cvp analysis

Cost Behavior and Cost-Volume Relationships

Cost Behavior and Cost-Volume Relationships

Product and Period Costs• Product costs: Costs related to getting a product or service

ready for sale.– Appear “above the line” for gross margin in income statements– These costs can be inventoried

• They flow through the inventory account in the balance sheet • Sometime called “Inventoriable costs.”

• Period costs: Costs that are not product costs. Related to marketing and administration – Appear “below the line” for gross margin– These costs are expensed in the period they are incurred.– These costs do not flow through inventory accounts

Period Costs

Product Costs

A Traditional Income Statement

Usefulness for Internal Decisions

• The statement only considers expenses– Cost versus expense

• An expense is a cost recognized in the income statement

• The gross margin income statement mingles– Relevant & non relevant costs– Variable and fixed costs– Direct and indirect costs

Service Firms

• Products are not tangible or storable– Hotels, restaurants, consulting, airlines, gyms,

universities, museums,…

• Generally, there is no inventory of their final product– Exceptions exist

• We can inventory costs of software projects that go across accounting periods

Flow of Costs: Service Settings

Merchandising Firms

• Examples include Wal Mart, Big Bazaar etc.• These firms

– Sell substantively the same product they purchase.– Carry inventory to make goods available in the

quantities, varieties and delivery schedules demanded by customers.

Inventory Equation

• Need to flow costs via inventory account– Cost of purchase is NOT the cost of goods sold

• We can capture flow as:Cost of beginning inventory

+ Cost of goods purchased during the period– Cost of ending inventory= Cost of goods sold (COGS) during the period

• Make inventory cost flow assumption– First In First Out (FIFO)– Last In First Out (LIFO)

Cost of beginning inventory $3,450,200+ Cost of goods purchased + 24,795,740- Cost of ending inventory - 3,745,600= Cost of goods sold = $24,500,340

Solution

Flow of Costs in Merchandising

Transportation in, stocking

Transportation in, stocking

Manufacturing Firms

• Use labor and equipment to transform raw materials into finished goods– Have work-in-process– Need inventory accounts for all three kinds of

stages in the production process

• Much variation in– Nature of production process– Relative amounts of different costs

Cost Terms in Manufacturing

Names for Groups of Costs

Cost Terms in Manufacturing Prime Costs

Prime Costs

Conversion Costs

Conversion Costs

To verify the amounts specified above, THREE calculations need to be made:To verify the amounts specified above, THREE calculations need to be made:

Calculate Raw Materials UsedCalculate Raw Materials Used11Procedure Result

22 Calculate Cost of Goods ManufacturedCalculate Cost of Goods Manufactured

33 Calculate Cost of Goods SoldCalculate Cost of Goods Sold

Beginning materials inventory $240,000+ Purchases + 1,200,000- Ending materials inventory - 320,000= Raw materials used = $1,120,000

Beginning WIP inventory $50,000+ Materials used + 1,120,000+ Labor cost + 845,000+ Manufacturing overhead + 760,500- Ending WIP inventory - 100,000= Cost of goods manufactured = 2,675,500

Beginning FG inventory $375,000+ COGM + 2,675,500- Ending FG inventory - 294,500= Cost of goods sold = $2,765,000

Calculation

Cost Hierarchy• The cost hierarchy broadens the principle of

variability– Allows us to consider multiple activities

• The cost hierarchy recognizes four types of costs – Unit-level costs– Batch-level costs – Product-level costs– Facility-level costs

Why the Cost Hierarchy?

• Allows us to compute a more accurate estimate of costs– Can extend concept to other “levels”

• Customer level costs, channel level costs,…

• However,– Difficult to assign many costs to hierarchy categories

• Need finer data on operations

– Wrong classification of levels introduces errors in cost estimation

Example: Deluxe Checks

Variable and Fixed Cost

BehaviorA variable cost changes in direct proportion to changes in the cost-driver level.

A variable cost changes in direct proportion to changes in the cost-driver level.

A fixed cost is not immediately affected by changes in the cost-driver.

A fixed cost is not immediately affected by changes in the cost-driver.

Think of variable costs on a per-unit basis.Think of variable costs on a per-unit basis.

The per-unit variable cost remains unchanged regardless of changes in the cost-driver.

The per-unit variable cost remains unchanged regardless of changes in the cost-driver.

Think of fixed costs on a total-cost basis.Think of fixed costs on a total-cost basis.

