate the payback periods of the two projects and state which is the most acceptable project. Solution Firstly, we need to calculate the payback periods for Projects A and B. Project A

Year Cash inflow Cumulative cash inflow Rs '000 Rs '000 1 100,000 100,000 2 200,000 300,000 3 100,000 400,000 4 150,000 550,000 5 150,000 700,000 Project A has a payback period of 3 years.

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Project B Year Cash inflow Cumulative cash inflow Rs '000 Rs '000 1 200,000 200,000 2 180,000 380,000 3 120,000 500,000 4 100,000 600,000 5 100,000 700,000 Project B has a payback period of between 2 and 3 years. Payback period = 2 years + (Rs. 20 million/Rs. 120 million 12 months) = 2 years + 2 months Since Ruby LLC has a payback period limit of two years, neither project should be invested in (as both payback periods are greater than two years). If, however, Ruby LLC did not have a payback limit, or it was three years or longer, it should invest in Project B because it has the shorter payback period of the two projects.

QUESTION A company is considering a project to purchase an item of equipment costing Rs. 900,000. This would be depreciated over six years to a residual value of Rs. 0, using the straight line method. The expected additional profit from using the equipment in each of the six years would be: Year 1 Rs. 40,000 Year 4 Rs. 150,000 Year 2 Rs. 80,000 Year 5 Rs. 100,000 Year 3 Rs. 100,000 Year 6 Rs. 40,000 Required Calculate the expected payback period, assuming that cash flows accrue at an even rate during each year. A 3 years 3 months B 3 years 4 months C 3 years 8 months D 3 years 9 months

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ANSWER Annual depreciation will be Rs. 900,000/6 years = Rs. 150,000. Year Annual cash inflows Cumulative cash inflows Rs Rs 0 (900,000) (900,000) 1 190,000 (710,000) 2 230,000 (480,000) 3 250,000 (230,000) 300,000 70,000 (There is no need to calculate cumulative cash flows after Year 3.) Payback = 3 years + (230,000/300,000) 12 months = 3 years 9 months. The correct answer is D. 2.5 What does payback mean? The payback for an investment is a measure of how long it will take to recover the initial cash spending on an investment. If an organisation has cash flow difficulties, payback may be an important consideration. Similarly, payback may be a way of avoiding investments in projects where the expected cash flows are difficult to estimate reliably, especially more than a few years into the future. However, payback does not measure the value of an investment, or the expected return on investment that it will provide. It ignores all cash flows and returns after payback has been achieved. Payback is often used as an initial step in appraising a project. However, a project should not be evaluated on the basis of payback alone. If a project passes the 'payback test' (ie it has a payback period that is less than the payback period limit of the company) then it should be evaluated further with a more sophisticated project appraisal technique, (such as the NPV or IRR methods).

3 Capital investment appraisal – ARR method

The accounting rate of return (ARR) method (also called the return on capital employed (ROCE) method or the return on investment (ROI) method) of appraising a project is used to estimate the accounting rate of return that the project should yield. If it exceeds a target rate of return, the project will be undertaken.

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The most widely used definition of ARR is: ARR = Average annual profit from investment ×100Average investment Unfortunately, there are several different definitions of ARR, including: ARR = Estimated total profits Estimated initial investment 100% OR ARR = Estimated average profits Estimated initial investment 100%

3.1 Example A company has a target accounting rate of return of 20% (using the first definition above), and is now considering the following project. Capital cost of asset Rs. 80,000,000Estimated life 4 years Estimated profit before depreciation Year 1 Rs. 20,000,000 Year 2 Rs. 25,000,000 Year 3 Rs. 35,000,000 Year 4 Rs. 25,000,000The capital asset would be depreciated by 25% of its cost each year, and will have no residual value. Required

Calculate the accounting rate of return of the project and state whether the project should be undertaken. Solution The annual profits after depreciation, and the mid-year net book value of the asset, would be as follows. Profit after Mid-year net ARR in the Year depreciation book value year Rs '000 Rs '000 % 1 0 70,000 0 2 5,000 50,000 10 3 15,000 30,000 50 4 5,000 10,000 50 As the table shows, the ARR is low in the early stages of the project, partly because of low profits in Year 1 but mainly because the NBV of the asset is much higher early on in its life. The project does not achieve the target ARR of 20% in its first two years, but exceeds it in years 3 and 4. Should it be undertaken?

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When the ARR from a project varies from year to year, it makes sense to take an overall or 'average' view of the project's return. In this case, we should look at the return over the four-year period. Rs '000 Total profit before depreciation over four years 105,000 Total profit after depreciation over four years 25,000 Average annual profit after depreciation 6,250 Original cost of investment 80,000 Average net book value over the four-year period ((80 million + 0)/2) 40,000 The project would not be undertaken because its ARR is Rs. 6.25 million/Rs. 40 million = 15.625% and so it would fail to yield the target return of 20%. 3.2 The ARR and the comparison of mutually exclusive projects The ARR method of capital investment appraisal can also be used to compare two or more projects which are mutually exclusive. The project with the highest ARR would be selected (provided that the expected ARR is higher than the company's target ARR). QUESTION ARR Arrow wants to buy a new item of equipment. Two models of equipment are available, one with a slightly higher capacity and greater reliability than the other. The expected costs and profits of each item are as follows. Equipment item Equipment item X Y Capital cost Rs. 80,000 Rs. 150,000 Life 5 years 5 years Profits before depreciation Rs Rs Year 1 50,000 50,000 Year 2 50,000 50,000 Year 3 30,000 60,000 Year 4 20,000 60,000 Year 5 10,000 60,000 Disposal value 0 0 ARR is measured as the average annual profit after depreciation, divided by the average net book value of the asset. Required

State whether equipment item Y should be selected if the company's target ARR is 30%.

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ANSWER

The correct answer is that X should be selected and so the statement is false. Item X Item Y Rs Rs Total profit over life of equipment Before depreciation 160,000 280,000 After depreciation 80,000 130,000Average annual profit after depreciation 16,000 26,000 Average investment = (capital cost + disposal value)/2 40,000 75,000 ARR 40% 34.7% Both projects would earn a return in excess of 30%, but since item X would earn a bigger ARR, it would be preferred to item Y, even though the profits from Y would be higher by an average of Rs. 10,000 a year. 3.3 The drawbacks and advantages to the ARR method of project

appraisal The ARR method has the serious drawback that it does not take account of the timing of the profits from a project. Whenever capital is invested in a project, money is tied up until the project begins to earn profits which pay back the investment. Money tied up in one project cannot be invested anywhere else, until the profits come in. Management should be aware of the benefits of early repayments from an investment, which will provide the money for other investments. There are a number of other disadvantages. (a) It is based on accounting profits which are subject to a number of

different accounting treatments (b) It is a relative measure rather than an absolute measure and hence takes no account of the size of the investment (c) It takes no account of the length of the project (d) Like the payback method, it ignores the time value of money There are, however, advantages to the ARR method. (a) It is quick and simple to calculate (b) It involves a familiar concept of a percentage return (c) Accounting profits can be easily calculated from financial statements

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(d) It looks at the entire project life (e) Managers and investors are accustomed to thinking in terms of profit, and so an appraisal method which employs profit may therefore be more easily understood

4 The principles of discounted cash flow

The basic principle of discounting involves calculating the present value of an investment (ie the value of an investment today). The term present value means the cash equivalent now of a sum to be received or to be paid in the future. The basic principle of discounting is that if we wish to have Rs. S in n years' time, we need to invest a certain sum now (year 0) at an interest rate of r% in order to obtain the required sum of money in the future. In day-to-day terms, we could say that if we wish to have Rs. 1,000 in five years' time, how much would we need to invest now at an interest rate of 4%? 4.1 Discounting Discounting starts with the future value, and converts a future value to a present value. For example, if a company expects to earn a (compound) rate of return of 10% on its investments, how much would it need to invest now to have the following investments? (a) Rs. 11,000 after 1 year (b) Rs. 12,100 after 2 years (c) Rs. 13,310 after 3 years The answer is Rs. 10,000 in each case, and we can calculate it by discounting. The discounting formula to calculate the present value (PV) of a future sum of money (future value, FV) at the end of n time periods is:

n1PV = FV (1+ r) (a) After 1 year, Rs. 11,000 1 = Rs. 10,0001.10

(b) After 2 years, Rs. 12,100 21 = Rs. 10,0001.10 (c) After 3 years, Rs. 13,310 31 = Rs. 10,0001.10

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Discounting can be applied to both money receivable and also to money payable at a future date. By discounting all payments and receipts from a capital investment to a present value, they can be compared on a common basis, at a value which takes account of when the various cash flows will take place. 4.2 Present values The term 'present value' simply means the cash equivalent now of a sum to be received or to be paid in the future. The discounting formula is FORMULA TO LEARN PV = FV n1(1+ r) where FV is the future value of the investment with interest PV is the present value of that sum r is the rate of return, expressed as a proportion n is the number of time periods (usually years) The rate r is sometimes called the cost of capital. Note that this equation is just a rearrangement of the compounding formula.

4.2.1 Example: Present values (a) Calculate the present value of Rs. 60,000 received at the end of year 6, if interest rates are 15% per annum. (b) Calculate the present value of Rs. 100,000 received at the end of year 5, if interest rates are 6% per annum. Solution The discounting formula, PV = FV

n11+ r is required. (a) FV = Rs. 60,000 n = 6 r = 0.15 PV = 60,000 611.15 = 60,000 0.432 = Rs. 25,920 (b) FV = Rs. 100,000 n = 5 r = 0.06

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PV = 100,000 511.06 = 100,000 0.747 = Rs. 74,700

4.3 Present value tables Now that you understand the principles of discounting and you are able to calculate present values, you will be happy to hear that you do not need to remember the formula for discounting. Refer to the present value tables in the Appendix to this book. The use of present value tables is best explained by means of an example. 4.3.1 Example: Present value tables (a) Calculate the present value of Rs. 60,000 at year 6, if interest rates are 15% per annum, using tables. (b) Calculate the present value of Rs. 100,000 at year 5, if interest rates are 6% per annum, using tables. Solution (a) Looking at the present value tables, look along the row n = 6 (year 6) and down column r = 15% (interest rates are 15% per annum). The required discount rate is 0.432. The present value of Rs. 60,000 at year 6, when interest rates are 15% is therefore: Rs. 60,000 0.432 = Rs. 25,920 (b) Looking at the present value tables, look along the row n = 5 (year 5) and down column r = 6% (interest rates are 6% per annum). The required discount rate is 0.747. The present value of Rs. 100,000 at year 5, when interest rates are 6% is therefore: Rs. 100,000 0.747 = Rs. 74,700 Do either of these present values look familiar? Well, both of them should be, as they are the same present values that we calculated in the previous example using the discounting formula!

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QUESTION Present values Today's date is 30 April 20X3 and Fred wishes to have Rs. 160,000 saved by 30 April 20X8. Required

Compute the amount to be invested if interest rates are 5%. You may use the present value tables. ANSWER 30 April 20X3 = Now 30 April 20X8 = time period 5 n = 5 r = 5% Present value = Rs. 160,000 discount rate (where n = 5 and r = 5%) = Rs. 160,000 0.784 = Rs. 120,544

5 Annuities and perpetuities

An annuity is a constant sum of money received or paid each year for a given number of years. A perpetuity is an annuity which lasts forever. 5.1 Annuities An annuity is a constant sum of money received or paid each year for a given number of years.

For example, the present value of a three-year annuity of Rs. 100, which begins in one year's time when interest rates are 5%, is calculated as follows. Time Cash flow Discount factor Present value Rs 5% Rs 1 100 0.952 95.20 2 100 0.907 90.70 3 100 0.864 86.40 2.723 272.30 There is a rather long and complicated formula which can be used to calculate the present value of an annuity. Fortunately there are also annuity tables which

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calculate all of the annuity factors that you might ever need for Paper KE2. These are included at the end of this Study Text. In order to calculate the present value of a constant sum of money, we can multiply the annual cash flow by the sum of the discount factors for the relevant years. These total factors are known as cumulative present value factors or annuity factors. In the example above this is Rs. 100 × 2.723 = Rs. 272.30, which is the present value already calculated. Present value of an annuity = Annuity annuity factor

5.1.1 Example: Annuity tables

Calculate the annuity factor (cumulative present value factor) of Rs. 1 per annum for five years at 11% interest. Solution Refer to the annuity tables at the back of this Study Text. Read across to the column headed 11% (r = 11%) and down to period 5 (n = 5). The annuity factor = 3.696. Now look back at the present value tables and look in the column n = 11%. The cumulative present value rates for n = 1 to 5 = 0.901 + 0.812 + 0.731 + 0.659 + 0.593 = 3.696. Can you see now why these annuity tables are also called cumulative present value tables? 5.1.2 Example: Present value of an annuity Abilash has to make an annual payment of Rs. 100,000 to a car hire company each year from 30 June 20X3 to 30 June 20X8. Required

Calculate the present value of Abilash's total payments, if today's date is 1 July 20X2. Use a discount rate of 7%. Solution The first payment will be in one year's time ie time 1. There will be six annual payments. Annuity factor (where n = 6, r = 7%) = 4.767 Present value of payments = Rs. 100,000 annuity factor = Rs. 100,000 4.767 = Rs. 47,670

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5.2 Perpetuities A perpetuity is an annuity which lasts forever. The present value of a perpetuity = annuityinterest rate * *expressed as a proportion eg 20% = 0.2

5.2.1 Example: A perpetuity Fred is to receive Rs. 35,000 per annum in perpetuity starting in one year's time. Required

Calculate the present value of this perpetuity if the annual rate of interest is 9%. Solution PV = annuityinterest rate PV = Rs. 35,0000.09 = Rs. 388,889

6 Working capital and profits

To be successful in business, organisations must make profits. Profits are needed in order to pay dividends to shareholders and to allow partners to make drawings. If an organisation makes a loss, the value of the business falls and if there are long-term losses, the business may eventually collapse. Net profit measures how much the capital of an organisation has increased over a period of time. Profit is calculated by applying the matching concept, that is to say by matching the costs incurred with the sales revenue generated during a period. 6.1 The importance of cash In addition to being profitable, an organisation needs to have enough cash in order to pay for the following. Goods and services Capital investment (plant, machinery and so on) Labour costs Other expenses (rent, rates, taxation and so on) Dividends

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Net cash flow measures the difference in the payments leaving an organisation's bank account and the receipts that are paid into the bank account. 6.2 Net profit and net cash flow Net profit and net cash flow can differ, mainly due to timing differences. (a) Purchase of non-current assets Suppose an asset is purchased for Rs. 200,000 and depreciation is charged at 10% of the original cost.

Cash payment during the year = Rs. 200,000 (and this does not affect the statement of profit or loss) Depreciation charge = 10% × Rs. 200,000 = Rs. 20,000. This is charged to the statement of profit or loss and will reduce overall profits (b) Sale of non-current assets When an asset is sold there is usually a profit or loss on sale. Suppose an asset with a net book value of Rs. 15,000 is sold for Rs. 11,000, giving rise to a loss on disposal of Rs. 4,000. Increase in cash flow during the year = Rs. 11,000 sale proceeds. There will be no effect on the statement of profit or loss Loss on sale of non-current assets = Rs. 4,000. This will be recorded in the firm's statement of profit or loss and will reduce overall profits (c) Matching receipts from receivables and sales invoices raised If goods are sold on credit, the cash receipts will be the same as the value of the sales (ignoring early settlement discounts and bad debts). However, receipts may occur in a different period as a result of the timing of payments. (d) Matching payments to payables and cost of sales If materials are bought on credit, the cash payments to suppliers will be the same as the value of materials purchased. Again, the payments may be in different periods, due to timing. Materials purchased are matched against sales in a particular period to calculate profit, demonstrating that profit and cash flow will differ in a particular period.

6.3 Cash flow in capital investment appraisal In a capital investment appraisal situation, the driver of long-term value is cash flow. In particular, the timing and amount of cash received or paid is used in the evaluation rather than an assessment of profit (or loss), which is a short-term measure often used to assess value.

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7 Net present value (NPV) method

Discounted cash flow involves discounting future cash flows from a project in order to decide whether the project will earn a satisfactory rate of return. The two main discounted cash flow methods are the net present value (NPV) method and the internal rate of return (IRR) method. Discounted cash flow methods can be used to appraise capital investment projects. Discounted cash flow (DCF) involves the application of discounting arithmetic to the estimated future cash flows (receipts and expenditures) from a capital investment project, in order to decide whether the project is expected to earn a satisfactory rate of return. The two main discounted cash flow methods are as follows. The net present value method The internal rate of return method 7.1 The net present value (NPV) method The net present value (NPV) method calculates the present values of all items of income and expenditure related to an investment at a given rate of return, and then calculates a net total. If it is positive, the investment is considered to be acceptable. If it is negative, the investment is considered to be unacceptable. 7.2 The cost of capital The cost of capital has two aspects to it. (a) It is the cost of funds that a company raises and uses. (b) The return that investors expect to be paid for putting funds into the company. It is therefore the minimum return that a company should make from its own investments, to earn the cash flows out of which investors can be paid their return. The cost of capital can therefore be measured by studying the returns required by investors, and used to derive a discount rate for discounted cash flow analysis and investment appraisal.

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7.2.1 Example: The net present value of a project Dog Co is considering whether to spend Rs. 5,000 on an item of equipment which will last for two years. The excess of cash received over cash expenditure from the equipment would be Rs. 3,000 in the first year and Rs. 4,000 in the second year. Required

Calculate the net present value of the investment in the equipment at a discount rate of 15%. Solution In this example, an outlay of Rs. 5,000 now promises a net cash inflow of Rs. 3,000 during the first year and Rs. 4,000 during the second year. It is a convention in DCF, however, that cash flows spread over a year are assumed to occur at the end of the year, so that the cash flows of the project are as follows. The initial cost occurs at time 0, now, and therefore the discount factor is 1.00 as Rs. 5,000 is the present value of the expenditure now. Rs Year 0 (now) (5,000) Year 1 (at the end of the year) 3,000 Year 2 (at the end of the year) 4,000 A net present value statement is drawn up as follows. Year Cash flow Discount factor Present value Rs 15% Rs 0 (5,000) 1.000 (5,000) 1 3,000 0.870 2,610 2 4,000 0.756 3,024 Net present value + 634 The project has a positive net present value, so it is acceptable. 7.3 The timing of cash flows Note that annuity tables and the formulae both assume that the first payment or receipt is a year from now. Always check examination and assessment questions for when the first payment falls. For example, if there are five equal annual payments starting now, and the interest rate is 8%, we should use a factor of 1 (for today's payment) + 3.312 (for the other four payments) = 4.312.

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7.4 Cash v profit Remember that it is cash flow figures that must be included in your calculations. If depreciation has been deducted to arrive at a profit figure, it must be added back to give the net cash inflow. QUESTION NPV (1) Manel LLC is considering whether to make an investment costing Rs. 28 million which would earn a profit of Rs. 2.4 million per annum for each of the next five years, after charging depreciation at the straight-line rate over five years, to a residual value of Rs. 0. Required

Calculate the net present value of the investment at a cost of capital of 11%. ANSWER

Year Profit Depreciation Cash flow Discount factor Present value Rs '000 11% Rs '000 0 (28,000) 1.000 (28,000) 1 2,400 5,600 8,000 0.901 7,208 2 2,400 5,600 8,000 0.812 6,496 3 2,400 5,600 8,000 0.731 5,848 4 2,400 5,600 8,000 0.659 5,272 5 2,400 5,600 8,000 0.593 4,744 NPV 1,568 WORKING Cash flow = Rs. 2,400,000 profit per annum + Rs. 5,600,000 depreciation per annum* = Rs. 8,000 per annum * Depreciation = Rs. 28,000,000/5 years = Rs. 5,600,000 per annum. The important point to note is that depreciation is a non-cash expense. The actual cash spending occurs in Year 0, when the investment is made. Alternatively, you could treat the cash inflows of Rs. 8,000 for five years as an annuity. Year Cash flow Discount factor Present value Rs '000 11% Rs '000 0 (28,000) 1.000 (28,000) 1-5 8,000 3.696 29,568 1,568

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QUESTION NPV (2) Natural Oil LLC is considering a project which would cost Rs. 50 million now and yield Rs. 9 million per annum every year in perpetuity, starting a year from now. The cost of capital is 15%. Required

Calculate the net present value of the project. ANSWER

Year Cash flow Discount factor Present value Rs '000 15% Rs '000 0 (50,000) 1.0 (50,000) 1 - 9,000 1/0.15 60,000 NPV 10,000 The net present value of the project is Rs. 10 million. 7.5 What does a net present value mean? The net present value is a measure of the value in terms of 'today's money' of the net benefits from a proposed investment. The discount rate is the rate of return that will be sufficient to cover the cost of the organisation's capital. If an investment with a positive NPV goes ahead it will add value to the organisation, because the value of its net returns will be more than are needed to satisfy the providers of capital to the organisation. In theory, the value of the organisation should increase by the amount of the NPV if the investment goes ahead.