Total fixed costs remain unchanged regardless of changes in the cost-driver.

Total fixed costs remain unchanged regardless of changes in the cost-driver.

Examples of Variable Costs

Direct material consumed.Direct LabourDirect Expenses/overheadsSelling commission based on number of units sold

Direct material consumed.Direct LabourDirect Expenses/overheadsSelling commission based on number of units sold

Examples of Fixed Cost

Salary of factory managerFactory RentDepreciation on machineryOffice & administrative costsSelling & distribution costs if fixed

Salary of factory managerFactory RentDepreciation on machineryOffice & administrative costsSelling & distribution costs if fixed

Committed Fixed Costs:Those fixed costs which cannot be reduced withoutcurtailing the organisation’s operations substantially

Committed Fixed Costs:Those fixed costs which cannot be reduced withoutcurtailing the organisation’s operations substantially

Discretionary Fixed Costs:Those fixed costs which can be reduced in difficult times

Discretionary Fixed Costs:Those fixed costs which can be reduced in difficult times

Relevant Range

The relevant range is the limitof cost-driver activity level within which aspecific relationship between costsand the cost driver is valid.

The relevant range is the limitof cost-driver activity level within which aspecific relationship between costsand the cost driver is valid.

Even within the relevant range, a fixed cost remains fixed only over a given period of time Usually the budget period.

Even within the relevant range, a fixed cost remains fixed only over a given period of time Usually the budget period.

Fixed Costs and Relevant Range

20 40 60 80 100 20 40 60 80 100

$115,000$115,000 100,000 100,000

60,000 60,000

Total Cost-Driver Activity in Thousands of Cases per Month

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Fix

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Costs

Relevant range$115,000$115,000 100,000 100,000

60,000 60,000

20 40 60 80 100

CVP Scenario

Per Unit Percentage of Sales Selling price $3.00 100%Variable cost of each item 2.10 70Selling price less variable cost $ .90 30%

Monthly fixed expenses: Rent $10,000 Depreciation 20,000 Other fixed expenses 15,000Total fixed expenses per month $ 45,000

Per Unit Percentage of Sales Selling price $3.00 100%Variable cost of each item 2.10 70Selling price less variable cost $ .90 30%

Monthly fixed expenses: Rent $10,000 Depreciation 20,000 Other fixed expenses 15,000Total fixed expenses per month $ 45,000

Cost-volume-profit (CVP) analysis is the study of the effects of output volume on revenue (sales), expenses (costs), and net income (net profit).Cost-volume-profit (CVP) analysis is the study of the effects of output volume on revenue (sales), expenses (costs), and net income (net profit).

Break-Even Point

The break-even point is the level of sales at which revenue equals expenses and net income is zero.The break-even point is the level of sales at which revenue equals expenses and net income is zero.

Sales - Variable expenses- Fixed expensesZero net income (break-even point)

Sales - Variable expenses- Fixed expensesZero net income (break-even point)

Contribution Margin Method

$45,000 fixed costs ÷ $.90= 50,000 units (break even)$45,000 fixed costs ÷ $.90= 50,000 units (break even)

Contribution margin Per UnitSelling price $3.00 Variable costs 2.10Contribution margin $ .90

Contribution margin Per UnitSelling price $3.00 Variable costs 2.10Contribution margin $ .90

Contribution margin ratioPer Unit %Selling price 100 Variable costs 70 Contribution margin 30


Contribution Margin Method

$45,000 fixed costs÷ 30% (contribution-margin percentage)= $150,000 of sales to break even

$45,000 fixed costs÷ 30% (contribution-margin percentage)= $150,000 of sales to break even

50,000 units × $3.00 = $150,000in sales to break even50,000 units × $3.00 = $150,000in sales to break even

Equation Method

Sales – variable expenses – fixed expenses = net income$3.00N – $2.10N – $45,000 = 0$.90N = $45,000N = $45,000 ÷ $.90N = 50,000 Units

Sales – variable expenses – fixed expenses = net income$3.00N – $2.10N – $45,000 = 0$.90N = $45,000N = $45,000 ÷ $.90N = 50,000 Units

Let N = number of unitsto be sold to break even.Let N = number of unitsto be sold to break even.