8 Capital investment appraisal – internal rate of return (IRR) method

The IRR method determines the rate of interest (internal rate of return) at which the NPV = 0. The internal rate of return is therefore the rate of return on an investment. The internal rate of return (IRR) method of evaluating investments is an alternative to the NPV method. The NPV method of discounted cash flow determines whether an investment earns a positive or a negative NPV when discounted at a given rate of interest. If the NPV is zero (that is, the present values of costs and benefits are equal) the return from the project would be exactly the rate used for discounting.

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The IRR method of discounted cash flow is a method which determines the rate of interest (the internal rate of return) at which the NPV is 0. The internal rate of return is therefore the rate of return on an investment. The IRR method will indicate that a project is viable if the IRR exceeds the

minimum acceptable rate of return. Thus if the company expects a minimum return of, say, 15%, a project would be viable if its IRR is more than 15%. 8.1 Example: The IRR method over one year If Rs. 500 is invested today and generates Rs. 600 in one year's time, the internal rate of return (r) can be calculated as follows. PV of cost = PV of benefits 500 = 600(1+ r) 500 (1 + r) = 600 1 + r = 600500 = 1.2 r = 0.2 = 20% The arithmetic for calculating the IRR is more complicated for investments and cash flows extending over a period of time longer than one year. An approximate IRR can be calculated using either a graphical method or by a technique known as the interpolation method. 8.2 Graphical approach A useful way to estimate the IRR of a project is to find the project's NPV at a number of discount rates and sketch a graph of NPV against discount rate. You can then use the sketch to estimate the discount rate at which the NPV is equal to zero (the point where the curve cuts the discount rate (horizontal) axis). 8.2.1 Example: graphical approach A project might have the following NPVs at the following discount rates.

Discount rate NPV % Rs '000 5 5,300 10 400 15 (1,700) 20 (2,900)

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This could be sketched on a graph as follows. NPV

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Figure 13.1: Net present values Reading from the graph, the IRR can be estimated as 11% (ie point A at which the curve crosses the horizontal axis). The graphical approach is a useful way of illustrating how the NPV of a project changes as the discount rate used varies. 8.3 The interpolation method Using the interpolation method, the IRR is calculated by first of all finding the NPV at each of two interest rates. Ideally, one interest rate should give a small positive NPV and the other a small negative NPV. The IRR would then be somewhere between these two interest rates: above the rate where the NPV is positive, but below the rate where the NPV is negative. However, it is possible to use two positive values or two negative values to extrapolate the IRR.

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The IRR, where the NPV is zero, can be calculated as follows. IRR = a% +

AA BNPV ×(b a) %NPV NPV where a is one interest rate b is the other interest rate NPVA is the NPV at rate a NPVB is the NPV at rate b

Using the information from the graphical approach example above, a = 10% b = 15% NPVA = Rs. 400,000 NPVB = Rs. (1,700,000) IRR = 10% + 400,000 × 15 10400,000+1,700,000 % = 10% + 0.95% = 10.95% QUESTION IRR (1) The net present value of an investment at 16% is +Rs. 50 million and at 20% is +Rs. 10 million. Required

Calculate the internal rate of return of this investment (to the nearest whole number). A 19% B 20% C 21% D 22% ANSWER The IRR in this example is greater than 20% because the NPV is still positive when discounted at 20% per annum. It can be estimated using extrapolation, rather than interpolation. The techniques are similar. IRR = a% +

BA BNPV ×(a b) %NPV NPV Where a = 20% b = 16% NPVA = NPV at rate a = Rs. 50,000,000 NPVB = NPV at rate b = Rs. 10,000,000

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IRR = 20% +

Rs. 10,000,000 ×(20 16)Rs. 50,000,000 10,000,000 % = 20% + 1% = 21% or = 16% +

Rs. 50,000,000 ×(20 16)Rs. 50,000,000 10,000,000 = 16% + 5% = 21% The correct answer is therefore C.

QUESTION IRR (2) The net present value of an investment at 18% is –Rs. 14,000,000 and at 14% is –Rs. 5,000,000. Required

Calculate the internal rate of return of this investment (to the nearest whole number). A 13% B 12% C 11% D 10% ANSWER The IRR in this example is less than 14% because the NPV is still negative when discounted at 14% per annum. It can be estimated using extrapolation. IRR = a% –

AB ANPV ×(b a) %NPV NPV Where a = 14% b = 18% NPVA = NPV at rate a = – Rs. 5,000,000 NPVB = NPV at rate b = – Rs. 14,000,000 IRR = 14% –

Rs. 5,000,000 ×(18 14)Rs. 14,000,000 Rs. 5,000,000 % = 14% – 2.2% = 11.8%.

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Or = 18% –

Rs. 14,000,000 ×(18 14)Rs. 14,000,000 Rs. 5,000,000 = 18% – 6.2% = 11.8% Rounding to the nearest % is sensible, given the uncertainty generally about estimating cash flows several years ahead and given also the use of annual intervals in discounting. The correct answer is therefore B.

8.4 The interpolation method, constant annual cash flows and annuity factors When the cash flows from a project are a constant amount each year, the IRR can be calculated (approximately) using the interpolation method and annuity factors. (Annuity factors are the value of Rs. 1 per annum at a discount rate of x% for each year from year 1 to year n.) An example will be used to illustrate the technique.

QUESTION IRR (3) An investment will cost Rs. 75 million and is expected to provide a cash return of Rs. 20 million each year for the next six years. Required

Calculate the IRR of the investment. The present value of Rs. 1 per annum at 14% for years 1 – 6 = Rs. 3.889 The present value of Rs. 1 per annum at 16% for years 1 – 6 = Rs. 3.685 ANSWER When the NPV of the investment is Rs. 0, the cumulative discount factor for Rs. 20 million each year from year 1 to year 6 = Rs. 75 million/Rs. 20 million = 3.750. The NPV at a discount rate of 14% would be positive, because the annuity factor at 14% (3.889) is higher than 3.750. The NPV at a discount rate of 16% would be negative, because the annuity factor at 16% (3.685) is lower than 3.750.

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The IRR can be calculated using the following formula, which is based on interpolation: IRR = a% +

CDFa CDFirr (b a) %CDFa CDFb where a is the lower discount rate b is the higher discount rate CDFa is the cumulative discount factor (annuity factor) at the lower discount rate CDFb is the cumulative discount factor (annuity factor) at the higher discount rate CDFirr is the cumulative discount factor (annuity factor) where the NPV = 0. Applying this formula:

IRR = 14% +

3.889 3.750 ×(16 14) %3.889 3.685 = 14% + [0.139/0.204] 2% = 15.36%.

Note: The calculation of the IRR in this example has used the interpolation method. In practice, the exact IRR could be obtained using a mathematical calculator. 8.5 What does the IRR of an investment mean? It was explained previously that, in theory, the value of an organisation should increase by the NPV of the investments that it undertakes (assuming that only investments with a positive NPV are selected). The IRR of an investment is a measure of the return that the investment is expected to achieve. If the IRR is more than the organisation's cost of capital, the investment should go ahead. However, unlike the NPV of investments, the IRR does not provide a measure of how much value the investment will create. A project with an NPV of +Rs. 1 million and an IRR of 15% is more valuable than a project with an NPV of +Rs. 100,000 and an IRR of 25%. The project with the higher NPV will create more value (by Rs. 900,000), even though it has a lower IRR.

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9 NPV v IRR (a) When cash flow patterns are conventional both methods gives the same accept or reject decision. (b) The IRR method is more easily understood. (c) NPV is technically superior to IRR and simpler to calculate. (d) IRR and accounting ROCE can be confused. (e) IRR ignores the relative sizes of investments. (f) Where cash flow patterns are non-conventional, there may be several IRRs which decision makers must be aware of to avoid making the wrong decision. (g) The NPV method is superior for ranking mutually exclusive projects in order of attractiveness. (h) The reinvestment assumption underlying the IRR method cannot be substantiated. (i) When discount rates are expected to differ over the life of the project, such variations can be incorporated easily into NPV calculations, but not into IRR calculations. (j) Despite the advantages of the NPV method over the IRR method, the IRR method is widely used in practice.

10 Non-financial factors

Managers must also consider the non-financial implications of their decisions. As well as financial considerations, any decision support information provided to management should also incorporate non-financial considerations. Here are some examples. (a) Impact on employee morale. Most investments affect employees' prospects, sometimes for the better, sometimes for the worse. A new cafeteria for employees would have a favourable impact, for example. (b) Impact on the community. This is a particularly important consideration if the investment results in loss of jobs, more jobs or elimination of small businesses. (c) Impact on the environment. The opening of a new mine, the development of products which create environmentally harmful waste and so on all have an impact on the environment. This can affect an organisation's image and

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reputation and hence its long-term growth and survival prospects. Some of these environmental effects can also impact directly on project cash flows because organisations have to pay fines, incur legal costs, incur disposal and clean-up costs and so on. (d) Ethical issues. Some investments might be legal but might not be in line with the ethics and code of conduct demanded by various stakeholder groups. (e) Learning. Many investments, particularly those which advance an organisation's technology, provide opportunities for learning. For example, investment in new computerised equipment to revolutionise a production process would enable an organisation to better use highly technical production methods. 500 people 20% In addition to the sale of the theatre tickets, it can be expected that members of the audience will also purchase confectionery both prior to the performance and during the interval. The contribution that this would yield to the theatre is unclear, but has been estimated as follows. Contribution from confectionery sales Probability Contribution of Rs. 3,000 per person 30% Contribution of Rs. 5,000 per person 50% Contribution of Rs. 10,000 per person 20%

Required (a) Using expected values as the basis of your decision, advise the theatre management whether it is financially worthwhile to engage MS for the concert. (b) Prepare a two-way data table to show the profit values that could occur from deciding to engage MS for the concert.

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The basic principle of discounting involves calculating the present value of an investment (ie the value of an investment today at time 0). The term present value means the cash equivalent now of a sum to be received or to be paid in the future. An annuity is a constant sum of money received or paid each year for a given number of years. A perpetuity is an annuity which lasts forever. To be successful in business, organisations must make profits. Profits are needed in order to pay dividends to shareholders and allow partners to make drawings. Discounted cash flow involves discounting future cash flows from a project in order to decide whether the project will earn a satisfactory rate of return. The two main discounted cash flow methods are the net present value (NPV)

method and the internal rate of return (IRR) method. The net present value (NPV) method calculates the present values of all items of income and expenditure related to an investment at a given rate of return, and then calculates a net total. If it is positive, the investment is considered to be acceptable. If it is negative, the investment is considered to be unacceptable. The IRR method determines the rate of interest (internal rate of return) at which the NPV = 0. The internal rate of return is therefore the rate of return on an investment. The payback period is the time that is required for the cash inflows from a capital investment project to equal the cash outflows. The accounting rate of return has several different definitions. The most common definition is Average annual profit from investment ×100%Average investment The accounting rate of return (ARR) method (also called the return on capital employed (ROCE) method or the return on investment (ROI) method) of appraising a project is used to estimate the accounting rate of return that the project should yield. If it exceeds a target rate of return, the project will be undertaken. Managers must also consider the non-financial implications of their decisions.

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1 Define the term 'present value'. 2 An annuity is a sum of money received every year.

True False

3 Define the term 'perpetuity'. 4 State the two usual methods of capital expenditure appraisal using discounted cash flow methods. 5 Define the term 'payback period'. 6 A company is proposing to launch a new product. Incremental net cash inflows of Rs. 36,000 per annum for five years are expected, starting at Time 1. An existing machine, with a net book value of Rs. 85,000, would be used to manufacture the new product. The machine could otherwise be sold now, Time 0, for Rs. 60,000. The machine, if used for the manufacture of the new product, would be depreciated on a straight-line basis over five years, starting at Time 1.

Identify the relevant amounts that should be used, at Time 0 and Time 1, in the discounted cash flow appraisal of the project. Time 0 Time 1 A Rs. 0 Rs. 19,000 B Rs. 0 Rs. 24,000 C (Rs. 60,000) Rs. 36,000 D (Rs. 85,000) Rs. 36,000

7 Calculate the present value, at a discount rate of 12% of a cash inflow of Rs. 80,000: (a) At the end of year 6 (b) At the beginning of year 6 8 A project would have a NPV of +Rs. 34,400 at a discount rate of 8% and an NPV of -Rs. 10,250 at a discount rate of 11%. Calculate the approximate internal rate of return using interpolation.

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9 An investment project has net present values as follows: Discount rate 11% per annum: net present value Rs. 35,170 positive Discount rate 15% per annum: net present value Rs. 6,040 positive. Calculate the best estimate of the internal rate of return. A 14.5% B 15.8% C 19.5% D 19.8%

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1 The amount of money which must be invested now for n years at an interest rate of r% to give a future sum of money at the time it will be due. 2 False It is a constant sum of money received or paid each year for a given number of years. 3 An annuity which lasts forever. 4 The net present value (NPV) method The internal rate of return (IRR) method 5 The payback period is the time that is required for the cash inflows of a capital investment project to equal the cash outflows. 6 The answer is C. 7 (a) Rs. 80,000 1/1.126 = Rs. 80,000 0.50663 = Rs. 40,530. (b) The beginning of Year 6 is the end of Year 5. Rs. 80,000 1/1.125 = Rs. 80,000 0.56743 = Rs. 45,394. 8 IRR = a % +

aa bNPV × b aNPV NPV %

= 8% + [34,400/34,400 – 10,250] (11 – 8)% = 8% + [34,400/44,650] 3% = 8% + 2.3% = 10.3% 9 The answer is B. IRR = a % +

aa bNPV × b aNPV NPV

= 11% +

35,170 × (15 11)35,170 6,040 % = 11% + 4.8% = 15.8%

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Knowledge Component D Risk and uncertainty 4.1 Introduction to risk and uncertainty 4.1.1 Explain the concept of risk and uncertainty 4.2 Basic decision-making tools under risk 4.2.2 Calculate summary measures of central tendency and dispersion for both grouped and ungrouped data 4.2.2 Demonstrate the use of probability in decision making 4.2.2 Analyse outcomes using the basic decision tools under risk

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INTRODUCTION Decision making for the long term is similar in many respects to short-term decision making, and relevant costs must be used to assess whether a proposed investment should go ahead or not (assuming that the decision will be made on financial considerations only). In addition, however, the financial assessment of long-term investments should also take into consideration the time value of money. Investments should be expected to earn a return, and the size of the return should be expected to increase with time. Cash flow considerations may also be important, and a business may not want to invest in a project where it may take a long time to earn the investment returns. This chapter explains how long-term decisions should take into consideration the time value of money, and possibly also the cash payback period. It introduces the technique of discounted cash flow, which is extremely important in financial management.

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CHAPTER CONTENTS

LEARNING OUTCOME1 The concept of probability 2 Probability distribution 3 Normal distribution 4 Standard deviation on a normal distribution 5 Using normal distribution to calculate distribution probabilities

4.1.14.1.14.1.14.1.14.1.1, 4.2.26 Risk and uncertainty 4.2.17 Allowing for uncertainty 4.2.18 Expected values 4.2.19 Decision rules 4.2.1, 4.2.3

1 The concept of probability

1.1 Introducing probability Probability is a measure of likelihood and can be stated as a percentage, a ratio or, more usually, as a number from 0 to 1. Consider the following. Probability = 0 = impossibility Probability = 1 = certainty Probability = 1/2 = a 50% chance of something happening Probability = 1/4 = a 1-in-4 chance of something happening

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1.2 Expressing probabilities In statistics, probabilities are more commonly expressed as proportions than as percentages. Consider the following possible outcomes.

Probability as a Probability as Possible outcome percentage a proportion % A 15.0 0.150 B 20.0 0.200 C 32.5 0.325 D 7.5 0.075 E 12.5 0.125 F 12.5 0.125 100.0 1.000 It is useful to consider how probability can be quantified. A businessman might estimate that if the selling price of a product is raised by 20c, there would be a 90% probability that demand would fall by 30%, but how would he have reached his estimate of 90% probability?

1.3 Assessing probabilities There are several ways of assessing probabilities. They may be measurable with mathematical certainty – If a coin is tossed, there is a 0.5 probability that it will come down heads, and a 0.5 probability that it will come down tails. – If a die is thrown, there is a one-sixth probability that a 6 will turn up. They may be measurable from an analysis of past experience Probabilities can be estimated from research or surveys. It is important to note that probability is a measure of the likelihood of an event happening in the long run, or over a large number of times. The rules of probability, in Section 2, will go through in detail how to calculate probabilities in various situations.

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1.4 The rules of probability

1.4.1 Setting the scene It is the year 2020 and examiners are extinct. A mighty but completely fair computer churns out examinations that are equally likely to be easy or difficult. There is no link between the number of questions on each paper, which is arrived at on a fair basis by the computer, and the standard of the paper. You are about to take five examinations. 1.4.2 Simple probability It is vital that the first examination is easy, as it covers a subject which you have tried, but unfortunately failed, to understand. What is the probability that it will be an easy examination? Obviously (let us hope), the probability of an easy paper is 1/2 (or 50% or 0.5). This reveals a very important principle (which holds if each result is equally likely). FORMULA TO LEARN

Probability of achieving the desired result = Number of ways of achieving desired resultTotal number of possible outcomes Let us apply the principle to our example. Total number of possible outcomes = 'easy' or 'difficult' = 2 Total number of ways of achieving the desired result (which is 'easy') = 1 The probability of an easy examination, or P(easy examination) = 1/2 1.4.3 Example: Simple probability Suppose that a dice is rolled. Required

Calculate the probability that it will show a six. Solution P(heads) = Number of ways of achieving desired resultTotal number of possible outcomes = 16 or 16.7% or 0.167

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1.4.4 Example: Simple probability 2 Suppose a box contains three red balls and two blue balls. You close your eyes and pick a ball from the box. Required

Calculate the probability that it will be a blue ball. Solution P(blue) = Number of ways of achieving desired resultTotal number of possible outcomes = 25 or 40% or 0.4 1.5 Venn diagrams A Venn diagram is a pictorial method of showing probability. We can show all the possible outcomes (E) and the outcome we are interested in (A).

A

E

Figure 8.1: Venn diagram

1.6 Complementary outcomes You are desperate to pass more of the examinations than your sworn enemy but, unlike you, he is more likely to pass the first examination if it is difficult. (He is very strange!) What is the probability of the first examination being more suited to your enemy's requirements? We know that the probability of certainty is one. The certainty in this scenario is that the examination will be easy or difficult. P(easy or difficult examination) = 1 From section 2.2, P(easy examination) = 1/2 P(not easy examination) = P(difficult examination) = 1 – P(easy examination) = 1 – 1/2 = ½

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FORMULA TO LEARN P (A) = 1 – P(A), where A is 'not A'. 1.6.1 Venn diagram: Complementary outcomes

A

Figure 8.2: Venn diagram – complementary outcomes The probability of not A is shown by the shaded region. 1.6.2 Example: Complementary outcomes If there is a 25 per cent chance of the Rainbow Party winning the next general election, use the law of complementary events to calculate the probability of the Rainbow Party not winning the next election. Solution P(winning) = 25% = 1/4 P(not winning) = 1 – P(winning) = 1 –1/4 = 3/4 1.7 The simple addition or OR law The simple addition law for two mutually exclusive events, A and B, is as follows. P(A or B) = P (A B) = P(A) + P(B) The time pressure in the second examination is enormous. The computer will produce a paper which will have between five and twelve questions. You know that, easy or difficult, the examination must have six questions at the most for you to have any hope of passing it. What is the probability of the computer producing an examination with six or fewer questions? In other words, what is the probability of an examination with exactly five or exactly six questions?

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Don't panic. Let us start by using the basic principle. P(5 questions) = Total number of ways of achieving a five question examinationTotal number of possible outcomes (= 5, 6, 7, 8, 9, 10, 11 or 12 questions) = 18 Likewise, P(6 questions) = 18 Either five questions or six questions would be acceptable, so the probability of you passing the examination must be greater than if just five questions or just six questions were acceptable. We therefore add the two probabilities together so that the probability of passing the examination has increased. So P(5 or 6 questions) = P(5 questions) + P(6 questions) = 18 + 18 = 2 1=8 4 =0.25 Mutually exclusive outcomes are outcomes where the occurrence of one of the outcomes excludes the possibility of any of the others happening. In the example the outcomes are mutually exclusive; it is impossible to have five questions and six questions in the same examination. 1.7.1 Venn diagram: Mutually exclusive outcomes

A B

Figure 8.3: Venn diagram – mutually exclusive outcomes

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1.7.2 Example: Mutually exclusive outcomes The delivery of an item of raw material from a supplier may take up to six weeks from the time the order is placed. The probabilities of various delivery times are as follows. Delivery time Probability 1 week 0.10 > 1, 2 weeks 0.25 > 2, 3 weeks 0.20 > 3, 4 weeks 0.20 > 4, 5 weeks 0.15 > 5, 6 weeks 0.10 1.00 Required Calculate the probability that a delivery will take the following times. (a) Two weeks or less (b) More than three weeks Solution (a) P ( 1 or > 1, 2 weeks) = P ( 1 week) + P (>1, 2 weeks) = 0.10 + 0.25 = 0.35 (b) P (> 3, 6 weeks) = P (> 3, 4 weeks) + P (> 4, 5 weeks) + P (> 5, 6 weeks) = 0.20 + 0.15 + 0.10 = 0.45 1.8 The simple multiplication or AND law The simple multiplication law for two independent events, A and B, is as follows. P(A and B) = P (A B) = P(A)P(B) P(A and B) = 0 when A and B have mutually exclusive outcomes. You still have three examinations to sit: astrophysics, geography of the moon and computer art. Stupidly, you forgot to revise for the astrophysics examination, which will have between 15 and 20 questions. You think that you may scrape through this paper if it is easy and if there are only 15 questions. What is the probability that the paper the computer produces will exactly match your needs? Do not forget that there is no link between the standard of the examination and the number of questions, ie they are independent events.

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The best way to approach this question is diagrammatically, showing all the possible outcomes. Number of questions

Type of paper

15 16 17 18 19 20

Easy (E) E and 15* E and 16 E and 17 E and 18 E and 19 E and 20 Difficult (D) D and 15 D and 16 D and 17 D and 18 D and 19 D and 20 The diagram shows us that, of the twelve possible outcomes, there is only one 'desired result' (which is asterisked). We can therefore calculate the probability as follows. P(easy paper and 15 questions) =1/12. The answer can be found more easily as follows. P(easy paper and 15 questions) = P(easy paper) P(15 questions) = 1/2 1/6 = 1/12. The number of questions has no effect on, nor is it affected by whether it is an easy or difficult paper. (Note that P(15 questions) = 1/6 because there could be six different numbers of questions, either 15 or 16 or 17 or 18 or 19 or 20; only one of these six possible scenarios has 15 questions exactly.)

Independent events are events where the outcome of one event in no way affects the outcome of the other events. 1.8.1 Example: Independent events A die is thrown, and a coin is tossed simultaneously. Required

Calculate the probability of throwing a 5 and getting heads on the coin. Solution The probability of throwing a 5 on a die is 1/6. (There are six faces on a die and only one contains a six.) The probability of a tossed coin coming up heads is 1/2 The probability of throwing a 5 and getting heads on a coin is 1/2 1/6 = 1/12

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1.9 The general rule of addition The general rule of addition for two events, A and B, which are not mutually exclusive, is as follows. P(A or B) = P (A B) = P(A) + P(B) – P(A and B) The three examinations you still have to sit are placed face down in a line in front of you at the final examination sitting. There is an easy astrophysics paper, a difficult geography of the moon paper and a difficult computer art paper. Without turning over any of the papers you are told to choose one of them. What is the probability that the first paper that you select is difficult or is the geography of the moon paper? Let us think about this carefully. There are two difficult papers, so P(difficult) = 2/3 There is one geography of the moon paper, so P(geography of the moon) = 1/3 If we use the OR law and add the two probabilities, then we will have double counted the difficult geography of the moon paper. It is included in the set of difficult papers and in the set of geography of the moon papers. In other words, we are not faced with mutually exclusive outcomes, because the occurrence of a geography of the moon paper does not exclude the possibility of the occurrence of a difficult paper. We therefore need to take account of this double counting. P(difficult paper or geography of the moon paper) = P(difficult paper) + P(geography of the moon paper) – P(difficult paper and geography of the moon paper). Using the general rule of addition, P(difficult paper or geography of the moon paper) = 2/3 + 1/3 – (1/3) = 2/3. Since it is perfectly possible to have an examination which is difficult and about the geography of the moon, these two events are not mutually exclusive. 1.9.1 Venn diagram: General rule of addition We can show how to calculate P(A B) from three diagrams.

A B

Figure 8.4a: Venn diagram – general rules of addition

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The shaded area in Figure 8.4a is the probability of A and not B = P(A) – P(A B) A B

Figure 8.4b: Venn diagram – general rules of addition The shaded area is the probability of A and B = P (A B)

A B

Figure 8.4c: Venn diagram – general rules of addition The shaded area is the probability of B and not A = P (B) – (A B) If we add these three sections together we get the formula for the probability of A or B = P(A) + P(B) – P (A B) QUESTION General rule of addition If one card is drawn from a normal pack of 52 playing cards, calculate the probability of getting an ace or a spade. Probability

Ace Spade Ace of spades Ace or spade ANSWER

Probability

Ace Spade Ace of spades Ace or spade

524 52

13 521 13

4 WORKING P(ace or spade) = 4 13 1 16 4+ = =52 52 52 52 13

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1.10 The general rule of multiplication The general rule of multiplication for two dependent events, A and B is: P(A and B) = P(A) P(B|A) = P(B) P(A|B) Computer art is your last examination. Understandably you are very tired and you are uncertain whether you will be able to stay awake. You believe that there is a 70% chance of your falling asleep if it becomes too hot and stuffy in the examination hall. It is well known that the air conditioning system serving the examination hall was installed in the last millennium and is therefore extremely unreliable. There is a 1-in-4 chance of it breaking down during the examination, thereby causing the temperature in the hall to rise. What is the likelihood that you will drop off? The scenario above has led us to face what is known as conditional probability. We can rephrase the information provided as 'the probability that you will fall asleep, given that it is too hot and stuffy, is equal to 70%' and we can write this as follows. P(fall asleep | too hot and stuffy) = 70%. (You can read the '|' symbol as 'given' so this means the probability of falling asleep given that it is hot and stuffy.) Dependent or conditional events are events where the outcome of one event depends on the outcome of the others. Whether you fall asleep is conditional upon whether the hall becomes too hot and stuffy. The events are not, therefore, independent and so we cannot use the simple multiplication law. So: P(it becomes too hot and stuffy and you fall asleep) = P(too hot and stuffy) P(fall asleep | too hot and stuffy) = 25% 70% = 0.25 0.7 = 0.175 = 17 2

1 % When A and B are independent events, then P(B|A) = P(B) since, by definition, the occurrence of B (and therefore P(B)) does not depend upon the occurrence of A. Similarly, P(A|B) = P(A).

1.10.1 Example: Conditional probability The board of directors of Shuttem LLC has warned that there is a 60% probability that a factory will be closed down unless its workforce improves its productivity. The factory's manager has estimated that the probability of success in agreeing a productivity deal with the workforce is only 30%.

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Required

Assess the likelihood that the factory will be closed. Solution If outcome A is the shutdown of the factory and outcome B is the failure to improve productivity: P(A and B) = P(B) P(A|B) = 0.7 0.6 = 0.42 Contingency tables can be useful for dealing with conditional probability. 1.10.2 Example: Contingency tables A cosmetics company has developed a new anti-dandruff shampoo which is being tested on volunteers. Seventy percent of the volunteers have used the shampoo, whereas others have used a normal shampoo, believing it to be the new anti-dandruff shampoo. Two-sevenths of those using the new shampoo showed no improvement, whereas one-third of those using the normal shampoo had less dandruff. Required A volunteer shows no improvement. Calculate the probability that s/he used the normal shampoo. Solution The problem is solved by drawing a contingency table, showing 'improvement' and 'no improvement', 'volunteers using normal shampoo' and 'volunteers using the new shampoo'. Let us suppose that there were 1,000 volunteers (we could use any number). We could depict the results of the test on the 1,000 volunteers as follows.

New shampoo Normal shampoo

Total Improvement ***500 ****100 600 No improvement **200 *** 200 400 *700 300 1,000 * 70% 1,000 ** 27 700 *** Balancing figure **** 13 300 We can now calculate P (shows no improvement)

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P(shows no improvement) = 4001,000 P(used normal shampoo | shows no improvement) = 200400 = 12 Other probabilities are just as easy to calculate. P (shows improvement | used new shampoo) = 500700 = 57 P (used new shampoo | shows improvement) = 500600 = 56 QUESTION Independent events The independent probabilities that the three sections of a management accounting department will encounter one computer error in a week are respectively 0.1, 0.2 and 0.3. There is never more than one computer error encountered by any one section in a week. Required

Calculate the probability that there will be the following number of errors encountered by the management accounting department next week. (a) At least one computer error (b) One and only one computer error ANSWER (a) The probability of at least one computer error is 1 minus the probability of no error. The probability of no error is 0.9 0.8 0.7 = 0.504. (Since the probability of an error is 0.1, 0.2 and 0.3 in each section, the probability of no error in each section must be 0.9, 0.8 and 0.7 respectively.) The probability of at least one error is 1 – 0.504 = 0.496. (b) Y = yes, N = no Section 1 Section 2 Section 3 (i) Error? Y N N (ii) Error? N Y N (iii) Error? N N Y Probabilities (i) 0.1 × 0.8 × 0.7 = 0.056 (ii) 0.9 × 0.2 × 0.7 = 0.126 (iii) 0.9 × 0.8 × 0.3 = 0.216 Total 0.398 The probability of only one error only is 0.398.

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QUESTION General rule of addition In a student survey, 60% of the students are male and 75% are CA Sri Lanka candidates. Required

Calculate the probability that a student chosen at random is either female or a CA Sri Lanka candidate. A 0.85 B 0.30 C 0.40 D 1.00 ANSWER P(male) = 60% = 0.6 P(female) = 1 – 0.6 = 0.4 P(CA Sri Lanka candidate) = 75% = 0.75 We need to use the general rule of addition to avoid double counting. P(female or CA Sri Lanka candidate) = P(female) + P(CA Sri Lanka candidate) – P(female and CA Sri Lanka candidate) = 0.4 + 0.75 – (0.4 0.75) = 1.15 – 0.3 = 0.85 The correct answer is A. You should have been able to eliminate options C and D immediately. 0.4 is the probability that the candidate is female and 1.00 is the probability that something will definitely happen – neither of these options are likely to correspond to the probability that the candidate is either female or a CA Sri Lanka candidate. 1.11 Arithmetic mean of ungrouped data The arithmetic mean is the best-known type of average and is widely understood. It is used for further statistical analysis. Arithmetic mean of ungrouped data = Sum of values of itemsNumber of items The arithmetic mean of a variable x is shown as x ('x bar').

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1.11.1 Example: The arithmetic mean The demand for a product on each of 20 days was as follows (in units). 3 12 7 17 3 14 9 6 11 10 1 4 19 7 15 6 9 12 12 8 The arithmetic mean of daily demand is x . Sum of demand 185x = =Number of days 20 = 9.25 units In this example, demand on any one day is never actually 9.25 units. The arithmetic mean is merely an average representation of demand on each of the 20 days. 1.12 Arithmetic mean of data in a frequency distribution In an assessment you could be asked to calculate the arithmetic mean of a frequency distribution. In our previous example, the frequency distribution would be shown as follows.

Daily demand Frequency Demand frequency

x f fx 1 1 1 3 2 6 4 1 4 6 2 12 7 2 14 8 1 8 9 2 18 10 1 10 11 1 11 12 3 36 14 1 14 15 1 15 17 1 17 19 1 19 20 185 185x = 20 = 9.25

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1.13 Sigma,

means 'the sum of' and is used as shorthand to mean 'the sum of a set of values'. In the previous example: (a) f would mean the sum of all the frequencies, which is 20. (b) fx would mean the sum of all the values of 'frequency multiplied by daily demand', that is, all 14 values of fx, so fx = 185.

1.14 Arithmetic mean of grouped data in class intervals

The arithmetic mean of grouped data,

fx fxx = or n f where n is the number of values recorded, or the number of items measured. This formula will be given to you in your exam. You might also be asked to calculate (or at least approximate) the arithmetic mean of a frequency distribution, where the frequencies are shown in class intervals. 1.14.1 Example: The arithmetic mean of grouped data Using the example in Section 7.1.1, the frequency distribution might have been shown as follows.

Daily demand Frequency > 0 5 4 > 5 10 8 >10 15 6 >15 20 2 20 There is, of course, an extra difficulty with finding the average now; as the data have been collected into classes, a certain amount of detail has been lost and the values of the variables to be used in the calculation of the mean are not clearly specified. 1.14.2 The mid-point of class intervals To calculate the arithmetic mean of grouped data we therefore need to decide on a value which best represents all of the values in a particular class interval. This value is known as the mid-point. The mid-point of each class interval is conventionally taken, on the assumption that the frequencies occur evenly over the class interval range. In the example above, the variable is discrete, so the first class includes 1, 2, 3, 4 and 5, giving a mid-point of 3. With a continuous variable, the mid-points would have been 2.5,

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7.5 and so on. Once the value of x has been decided, the mean is calculated using the formula for the arithmetic mean of grouped data. Daily demand Mid point Frequency

x f fx > 0 5 3 4 12 > 5 10 8 8 64 >10 15 13 6 78 >15 20 18 2 36 f = 20 fx = 190 Arithmetic mean

fx 190x = or f 20 = 9.5 units Because the assumption that frequencies occur evenly within each class interval is not quite correct in this example, our approximate mean of 9.5 is not exactly correct, and is in error by 0.25 (9.5 – 9.25). As the frequencies become larger,

the size of this approximating error should become smaller.

1.14.3 Example: The arithmetic mean of combined data Suppose that the mean age of a group of five people is 27 and the mean age of another group of eight people is 32. How would we find the mean age of the whole group of 13 people? FORMULA TO LEARN

Arithmetic mean = Sum of values of itemsNumber of items The sum of the ages in the first group is 5 27 = 135 The sum of the ages in the second group is 8 32 = 256 The sum of all 13 ages is 135 + 256 = 391 The mean age is therefore 39113 = 30.08 years. QUESTION Mean The mean weight of 10 units at 5 kg, 10 units at 7 kg and 20 units at X kg is 8 kg. Required

Calculate the value of X.

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ANSWER The value of X is 10. WORKINGS Mean = Sum of values of itemsNumber of items Sum of first 10 units = 5 10 = 50 kg Sum of second 10 units = 7 10 = 70 kg Sum of third 20 units = 20 X = 20X Sum of all 40 units = 50 + 70 + 20X = 120 + 20X Arithmetic mean = 8 = 120+20X40 8 40 = 120 + 20X 320 = 120 + 20X (subtract 120 from both sides) 320 – 120 = 20X 200 = 20X 10 = X (divide both sides by 20) 1.15 The advantages and disadvantages of the arithmetic mean Advantages of the arithmetic mean It is easy to calculate. It is widely understood. It is representative of the whole set of data. It is supported by mathematical theory and is suited to further statistical analysis. Disadvantages of the arithmetic mean

Its value may not correspond to any actual value. For example, the 'average' family might have 2.3 children, but no family has exactly 2.3 children. An arithmetic mean might be distorted by extremely high or low values. For example, the mean of 3, 4, 4 and 6 is 4.25, but the mean of 3, 4, 4, 6 and 15 is 6.4. The high value, 15, distorts the average and in some circumstances the mean would be a misleading and inappropriate figure.

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QUESTION Definite variables For the week ended 15 November, the wages earned by the 69 operators employed in the machine shop of Mermaid LLC were as follows. Wages Number of operatives Under Rs. 60 3 Rs. 60 and under Rs. 70 11 Rs. 70 and under Rs. 80 16 Rs. 80 and under Rs. 90 15 Rs. 90 and under Rs. 100 10 Rs. 100 and under Rs. 110 8 Over Rs. 110 6 69 Required

Calculate the arithmetic mean wage of the machine operators of Mermaid LLC for the week ended 15 November. ANSWER The mid point of the range 'under Rs. 60' is assumed to be Rs. 55 and that of the range over Rs. 110 to be Rs. 115, since all other class intervals are Rs. 10. This is obviously an approximation which might result in a loss of accuracy, but there is no better alternative assumption to use. Because wages can vary in steps of 1c, they are virtually a continuous variable and hence the mid-points of the classes are halfway between their end points.

Mid-point of class Frequency x f fx Rs 55 3 165 65 11 715 75 16 1,200 85 15 1,275 95 10 950 105 8 840 115 6 690 69 5,835

Arithmetic mean = fxf = 5,83569 = Rs. 84.57

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1.16 The mode

1.16.1 The modal value The mode or modal value is an average which means 'the most frequently occurring value'. 1.16.2 Example: The mode The daily demand for inventory in a ten-day period is as follows.

Demand Number of days units 6 3 7 6 8 1 10 The mode is 7 units, because it is the value which occurs most frequently.

1.17 The mode of a grouped frequency distribution The mode of a grouped frequency distribution can be calculated from a histogram. 1.17.1 Example: Finding the mode from a histogram Consider the following grouped frequency distribution Class interval Frequency 0 and less than 10 0 10 and less than 20 50 20 and less than 30 150 30 and less than 40 100 (a) The modal class (the one with the highest frequency) is '20 and less than 30'. But how can we find a single value to represent the mode? (b) What we need to do is draw a histogram of the frequency distribution.

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The modal class is always the class with the tallest bar. This may not be the class with the highest frequency if the classes do not all have the same width. (c) We can estimate the mode graphically as follows. Step 1 Join with a straight line the top left-hand corner of the bar for the modal class and the top left hand corner of the next bar to the right. Step 2 Join with a straight line the top right-hand corner of the bar for the modal class and the top right hand corner of the next bar to the left. (d) Where these two lines intersect, we find the estimated modal value. In this example it is approximately 26.7.

(e) We are assuming that the frequencies occur evenly within each class interval but this may not always be correct. It is unlikely that the 150 values in the modal class occur evenly. Hence the mode in a grouped frequency distribution is only an estimate.

The advantages and disadvantages of the mode Advantages of the mode

It is easy to find It is not influenced by a few extreme values It can be used for data which are not even numerical (unlike the mean and median) It can be the value of an actual item in the distribution Disadvantages of the mode

It may be unrepresentative; it takes no account of a high proportion of the data, only representing the most common value It does not take every value into account

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There can be two or more modes within a set of data If the modal class is only very slightly bigger than another class, just a few more items in this other class could mean a substantially different result, suggesting some instability in the measure 1.18 The median 1.18.1 The middle item of a distribution The median of a set of ungrouped data is found by arranging the items in ascending or descending order of value, and selecting the item in the middle of the range. A list of items in order of value is called an array. The median is the value of the middle member of an array. The middle item of an odd number of items is calculated as the th(n +1)2 item. 1.18.2 Example: The median (a) The median of the following nine values: 8 6 9 12 15 6 3 20 11 is found by taking the middle item (the fifth one) in the array: 3 6 6 8 9 11 12 15 20 The median is 9. (b) Consider the following array. 1 2 2 2 3 5 6 7 8 11 The median is 4 because, with an even number of items, we have to take the arithmetic mean of the two middle ones (in this example, (3 + 5)/2 = 4). QUESTION Median The following times taken to produce a batch of 100 units of Product X have been noted. 21 mins, 17 mins, 24 mins, 11 mins, 37 mins, 27 mins, 20 mins, 15 mins, 17 mins, 23 mins, 29 mins, 30 mins 24 mins, 18 mins, 17 mins, 21 mins, 24 mins, 20 mins What is the median time?

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ANSWER The times can be arranged as follows. 11, 15, 17, 17, 17, 18, 20, 20, 21, 21, 23, 24, 24, 24, 27, 29 30, 37 There are eighteen items which is an even number, therefore the median is the arithmetic mean of the two middle items (ie ninth and tenth items) = 21 mins. QUESTION Median The following scores are observed for the times taken to complete a task, in minutes. 12, 34, 14, 15, 21, 24, 9, 17, 11, 8 What is the median score? A 14.00 B 14.10 C 14.50 D 14.60 ANSWER The first thing to do is to arrange the scores in order of magnitude. 8, 9, 11, 12, 14, 15, 17, 21, 24, 34 There are ten items, and so median is the arithmetic mean of the 5th and 6th items. = 14+15 29=2 2 = 14.50 The correct answer is therefore C. You could have eliminated options B and D straight away. Since there are ten items, and they are all whole numbers, the average of the 5th and 6th items is either going to be a whole number (14.00) or 'something and a half' (14.50).

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1.19 Finding the median of an ungrouped frequency distribution The median of an ungrouped frequency distribution is found in a similar way. Consider the following distribution. Value Frequency Cumulative

frequency x f 8 3 3 12 7 10 16 12 22 17 8 30 19 5 35 35 The median would be the (35 + 1)/2 = 18th item. The 18th item has a value of 16, as we can see from the cumulative frequencies in the right hand column of the above table. 1.20 Finding the median of a grouped frequency distribution The median of a grouped frequency distribution can be established from an ogive. Finding the median of a grouped frequency distribution from an ogive is best explained by means of an example. 1.20.1 Example: The median from an ogive Construct an ogive of the following frequency distribution and hence establish the median.

Class Frequency Cumulative frequency Rs.

340, < 370 17 17 370, < 400 9 26 400, < 430 9 35 430, < 460 3 38 460, < 490 2 40 40

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Solution

The median is at the 1/2 40 = 20th item. Reading off from the horizontal axis on the ogive, the value of the median is approximately Rs. 380. Note that, because we are assuming that the values are spread evenly within each class, the median calculated is only approximate.