Equation Method

S – .70S – $45,000 = 0.30S = $45,000S = $45,000 ÷ .30S = $150,000

S – .70S – $45,000 = 0.30S = $45,000S = $45,000 ÷ .30S = $150,000

Let S = sales in dollarsneeded to break even.Let S = sales in dollarsneeded to break even.

Shortcut formulas:Break-even volume in units = fixed expenses unit contribution margin

Break-even volume in sales = fixed expenses contribution margin ratio

Shortcut formulas:Break-even volume in units = fixed expenses unit contribution margin

Break-even volume in sales = fixed expenses contribution margin ratio

Target Net Profit

Managers use CVP analysis to determine the total sales, in units and dollars, needed To reach a target net profit.

Managers use CVP analysis to determine the total sales, in units and dollars, needed To reach a target net profit.

Target sales – variable expenses – fixed expenses target net income

Target sales – variable expenses – fixed expenses target net income

$9,000 per month is the minimumacceptable net income.

$9,000 per month is the minimumacceptable net income.

Target sales volume in units =(Fixed expenses + Target net income)÷ Contribution margin per unit

Target sales volume in units =(Fixed expenses + Target net income)÷ Contribution margin per unit

($45,000 + $9,000) ÷ $.90 = 60,000 units($45,000 + $9,000) ÷ $.90 = 60,000 units

Target Net Profit

Selling price $3.00 Variable costs 2.10 Contribution margin per unit $ .90

Selling price $3.00 Variable costs 2.10 Contribution margin per unit $ .90

Target sales dollars = sales price X sales volume in unitsTarget sales dollars = $3.00 X 60,000 units = $180,000.Target sales dollars = sales price X sales volume in unitsTarget sales dollars = $3.00 X 60,000 units = $180,000.

Sales volume in dollars = 45,000 + $9,000 = $180,000 .30

Sales volume in dollars = 45,000 + $9,000 = $180,000 .30

Target Net Profit

Target sales volume in dollars = Fixed expenses + target net incomecontribution margin ratio

Target sales volume in dollars = Fixed expenses + target net incomecontribution margin ratio



Margin of Safety

The excess of actual sales revenue over the break even sales revenue.The excess of actual sales revenue over the break even sales revenue.

Margin of safety divided by actual sales revenue gives the Margin of Safety Ratio.Higher the Margin of Safety Ratio, better it is.

Margin of safety divided by actual sales revenue gives the Margin of Safety Ratio.Higher the Margin of Safety Ratio, better it is.

Example

A company had incurred fixed expenses of Rs.4,50,000 with sales of Rs.15,00,000 and earned a profit of Rs.3,00,000 during the first halfof the year. In the Second half, it suffered a loss of Rs.1,50,000.

Compute:i. The profit volume ratio, break even point and margin of safety

for the first half.ii. Sales volume of second half assuming that the selling price and

fixed expenses remained unchanged.iii. The margin of safety and breakeven point for the whole year.

A company had incurred fixed expenses of Rs.4,50,000 with sales of Rs.15,00,000 and earned a profit of Rs.3,00,000 during the first halfof the year. In the Second half, it suffered a loss of Rs.1,50,000.

Compute:i. The profit volume ratio, break even point and margin of safety

for the first half.ii. Sales volume of second half assuming that the selling price and

fixed expenses remained unchanged.iii. The margin of safety and breakeven point for the whole year.

Assumptions of CVP Analysis

• Costs can be classified between Variable and Fixed costcomponents.

• The relationship of revenues and variable costs with output is linear.

• No changes in efficiency or productivity.

• Sales mix remains constant.

• Inventory level does not change significantly.

• Costs can be classified between Variable and Fixed costcomponents.

• The relationship of revenues and variable costs with output is linear.

• No changes in efficiency or productivity.

• Sales mix remains constant.

• Inventory level does not change significantly.

Operating Leverage

Operating leverage: a firm’s ratio of fixed costs to variable costs. Operating leverage: a firm’s ratio of fixed costs to variable costs.

Margin of safety = planned unit sales – break-even sales How far can sales fall below the planned level before losses occur?Margin of safety = planned unit sales – break-even sales How far can sales fall below the planned level before losses occur?

Highly leveraged firms have high fixed costs and low variable costs. A small change in sales volume = a large change in net income.Highly leveraged firms have high fixed costs and low variable costs. A small change in sales volume = a large change in net income.

Low leveraged firms have lower fixed costs and higher variable costs. Changes in sales volume will have a smaller effect on net income.Low leveraged firms have lower fixed costs and higher variable costs. Changes in sales volume will have a smaller effect on net income.