1.21 The advantages and disadvantages of the median Advantages of the median

It is easy to understand It is unaffected by extremely high or low values It can be the value of an actual item in the distribution Disadvantages of the median

It fails to reflect the full range of values It is unsuitable for further statistical analysis Arranging data into order of size can be tedious The arithmetic mean, mode and median of a grouped frequency distribution can only be estimated approximately Each type of average has a number of advantages and disadvantages that you need to be aware of

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1.22 The variance and the standard deviation The variance, 2, is the average of the squared differences from the mean. is the Greek letter sigma (in lower case). The variance is therefore called 'sigma squared'. 1.23 Calculation of the variance for ungrouped data Step 1 Difference between value (x) and mean ( x ) x – x Step 2 Square of the difference (x – x )2 Step 3 Sum of the squares of the difference (x – x )2 Step 4 Average of the sum (= variance = 2 ) 2(x x)n 1.24 Calculation of the variance for grouped data Step 1 Difference between value and mean (x – x ) Step 2 Square of the difference (x – x )2 Step 3 Sum of the squares of the difference f(x – x )2 Step 4 Average of the sum (= variance = 2)

2f x xf 1.25 The standard deviation The units of the variance are the square of those in the original data because we squared the differences. We therefore need to take the square root to get back to the units of the original data. The standard deviation = square root of the variance. The standard deviation measures the spread of data around the mean. In general, the larger the standard deviation value in relation to the mean, the more dispersed the data. The standard deviation, which is the square root of the variance, is a very important measure of spread used in statistics. Make sure you understand how to calculate the standard deviation of a set of data.

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There are a number of formulae which you may use to calculate the standard deviation; use whichever one you feel comfortable with. The standard deviation formulae are as follows. FORMULA TO LEARN

Standard deviation (for ungrouped data) = 2(x x)n = 2 2x xn

Standard deviation (for grouped data) =

2f(x x)f =

22fx fxf f The key to these calculations is to set up a table with totals as shown below and then use the totals in the formulae given to you.

1.26 Example: The variance and the standard deviation The hours of overtime worked in a particular quarter by the 60 employees of ABC Co are as follows. Hours Frequency

More than Not more than 0 10 3 10 20 6 20 30 11 30 40 15 40 50 12 50 60 7 60 70 6 60 Required

Calculate the variance and the standard deviation of the frequency distribution that follows.

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Solution Using the formula provided, the calculation is as follows. Midpoint

x f fx x² fx² 5 3 15 25 75 15 6 90 225 1,350 25 11 275 625 6,875 35 15 525 1,225 18,375 45 12 540 2,025 24,300 55 7 385 3,025 21,175 65 6 390 4,225 25,350 f = 60 fx = 2,220 fx2 = 97,500 Mean =

fxf = 2,22060 = 37

Variance =

22 2fx fx 97,500= (37)f f 60 = 256 hours Standard deviation = 256 = 16 hours QUESTION Variance and standard deviation

Calculate the variance and the standard deviation of the following frequency distribution. Frequency of

Value occurrence 5 4 15 6 25 8 35 20 45 6 55 6 50 ANSWER

x f fx x2 fx2 5 4 20 25 100 15 6 90 225 1,350 25 8 200 625 5,000 35 20 700 1,225 24,500 45 6 270 2,025 12,150 55 6 330 3,025 18,150 f = 50 fx = 1610 fx2 = 61,250

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Mean = 1,61050 = 32.2 Variance = 61,25050 – (32.2)2 = 188.16 Standard deviation = 188.16 = 13.72 1.27 The main properties of the standard deviation The standard deviation's main properties are as follows. (a) It is based on all the values in the distribution and so is more comprehensive than dispersion measures based on quartiles, such as the quartile deviation. (b) It is suitable for further statistical analysis. (c) It is more difficult to understand than some other measures of dispersion. The importance of the standard deviation lies in its suitability for further statistical analysis (eg using the normal distribution). 1.28 The mean and standard deviation The effect on the mean and the standard deviation if the data of a set are increased or multiplied by a constant is explained below. (a) If each data of a set is increased by a constant, the mean of the set is increased by that constant, but the standard deviation is unaltered. (b) If each data of a set is multiplied by a constant, both the mean and the standard deviation are multiplied by that constant. 1.29 The variance and the standard deviation of several items

together You may need to calculate the variance and standard deviation for n items together, given the variance and standard deviation for one item alone. 1.30 Example: Several items together The daily demand for an item of inventory has a mean of 6 units, with a variance of 4 and a standard deviation of 2 units. Demand on any one day is unaffected by demand on previous days or subsequent days.

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Required

Calculate the arithmetic mean, the variance and the standard deviation of demand for a five-day week. Solution If we let Arithmetic mean = x = 6 Variance = 2 = 4 Standard deviation = = 2 Number of days in week = n = 5 The following rules apply to x , 2 and when we have several items together. Arithmetic mean = n x = 5 × 6 = 30 units Variance = n2 = 5 × 4 = 20 units Standard deviation = 2nσ = 20 = 4.47 units 1.31 Comparing the spreads of two distributions The spreads of two distributions can be compared using the coefficient of variation. FORMULA TO LEARN

Coefficient of variation (coefficient of relative spread) = Standard deviationmean The bigger the coefficient of variation, the wider the spread. For example, suppose that two sets of data, A and B, have the following means and standard deviations. A B Mean 120 125 Standard deviation 50 51 Coefficient of variation (50/120) 0.417 (51/125) 0.408 Although B has a higher standard deviation in absolute terms (51 compared to 50), its relative spread is less than A's since the coefficient of variation is smaller.

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QUESTION Variance The number of new orders received by five salesmen last week is: 1, 3, 5, 7, 9. Required

Calculate the variance of the number of new orders received. A 2.40 B 2.83 C 6.67 D 8.00 ANSWER x 2x x 1 16 3 4 5 0 7 4 9 16 x = 25 2x x = 40 X 25x = 5 = 5 2x x 40=n 5 = 8 The correct answer is therefore D.

2 Probability distribution

2.1 Discrete probability distributions

Formulae can be used to find the mean and standard deviation of discrete probability distributions. A probability distribution is an analysis of the proportion of times each particular value occurs in a set of items. Probability distributions arise when a random variable (X) exists that may take any of a given range of values that can't be predicted with certainty but can be assigned probabilities.

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A probability distribution is said to be discrete if the possible outcomes are each one of a fixed number of numerical values. We have already looked at examples of this in the previous chapter, such as the six numerical outcomes when a die is thrown. 2.1.1 Mean of a discrete probability distribution We looked at the mean of certain probability distributions when we covered expected values in a business context in the previous chapter. However we will re-visit this again here as we will follow on with a look at the standard deviation which utilises the mean. You should also notice the similarities with the mean and standard deviation formulae we looked at in Chapter 1. Consider a discrete random variable (X), which can take specific values of x. The mean or expected value (E) of this random variable can be defined as follows: E(X) = xp Where p is the probability that that X = x. The summation covers all values of x assigned a probability. Note that, as we will see later when we look at normal distributions, the mean E(X) is often represented by the symbol ''. 2.1.2 Variance and standard deviation of a discrete probability distribution You will remember that we covered variance and standard deviation in general in Chapter 1. Look back at this now if you want to remind yourself of the purpose of these measures. The variance (V) of a discrete probability distribution can be expressed as follows: V(X) = x 2p – E(X) 2 So, to calculate the variance, multiply the square of each value by its probability before subtracting the square of the expected value (as described in 2.1.1). The standard deviation () is then simply the square root of the variance. = V(X) 2.1.3 Example: mean and standard deviation of discrete variables The sales for the period of product Q may be as follows. Units Probability100 0.2 150 0.4 200 0.3 250 0.1 1.0

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Required

Calculate the mean (expected value) and standard deviation of sales units. Solution

Sales units Probability (x) (p) 100 0.2 150 0.4 200 0.3 250 0.1 The mean = E(X) = 165 The variance = V(X) = x 2p – E(X) 2 = 29,250 – 1652 = 29,250 – 27,225 = 2,025 The standard deviation () = V(X) = 2025 = 45. 2.2 Converting frequency distributions into probability distributions If we convert the frequencies in a frequency distribution table into proportions, we get a probability distribution.

Marks out of 10 Number of students Proportion or probability(statistics test) (frequency distribution) (probability distribution) 0 0 0.00 1 0 0.00 2 1 0.02* 3 2 0.04 4 4 0.08 5 10 0.20 6 15 0.30 7 10 0.20 8 6 0.12 9 2 0.04 10 0 0.00 50 1.00

* 1/50 = 0.02 2.3 Graphing probability distributions A graph of the probability distribution would be the same as the graph of the frequency distribution, but with the vertical axis marked in proportions as well as in numbers.

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Number or

proportion

of students

Graph of probability/frequency

distribution

1 2 3 4 5 6 7 8 9 10 Marks

5 =0.1

10 =0.2

15 =0.3

Figure 9.1: Graph of probability/frequency distribution (a) The area under the curve in the frequency distribution represents the total number of students whose marks have been recorded, 50 people. (b) The area under the curve in a probability distribution is 100%, or 1 (the total of all the probabilities). There are a number of different probability distributions but the only one that you need to know about for the KE2 exam is the normal distribution.

3 Normal distribution

The normal distribution is a probability distribution which often applies to continuous variables, such as distance and time. 3.1 Introduction In calculating P(x), x can be any value, and does not have to be a whole number. The normal distribution can also apply to discrete variables which can take many possible values. For example, the volume of sales, in units, of a product might be any whole number in the range 100–5,000 units. There are so many possibilities within this range that the variable is, for all practical purposes, continuous.

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3.2 Graphing the normal distribution The normal distribution can be drawn as a graph, and it would be a bell-shaped curve.

Normal distribution

Area under the curve

= 100% of all probabilities

μ x Figure 9.2: Graphing the normal distribution

3.3 Properties of the normal distribution Properties of the normal distribution are as follows. • It is symmetrical and bell-shaped • It has a mean, (pronounced 'mew') • The area under the curve totals exactly 1 • The area to the left of = area to the right of = 0.5 3.4 Importance of the normal distribution The normal distribution is important because, in the practical application of statistics, it has been found that many probability distributions are close enough to a normal distribution to be treated as such without any significant loss of accuracy. This means that the normal distribution can be used as a tool in business decision making involving probabilities.

4 Standard deviation on a normal distribution

4.1 Introduction For any normal distribution, the dispersion around the mean () of the frequency of occurrences can be measured exactly in terms of the standard deviation (). (a) The entire normal frequency curve represents all the possible outcomes and their frequencies of occurrence. Since the normal curve is symmetrical, 50% of occurrences have a value greater than the mean value (), and 50% of occurrences have a value less than the mean value.

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Frequency

(%)

μ or x

50 % ofoccurrences

50 % ofoccurrences

Figure 9.3: Normal distribution (b) About 68% of frequencies have a value within one standard deviation either side of the mean.

μ

34%

1σ

34%

1σ

Figure 9.4: Distribution, one standard deviation (c) 95% of the frequencies in a normal distribution occur in the range 1.96 standard deviations from the mean.

μ

47.5%

1.96σ

47.5%

1.96σ

Figure 9.5: Distribution, 1.96 standard deviations You will not need to remember these precise figures as a normal distribution table can be used to find the relevant proportions, and this will be given to you in the exam.

4.2 Normal distribution tables Although there is an infinite number of normal distributions, depending on values of the mean and the standard deviation , the relative dispersion of frequencies around the mean, measured as proportions of the total population, is exactly the same for all normal distributions. In other words, whatever the normal distribution, 47.5% of outcomes will always be in the range

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between the mean and 1.96 standard deviations below the mean, 49.5% of outcomes will always be in the range between the mean and 2.58 standard deviations below the mean and so on. A normal distribution table gives the proportion of the total between the mean and a point above or below the mean for any multiple of the standard deviation. 4.2.1 Example: Normal distribution tables What is the probability that a randomly picked item will be in the shaded area of the diagram below?

μ

1.96σ

Figure 9.6: Distribution example Look up 1.96 in the normal distribution table and you will obtain the value .475. This means there is a 47.5% probability that the item will be in the shaded area. Since the normal distribution is symmetrical, 1.96 below the mean will also correspond to an area of 47.5%.

μ

47.5%

1.96σ

47.5%

1.96σ

Figure 9.7: Distribution example - answer The total shaded area = 47.5% × 2 = 95% In section 4.1(c) we said that 95% of the frequencies in a normal distribution lie in the range 1.96 standard deviations from the mean; however, we did not say what this figure was based on. It was, of course, based on the corresponding value in the normal distribution tables (when z = 1.96) as shown above. We can also show that 99% of the frequencies occur in the range 2.58 standard deviations from the mean.

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Using the normal distribution table, a z score of 2.58 corresponds to an area of 0.4949 (or 49.5%). Remember, the normal distribution is symmetrical.

μ

49.5%

2.58σ

49.5%

2.58σ

Figure 9.8: 2.58 Standard deviations 49.5% 2 = 99% If mean, + 2.58 = 49.5% and mean, 2.58 = 49.5% Range = mean 2.58 = 99.0% Therefore, 99% of frequencies occur in the range mean () 2.58 standard deviations (), as proved by using normal distribution tables. QUESTION 68% of frequencies

Compute the percentage (to the nearest whole number) of frequencies which have a value within one standard deviation either side of the mean, . ANSWER One standard deviation corresponds to z = 1 If z = 1, we can look this value up in normal distribution tables to get a value (area) of 0.3413. One standard deviation above the mean can be shown on a graph as follows.

μ

34.13%

1σ

Figure 9.9 The normal distribution is symmetrical, and we must therefore show the area corresponding to one standard deviation below the mean on the graph also.

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1 The area one standard deviation below the mean 2 The area one standard deviation above the mean

μ

34.13%

1σ

34.13%

1σ

1 2

Figure 9.10 Area one standard deviation above and below the mean = 1 + 2 = 34.13% + 34.13% = 68.26% ≈ 68%

5 Using normal distribution to calculate distribution probabilities

FORMULA TO LEARN z = σ μx This formula is given to you in the normal distribution table. The normal distribution can be used to calculate probabilities. Sketching a graph of a normal distribution curve often helps in normal distribution problems. z = σ μx where z = the number of standard deviations above or below the mean (z score) x = the value of the variable under consideration = the mean = the standard deviation 5.1 Introduction In order to calculate probabilities, we need to convert a normal distribution (X) with a mean and standard deviation to the standard normal distribution (z) before using the table to find the probability figure.

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5.2 Example: Calculating z Calculate the following z scores and identify the corresponding proportions using normal distribution tables. (a) x = 100, = 200, = 50 (b) x = 1,000, = 1,200, = 200 (c) x = 25, = 30, = 6 Solution (a) z = σμ_x

= 50200100 = 2 A z score of 2 corresponds to a proportion of 0.4772 or 47.72%. (b) z = σμ_x = 2001,2001,000 = 1 A z score of 1 corresponds to a proportion of 0.3413 or 34.13%. (c) z = σμ_x = 63025 = 0.8333 0.8333 corresponds to a proportion of 0.2967 or 29.67%

5.3 Example: Using the normal distribution to calculate probabilities A frequency distribution is normal, with a mean of 100 and a standard deviation of 10.

Required Calculate the proportion of the total frequencies which will be: (1) Above 80 (6) Below 95 (2) Above 90 (7) Below 108 (3) Above 100 (8) In the range 80–110 (4) Above 115 (9) In the range 90–95 (5) Below 85

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Solution (1) If the value (x) is below the mean (), the total proportion is 0.5 plus proportion between the value and the mean (area (a)).

μ

100

0.50a

b

μ

80 Figure 9.11 The proportion of the total frequencies which will be above 80 is calculated as follows.

1010080 = 2 standard deviations below the mean. From the tables, where z = 2, the proportion is 0.4772. The proportion of frequencies above 80 is 0.5 + 0.4772 = 0.9772. (2) The proportion of the total frequencies which will be above 90 is calculated as follows. 1010090 = 1 standard deviation below the mean. From the tables, when z = 1, the proportion is 0.3413. The proportion of frequencies above 90 is 0.5 + 0.3413 = 0.8413. (3) 100 is the mean. The proportion above this is 0.5. (The normal curve is symmetrical and 50% of occurrences have a value greater than the mean, and 50% of occurrences have a value less than the mean.) (4) If the value is above the mean, the proportion (b) is 0.5 minus the proportion between the value and the mean (area (a)).

μ

100

b

x

115

a

Figure 9.12

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The proportion of the total frequencies which will be above 115 is calculated as follows. 115–10010 = 1.5 standard deviations above the mean. From the tables, where z = 1.5, the proportion is 0.4332. The proportion of frequencies above 115 is therefore 0.5 – 0.4332 = 0.0668. (5) If the value is below the mean, the proportion (b) is 0.5 minus the proportion between the value and the mean (area (a)).

μ

100

b

x

85

a

Figure 9.13 The proportion of the total frequencies which will be below 85 is calculated as follows.

1010085 = 1.5 standard deviations below the mean. The proportion of frequencies below 85 is therefore the same as the proportion above 115 = 0.0668. (6) The proportion of the total frequencies which will be below 95 is calculated as follows. 1010095 = 0.5 standard deviations below the mean. When z = 0.5, the proportion from the tables is 0.1915. The proportion of frequencies below 95 is therefore 0.5 – 0.1915 = 0.3085. (7) If the value is above the mean, the proportion required is 0.5 plus the proportion between the value and the mean (area (a)).

μ

100

b

x

108

a

0.50

Figure 9.14

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The proportion of the total frequencies which will be below 108 is calculated as follows. 10100108 = 0.8 standard deviations above the mean. From the tables for z = 0.8 the proportion is 0.2881. The proportion of frequencies below 108 is 0.5 + 0.2881 = 0.7881. (8) The proportion of the total frequencies which will be in the range 80–110 is calculated as follows. The range 80 to 110 may be divided into two parts: (i) 80 to 100 (the mean); (ii) 100 to 110.

μ

100 11080 Figure 9.15 The proportion in the range 80 to 100 is (2 standard deviations) 0.4772 The proportion in the range 100 to 110 is (1 standard deviation) 0.3413 The proportion in the total range 80 to 110 is 0.4772 + 0.3413 = 0.8185. (9) The range 90 to 95 may be analysed as: (i) The proportion above 90 and below the mean (ii) Minus the proportion above 95 and below the mean

90 95 100 90 100 95 100

= minus

Figure 9.16 Proportion above 90 and below the mean (1 standard deviation) 0.3413 Proportion above 95 and below the mean (0.5 standard deviations) 0.1915 Proportion between 90 and 95 0.1498

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QUESTION Normal distribution and proportions The salaries of employees in an industry are normally distributed, with a mean of Rs. 14,000 and a standard deviation of Rs. 2,700. Required (a) Calculate the proportion of employees who earn less than Rs. 12,000. (b) Calculate the proportion of employees who earn between Rs. 11,000 and Rs. 19,000. ANSWER

(a)

14,00012,000

Required

area

z = 2,70014,00012,000 = 0.74 From normal distribution tables, the proportion of salaries between Rs. 12,000 and Rs. 14,000 is 0.2704 (from tables). The proportion of salaries less than Rs. 12,000 is therefore 0.5 – 0.2704 = 0.2296. (b)

14,000

1 2

19,00011,000 1 z = 2,70014,00011,000 = 1.11 2 z = 2,70014,00019,000 = 1.85

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The proportion with earnings between Rs. 11,000 and Rs. 14,000 is 0.3665 (from tables, where z = 1.11). The proportion with earnings between Rs. 14,000 and Rs. 19,000 is 0.4678 (from tables, where z = 1.85). The required proportion is therefore 0.3665 + 0.4678 = 0.8343. Note that the normal distribution is, in fact, a way of calculating probabilities. In this question, for example, the probability that an employee earns less than Rs. 12,000 (part (a)) is 0.2296 (or 22.96%); the probability that an employee earns between Rs. 11,000 and Rs. 19,000 is 0.8343 (or 83.43%). Make sure you always draw a sketch of a normal distribution to identify the areas that you are concerned with. If you are given the variance of a distribution, remember to first calculate the standard deviation by taking its square root. QUESTION Normal distribution The specification for the width of a widget is a minimum of 42mm and a maximum of 46.2mm. A normally distributed batch of widgets is produced with a mean of 45mm and a variance of 4mm. Required (a) Calculate the percentage of parts that are too small. (b) Calculate the percentage of parts that are too big. ANSWER (a)

45mm42mm

Required

area

= 4 = 2 z = 2 4542 = – 1.5 Proportion of widgets between 42mm and 45mm = 0.4332 Proportion of widgets smaller than 42mm = 0.5 – 0.4332 = 0.0668 = 6.68%

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(b) Required

area

46.2mm45.mm z = 2 4546.2 = 0.6 Proportion of widgets between 45mm and 46.2mm = 0.2257 Proportion of widgets bigger than 46.2mm = 0.5 – 0.2257 = 0.2743 = 27.43% QUESTION Standard deviation A population is normally distributed with a mean of 120 and a standard deviation of 15. Required

Calculate the value of the variable where 75% of the population falls below that. ANSWER 50% of the population is below 120. 25% of the population is below x. From the normal distribution table, a value of 0.25 equates to a z value of 0.67. z = σμx

0.67 = 15120x 0.67 × 15 = x – 120 10.05 = x – 120 x = 10.05 + 120 = 130.05 75% of the population is below 130.05.