Sales Mix Analysis

Sales mix is the relative proportions orcombinations of quantities of productsthat comprise total sales.

Sales mix is the relative proportions orcombinations of quantities of productsthat comprise total sales.

Sales Mix AnalysisRamos Company Example

Sales in units 300,000 75,000 375,000Sales @ $8 and $5 $2,400,000 $375,000 $2,775,000Variable expenses @ $7 and $3 2,100,000 225,000 2,325,000 Contribution margins @ $1 and $2 $ 300,000 $150,000 $ 450,000Fixed expenses 180,000 Net income $ 270,000

Sales in units 300,000 75,000 375,000Sales @ $8 and $5 $2,400,000 $375,000 $2,775,000Variable expenses @ $7 and $3 2,100,000 225,000 2,325,000 Contribution margins @ $1 and $2 $ 300,000 $150,000 $ 450,000Fixed expenses 180,000 Net income $ 270,000

Wallets(W)

Key Cases(K) Total

How much units of Wallets and Key Cases should the company sell to break even?

Sales Mix Analysis

Break-even point for a constant sales mix of 4 units of W for every unit of K.sales – variable expenses - fixed expenses = zero net income[$8(4K) + $5(K)] – [$7(4K) + $3(K)] – $180,000 = 0 32K + 5K - 28K - 3K - 180,000 = 06K = 180,000 K = 30,000W = 4K = 120,000

Break-even point for a constant sales mix of 4 units of W for every unit of K.sales – variable expenses - fixed expenses = zero net income[$8(4K) + $5(K)] – [$7(4K) + $3(K)] – $180,000 = 0 32K + 5K - 28K - 3K - 180,000 = 06K = 180,000 K = 30,000W = 4K = 120,000

Let K = number of units of K to break even, and4K = number of units of W to break even.Let K = number of units of K to break even, and4K = number of units of W to break even.

Sales Mix Analysis

If the company sells only key cases:break-even point = fixed expenses

contribution margin per unit = $180,000

$2 = 90,000 key cases

If the company sells only key cases:break-even point = fixed expenses


$2 = 90,000 key cases

If the company sells only wallets:break-even point = fixed expenses


$1 = 180,000 wallets

If the company sells only wallets:break-even point = fixed expenses


$1 = 180,000 wallets

Sales Mix Analysis

Suppose total sales were equal to the budget of 375,000 units.Suppose total sales were equal to the budget of 375,000 units.

However, Ramos sold only 50,000 key casesAnd 325,000 wallets.What is net income?

However, Ramos sold only 50,000 key casesAnd 325,000 wallets.What is net income?

Sales Mix Analysis

Ramos Company Example

Sales in units 325,000 50,000 375,000 Sales @ $8 and $5 $2,600,000 $250,000 $2,850,000 Variable expenses @ $7 and $3 2,275,000 150,000 2,425,000 Contribution margins @ $1 and $2 $ 325,000 $100,000 $ 425,000 Fixed expenses 180,000 Net income $ 245,000

Sales in units 325,000 50,000 375,000 Sales @ $8 and $5 $2,600,000 $250,000 $2,850,000 Variable expenses @ $7 and $3 2,275,000 150,000 2,425,000 Contribution margins @ $1 and $2 $ 325,000 $100,000 $ 425,000 Fixed expenses 180,000 Net income $ 245,000

Wallets(W)

Key Cases(K) Total

Example

The Garware Paints Ltd. presents you the following income statement for the first quarter

Product Total X Y Z Sales 100,000 60,000 40,000 200,000 Variable Costs 80,000 42,000 24,000 146,000 Contribution 20,000 18,000 16,000 54,000 Fixed costs 27,000 Net Income 27,000 P/V ratio 0.27Break Even sales 100,000 Sales mix percent 0.50 0.30 0.20 1.00

If Rs.40,000 of the sales shown for the product X could be shifted to product Y and Z equally, how would the net income, P/V ratio and BEP change.

Impact of Income Taxes

Suppose that a company earns $480 before taxes and pays income tax at a rate of 40%.Suppose that a company earns $480 before taxes and pays income tax at a rate of 40%.

What is the after-tax income?What is the after-tax income?


Target income before taxes = Target after-tax net income 1 – tax rate

Target income before taxes = $ 288 = $480 1 – 0.40

Suppose the target net incomeafter taxes was $288.