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6 Risk and uncertainty Risk and uncertainty

in decision making

Measuring risk••

Standard deviationSpread

Techniques•••••

Pay off tablesJoint probabilitiesDecision treesSensitivity analysisSimulation

Decision methods•••

MaximaxMaximinMinimax regret

Risk preference•••

Risk seekerRisk averseRisk neutral

Risk vsuncertainty

Value of perfectinformation

Expected values• Σpx

6.1 What are risk and uncertainty? An example of a risky situation is one in which we can say that there is a 70% probability that returns from a project will be in excess of $100,000 but a 30% probability that returns will be less than $100,000. If no information can be provided on the returns from the project, we are faced with an uncertain situation. Risk involves situations or events that may or may not occur, but whose probability of occurrence can be calculated statistically and the frequency of their occurrence predicted from past records. Thus insurance deals with risk. Uncertain events are those whose outcome cannot be predicted with statistical confidence. 6.2 Risk and capital investment decisions In general, risky projects are those that have future cash flows, and hence project returns, that are likely to be variable. The greater the variability, the greater the risk. The problem of risk is more acute with capital investment decisions for the following reasons. (a) Estimates of capital expenditure might be for several years ahead, such as those for major construction projects. Actual costs may escalate well above budget as the work progresses.

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(b) Estimates of benefits will be for several years ahead, sometimes 10, 15 or 20 years ahead or even longer, and such long-term estimates can at best be approximations. 6.3 Risk preference A risk seeker is a decision maker who is interested in the best outcomes no matter how small the chance that they may occur. A risk neutral decision maker is concerned with what will be the most likely outcome. A risk averse decision maker acts on the assumption that the worst outcome might occur.

6.3.1 Example This has clear implications for managers and organisations. A risk-seeking manager working for an organisation that is characteristically risk averse is likely to make decisions that are not congruent with the goals of the organisation. There may be a role for the management accountant here, who could be instructed to present decision-making information in such a way as to ensure that the manager considers all of the possibilities, including the worst. What is an acceptable amount of risk will vary from organisation to organisation. For large public companies it is largely a question of what is acceptable to the shareholders. A 'safe' investment will attract investors who are to some extent risk averse, and so the company will be obliged to follow relatively 'safe' policies. A company that is recognised as being an innovator or a 'growth' inventory in a relatively new market will attract investors who are looking for high performance, and are prepared to accept some risk in return. Such companies will be expected to make 'bolder' (more risky) decisions. The risk of an individual strategy should also be considered in the context of the overall 'portfolio' of investment strategies adopted by the company. (a) If a strategy is risky, but its outcome is not related to the outcome of

other strategies, then adopting that strategy will help the company to spread its risks. (b) If a strategy is risky, but is inversely related to other adopted strategies (so that if strategy A does well, other adopted strategies will do badly and vice versa) then adopting strategy A would actually reduce the overall risk of the company's investment portfolio.

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7 Allowing for uncertainty

Management accounting directs its attention towards the future and the future is uncertain. For this reason, a number of methods of taking uncertainty into consideration have evolved.

7.1 Market research This approach simply involves estimating outcomes in a conservative manner in order to provide a built-in safety factor. Market research is the systematic process of gathering, analysing and reporting data about markets to investigate, describe, measure, understand or explain a situation or problem facing a company or organisation.

Market research involves tackling problems. The assumption is that these problems can be solved, no matter how complex the issues are, if the researcher follows a line of enquiry in a systematic way, without losing sight of the main objectives. Gathering and analysing all the facts will ultimately lead to better decision making.

7.1.1 The role of market research In the last 20 years or so market research has become a much more widespread activity. Organisations – in the private sector, the public sector and the not-for-profit sector – rely on research to inform and improve their planning and decision making. Market research enables organisations to understand the needs and opinions of their customers and other stakeholders. Armed with this knowledge they are able to make better quality decisions and provide better products and better services. Thus, research influences what is provided and the way it is provided. It reduces uncertainty and monitors performance. A management team which possesses accurate information relating to the marketplace will be in a strong position to make the best decisions in an increasingly competitive world. Decision makers need data to reduce uncertainty and risk when planning for the future and to monitor business performance. Market researchers provide the data that helps them to do this.

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7.1.2 Types of data collected Data can be either primary (collected at first hand from a sample of respondents), or secondary (collected from previous surveys, other published facts and opinions, or from experts). Secondary research is also known as desk research, because it can be carried out from one's desk. More importantly for research practice and analysis, data can be either quantitative or qualitative. Quantitative data usually deals with numbers and typically provides the decision maker with information about how many customers, competitors etc act in a certain way. Quantitative data can, for example, tell the researcher what people need or consume, or where, when and how people buy goods or consumer services. Qualitative data tells us why consumers think/buy or act the way they do. Qualitative data is used in consumer insight (eg understanding what makes consumers prefer one brand to another), media awareness (eg how much of an advertisement is noticed by the public), new product development studies and for many other reasons. Qualitative research has as its specific purpose the uncovering and understanding of thought and opinion. It is carried out on relatively small samples and unstructured or semi-structured techniques, such as individual in depth interviews and group discussions (also known as focus groups), are used. 7.2 Conservatism This approach simply involves estimating outcomes in a conservative manner in order to provide a built-in safety factor. However, the method fails to consider explicitly a range of outcomes and, by concentrating only on conservative figures, may also fail to consider the expected or most likely outcomes. Conservatism is associated with risk aversion and prudence (in the general sense of the word). In spite of its shortcomings it is probably the most widely used method in practice.

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8 Expected values

Expected values indicate what an outcome is likely to be in the long term with repetition. Fortunately, many business transactions do occur over and over again. Although the outcome of a decision may not be certain, there is some likelihood that probabilities could be assigned to the various possible outcomes from an analysis of previous experience. 8.1 Expected values Where probabilities are assigned to different outcomes, we can evaluate the worth of a decision as the expected value (EV), or weighted average, of these outcomes. The principle is that when there are a number of alternative decisions, each with a range of possible outcomes, the optimum decision will be the one which gives the highest expected value. 8.1.1 Example: Expected values Suppose a manager has to choose between mutually exclusive options A and B, and the probable outcomes of each option are as follows.

Option A Option B Probability Profit Probability Profit Rs '000 Rs '000 0.8 5,000 0.1 (2,000) 0.2 6,000 0.2 5,000 0.6 7,000 0.1 8,000 The EV of profit of each option would be measured as follows. _______________Option A________________ _______________Option B_____________

Prob. Profit EV of profit

Prob. Profit EV of profit Rs '000 Rs '000 Rs '000 Rs '000 0.8 5,000 4,000 0.1 (2,000) = (200) 0.2 6,000 1,200 0.2 5,000 = 1,000 EV 5,200 0.6 7,000 = 4,200 0.1 8,000 = 800 EV = 5,800 In this example, since it offers a higher EV of profit, option B would be selected in preference to A, unless further risk analysis is carried out.

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8.1.2 Example: Expected values and pay-off tables IB Newsagents stocks a weekly lifestyle magazine. The owner buys the magazines for Rs. 300 each and sells them at the retail price of Rs. 500 each. At the end of the week unsold magazines are obsolete and have no value. The estimated probability distribution for weekly demand is shown below. Weekly demand in units Probability 20 0.20 30 0.55 40 0.25 1.00 Required

Calculate the expected value of demand. If the owner is to order a fixed quantity of magazines per week, calculate how many that should be. Assume no seasonal variations in demand. Solution EV of demand (units per week) = (20 0.20) + (30 0.55) + (40 0.25) = 30.5 units per week The next step is to set up a decision matrix of possible strategies (numbers bought) and possible demand. The 'pay-off' from each combination of action and outcome is then computed. No sale = cost of Rs. 300 per magazine Sale = profit of Rs. 200 per magazine (Rs. 500 – Rs. 300)

Probability

Outcome (number

demanded) Decision (number bought) 20 30 40 Rs '000 Rs '000 Rs '000 0.20 20 4.00 1.00* (2.00) 0.55 30 4.00 6.00 3.00 0.25 40 4.00 6.00 8.00 1 EV 4.00 5.00** 3.25 * Buy 30 and sell only 20 gives a profit of (20 Rs. 500) – (30 Rs. 300) = Rs. 1.000 ** (0.2 Rs. 1,000) + (0.55 Rs. 6,000) + (0.25 Rs. 6,000) = Rs. 5,000 The strategy which gives the highest expected pay-off is to stock 30 magazines each week.

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QUESTION EVs A manager has to choose between mutually exclusive options C and D and the probable outcomes of each option are as follows. Option C Option D

Probability Cost Probability Cost Rs Mn Rs Mn 0.29 15 0.03 14 0.54 20 0.30 17 0.17 30 0.35 21 0.32 24 Both options will produce an income of Rs. 30m. Required Identify which option should be chosen. ANSWER The answer is Option C. Do the workings yourself in the way illustrated above. Note that the probabilities are for costs not profits.

8.1.3 Limitations of expected values There are the following problems with using expected values in making investment decisions. An investment may be one-off, and 'expected' net present value (NPV) may never actually occur. Assigning probabilities to events is highly subjective. Expected values do not evaluate the range of possible NPV outcomes. Expected values are more valuable as a guide to decision making where they refer to outcomes which will occur many times over. Examples would include the probability that so many customers per day will buy a can of baked beans, the probability that a customer services assistant will receive so many phone calls per hour and so on. 8.2 Worst/most likely/best outcome estimates A more scientific version of conservatism is to measure the most likely outcome from a decision, and the worst and best possible outcomes. This will show the full range of possible outcomes from a decision, and might help managers to reject certain alternatives because the worst possible outcome might involve an unacceptable amount of loss. This requires the preparation of pay-off tables.

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8.2.1 Pay-off tables Pay-off tables identify and record all possible outcomes (or pay-offs) in situations where the action taken affects the outcomes. 8.2.2 Example: Worst/best possible outcomes Om LLC is trying to set the sales price for one of its products. Three prices are under consideration, and expected sales volumes and costs are as follows. Price per unit Rs. 4,000 Rs. 4,300 Rs. 4,400 Expected sales volume (units) Best possible 16,000 14,000 12,500 Most likely 14,000 12,500 12,000 Worst possible 10,000 8,000 6,000 Fixed costs are Rs. 20m and variable costs of sales are Rs. 2,000 per unit. Required

Identify which price should be chosen. Solution Here we need to prepare a pay-off table showing pay-offs (contribution) dependent on different levels of demand and different selling prices. Price per unit Rs. 4,000 Rs. 4,300 Rs. 4,400 Contribution per unit Rs. 2,000 Rs. 2,300 Rs. 2,400 Total contribution towards fixed costs Rs '000 Rs '000 Rs '000 Best possible 32,000 32,200 30,000 Most likely 28,000 28,750 28,800 Worst possible 20,000 18,400 14,400 (a) The highest contribution based on most likely sales volume would be at a price of Rs. 4,400, but arguably a price of Rs. 4,300 would be much better than Rs. 4,400, since the most likely profit is almost as good, the worst possible profit is not as bad and the best possible profit is better. (b) However, only a price of Rs. 4,000 guarantees that the company would not

make a loss, even if the worst possible outcome occurs. (Fixed costs of Rs. 20m would just be covered.) A risk averse management might therefore prefer a price of Rs. 4,000 to either of the other two prices. QUESTION Profitability possibilities A theatre has a seating capacity of 500 people and is considering engaging MS and their orchestra for a concert for one night only. The fee that would be charged by MS would be Rs. 10m. If the theatre engages MS, then this sum is payable regardless of the size of the theatre audience.

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Based on past experience of events of this type, the price of the theatre ticket would be Rs. 25,000 per person. The size of the audience for this event is uncertain, but based on past experience it is expected to be as follows. Probability 300 people 50% 400 people 30% 500 people 20% In addition to the sale of the theatre tickets, it can be expected that members of the audience will also purchase confectionery both prior to the performance and during the interval. The contribution that this would yield to the theatre is unclear, but has been estimated as follows. Contribution from confectionery sales Probability Contribution of Rs. 3,000 per person 30% Contribution of Rs. 5,000 per person 50% Contribution of Rs. 10,000 per person 20%

Required (a) Using expected values as the basis of your decision, advise the theatre management whether it is financially worthwhile to engage MS for the concert. (b) Prepare a two-way data table to show the profit values that could occur from deciding to engage MS for the concert.

ANSWER (a) Expected audience size Audience size Probability EV 300 0.5 150 400 0.3 120 500 0.2 100 370 Expected value of confectionery sales

Contribution/person Rs '000 Probability EV Rs '000 3 0.3 0.90 5 0.5 2.50 10 0.2 2.00 5.40 Expected spend per person = ticket price + EV of confectionery sales = 25K + 5.40K = Rs. 30.40K

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Expected total spend = 30.40 expected number of people = 30.40K 370 = Rs. 11,248K Expected profit = 11,248K – fixed costs 10,000K = Rs. 1,248K As the theatre is expected to make a profit of Rs. 1,248K, it is financially worthwhile to engage MS for the concert. (b) Two-way data table for profit values Two-way data table showing profit for a range of audience size based on Rs. 25,000 ticket per head and confectionery sales. Audience size 300 400 500 Rs Mn Rs Mn Rs Mn Rs. 3K/head (1,600) 1,200 4,000 Confectionery sales Rs. 5K/head (1,000) 2,000 5,000 Rs. 10K/head 500 4,000 7,500

9 Decision rules

The 'play it safe' basis for decision making is referred to as the maximin basis. This is short for 'maximise the minimum achievable profit'. A basis for making decisions by looking for the best outcome is known as the maximax basis, short for 'maximise the maximum achievable profit'. The 'opportunity loss' basis for decision making is known as minimax regret. In this last section we look at various decision-making processes when the business is faced with uncertainty. 9.1 The maximin decision rule The maximin decision rule suggests that a decision maker should select the alternative that offers the least unattractive worst outcome. This would mean choosing the alternative that maximises the minimum profits.

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Suppose a business person is trying to decide which of three mutually exclusive projects to undertake. Each of the projects could lead to varying net profit under three possible scenarios. Profits Project D E F I 100 80 60 Scenarios II 90 120 85 III (20) 10 85 The maximin decision rule suggests that he or she should select the 'smallest worst result' that could happen. This is the decision criterion that managers should 'play safe' and either minimise their losses or costs, or else go for the decision which gives the higher minimum profits. If he or she selects project D, the worst result is a loss of 20. The worst results for E and F are profits of 10 and 60 respectively. The best worst outcome is 60 and project F would therefore be selected (because this is a better 'worst possible' than either D or E). 9.1.1 Criticisms of maximin (a) It is defensive and conservative, being a safety first principle of avoiding the worst outcomes without taking into account opportunities for maximising profits. (b) It ignores the probability of each different outcome taking place. 9.2 Maximax The maximax criterion looks at the best possible results. Maximax means 'maximise the maximum profit'.

Using the information above, the maximum profit for D is 100, for E is 120 and for F is 85. Project E would be chosen if the maximax rule is followed. 9.2.1 Criticisms of maximax (a) It ignores probabilities. (b) It is over-optimistic. QUESTION Maximax and maximin A company is considering which one of three alternative courses of action, A, B and C, to take. The profit or loss from each choice depends on which one of four economic circumstances, I, II, III or IV, will apply. The possible profits and losses,

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in millions of rupees, are given in the following pay-off table. Losses are shown as negative figures. Action A B C I 70 60 70 Circumstance II (10) 20 (5) III 80 0 50 IV 60 100 115 Required

State which action would be selected using each of the maximax and maximin criteria. ANSWER (a) The best possible outcomes are as follows. A (circumstance III): 80 B (circumstance IV): 100 C (circumstance IV): 115 As 115 is the highest of these three figures, action C would be chosen using the maximax criterion. (b) The worst possible outcomes are as follows. A (circumstance II): (10) B (circumstance III): 0 C (circumstance II): (5) The best of these figures is 0 (neither a profit nor a loss), so action B would be chosen using the maximin criterion.

9.3 Minimax regret rule The minimax regret rule aims to minimise the regret from making the wrong decision. Regret is the opportunity lost through making the wrong decision. We first consider the extreme to which we might come to regret an action we had chosen. Regret for any combination of action and circumstances = profit for best action in those circumstances – profit for the action actually chosen in those circumstances

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The minimax regret decision rule is that the decision option selected should be the one which minimises the maximum potential regret for any of the possible outcomes. Using the example above, a table of regrets can be compiled as follows. Project D E F I 0 20* 40** Scenario II 30*** 0 35 III 105 75 0 Maximum regret 105 75 40 * 100 – 80 ** 100 – 60 *** 120 – 90 The lowest of maximum regrets is 40 with project F so project F would be selected if the minimax regret rule is used. 9.4 Contribution tables Questions requiring application of the decision rules often incorporate a number of variables, each with a range of possible values. For example, these variables might be: Unit price and associated level of demand Unit variable cost Each variable might have, for example, three possible values. Before being asked to use the decision rules, exam questions could ask you to work out contribution for each of the possible outcomes. (Alternatively, profit figures could be required if you are given information about fixed costs.) The number of possible outcomes = number of values of variable 1 number of values of variable 2 number of values of variable 3 etc So, for example, if there are two variables, each with three possible values, there are 3 3 = 9 outcomes. Perhaps the easiest way to see how to draw up contribution tables is to look at an example. 9.4.1 Example: Contribution tables and the decision rules Suppose the budgeted demand for product X will be 11,500 units if the price is Rs. 10,000, 8,500 units if the price is Rs. 12,000 and 5,000 units if the price is Rs. 14,000. Variable costs are estimated at Rs. 4,000, Rs. 5,000 or Rs. 6,000 per unit. A decision needs to be made on the price to be charged.

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Here is a contribution table showing the budgeted contribution for each of the nine possible outcomes. Demand Price Variable cost

Unit contribution

Total contribution Rs '000 Rs '000 Rs '000 Rs Mn 11,500 10 4 6 69.0 11,500 10 5 5 57.5 11,500 10 6 4 46.0 8,500 12 4 8 68.0 8,500 12 5 7 59.5 8,500 12 6 6 51.0 5,000 14 4 10 50.0 5,000 14 5 9 45.0 5,000 14 6 8 40.0 Once the table has been drawn up, the decision rules can be applied.

Required

Recommend which price should be charged. Solution

Maximin We need to maximise the minimum contribution. Demand/price

Minimum contribution 11,500/Rs. 10,000 Rs. 46m 8,500/Rs. 12,000 Rs. 51m 5,000/Rs. 14,000 Rs. 40m

Set a price of Rs. 12,000.

Maximax We need to maximise the maximum contribution. Demand/price

Maximum contribution 11,500/Rs. 10,000 Rs. 69m 8,500/Rs. 12,000 Rs. 68m 5,000/Rs. 14,000 Rs. 50m

Set a price of Rs. 10,000.

Minimax regret We need to minimise the maximum regret (lost contribution) of making the wrong decision.

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Variable cost Price R Rs. 10,000 Rs. 12,000 Rs. 14,000 4 – Rs. 1m Rs. 19m 5 Rs. 2m – Rs. 14.5m 6 Rs. 5m – Rs. 11m Minimax regret Rs. 5m Rs. 1m Rs. 19m Minimax regret strategy (price of Rs. 12,000) is that which minimises the maximum regret (Rs. 1m). Sample working At a variable cost of Rs. 4,000, the best strategy would be a price of Rs. 10,000. Choosing a price of Rs. 12,000 would mean lost contribution of Rs. 69m – Rs. 68m, while choosing a price of Rs. 14,000 would mean lost contribution of Rs. 69m – Rs. 50m.

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The arithmetic mean is the best known type of average and is widely understood. It is used for further statistical analysis. Arithmetic mean of ungrouped data = Sum of values of itemsNumber of items The arithmetic mean of grouped data, x = fxn or

fxf where n is the number of values recorded, or the number of items measured. This formula will be given to you in your exam.

The mode or modal value is an average which means 'the most frequently occurring value'. The mode of a grouped frequency distribution can be calculated from a histogram. The median is the value of the middle member of an array. The middle item of an odd number of items is calculated as the th(n +1)2 item. The median of a grouped frequency distribution can be established from an ogive. The variance, 2, is the average of the squared differences from the mean. The standard deviation, which is the square root of the variance, is a very important measure of spread used in statistics. Make sure you understand how to calculate the standard deviation of a set of data. The spreads of two distributions can be compared using the coefficient of

variation. The 'play it safe' basis for decision making is referred to as the maximin basis. This is short for 'maximise the minimum achievable profit'. A basis for making decisions by looking for the best outcome is known as the

maximax basis, short for 'maximise the maximum achievable profit'. The 'opportunity loss' basis for decision making is known as minimax regret. Probability is a measure of likelihood and can be stated as a percentage, a ratio or, more usually, as a number from 0 to 1. The simple addition law for two mutually exclusive events, A and B, is as follows. P(A or B) = P (A B) = P(A) + P(B) Mutually exclusive outcomes are outcomes where the occurrence of one of the outcomes excludes the possibility of any of the others happening.

CHA

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The simple multiplication law for two independent events, A and B, is as follows. P(A and B) = P (A B) = P(A)P(B) Independent events are events where the outcome of one event in no way affects the outcome of the other events. The general rule of addition for two events, A and B, which are not mutually exclusive, is as follows. P(A or B) = P (A B) = P(A) + P(B) – P(A and B) The general rule of multiplication for two dependent events, A and B is: P(A and B) = P(A) P(B|A) = P(B) P(A|B) Dependent or conditional events are events where the outcome of one event depends on the outcome of the others. Contingency tables can be useful for dealing with conditional probability. Formulae can be used to find the mean and standard deviation of discrete probability distributions. The normal distribution is a probability distribution which often applies to

continuous variables, such as distance and time. Properties of the normal distribution are as follows.