Target sales – Variable expenses – Fixed expenses= Target after-tax net income ÷ (1 – tax rate)Target sales – Variable expenses – Fixed expenses= Target after-tax net income ÷ (1 – tax rate)

$.50N – $.40N – $6,000 = $288 ÷ (1 – 0.40)$.10N = $6,000 + ($288/.6)$.06N = $3,600 + $288 = $3,888 N = $3,888/$.06 N = 64,800 units

$.50N – $.40N – $6,000 = $288 ÷ (1 – 0.40)$.10N = $6,000 + ($288/.6)$.06N = $3,600 + $288 = $3,888 N = $3,888/$.06 N = 64,800 units


Suppose target net income after taxes was $480Suppose target net income after taxes was $480

$.50N – $.40N – $6,000 = $480 ÷ (1 – 0.40)$.10N = $6,000 + ($480/.6) $.06N = $3,600 + $480 = $4080N = $4,080 ÷ $.06 N = 68,000 units

$.50N – $.40N – $6,000 = $480 ÷ (1 – 0.40)$.10N = $6,000 + ($480/.6) $.06N = $3,600 + $480 = $4080N = $4,080 ÷ $.06 N = 68,000 units

Q. State whether P/V ratio will increase or decrease or remain unchanged in the following situations (Consider all situations independently keeping other things constant):

An increase in physical sales volumeNo Change

An increase in fixed costsNo Change

A decrease in variable cost per unitIncrease.

A decrease in contribution margin per unitDecrease

An increase in Selling priceIncrease

A decrease in fixed costsNo change

A 10% increase in both variable costs and selling priceNo Change

A 10% increase in selling price and 10% decrease in physical sales volumeIncrease

A 50% increase in variable cost and 50% decrease in fixed costsDecrease

An increase in angle of incidenceIncrease

Example

S Ltd. furnishes the following data relating to the year 2012:

Ist Half of the yearIInd Half of the year

Sales 45,000 50,000 Total Cost 40,000 43,000

Assuming that there is no change in prices and variable costs per unit and that the fixed expenses are incurred equally in the two half year periods, calculate for the entire year:

i. The profit volume ratioii. Fixed expensesiii. Break even salesiv. Margin of safety ratio

ExampleM Ltd. manufactures three products P, Q and R. The unit selling price of these products are Rs.100, Rs.80 and Rs.50 respectively. The corresponding unit variable costs are Rs.50, Rs.40 and Rs.20. The proportions (quantity wise) in which these products are manufactured and sold are 20%, 30% and 50% respectively. The total fixed costs are Rs.14,80,000.

Given the above information you are required to work out overall break even quantity and product wise break up of such quantity.

Example

Two competing companies HERO Ltd. and ZERO Ltd. sell same type of product in the same market. Their forecasted Profit and Loss A/c for the year ending Mar 2011 are as follows:

HERO ZERO

Sales 500,000 500,000

Less: Variable Costs 400,000 300,000

Fixed costs 50,000 150,000

Forecasted net profit 50,000 50,000

You are required to state which company is likely greater profits in the conditions of:a. Low demandb. High Demand.

Example

A Japanese soft drink is planning to establish a subsidiary company in India to produce mineral water.Based on the estimated annual sales of 40,000 bottles of mineral water, cost studies produced the following estimates for Indian Subsidiary:

Total Annual CostsPercent of total annual cost which is variable

Material 210,000 100%Labour 150,000 80%Factory overheads 92,000 60%Administration expenses 40,000 35%

The Indian production will be sold by the manufacturer's representatives who will receive a commission of 8% of the sale price.i. What should be the selling price per bottle to earn a net profit of 10% on sales.ii. What will be the break even point in units and in Rupee sales at the above

computed selling price.

ExampleSuppose a Holiday Inn Hotel has annual fixed costs applicable to its rooms of $1.2 million for its 300-room hotel, average daily room rents of $50, and average variable costs of $10 for each room rented. It operates 365 days per year.

What is the amount of net income on rooms that will be generated if the hotel is half full throughout the entire year?

What is the break even point in number of room days?

What is the percentage of occupancy needed to break even?

Ans: $990,000, 30,000 room days27.4%

ExampleGeneral Hospital has total variable costs of 90% of total revenues and fixed costs of $5 million per year. There are 50,000 patient-days estimated for next year. What is the average daily revenue per patient necessary to breakeven?

Ans: $1,000 average daily revenue per patient necessary to breakeven

ExampleBerea Company currently sells 19,000 units. Total fixed costs are $84,000, and the contribution margin per unit is $6.00. Berea’s tax rate is 40%. What is the margin of safety in units?

Ans: 5,000 units

EaxmpleMuy Mal Company, a producer of salsa, has the following information:

Income tax rate 30%Selling price per unit $5.00 Variable cost per unit $3.00 Total fixed costs $90,000.00

How many number of units must be sold to obtain a targeted after-tax income of $14,000?

Ans: 55,000 units

ExampleBonnie and Clyde started the BC Restaurant in 20X0. They rented a building, bought equipment, and hired two employees to work full time at a fixed monthly salary. Utilities and other operating charges remain fairly constant during each month. During the past two years, the business has grown with average sales increasing 1% a month. This situation pleases both Bonnie and Clyde, but they do not understand how sales can grow by one percent a month while profits are increasing at an even faster pace. They are afraid that one day they will wake up to increasing sales but decreasing profits. Required: Explain why the profits have increased at a faster rate than sales.

Linear-cost Behavior

Costs are assumed to be fixed or variable within the relevant range of activity

Step Cost Behavior Patterns

Step costs change abruptly at intervalsof activity because the resources andtheir costs come in indivisible chunks.

Step Cost Behavior Patterns

Mixed-Cost Behavior Patterns

Mixed costs contain elements of bothfixed- and variable-cost behavior.

The fixed-cost element is unchangedover a range of cost-driver activity.

The variable-cost element variesproportionately with cost-driver activity.

Mixed-Cost Behavior PatternsParkview Medical Center Predicted costs = fixed + variable

costs (patient-days) Predicted costs = $10,000 + $5(4,000)

Predicted costs = $30,000

Distribution channels

Choice of process and product design

Quality levels

Product features

Management’s Influence on Cost Behavior

Capacity Decisions

They are the fixed costs of being ableto achieve a desired level of production orto provide a desired level of service whilemaintaining product or service attributes.

Committed Fixed Costs

Salaries of key personnel

Committed fixed costs arisefrom the possession of facilities,

equipment, and a basic organization.

Lease payments

Property taxes

Discretionary Fixed Costs

Discretionary fixed costs are costs fixed at certain levels only because management decided that these levels of cost

should be incurred to meet the organization’s goals.

These discretionary fixed costs have no obvious relationship to levels of output activity but

are determined as part of the periodic planning process.

Each planning period, management will determine how much to spend on discretionary items. These costs

then become fixed until the next planning period.

Examples of DiscretionaryFixed Costs

Advertising and promotion

Research and development

Management salaries

Employee training

Technology Decisions

Choice of technology (e-commerce versusin-store or mail-order sales) positions theorganization to meet its current goals andto respond to changes in the environment.

Cost Functions

Planning and controlling the activitiesof an organization require accurate

and useful estimates of futurefixed and variable costs.

Cost Functions

Understanding relationships between costsand their cost drivers allows managers to...

Make better operating, marketing, And production decisions

Plan and evaluate actions

Determine appropriate costs for short-run and long-run decisions.

Cost Functions

The first step in estimating or predictingcosts is measuring cost behavior as afunction of appropriate cost drivers.

The second step is to use these costmeasures to estimate future costs atexpected levels of cost-driver activity.

Cost Function EquationLet:Y = Total cost F = Fixed costV = Variable cost per unitX = Cost-driver activity in number of units

Mixed-cost function:Y = F + VX

Y = $10,000 + $5.00X

The mixed-cost function is called a linear-cost function.

Developing Cost Functions

A cost function’s estimates of costsat actual levels of activity must reliablyconform with actually observed costs.

The cost function must be believable.

Choice of Cost Drivers: Activity Analysis

Choosing a cost function startswith choosing cost drivers.

Managers use activity analysis toidentify appropriate cost drivers.

Activity analysis directs managementaccountants to the appropriate

cost drivers for each cost.

Methods of Measuring Cost Functions

1. Engineering analysis 2. Account analysis 3. High-low analysis 4. Visual-fit analysis 5. Least-squares regression analysis

Engineering Analysis

Engineering analysis measures cost behavior according to what costs should be,

not by what costs have been.

Engineering analysis entails a systematicreview of materials, supplies, labor,

support services, and facilitiesneeded for products and services.