It is symmetrical and bell-shaped It has a mean, (pronounced 'mew') The area under the curve totals exactly 1 The area to the left of = area to the right of = 0.5

If you are given the variance of a distribution, remember to first calculate the standard deviation by taking its square root. Management accounting directs its attention towards the future and the future is

uncertain. For this reason, a number of methods of taking uncertainty into consideration have evolved. Expected values indicate what an outcome is likely to be in the long term with repetition. Fortunately, many business transactions do occur over and over again.

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1 A manager is trying to decide which of three mutually exclusive projects to undertake. Each of the projects could lead to varying net costs which the manager calls outcomes I, II and III. The following pay-off table or matrix has been constructed. Outcomes (Net profit)

Project I (Worst) II (Most likely) III (Best) A 60 70 120 B 85 75 140 C 100 120 135 Using the minimax regret decision rule, decide which project should be undertaken? 2 If the decision maker is trying to maximise the figure, what figure would the decision maker choose at point B in the diagram below? A 40,000 C 13,900 B 11,800 D 22,000

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D

0.9

0.1

0.8

0.2 33,000

14,000

22,000

40,000

11,000 3 Given the probability distribution shown below, assign ranges of numbers in order to run a simulation model. Probability Numbers assigned Probability Numbers assigned 0.132 …………………….. 0.083 …………………….. 0.410 …………………….. 0.060 …………………….. 0.315 ……………………..

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4 AB can choose from five mutually exclusive projects. The projects will each last for one year only and their net cash inflows will be determined by the prevailing market conditions. The forecast net cash inflows and their associated probabilities are shown below. Market conditions Poor Good Excellent Probability 0.20 0.40 0.40 Rs Mn Rs Mn Rs Mn Project L 550 480 580 Project M 450 500 570 Project N 420 450 480 Project O 370 410 430 Project P 590 580 430 Based on the expected value of the net cash inflows, which project should be undertaken?

5 Insert the formulae in the box below into the correct position. (a) The arithmetic mean of ungrouped data = (b) The arithmetic mean of grouped data = or • nx • nfx • ffx

6 The mean weight of a group of components has been calculated as 133.5. The individual weights of the components were 143, 96, x, 153.5, 92.5, y, 47. When y = 4x, compute the value of x.

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7 Calculate the mid-points for both discrete and continuous variables in the table below. Class interval Mid-point Mid-point

(Discrete data) (Continuous data) 25 < 30 30 < 35 35 < 40 40 < 45 45 < 50 50 < 55 55 < 60 60 < 65 8 The standard deviation of a sample of data is 36. What is the value of the variance? 9 Complete the following equations using the symbols in the box below. (a) Price index = 100 (b) Quantity index = 100 P1 P0 Q1 Q0

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1 A table of regrets can be compiled, as follows, showing the amount of profit that might be forgone for each project, depending on whether the outcome is I, II or III.

Outcome Maximum I II III Project A 40* 50 20 50 Project B 15** 45 0 45 Project C 0 0 5 5 * 100 – 60 ** 100 – 85 etc The maximum regret is 50 with project A, 45 with B and 5 with C. The lowest of these three maximum regrets is 5 with C, and so project C would be selected if the minimax regret rule is used.

2 The answer is D. Choice between ((0.2 33,000) + (0.8 14,000)) = 17,800 at C, 22,000, and ((0.1 40,000) + (0.9 11,000)) = 13,900 at D. 3 Probability Numbers assigned Probability Numbers assigned 0.132 000–131 0.083 857–939 0.410 132–541 0.060 940–999 0.315 542–856 4

EV Rs Mn Project L (550 0.20 + 480 0.40 + 580 0.40) 534 Project M (450 0.20 + 500 0.40 + 570 0.40) 518 Project N (420 0.20 + 450 0.40 + 480 0.40) 456 Project O (370 0.20 + 410 0.40 + 430 0.40) 410 Project P (590 0.20 + 580 0.40 + 430 0.40) 522 Project L has the highest EV of expected cash inflows and should therefore be undertaken. 5 (a) nx

(b) nfx or ffx

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6 Mean = Total7 So Total = 7 × 133.5 = 934.5 934.5 = 143 + 96 + x + 153.5 + 92.5 + y + 47 934.5 = 532 + x + y y = 4x So 934.5 = 532 + x + 4x 5x = 934.5 – 532 5x = 402.5 x = 80.5 7 Class interval Mid-point Mid-point (Discrete data) (Continuous data) 25 < 30 27 27.5 30 < 35 32 32.5 35 < 40 37 37.5 40 < 45 42 42.5 45 < 50 47 47.5 50 < 55 52 52.5 55 < 60 57 57.5 60 < 65 62 62.5 8 The variance is the square of the standard deviation. 362 = 1,296 9 (a) Price index = 10PP 100 (b) Quantity index = 10QQ 100

80.5

1,296

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Knowledge Component E Working capital management 5.1 Material management 5.1.1 Illustrate the inventory control process 5.1.2 Calculate inventory related costs for a manufacturing organisation 5.1.3 Calculate inventory control levels and EOQ 5.1.4 Calculate the cost of issued stocks and closing inventory using FIFO, LIFO and weighted average cost methods

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INTRODUCTION The investment in inventory is a very important one for most businesses, both in terms of monetary value and relationships with customers (no inventory, no sale, loss of customer goodwill). It is therefore vital that management establish and maintain an effective inventory control system. This chapter will concentrate on an inventory control system for materials, but similar problems and considerations apply to all forms of inventory.

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CHAPTER CONTENTS

LEARNING OUTCOME1 What is inventory control? 5.1.12 The ordering, receiving, purchasing, issuing and storage methods 5.1.1

3 Centralised and decentralised storing 5.1.14 Periodic vs perpetual stock taking 5.1.15 Inventory related costs 5.1.26 Inventory control levels and EOQ 5.1.37 Inventory valuation 5.1.48 FIFO (first in, first out) 5.1.49 LIFO (last in, first out) 5.1.410 AVCO (cumulative weighted average pricing) 5.1.4

1 What is inventory control?

1.1 Introduction

Inventory control includes the functions of inventory ordering and purchasing, receiving goods into store, storing and issuing inventory and controlling levels of inventory. Classifications of inventories

Raw materials Spare parts/consumables Work in progress Finished goods This chapter will concentrate on an inventory control system for materials, but similar problems and considerations apply to all forms of inventory. Controls should cover the following functions. The ordering of inventory The purchase of inventory The receipt of goods into store Storage The issue of inventory and maintenance of inventory at the most appropriate level

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1.2 Qualitative aspects of inventory control We may wish to control inventory for the following reasons. Holding costs of inventory may be expensive. Production will be disrupted if we run out of raw materials. Unused inventory with a short shelf life may incur unnecessary expenses. If manufactured goods are made out of low quality materials, the end product will be of low quality also. It may therefore be necessary to control the quality of inventory, in order to maintain a good reputation with consumers.

2 The ordering, receiving, purchasing, issuing and storage methods

2.1 Ordering and receiving materials Every movement of a material in a business should be documented using the following as appropriate: purchase requisition; purchase order; goods received note (GRN); materials requisition note; materials transfer note and materials returned note. Proper records must be kept of the physical procedures for ordering and receiving a consignment of materials. However, not all companies will need to follow all of these steps as much of it may be done electronically. As electronic functions are becoming increasing popular then these steps will be required less and less. The steps ensure the following: That enough inventory is held That there is no duplication of ordering That quality is maintained That there is adequate record-keeping for accounts purposes 2.2 Purchase requisition Current inventories run down to the level where a reorder is required. The stores department issues a purchase requisition which is sent to the purchasing department, authorising the department to order further inventory.

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PURCHASE REQUISITION

Department/job number:

Suggested Supplier:

Req. No.

Date

Requested by:

Latest date required:

QuantityCode

numberDescription Estimated Cost

Unit Rs

Authorised signature: Figure 4.1: Purchase requisition form

2.3 Purchase order The purchasing department draws up a purchase order which is sent to the supplier. (The supplier may be asked to return an acknowledgement copy as confirmation of his acceptance of the order.) Copies of the purchase order must be sent to the accounts department and the storekeeper (or receiving department). Our Order Ref:

To

Date

(Address) Please deliver to the above address

Ordered by:

Passed and checked by:

Total Order Value Rs

Subtotal

VAT

(@ 12%)

Total

Purchase Order/Confirmation

Figure 4.2: Purchase order

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2.4 Quotations The purchasing department may have to obtain a number of quotations if either a new inventory line is required, the existing supplier's costs are too high or the existing supplier no longer stocks the goods needed. Trade discounts (reduction in the price per unit given to some customers) should be negotiated where possible. 2.5 Delivery note The supplier delivers the consignment of materials, and the storekeeper signs a delivery note for the carrier. The packages must then be checked against the copy of the purchase order, to ensure that the supplier has delivered the types and quantities of materials which were ordered. (Discrepancies would be referred to the purchasing department.) 2.6 Goods received note If the delivery is acceptable, the storekeeper prepares a goods received note (GRN), an example of which is shown below.

DATE:

OUR ORDER NO:

SUPPLIER AND SUPPLIER’S ADVICE NOTE NO:

TIME:

QUANTITY CAT NO DESCRIPTION

RECEIVED IN GOOD CONDITION: (INITIALS)

GOODS RECEIVED NOTE WAREHOUSE COPY

NO 5565

WAREHOUSE A

Figure 4.3: Goods Received Note (GRN) A copy of the GRN is sent to the accounts department, where it is matched with the copy of the purchase order. The supplier's invoice is checked against the purchase order and GRN, and the necessary steps are taken to pay the supplier. The invoice may contain details relating to discounts such as trade discounts, quantity discounts (order in excess of a specified amount) and settlement discounts (payment received within a specified number of days).

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QUESTION Ordering materials

Discuss the possible consequences of a failure of control over ordering and receipt of materials. ANSWER (a) Incorrect materials being delivered, disrupting operations (b) Incorrect prices being paid (c) Deliveries other than at the specified time (causing disruption) (d) Insufficient control over quality (e) Invoiced amounts differing from goods actually received or prices agreed You may, of course, have thought of equally valid consequences. 2.7 Materials requisition note Materials can only be issued against a materials/stores requisition. This document must record not only the quantity of goods issued, but also the cost centre or the job number for which the requisition is being made. The materials requisition note may also have a column, to be filled in by the cost department, for recording the cost or value of the materials issued to the cost centre or job.

Materials requisition note

Date required Cost centre No/ Job No

Quantity Item code Description

Signature of requisitioning

Manager/Foreman Date

Rs

Figure 4.4: Materials requisition note

2.8 Materials transfers and returns Where materials, having been issued to one job or cost centre, are later transferred to a different job or cost centre, without first being returned to stores, a materials transfer note should be raised. Such a note must show not only the

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job receiving the transfer, but also the job from which it is transferred. This enables the appropriate charges to be made to jobs or cost centres. Material returns must also be documented on a materials returned note. This document is the 'reverse' of a requisition note, and must contain similar information. In fact it will often be almost identical to a requisition note. It will simply have a different title and perhaps be a distinctive colour, such as red, to highlight the fact that materials are being returned. 2.9 Computerised inventory control systems Many inventory control systems these days are computerised. Computerised inventory control systems vary greatly, but most will have the features outlined below. (a) Data must be input into the system. For example, details of goods received may simply be written on to a GRN for later entry into the computer system. Alternatively, this information may be keyed in directly to the computer: a GRN will be printed and then signed as evidence of the transaction, so that both the warehouse and the supplier can have a hard copy record in case of dispute. Some systems may incorporate the use of devices such as bar code readers. Other types of transaction which will need to be recorded include the following. (i) Transfers between different categories of inventory (for example, from work in progress to finished goods) (ii) Despatch, resulting from a sale, of items of finished goods to customers (iii) Adjustments to inventory records if the amount of inventory revealed in a physical inventory count differs from the amount appearing on the inventory records (b) An inventory master file is maintained. This file will contain details for every category of inventory and will be updated for new inventory lines. A database file may be maintained. The file may also hold details of inventory movements over a period, but this will depend on the type of system in operation. In a batch system, transactions will be grouped and input in one operation and details of the movements may be held in a separate transactions file, the master file updated in total only. In an online system, transactions may be input directly to the master file, where the record of movements is thus likely to be found. Such a system will mean that the inventory records are constantly up to date, which will help in monitoring and controlling inventory.

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The system may generate orders automatically once the amount in inventory has fallen to the reorder level. (c) The system will generate outputs. These may include, depending on the type of system, any of the following. (i) Hard copy records, for example a printed GRN, of transactions entered into the system. (ii) Output on a Computer screen in response to an enquiry (for example the current level of a particular line of inventory, or details of a particular transaction). (iii) Various printed reports, devised to fit in with the needs of the organisation. These may include inventory movement reports, detailing over a period the movements on all inventory lines, listings of GRNs, despatch notes and so forth. A computerised inventory control system is usually able to give more up-to-date information and more flexible reporting than a manual system but remember that both manual and computer-based inventory control systems need the same types of data to function properly. QUESTION Inventory master file

List the type of information that should be held on an inventory master file. ANSWER Here are some examples. (a) Inventory code number, for reference (e) Cost per unit (b) Brief description of inventory item (f) Selling price per unit (if finished goods) (c) Reorder level (g) Amount in inventory (d) Reorder quantity (h) Frequency of usage

2.10 Other systems of stores control and reordering 2.10.1 Order cycling method

Under the order cycling method, quantities on hand of each stores item are reviewed periodically (every one, two or three months). For low-cost items, a technique called the 90-60-30 day technique can be used, so that when inventories fall to 60 days' supply, a fresh order is placed for a 30 days' supply so as to boost inventories to 90 days' supply. For high-cost items, a more stringent stores control procedure is advisable so as to keep down the costs of inventory holding.

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2.10.2 Two-bin system

The two-bin system of stores control (or visual method of control) is one whereby each stores item is kept in two storage bins. When the first bin is emptied, an order must be placed for re-supply; the second bin will contain sufficient quantities to last until the fresh delivery is received. This is a simple system which is not costly to operate but it is not based on any formal analysis of inventory usage and may result in the holding of too much or too little inventory. 2.10.3 Classification of materials

Materials items may be classified as expensive, inexpensive or in a middle-cost range. Because of the practical advantages of simplifying stores control procedures without incurring unnecessary high costs, it may be possible to segregate materials for selective stores control. (a) Expensive and medium-cost materials are subject to careful stores control procedures to minimise cost. (b) Inexpensive materials can be stored in large quantities because the cost savings from careful stores control do not justify the administrative effort required to implement the control. This selective approach to stores control is sometimes called the ABC method, whereby materials are classified A, B or C according to their expense: group A being the expensive, group B the medium-cost and group C the inexpensive materials. 2.10.4 Pareto (80/20) distribution A similar selective approach to stores control is the Pareto (80/20) distribution which is based on the finding that in many stores, 80% of the value of stores is accounted for by only 20% of the stores items; inventories of these more expensive items should be controlled more closely.

3 Centralised and decentralised storing Centralised storage is where inventory is distributed from one larger primary location. For example, if a warehouse is centrally located amongst it’s customer base then it would be quick, cheap and easy to supply them from that one central point, hence the term ‘Centralised Storage’. Decentralised storage is in contrast to centralised storage as it has several smaller warehouses which are located in numerous locations. This allows businesses to be more efficient in supplying different markets, faster at supplying on a wider scale and can hold many different products.

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4 Periodic vs perpetual stock taking

The inventory count (stocktake) involves counting the physical inventory on hand at a certain date, and then checking this against the balance shown in the inventory records. The inventory count can be carried out on a continuous or periodic basis. Periodic stocktaking is a process whereby all inventory items are physically counted and valued at a set point in time, usually at the end of an accounting period. Continuous stocktaking is counting and valuing selected items at different times on a rotating basis. This involves a specialist team counting and checking a number of inventory items each day, so that each item is checked at least once a year. Valuable items or items with a high turnover could be checked more frequently.

4.1 Advantages of continuous stocktaking compared to periodic

stocktaking (a) The annual stocktaking is unnecessary and the disruption it causes is avoided. (b) Regular skilled stocktakers can be employed, reducing likely errors. (c) More time is available, reducing errors and allowing investigation. (d) Deficiencies and losses are revealed sooner than they would be if stocktaking were limited to an annual check. (e) Production hold-ups are eliminated because the stores staff are at no time so busy as to be unable to deal with material issues to production departments. (f) Staff morale is improved, and standards raised. (g) Control over inventory levels is improved, and there is less likelihood of overstocking or running out of inventory. 4.2 Inventory discrepancies There will be occasions when inventory checks disclose discrepancies between the physical amount of an item in inventory and the amount shown in the inventory records. When this occurs, the cause of the discrepancy should be investigated, and appropriate action taken to ensure that it does not happen again.

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4.3 Perpetual inventory

Perpetual inventory refers to an inventory recording system whereby the records (bin cards and stores ledger accounts) are updated for each receipt and issue of inventory as it occurs. This means that there is a continuous record of the balance of each item of inventory. The balance on the stores ledger account therefore represents the inventory on hand and this balance is used in the calculation of closing inventory in monthly and annual accounts. In practice, physical inventories may not agree with recorded inventories and therefore continuous stocktaking is necessary to ensure that the perpetual inventory system is functioning correctly and that minor inventory discrepancies are corrected. 4.4 Obsolete, deteriorating and slow-moving inventories and

wastage

Obsolete inventories are those items which have become out-of-date and are no longer required. Obsolete items are written off and disposed of. Inventory items may be wasted because, for example, they get broken. All wastage should be noted on the inventory records immediately so that physical inventory equals the inventory balance on records and the cost of the wastage written off. Slow-moving inventories are inventory items which are likely to take a long time to be used up. For example, 5,000 units are in inventory, and only 20 are being used each year. This is often caused by overstocking. Managers should investigate such inventory items and, if it is felt that the usage rate is unlikely to increase, excess inventory should be written off as for obsolete inventory, leaving perhaps four or five years' supply in inventory.

5 Inventory related costs

5.1 Objectives of storing materials

Speedy issue and receipt of materials Full identification of all materials at all times Correct location of all materials at all times Protection of materials from damage and deterioration Provision of secure stores to avoid pilferage, theft and fire Efficient use of storage space Maintenance of correct inventory levels Keeping correct and up-to-date records of receipts, issues and inventory levels

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5.2 Recording inventory levels One of the objectives of storekeeping is to maintain accurate records of current inventory levels. This involves the accurate recording of inventory movements (issues from, and receipts into, stores). The most frequently encountered system for recording inventory movements is the use of bin cards and stores ledger accounts. 5.2.1 Bin cards A bin card shows the level of inventory of an item at a particular stores location. It is kept with the actual inventory and is updated by the storekeeper as inventories are received and issued. A typical bin card is shown below.

Bin card

Part code no

Bin number

Location

Stores ledger no

Receipts Receipts

Date Quantity G.R.N. No. Date Quantity Req. No.

Inventory

balance

Figure 4.5: Bin card The use of bin cards is decreasing, partly due to the difficulty in keeping them updated and partly due to the merging of inventory recording and control procedures, frequently using computers. 5.2.2 Stores ledger accounts A typical stores ledger account is shown below. Note that it shows the value of inventory.

Stores ledger account

Material

Code

Maximum Quantity

Minimum Quantity

Date Receipts

G.R.N

No.Quantity

Unit

price

Rs

Amount

Rs

Stores

Req.