Account Analysis

The simplest method of account analysis selects a plausiblecost driver and classifies each account as a variable or fixed cost.

Supervisor’s salary and benefits $ 3,800 $3,800 Hourly workers’ wages and benefits 14,674 $14,674Equipment depreciation and rentals 5,873 5,873 Equipment repairs 5,604 5,604 Cleaning supplies 7,472 7,472 Total maintenance costs $37,423 $9,673 $27,750

Monthly cost Amount Fixed Variable

Parkview Medical Center

Account Analysis Example

Fixed cost per month = $9,673

Variable cost per patient-day= $27,750 ÷ 3,700

= $7.50 per patient-day

3,700 patient-days

Y = $9,673 + ($7.50 × patient-days)

High-Low Method

Focus on the highest- and lowest-activity points.

Plot historical data points on a graph.

High month: AprilMaintenance cost: $47,000

Number of patient-days: 4,900

Low month: SeptemberMaintenance cost: $17,000

Number of patient-days: 1,200

High-Low Method Example

The point at which the line intersects the Y axis is the intercept, F, or estimate of Fixed Costs, and the slope of the line measures the variable cost.


Variable costs = Change in costs change in activity

V = ($47,000 – $17,000) ÷ (4,900 – 1,200) = $30,000 ÷ 3,700 = $8.1081

What is the variable cost (V)?Using algebra to solve for variable and fixed costs.


F = Total mixed cost – total variable costAt X (high) F = $47,000 - ($8.1081× 4,900 patient days)

= $47,000 – $39,730 = $7,270 a month

At X (low) F = $17,000 = ($8.1081× 1,200 patient days)= $17,000 – $9,730 = $7,270 a month

Cost function measured by high-low method: Y = $7,270

per month + ($8.1081 × patient-days)

What is the fixed cost (F)?

Visual-Fit Method

In the visual-fit method, the cost analystvisually fits a straight line through a plot

of all of the available data, not justbetween the high point and the

low point, making it more reliablethan the high-low method.

Least-Squares Regression Method

Regression analysis measuresa cost function more objectivelyby using statistics to fit a cost

function to all the data.

Regression analysis measurescost behavior more reliably than

other cost measurement methods.

Coefficient of Determination

One measure of reliability,or goodness of fit, is the

coefficient of determination,R² (or R-squared).

The coefficient of determinationmeasures how much of the

fluctuation of a cost is explainedby changes in the cost driver.

ExamplePresented below is the production data for the first six months of the year showing the mixed costs incurred by Euclid Company.

Month Cost Units

January $7,500 4,000February 13,000 7,500March 11,500 9,000April 11,700 11,500May 13,500 12,000June 11,850 6,000

Euclid Company uses the high low method to analyze mixed costs. ‑

What shall be cost function?

ExampleThe Reynolds Company used regression analysis to predict the annual cost of utilities. The results were as follows:

Utilities CostExplained by Direct Labor Hours

Constant $7,650 Standard error of Y estimate $245.20 R squared ‑ 0.8650 No. of observations 30 Degrees of freedom 28

X coefficient(s) 8.437 Standard error of coefficient(s) 0.917

What shall be the estimated total cost for 1,000 units?

Example:The cost of the maintenance department at Forest Manufacturing has always been charged to the production departments based upon number of employees. Recently, an activity analysis of possible cost drivers was performed which indicated that the square feet of space may also be a predictor of costs to be assigned to each department. Given the following data, compare the different amounts of maintenance department cost that would be allocated to each of the production departments if the cost driver used is (a) number of employees, and (b) the square feet of space.

Dept. X Dept. Y Dept. ZNumber of employees 300 250 50Square feet of space 15,000 25,000 10,000

Total production department cost: $ 1,000,000

Example

Two manufacturing companies which have the following operating details decided to merge:

Company 1 Company 2Capacity Utiliation (%) 90 60Sales (Rs. Lakhs) 540 300

Variable Costs (Rs.Lakhs) 396 225Fixed Costs 80 50

Assuming that the proposal is implemented, calculate:

i. Break even sales for the merged plant and the capacity utilization at that stage.ii. Profitability of the merged plant at 80% capacity utilization.iii. Sales turnover of the merged plant to earn a profit of Rs.75 Lakhiv. When the merged plant is working at a capacity to earn a profit of Rs.75 lakhs, what

percentage increase in selling price is required to sustain an increase of 5% in fixed overheads.

ExampleABC Ltd. has installed capacity of 1,20,000 units per annum. The cost structure of the product manufactured is as under:

Variable Cost:Materials Rs.8Labour Rs.8Overheads Rs.3

Fixed overheads Rs.168750 per annumSemi variable overheads Rs.48,000 at 60% capacity and Rs.60,000 at 80% capacity.

The capacity utilization for next year is estimated at 60% for first two months , 70% for next six months and 80% for rest of the year. Company is planning to have a profit of 25% on sales.

Compute the selling price per unit and break even point in units at the computed selling price.

Example:XYZ School has a total of 150 students. The school plans a picnic to places like Zoo, Planetarium etc. A private bus operator has come forward to lease out the bus(es). Each bus will have 50 seats for students besides 2 seats reserved for teachers. There will be two teachers per bus and each teacher will be paid an allowance of Rs.50. The following are other cost estimates:

Cost per StudentBreak fast Rs.5Lunch Rs.10Tea Rs.3Entrance at Zoo Rs.2

Rent per bus is Rs.650. Special permit of Rs.50 per bus is also required to be paid. Block entrance fees at planetarium is Rs.250. Prizes to students for games Rs.250.

School charges Rs.45 per student. Compute the break even point.

Example

6000 pen drives of 2GB to be sold in a perfectly competitive market to earn Rs.1,06,000 of profit, whereas in monopoly only 1200 units are required to be sold to earn the same profit. The fixed costs for the period are Rs.74,000. The contribution per unit in monopoly market is as high as three fourth of it variable costs. Determine the target selling price per unit under each market condition.

Example

Paints Ltd. manufactures 2,00,000 tins of paints annually at normal capacity. It incurs the following manufacturing cost per unit:

Direct material Rs.7.80Direct Labour Rs.2.10Variable overhead Rs.2.50Fixed overhead Rs.4.00

Each unit is sold for Rs.21 with an additional variable selling overhead incurred at Rs.0.60 per unit. During the next quarter only 10,000 units can be produced and sold. Management plans to shut down the plant estimating that the fixed manufacturing costs can be reduced to Rs.74,000 for the quarter. When the plant is operating, the fixed overheads are incurred at uniform rate through out the year. Additional costs plant shut down for the quarter are estimated at Rs.14,000.

You are required to advise whether it is more economical to shut down the plant during the quarter rather than operate the plant.

ExampleEntertain U Ltd hires an air conditioned theatre to stage plays on weekend evenings. One play is staged per evening. The following are the seating arrangements:VIP Rows – First 3 rows of 10 seats per row, priced at Rs 320 per seat.Middle Level – The next 18 rows of 20 seats per row, priced at Rs 220 per seat.Last Level – 6 rows of 30 seats per row, priced at Rs 120 per seat.For each evening, a drama troupe has to be hired at Rs 71,000, rent has to be paid to theatre at Rs 14,000 per evening and air conditioning and other stage arrangement charges work out to Rs 7,400 per evening. Every time a play is staged, the drama troupe’s friends and guests occupy the first row of the VIP class, free of charge by virtue of passes granted to these guests. The troupe ensures that 50% of the remaining seats in the VIP class and 50% of the seats of the other two classes are sold to outsiders in advance and the money is passed on to Entertain U. The troupe also finds for every evening, a sponsor who puts up his advertisement banner near the stage and pays Entertain U a sum of Rs 9,000 per evening. Entertain U supplies snacks during the interval, free of charge to all guests in the hall, including the VIP free guests. The snacks cost Entertain U Rs 20 per person. Entertain U sells the remaining tickets and observes that for every one seat demanded from the last level, there are 3 seats demanded from middle level and 1 seat demanded from the VIP level. You may assume that in case any level is filled, the visitor buys the next higher or lower level, subject to availability.You are required to calculate the number of seats that Entertain U has to sell in order to break-even and give the category wise total seat occupancy at BEP.

CVP Analysis and Environmental Factors:

Economy-Industry relationship

Industry-Company relationship

Controllable factors affecting Sales-Profit Analysis:Advertising outlays

Market research expenditures

New product development

Extension of marketing territories

cvp analysis

Documents

fixed costs

inventory cost of goods

inventoriable costs

groups of costs cost

levelscustomer level

channel level costs

costdriver level

income statementsthese