No

QuantityUnit

price

Rs

Amount

RsQuantity

Unit

price

Rs

Amount

Rs

Issues Inventory

Figure 4.6: Stores ledger account

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The above illustration shows a card for a manual system, but even when the inventory records are computerised, the same type of information is normally included in the computer file. The running balance on the stores ledger account allows inventory levels and valuation to be monitored. 5.2.3 Free inventory Managers need to know the free inventory balance in order to obtain a full picture of the current inventory position of an item. Free inventory represents what is really available for future use and is calculated as follows. Materials in inventory X + Materials on order from suppliers X – Materials requisitioned, not yet issued (X) Free inventory balance X Knowledge of the level of physical inventory assists inventory issuing, inventory counting and controlling maximum and minimum inventory levels: knowledge of the level of free inventory assists ordering. QUESTION Units on order A wholesaler has 8,450 units outstanding for Part X100 on existing customers' orders; there are 3,925 units in inventory and the calculated free inventory is 5,525 units. Required

Calculate how many units the wholesaler has on order with his supplier. A 9,450 B 10,050 C 13,975 D 17,900 ANSWER The correct answer is B. Free inventory balance = units in inventory + units on order – units ordered, but not yet issued 5,525 = 3,925 + units on order – 8,450 Units on order = 10,050

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5.3 Identification of materials: inventory codes (materials codes) Materials held in stores are coded and classified. Advantages of using code numbers to identify materials are as follows. (a) Ambiguity is avoided. (b) Time is saved. Descriptions can be lengthy and time-consuming. (c) Production efficiency is improved. The correct material can be accurately identified from a code number. (d) Computerised processing is made easier. (e) Numbered code systems can be designed to be flexible, and can be expanded to include more inventory items as necessary. The digits in a code can stand for the type of inventory, supplier, department and so forth. 6 Inventory control levels and EOQ

6.1 Inventory costs

Inventory costs include purchase costs, holding costs, ordering costs and costs of running out of inventory. The costs of purchasing inventory are usually one of the largest costs faced by an organisation and, once obtained, inventory has to be carefully controlled and checked. 6.1.1 Reasons for holding inventories

To ensure sufficient goods are available to meet expected demand To provide a buffer between processes To meet any future shortages To take advantage of bulk purchasing discounts To absorb seasonal fluctuations and any variations in usage and demand To allow production processes to flow smoothly and efficiently As a necessary part of the production process (such as when maturing cheese) As a deliberate investment policy, especially in times of inflation or possible shortages

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6.1.2 Holding costs If inventories are too high, holding costs will be incurred unnecessarily. Such costs occur for a number of reasons. (a) Costs of storage and stores operations. Larger inventories require more storage space and possibly extra staff and equipment to control and handle them. (b) Interest charges. Holding inventories involves the tying up of capital (cash) on which interest must be paid. (c) Insurance costs. The larger the value of inventories held, the greater insurance premiums are likely to be. (d) Risk of obsolescence. The longer an inventory item is held, the greater is the risk of obsolescence. (e) Deterioration. When materials in store deteriorate to the extent that they are unusable, they must be thrown away; there is the likelihood that disposal costs would also be incurred. 6.1.3 Costs of obtaining inventory On the other hand, if inventories are kept low, small quantities of inventory will have to be ordered more frequently, thereby increasing the following ordering or procurement costs. (a) Clerical and administrative costs associated with purchasing, accounting for and receiving goods (b) Transport costs (c) Production run costs, for inventory which is manufactured internally rather than purchased from external sources 6.1.4 Stockout costs (running out of inventory) An additional type of cost which may arise if inventory are kept too low is the type associated with running out of inventory. There are a number of causes of stockout costs. Lost contribution from lost sales Loss of future sales due to disgruntled customers Loss of customer goodwill Cost of production stoppages Labour frustration over stoppages Extra costs of urgent, small quantity, replenishment orders

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6.1.5 Objective of inventory control The overall objective of inventory control is, therefore, to maintain inventory levels so that the total of the following costs is minimised. Holding costs Stockout costs Ordering costs 6.2 Inventory control levels

Inventory control levels can be calculated in order to maintain inventories at the optimum level. The three critical control levels are reorder level, minimum level and maximum level. Based on an analysis of past inventory usage and delivery times, inventory control levels can be calculated and used to maintain inventory at their optimum level (in other words, a level which minimises costs). These levels will determine 'when to order' and 'how many to order'. 6.2.1 Reorder level When inventories reach this level, an order should be placed to replenish inventories. The reorder level is determined by consideration of the following. The maximum rate of consumption The maximum lead time The maximum lead time is the time between placing an order with a supplier, and the inventory becoming available for use. FORMULA TO LEARN

Reorder level = maximum usage maximum lead time 6.2.2 Minimum level This is a warning level to draw management attention to the fact that inventories are approaching a dangerously low level and that stockouts are possible. FORMULA TO LEARN

Minimum level = reorder level – (average usage average lead time)

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6.2.3 Maximum level This also acts as a warning level to signal to management that inventories are reaching a potentially wasteful level. FORMULA TO LEARN

Maximum level = reorder level + reorder quantity – (minimum usage minimum lead time) This graph shows the varying levels of inventory over a time period.

Inventory

level

Time period

maximum level

reorder level

minimum level Figure 4.7: Inventory over time

QUESTION Maximum inventory level A large retailer with multiple outlets maintains a central warehouse. The following information is available for Part Number SF525. Average usage 350 per day Minimum usage 180 per day Maximum usage 420 per day Lead time for replenishment 11–15 days Re-order quantity 6,500 units Re-order level 6,300 units Required (a) Based on the data above, calculate the maximum level of inventory. A 5,250 B 6,500 C 10,820 D 12,800 (b) Based on the data above, calculate the approximate number of Part Number SF525 carried as buffer inventory. A 200 B 720 C 1,680 D 1,750

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ANSWER (a) Maximum inventory level = reorder level + reorder quantity – (min usage min lead time) = 6,300 + 6,500 – (180 11) = Rs. 10,820 The correct answer is C. Using good MCQ technique, if you were resorting to a guess you should have eliminated option A. The maximum inventory level cannot be less than the reorder quantity. (b) Buffer inventory = minimum level Minimum level = reorder level – (average usage average lead time) = 6,300 – (350 13) = 1,750. The correct answer is D. Option A could again be easily eliminated. With minimum usage of 180 per day, a buffer inventory of only 200 would not be much of a buffer! 6.2.4 Reorder quantity This is the quantity of inventory which is to be ordered when inventory reaches the reorder level. If it is set so as to minimise the total costs associated with holding and ordering inventory, then it is known as the economic order quantity (EOQ). 6.2.5 Average inventory The formula for the average inventory level assumes that inventory levels fluctuate evenly between the minimum (or safety) inventory level and the highest possible inventory level (the amount of inventory immediately after an order is received, ie safety inventory + reorder quantity). FORMULA TO LEARN

Average inventory = safety inventory + ½ reorder quantity

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QUESTION Average inventory A component has a safety inventory of 500, a re-order quantity of 3,000 and a rate of demand which varies between 200 and 700 per week. Required

Calculate the approximate average inventory. A 2,000 B 2,300 C 2,500 D 3,500 ANSWER The answer is A. Average inventory = safety inventory + ½ reorder quantity = 500 + (0.5 3,000) = Rs. 2,000 6.3 Economic order quantity (EOQ) The economic order quantity (EOQ) is the order quantity which minimises inventory costs. The EOQ can be calculated using a table, graph or formula. EOQ = 0H2C DC This is explained in Section 4.3.3. Economic order theory assumes that the average inventory held is equal to one half of the reorder quantity (although as we saw in the last section, if an organisation maintains some sort of buffer or safety inventory then average inventory = buffer inventory + half of the reorder quantity). We have seen that there are certain costs associated with holding inventory. These costs tend to increase with the level of inventories, and so could be reduced by ordering smaller amounts from suppliers each time. On the other hand, as we have seen, there are costs associated with ordering from suppliers: documentation, telephone calls, payment of invoices, receiving goods into stores and so on. These costs tend to increase if small orders are placed, because a larger number of orders would then be needed for a given annual demand.

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6.3.1 Example: Economic order quantity Suppose a company purchases raw material at a cost of Rs. 16 per unit. The annual demand for the raw material is 25,000 units. The holding cost per unit is Rs. 6.40 and the cost of placing an order is Rs. 32. We can tabulate the annual relevant costs for various order quantities as follows. Order quantity (units) 100 200 300 400 500 600 800 1,000Average inventory (units) (a) 50 100 150 200 250 300 400 500Number of orders (b) 250 125 83 63 50 42 31 25 Annual holding Rs Rs Rs Rs Rs Rs Rs Rs cost (c) 320 640 960 1,280 1,600 1,920 2,560 3,200Annual order cost (d) 8,000 4,000 2,656 2,016 1,600 1,344 992 800Total relevant cost 8,320 4,640 3,616 3,296 3,200 3,264 3,552 4,000Notes (a) Average inventory = Order quantity 2 (ie assuming no safety inventory) (b) Number of orders = annual demand order quantity (c) Annual holding cost = Average inventory Rs. 6.40 (d) Annual order cost = Number of orders Rs. 32 You will see that the economic order quantity is 500 units. At this point the total annual relevant costs are at a minimum. 6.3.2 Example: Economic order quantity graph We can present the information tabulated in Section 4.3.1 in graphical form. The vertical axis represents the relevant annual costs for the investment in inventories, and the horizontal axis can be used to represent either the various order quantities or the average inventory levels; two scales are actually shown on the horizontal axis so that both items can be incorporated. The graph shows that, as the average inventory level and order quantity increase, the holding cost increases. On the other hand, the ordering costs decline as inventory levels and order quantities increase. The total cost line represents the sum of both the holding and the ordering costs.

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Economic order quantity graph

100 200 300 400 500 600 700 800 900 1,0000

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

Annual costs

(Rs)

X

100 200 300 400 500Average inventory level (units)

Order quantity (units)

Order costs

Holding costs

Total costs

Figure 4.8: Re-order quantities Note that the total cost line is at a minimum for an order quantity of 500 units and occurs at the point where the ordering cost curve and holding cost curve intersect. The EOQ is therefore found at the point where holding costs equal ordering costs.

6.3.3 EOQ formula The formula for the EOQ will be provided in your examination. FORMULA TO LEARN

EOQ = 0H2C DC (given to you in the exam) where CH = cost of holding one unit of inventory for one time period C0 = cost of ordering a consignment from a supplier D = demand during the time period

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QUESTION EOQ

Calculate the EOQ using the formula and the information in Section 4.3.1. ANSWER EOQ = 6.40 Rs. 25,00032 Rs. 2 = 250,000 = 500 units QUESTION EOQ and holding costs A manufacturing company uses 25,000 components at an even rate during a year. Each order placed with the supplier of the components is for 2,000 components, which is the economic order quantity. The company holds a buffer inventory of 500 components. The annual cost of holding one component in inventory is Rs. 2. Required

Calculate the total annual cost of holding inventory of the component. A Rs. 2,000 B Rs. 2,500 C Rs. 3,000 D Rs. 4,000 ANSWER The correct answer is C. [Buffer inventory + (EOQ/2)] × Annual holding cost per component = [500 + (2,000/2)] × Rs. 2 = Rs. 3,000

6.4 Bulk discounts The solution obtained from using the simple EOQ formula may need to be modified if bulk discounts (also called quantity discounts) are available. The following graph shows the effect that discounts granted for orders of certain sizes may have on total costs.

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Total

costs

per

order

A B C Quantity

purchased

per orderEOQ Figure 4.10: Effect of bulk discounts The graph above shows the following. Differing bulk discounts are given when the order quantity exceeds A, B and C The minimum total cost (ie when quantity B is ordered rather than the EOQ) To decide mathematically whether it would be worthwhile taking a discount and ordering larger quantities, it is necessary to minimise the total of the following. Total material costs Inventory holding costs Ordering costs The total cost will be minimised at one of the following. At the pre-discount EOQ level, so that a discount is not worthwhile At the minimum order size necessary to earn the discount 6.4.1 Example: Bulk discounts The annual demand for an item of inventory is 45 units. The item costs Rs. 200 a unit to purchase, the holding cost for one unit for one year is 15% of the unit cost and ordering costs are Rs. 300 an order. The supplier offers a 3% discount for orders of 60 units or more, and a discount of 5% for orders of 90 units or more. Required

Calculate the cost-minimising order size. Solution (a) The EOQ, ignoring discounts, is 200of15% 453002 = 30 Rs Purchases (no discount) 45 Rs. 200 9,000 Holding costs (W1) 450 Ordering costs (W2) 450 Total annual costs 9,900

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WORKINGS (1) Holding costs Holding costs = Average stock holding cost for one unit of inventory per annum Average inventory = Order quantity 2 = 30 2 = 15 units Holding cost for one unit of inventory per annum = 15% Rs. 200 = Rs. 30 Holding costs = 15 units Rs. 30 = Rs. 450 (2) Ordering costs Ordering costs = Number of orders ordering costs per order (Rs. 300) Number of orders = Annual demand order quantity = 45 30 = 1.5 orders ordering costs = 1.5 orders Rs. 300 = Rs. 450 (b) With a discount of 3% and an order quantity of 60, unit costs are as follows. Rs Purchases Rs. 9,000 97% 8,730 Holding costs (W3) 873 Ordering costs (W4) 225 Total annual costs 9,828 WORKINGS (3) Holding costs Holding costs = Average inventory holding cost for one unit of inventory per annum Average inventory = Order quantity 2 = 60 2 = 30 units Holding cost for one unit of inventory per annum = 15% 97% Rs. 200 = Rs. 29.10 Note. 97% = 100% – 3% discount Holding costs = 30 units Rs. 29.10 = Rs. 873

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(4) Ordering costs Ordering costs = Number of orders ordering costs per order (Rs. 300) Number of orders = Annual demand order quantity = 45 60 = 0.75 orders Ordering costs = 0.75 orders Rs. 300 = Rs. 225 (c) With a discount of 5% and an order quantity of 90, unit costs are as follows. Rs Purchases Rs. 9,000 95% 8,550.0 Holding costs (W5) 1,282.5 Ordering costs (W6) 150.0 Total annual costs 9,982.5 WORKINGS (5) Holding costs Holding costs = Average inventory holding cost for one unit of inventory per annum Average inventory = order quantity 2 = 90 2 = 45 units Holding cost for one unit of inventory per annum = 15% 95% Rs. 200 = Rs. 28.50 Note. 95% = 100% – 5% discount Holding costs = 45 units Rs. 28.50 = Rs. 1,282.50 (6) Ordering costs Ordering costs = Number of orders ordering costs per order (Rs. 300) Number of orders = Annual demand order quantity = 45 90 = 0.5 orders ordering costs = 0.5 orders Rs. 300 = Rs. 150

The cheapest option is to order 60 units at a time.

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Note that the value of CH varied according to the size of the discount, because CH was a percentage of the purchase cost. This means that total holding costs are reduced because of a discount. This could easily happen if, for example, most of CH was the cost of insurance, based on the cost of inventory held. QUESTION Discounts A company uses an item of inventory as follows. Purchase price: Rs. 96 per unit Annual demand: 4,000 units Ordering cost: Rs. 300 Annual holding cost: 10% of purchase price Economic order quantity: 500 units Required

State whether the company should order 1,000 units at a time in order to secure an 8% discount by calculating the total annual inventory cost. ANSWER The total annual cost at the economic order quantity of 500 units is as follows. Rs Purchases 4,000 Rs. 96 384,000 Ordering costs Rs. 300 (4,000/500) 2,400 Holding costs Rs. 96 10% (500/2) 2,400 388,800 The total annual cost at an order quantity of 1,000 units would be as follows. Rs Purchases Rs. 384,000 92% 353,280 Ordering costs Rs. 300 (4,000/1,000) 1,200 Holding costs Rs. 96 92% 10% (1,000/2) 4,416 358,896 The company should order the item 1,000 units at a time, saving Rs. (388,800 – 358,896) = Rs. 29,904 a year.

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7 Inventory valuation

The correct pricing of issues and valuation of inventory are of the utmost importance because they have a direct effect on the calculation of profit. Several different methods can be used in practice. 7.1 Valuing inventory in financial accounts You may be aware from your studies for the Foundations of Financial Accounting paper that, for financial accounting purposes, inventories are valued at the lower of cost and net realisable value. In practice, inventories will probably be valued at cost in the stores records throughout the course of an accounting period. Only when the period ends will the value of the inventory in hand be reconsidered so that items with a net realisable value below their original cost will be revalued downwards, and the inventory records altered accordingly. 7.2 Charging units of inventory to cost of production or cost of

sales It is important to be able to distinguish between the way in which the physical items in inventory are actually issued. In practice, a storekeeper may issue goods in the following way. The oldest goods first The latest goods received first Randomly Those which are easiest to reach By comparison the cost of the goods issued must be determined on a consistently applied basis, and must ignore the likelihood that the materials issued will be costed at a price different to the amount paid for them. This may seem a little confusing at first, and it may be helpful to explain the point further by looking at an example. 7.3 Example: inventory valuation Suppose that there are three units of a particular material in inventory.

Units Date received Purchase cost A June 20X1 Rs. 100 B July 20X1 Rs. 106 C August 20X1 Rs. 109 In September, one unit is issued to production. As it happened, the physical unit actually issued was B. The accounting department must put a value or cost on the material issued, but the value would not be the cost of B, Rs. 106. The principles

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used to value the materials issued are not concerned with the actual unit issued, A, B, or C. Nevertheless, the accountant may choose to make one of the following assumptions. (a) The unit issued is valued as though it were the earliest unit in inventory, ie at the purchase cost of A, Rs. 100. This valuation principle is called FIFO, or first in, first out. (b) The unit issued is valued as though it were the most recent unit received into inventory, ie at the purchase cost of C, Rs. 109. This method of valuation is LIFO, or last in, first out. (c) The unit issued is valued at an average price of A, B and C, ie Rs. 105. (It may be that each item of inventory is marked with the purchase cost, as it is received. This method is known as the specific price method. In the majority of cases this method is not practical.)

7.4 A chapter example In the following sections we will consider each of the pricing methods detailed above (and a few more), using the following transactions to illustrate the principles in each case. TRANSACTIONS DURING MAY 20X3 Market value per unit on date Quantity Unit cost Total cost of transaction Units Rs Rs Rs Opening balance, 1 May 100 2.00 200 Receipts, 3 May 400 2.10 840 2.11 Issues, 4 May 200 2.11 Receipts, 9 May 300 2.12 636 2.15 Issues, 11 May 400 2.20 Receipts, 18 May 100 2.40 240 2.35 Issues, 20 May 100 2.35 Closing balance, 31 May 200 2.38 1,916

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8 FIFO (first in, first out)

FIFO assumes that materials are issued out of inventory in the order in which they were delivered into inventory: issues are priced at the cost of the earliest delivery remaining in inventory. 8.1 Example: FIFO Using FIFO, the cost of issues and the closing inventory value in the transactions in Section 6.4 would be as follows. Quantity Date of issue issued Value Units Rs Rs 4 May 200 100 o/s at Rs. 2 200 100 at Rs. 2.10 210 410 11 May 400 300 at Rs. 2.10 630 100 at Rs. 2.12 212 842 20 May 100 100 at Rs. 2.12 212 Cost of issues 1,464 Closing inventory value 200 100 at Rs. 2.12 212 100 at Rs. 2.40 240 452 1,916 Notes (a) The cost of materials issued plus the value of closing inventory equals the cost of purchases plus the value of opening inventory (Rs. 1,916). (b) The market price of purchased materials is rising dramatically. In a period of inflation, there is a tendency with FIFO for materials to be issued at a cost lower than the current market value, although closing inventories tend to be valued at a cost approximating to current market value. FIFO is therefore essentially a historical cost method, with materials included in cost of production being valued at historical cost.

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8.2 Advantages and disadvantages of the FIFO method

Advantages Disadvantages It is a logical pricing method which probably represents what is physically happening: in practice the oldest inventory is likely to be used first. FIFO can be cumbersome to operate because of the need to identify each batch of material separately.

It is easy to understand and explain to managers. Managers may find it difficult to compare costs and make decisions when they are charged with varying prices for the same materials. The inventory valuation can be near to a valuation based on replacement cost. In a period of high inflation, inventory issue prices will lag behind current market value. QUESTION FIFO

Record below in as much detail as possible the receipts, issues and inventory using the information in Sections 6.4 and 7.1. Receipts Issues Inventory Date Quantity Unit price Rs AmountRs Quantity Unit priceRs AmountRs Quantity Unit priceRs Amount Rs

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ANSWER Receipts Issues Inventory Date Quantity Unit price Rs AmountRs Quantity Unit priceRs Amount Rs Quantity Unit priceRs Amount Rs1.5.X3 100 2.00 200.00 3.5.X3 400 2.10 840.00 100 2.00 200.00 400 2.10 840.00 500 1,040.00 4.5.X3 100 2.00 200.00 100 2.10 210.00 300 2.10 630.00 9.5.X3 300 2.12 636.00 300 2.10 630.00 300 2.12 636.00 600 1,266.00 11.5.X3 300 2.10 630.00 100 2.12 212.00 200 2.12 424.00 18.5.X3 100 2.40 240.00 200 2.12 424.00 100 2.40 240.00 300 664.00 20.5.X3 100 2.12 212.00 100 2.12 212.00 100 2.40 240.00 31.5.X3 200 452.00

Note that this type of record is called a perpetual inventory system as it shows each receipt and issue of inventory as it occurs. 9 LIFO (last in, first out)

LIFO assumes that materials are issued out of inventory in the reverse order to which they were delivered: the most recent deliveries are issued before earlier ones, and issues are priced accordingly. 9.1 Example: LIFO Using LIFO, the cost of issues and the closing inventory value in the example above, would be as follows.

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Date of issue

Quantity issued

Valuation

Units Rs Rs 4 May 200 200 at Rs. 2.10 420 11 May 400 300 at Rs. 2.12 636 100 at Rs. 2.10 210 846 20 May 100 100 at Rs. 2.40 240 Cost of issues 1,506 Closing inventory value 200 100 at Rs. 2.10 210 100 at Rs. 2.00 200 410 1,916 Notes (a) The cost of materials issued plus the value of closing inventory equals the cost of purchases plus the value of opening inventory (Rs. 1,916). (b) In a period of inflation there is a tendency with LIFO for the following to occur. (i) Materials are issued at a price which approximates to current market value (or economic cost). (ii) Closing inventories become undervalued when compared to market value. 9.2 Advantages and disadvantages of the LIFO method Advantages Disadvantages Inventories are issued at a price which is close to current market value. The method can be cumbersome to operate because it sometimes results in several batches being only part-used in the inventory records before another batch is received. Managers are continually aware of recent costs when making decisions, because the costs being charged to their department or products will be current costs.

LIFO is often the opposite to what is physically happening and can therefore be difficult to explain to managers. As with FIFO, decision making can be difficult because of the variations in prices.

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9.3 Changing from LIFO to FIFO or from FIFO to LIFO You may get an assessment question which asks you what would happen to closing inventory values or gross profits if a business changed its method from LIFO to FIFO or vice versa. You may find it easier to think about this using diagrams. Let's consider a very simple example, where four barrels of inventory are purchased during a month of rising prices, and two are used. There is no opening inventory. Cost 1 Jan Rs. 100 per barrel 19 Jan Rs. 150 per barrel LIFO – these barrels would be left as closing inventory Rs. 250

FIFO – these barrels would be issued to production first (and charged to cost of sales) Rs. 250) 20 Jan Rs. 200 per barrel 31 Jan Rs. 250 per barrel LIFO – these barrels would be issued to

production first (and charged to cost of sales) Rs. 450

FIFO – these barrels would be left as closing inventory Rs. 450

Notice the rising prices

As you can see, during a period of rising prices, the closing inventory value using LIFO would be Rs. 250 – but using FIFO would be higher, at Rs. 450. The charge to cost of sales will be lower using FIFO and therefore the gross profit will be higher. 10 AVCO (cumulative weighted average pricing)

The cumulative weighted average pricing method (or AVCO) calculates a weighted average price for all units in inventory. Issues are priced at this average cost, and the balance of inventory remaining would have the same unit valuation. The average price is determined by dividing the total cost by the total number of units. A new weighted average price is calculated whenever a new delivery of materials is received into store. This is the key feature of cumulative weighted average pricing.

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10.1 Example: AVCO In our example, issue costs and closing inventory values would be as follows. Total inventory Unit Date Received Issued Balance value cost Units Units Units Rs Rs Rs Opening inventory 100 200 2.00 3 May 400 840 2.10 * 500 1,040 2.08 4 May 200 (416) 2.08 416 300 624 2.08 9 May 300 636 2.12 * 600 1,260 2.10 11 May 400 (840) 2.10 840 200 420 2.10 18 May 100 240 2.40 * 300 660 2.20 20 May 100 (220) 2.20 220 1,476 Closing inventory 200 440 2.20 440 value 200 440 2.20 440 1,916 * A new inventory value per unit is calculated whenever a new receipt of materials occurs. Notes (a) The cost of materials issued plus the value of closing inventory equals the cost of purchases plus the value of opening inventory (Rs. 1,916). (b) In a period of inflation, using the cumulative weighted average pricing system, the value of material issued will rise gradually, but will tend to lag a little behind the current market value at the date of issue. Closing inventory values will also be a little below current market value. 10.2 Advantages and disadvantages of AVCO

Advantages Disadvantages Fluctuations in prices are smoothed out, making it easier to use the data for decision making. The resulting issue price is rarely an actual price that has been paid, and can run to several decimal places. It is easier to administer than FIFO and LIFO, because there is no need to identify each batch separately. Prices tend to lag a little behind current market values when there is gradual inflation.

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QUESTION Inventory valuation methods Shown below is an extract from records for inventory code no 988988. Receipts Issues Balance Date Qty Value Total Qty Value Total Qty Value Total Rs Rs Rs Rs Rs Rs 5 June 30 2.50 75 8 June 20 3.00 60 10 June 10 A 14 June 20 B 18 June 40 2.40 96 20 June 6 C D Required (a) Calculate the values that would be entered on the stores ledger card for A, B, C and D in a cumulative weighted average pricing system. A Rs. C Rs. B Rs. D Rs. (b) Calculate the values that would be entered on the stores ledger card for A, B, C and D in a LIFO system. A Rs. C Rs. B Rs. D Rs. ANSWER (a) A Rs. 27 C Rs. 15

B Rs. 54 D Rs. 135 WORKINGS Rs 8 June Inventory balance 30 units Rs. 2.50 75 20 units Rs. 3.00 60 50 135 Weighted average price = Rs. 135/50 = Rs. 2.70 Rs 10 June Issues 10 units Rs. 2.70 27 14 June Issues 20 units Rs. 2.70 54 18 June Inventory balance 20 units Rs. 2.70 54 Remaining receipts 40 units Rs. 2.40 96 60 150

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Weighted average price = Rs. 150/60 = Rs. 2.50 Rs 20 June Issues 6 units Rs. 2.50 15 Inventory balance 54 units Rs. 2.50 135 (b) A Rs. 30 C Rs. 1 4.40 B Rs. 55 D Rs. 131 .60 WORKINGS Rs 10 June 10 units Rs. 3.00 30 14 June Remaining 10 units Rs. 3.00 30 10 units Rs. 2.50 25 55 20 June Issues: 6 units Rs. 2.40 14.40 Balance: 34 units Rs. 2.40 81.60 20 units Rs. 2.50 50.00 54 131.60

10.3 Periodic weighted average The periodic weighted average pricing method calculates an average price at the end of the period, based on the total purchases in that period. FORMULA TO LEARN Periodic weighted average = Cost of opening inventory + total cost of receiptsUnits of opening inventory + total units received

10.3.1 Example: Periodic weighted average A wholesaler had the following receipts and issues during May. Receipts units Issues units Rs/unit 4 May 800 30 6 May 400 13 May 600 35 14 May 400 23 May 600 40 25 May 400 29 May 400 2,000 1,600

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Calculate the value of closing inventory at the end of May using the periodic weighted average. Periodic weighted average = (800 × Rs. 30) + (600 × Rs. 35) + (600 × Rs. 40)800 + 600 + 600 = Rs. 34.50 per unit Value of closing inventory = 400 units Rs. 34.50 = Rs. 13,800

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Inventory control includes the functions of inventory ordering and purchasing, receiving goods into store, storing and issuing inventory and controlling levels of inventory. Every movement of material in a business should be documented using the following as appropriate: purchase requisition; purchase order; goods received note (GRN); materials requisition note; materials transfer note and materials returned note. The inventory count (stocktake) involves counting the physical inventory on hand at a certain date, and then checking this against the balance shown in the inventory records. The inventory count can be carried out on a continuous or

periodic basis. Perpetual inventory refers to an inventory recording system whereby the records (bin cards and stores ledger accounts) are updated for each receipt and issue of inventory as it occurs. Obsolete inventories are those items which have become out-of-date and are no longer required. Obsolete items are written off and disposed of. Inventory costs include purchase costs, holding costs, ordering costs and costs of running out of inventory. Inventory control levels can be calculated in order to maintain inventories at the optimum level. The three critical control levels are reorder level, minimum level and maximum level. The economic order quantity (EOQ) is the order quantity which minimises inventory costs. The EOQ can be calculated using a table, graph or formula. EOQ = HoC D2C The correct pricing of issues and valuation of inventory are of the utmost importance because they have a direct effect on the calculation of profit. Several different methods can be used in practice. FIFO assumes that materials are issued out of inventory in the order in which they were delivered into inventory: issues are priced at the cost of the earliest delivery remaining in inventory. LIFO assumes that materials are issued out of inventory in the reverse order to which they were delivered: the most recent deliveries are issued before earlier ones, and issues are priced accordingly.

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The cumulative weighted average pricing method (or AVCO) calculates a weighted average price for all units in inventory. Issues are priced at this average cost, and the balance of inventory remaining would have the same unit valuation. The average price is determined by dividing the total cost by the total number of units.

A new weighted average price is calculated whenever a new delivery of materials is received into store. This is the key feature of cumulative weighted average pricing.

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1 List six objectives of storekeeping. …………………………………… …………………………………… …………………………………… …………………………………… …………………………………… ……………………………………

2 Free inventory represents…………………………………………………………………………. 3 Free inventory is calculated as follows. (Delete as appropriate) (a) + – Materials in inventory X (b) + – Materials in order X (c) + – Materials requisitioned (not yet issued) X Free inventory balance X 4 Explain briefly how periodic inventory counting differs from continuous inventory counting. 5 Match up the following.

Reorder quantity Maximum usage maximum lead time�

Minimum level

Maximum level time)?

Average inventory Reorder level + reorder quantity – (minimum

usage minimum lead time)�

Reorder level – (average usage average lead)�

Safety inventory + reorder level12

6 EOQ = oH2C DC Where (a) CH = ………………………………………………….. (b) Co = ..………………………………………………… (c) D = ………………………………………………….

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7 Which of the following are true? I With FIFO, the inventory valuation will be very close to replacement cost. II With LIFO, inventories are issued at a price which is close to the current market value. III Decision making can be difficult with both FIFO and LIFO because of the variations in prices. IV A disadvantage of the weighted average method of inventory valuation is that the resulting issue price is rarely an actual price that has been paid and it may be calculated to several decimal places. A I and II only B I, II and III only C I and III only D I, II, III and IV 8 LIFO is essentially an historical cost method. True False 9 Fill in the blanks. When using ………………….. method of inventory valuation, issues are at a price which approximates to economic cost.

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1 Speedy issue and receipt of materials Full identification of all materials at all times Correct location of all materials at all times Protection of materials from damage and deterioration Provision of secure stores to avoid pilferage, theft and fire Efficient use of storage space Maintenance of correct inventory levels Keeping correct and up-to-date records of receipts, issues and inventory levels

2 Inventory that is readily available for future use. 3 (a) + (b) + (c) – 4 Periodic inventory counting. All inventory items physically counted and valued, usually annually.

Continuous inventory counting. Counting and valuing selected items at different times of the year (at least once a year). 5

Reorder quantity Maximum usage maximum lead time�

Minimum level

Maximum level time)

Average inventory Reorder level + reorder quantity – (minimum

usage minimum lead time)�

Reorder level – (average usage average lead)�

Safety inventory + reorder level12

6 (a) Cost of holding one unit of inventory for one time period (b) Cost of ordering a consignment from a supplier (c) Demand during the time period 7 The answer is D. All of the statements are true. 8 False. FIFO is an historical cost method 9 LIFO

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A ABC method of stores control, 573 Abnormal gain, 203 Abnormal loss, 203 Absorption base, 115 Absorption costing, 261 Absorption costing and marginal costing compared, 261 Absorption of overheads, 114 Accounting rate of return (ARR)

method, 464 Additive model, 363 Administration overhead, 30 Allocation, 99 AND law, 500 Annuity, 471 Annuity factors, 472 Annuity tables, 471 Arithmetic mean, 507 Arithmetic mean of combined data, 510 Arithmetic mean of grouped data, 509 Arithmetic mean of ungrouped data, 507 Array, 515 Attainable standards, 289 AVCO, 597 Average inventory, 582 Avoidable costs, 441 B Basic standard, 289 Batch, 177 Bill of materials, 167 Bin cards, 576 Blanket absorption rates, 118 Blanket overhead absorption rate, 118 Bonus schemes, 88 Breakeven chart, 424 Breakeven charts, 431 Breakeven point, 407 Budget, 331, 332 Budget committee, 333 Budget cost allowance, 379, 384 Budget manual, 334 Budget period, 333 Budget preparation, 333

Budget variance, 384 Budgetary control, 382 Budgeted income statement, 349 Budgeted statement of financial position, 349 Budgeting, 330 Budgets and standards compared, 291 Bulk discounts, 586 By-product, 242 C C/S ratio, 409, 410 Capital investment appraisal – net present value method, 475 Capital investment appraisal – payback method, 461, 464, 485 Cash budget, 342 Cash v profit, 477 Coefficient of determination, 66, 72 Coefficient of rank correlation, 67 Coefficient of variation, 523 Complementary outcomes, 497 Conditional events, 504 Conditional probability, 504 Conservatism, 542, 543 Contingency tables, 505 Continuous stocktaking, 574 Contract, 180 Contract accounts, 181 Contract costing, 180 Contribution, 264 Contribution breakeven chart, 408, 427 Contribution tables, 552 Control, 17, 370 Controllable cost, 46 Corporate planning, 14, 368 Correlation, 54, 61 Correlation and causation, 66 Correlation coefficient, 61 Correlation in a time series, 64 Cost accounting, 6 Cost accounts, 6 Cost behaviour, 35 Cost behaviour assumptions, 43 Cost behaviour patterns, 26, 35 Cost of capital, 469, 475 Cost per service unit, 184

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Cost plus pricing, 135, 170 Cost-volume-profit analysis (CVP),

406 Cumulative present value factors, 472 Cumulative weighted average pricing, 597 Current standards, 289 Curvilinear variable costs, 39 D Data, 8 Day-rate system, 80 Decision support information, 485 Decision-making, 18, 370 Delivery note, 569 Departmental absorption rates, 118 Departmental/functional budgets, 337 Dependent events, 504 Deseasonalisation, 366 Deteriorating inventory, 575 Direct expenses, 28 Direct labour efficiency variance,

298 Direct labour idle time variance,

299 Direct labour rate variance, 297 Direct labour total variance, 297 Direct material, 28 Direct material price variance, 295 Direct material total variance, 295 Direct material usage variance,

295 Direct wages, 29 Discounted cash flow (DCF), 475 Discounting, 468 Discounting formula, 469 Distribution overhead, 30 Double loop feedback, 388 E Economic Order Quantity (EOQ), 583 Effectiveness, 19, 372 Efficiency, 19, 372 EOQ (Economic Order Quantity), 583 Equivalent units, 219 Expected idle time, 301

F Feedback, 388, 389 Feedforward control, 390 FIFO, 593 FIFO (first in, first out) method, 225 Financial accounts, 4 Financial information, 12 Finished goods inventory budget, 336 First in, first out, 593 Fixed budget, 375 Fixed costs, 26, 35, 36 Flexible budget, 375, 376 Focus groups, 543 Forecast, 332 Free inventory, 577 Full cost-plus pricing, 136 Function costing, 182 Functional budgets, 337 G General rule of multiplication, 504 Goods received note (GRN), 569 GRN, 569 Group bonus scheme, 90 Grouped data, 520 Guaranteed minimum wage, 83 H High day-rate system, 85 Higher-level feedback, 388 High-low method, 43, 47, 52, 61, 355, 377 Holding costs, 579 I Ideal standard, 288 Idle time, 81 Idle time ratio, 83 Idle time variance, 299 Incremental budgeting, 391 Incremental costs, 44, 441 Independent events, 501 Indirect cost, 27 Indirect expenses, 30 Indirect materials, 29 Indirect wages, 30

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Individual bonus schemes, 88 Information, 8 Internal rate of return (IRR) method – graphical approach, 479 International Accounting Standard 2 (IAS 2), 113, 263 Inventory codes, 578 Inventory control, 566, 580 Inventory control levels, 578, 580 Inventory control systems, 571 Inventory costs, 578 Inventory count, 574 Inventory discrepancies, 574 Inventory valuation, 591 IRR, 481, 484 IRR method of discounted cash

flow, 479 Issue of materials, 570 J Job, 164 Job cost cards, 166 Job cost information, 167 Job cost sheets, 166 Job costing, 164 Job costing and computerisation, 171 Job costing for internal services, 174 Joint costs, 242 Joint products, 242 Joint products and common costs, 236 K Key budget factor, 335 Key factor, 439 L Labour budget, 336 Last in, first out, 595 Laws of probability, 496 Least squares method of linear regression analysis, 57, 351 LIFO, 595 Limiting budget factor, 335 Limiting factor, 439 Long-term strategic planning, 14,

368

M Machine usage budget, 336 Machinery user costs, 445 Management accounting, 7 Management accounts, 4 Management control, 19, 372 Management control system, 20, 373 Margin of safety, 413 Marginal costing, 260, 263, 377 Marginal costing and absorption costing compared, 261 Marginal costing principles, 132, 265 Marginal cost-plus pricing, 139 Marginal cost-plus pricing, 139 Market research, 542 Mark-up pricing, 139 Master budget, 349 Materials codes, 578 Materials inventory budget, 336 Materials requisition note, 570 Materials returned note, 571 Materials returns, 570 Materials transfer note, 570 Materials transfers, 570 Materials usage budget, 336 Materials variances and opening and closing inventory, 296 Maximax basis, 549 Maximax criterion, 550 Maximin decision rule, 549 Maximum level, 581 Median, 515 Median of an ungrouped frequency distribution, 517 Minimax regret rule, 551 Minimum level, 580 Mixed costs, 40 Modal value, 513 Mode, 513 Mode from a histogram, 513 Motivation and budgets, 331 Moving averages, 356 Multiplicative model, 364 Multi-product P/V charts, 434 Mutually exclusive outcomes, 499 Mutually exclusive projects, 466

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N Negative correlation, 56 Negative feedback, 388 Net present value (NPV) method, 475 Non-controllable costs, 46 Non-financial information, 12 Non-linear variable costs, 39 Normal distribution, 527 Normal distribution tables, 529 Normal idle time, 301 Normal loss, 203 NPV, 475 O Objectives, 13, 367 Obsolete inventory, 575 Operating statements, 306, 307 Operational control, 20, 372 OR law, 498 Order cycling method of stores control, 572 Ordering costs, 579 Ordering materials, 567 Over-absorption, 120 Overhead absorption, 114, 116, 126, 236 Overhead absorption rate, 118, 119 Overhead apportionment, 100 Overhead recovery, 114, 126 Overheads, 27, 98 Overtime, 29, 81, 91 Overtime premium, 81 P P/V graph, 428 P/V ratio, 408, 410 Pareto (80/20) distribution, 573 Partial correlation, 56 Payback period, 461 Pay-off tables, 547 Perfect correlation, 55 Performance standard, 288 Periodic stocktaking, 574 Perpetual inventory, 575 Perpetuity, 473 Piecework schemes, 83 Planning, 13, 17 Positive correlation, 56 Positive feedback, 388

Predetermined overhead absorption rate, 114 Present value of a perpetuity, 473 Present value of an annuity, 472 Present value tables, 470 Present values, 469 Principal budget factor, 335 Principles of discounted cash flow, 468 Probabilities, 544 Probability, 494 Probability distribution, 524 Probability of achieving the desired result, 496 Process costing, 200, 201 Process costing and closing work in progress, 219 Process costing and opening work in progress, 225 weighted average cost method, 232 Process costing framework, 202 Procurement costs, 579 Production, 29 Production budget, 336 Profit/volume (P/V) graph, 428 Profit/volume ratio, 408, 410 Project appraisal – payback method, 462 Proportional (multiplicative)

model, 364 Purchase order, 568 Purchase requisition, 567 Q Qualitative data, 543 Qualitative research, 543 Quantitative data, 543 R Rank correlation coefficient, 67 Raw materials purchases budget, 336 Receiving materials, 567 Rectification costs, 169 Regression lines and time series, 58, 352 Regret, 551 Relevant cost, 44, 440, 445 Remuneration methods, 80 Reorder level, 580

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Resource allocation, 332 Responsibility accounting, 331 Return on capital employed

(ROCE) method, 464 Return on investment (ROI)

method, 464 Risk, 540 Risk averse, 541 Risk neutral, 541 Risk preference, 541 Risk seeker, 541 Role of market research, 542 S Salaried labour, 86 Sales budget, 336 Sales variances, 304 Sales variances – significance, 306 Sales volume profit variance, 305 Scattergraph, 55 Scrap, 210 Seasonal variations, 362 Selling overhead, 30 Selling price variance, 304 Semi-fixed costs, 40 Semi-variable costs, 40 Separate absorption rates, 118 Service cost analysis, 185 Service cost analysis in service industry situations, 189 Service costing, 182 unit cost measures, 184 Shift premium, 81 Short-term tactical planning, 14, 369 Sigma , 509 Simple addition law, 498 Simple multiplication law, 500 Simple probability, 496 Single loop feedback, 388 Slow-moving inventories, 575 Split off point, 236 Standard cost, 285 Standard costing, 285, 287 Standard costing and new technology, 293

Standard Criticisms, 292 Standard deviation, 519 Standard deviation (for grouped data), 520 Standard deviation (for ungrouped data), 520 Standard operation sheet, 291 Standard product specification, 291 Standard resource requirements, 291 Step costs, 37 Step down method of reapportionment, 106 Stockout costs, 579 Storage of raw materials, 575 Stores ledger accounts, 576 Stores requisition, 570 Strategic information, 15, 374 Strategic planning, 19, 372 Strategy and organisational structure, 13, 368 Sunk cost, 443 T Tactical information, 16, 374 Target profit, 416 Throughput accounting (TA), 439 Tied ranks, 68 Time work, 80 Transfers and returns of materials, 570 Two-bin system of stores control, 573 U Uncertain events, 540 Uncontrollable cost, 46 Under-/over-absorbed overhead account, 124, 153 Under-absorption, 120 Ungrouped data, 520 User costs, 445 V Variable costing, 132 Variable costs, 35, 37 Variable overhead total variance, 302

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Variable production overhead efficiency variance, 303

Variable production overhead expenditure variance, 301, 302 Variance, 294, 304, 519 Variance for grouped data, 519 Variance for ungrouped data, 519 Variances, 294, 382, 383, 386 Venn diagrams, 497

W Wages control account, 151 Wages department, 82 Weighted average price, 597 Worst/most likely/best outcome estimates, 546 Z Z score, 532

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