Lecture 6

Dr. Haider Shah

Understand what are the primary tools for forecasting

Understand regression analysis and when and how to apply it

In previous lectures we have covered budget preparation

We will now look at how we could produce data to be placed in these budgets

Qualitative Methods

Quantitative methods using historical data

The following checks need to be applied

1. Data must be examined for one off costs. We only want base data which is likely to re-occur

2. Has the data been affected adversely by accounting policies

3. Is the time period appropriate. e.g long enough to reflect seasonal changes

4. Be able to identify dependent and independent variables

Y = a + bX (equation of straight line)

a

b

X

Y

Y = a + bX

Where:

Y = the dependent variable – depends on the value of X

X= the independent variablea = a constant a fixed amountb = a constant ( the number by which the

value of X should be multiplied to derive the value of Y

If there is a linear relationship between total costs and level of activity

Y will equal Total Costs X will equal Level of activity a will equal fixed cost b will equal variable cost per unit

Variable cost - linear:

TotalCost

Output

E.g. Direct Materials

10

30

UnitCost

Output

£3

Stepped Fixed Costs:TotalCost

Output

E.g.

TotalCost

Output

E.g.

Semi-Variable Costs:

Supervision PowerTelephone

Normal Operating

Range

(Relevant Range)

Variable Costs

Fixed Costs

Total Costs

Cost ClassificationCost Classification

Also called mixed costs. Comprise fixed and variable components.

Variable and fixed costs components need to be split for estimation purpose

We need some data which plot total cost against the cost driving activity.

The data can be used to help us split the total cost into variable

and fixed components

Regression analysis: Used for both Revenue & Costs estimates

Time series analysis Used for Revenue estimates mostly

High-Low Method Less sophisticated estimation method

Month Factory O/H Dir Lab Hours

January 15 9

February 20 19

March 14 11

April 16 14

May 25 23

June 20 12

July 20 12

August 23 22

September 14 7

October 22 13

November 18 15

December 18 17

4

16

12

20

8

24

12

28

84 2016 24

FactoryO/H (£)

Direct Labour hours

.

.

..

. ..

...

Fixed

Variable O/H rate

Total O/H (y)

Activity (hours) (x)

High £25 23

Low £14 7

Difference £11 16

= 11 = £0.6875 16

Fixed O/H = Total O/H – variable rate * Dir Lab Hours

Fixed O/H = 25 – 0.6875 * 23 = 9.1875

Y = a + bx Y = 9.1875 + 0.6875x

Variable Rate = Difference of y Difference of x

Also known as ‘least squares technique’ Historical data is collected from previous

periods and adjusted to a common price to remove inflation.

Provides information for activity levels (X) and associated costs (Y).

Identify fixed and variable cost elements

Month Truck maintenance(£)

Truck usage (hrs)

Jan 13,600 2,100

Feb 15,800 2,800

Mar 14,500 2,200

Apr 16,200 3,000

May 14,900 2,600

June 15,000 2,500

Total 90,000 15,200

X Y XY Xsq000 hrs £'000

1 2.1 13.6 28.56 4.412 2.8 15.8 44.24 7.843 2.2 14.5 31.90 4.844 3.0 16.2 48.60 9.005 2.6 14.9 38.74 6.766 2.5 15 37.50 6.25

15.2 90.0 229.54 39.10

Solution:

n=No. of pairs = 6

b = 6(229.54) - (15.2)(90)(6(39.1) - (15.2)sq)

=(1377.24 - 1368) (234.6 - 231.04)

= 9.243.56

= £2.60

a =(sumY/n) - (bsumX / n)

a = (90/6) - (2.6(15.2)/6)

a =8.41 approx = £8,410

Month

Output(units) 000s

Costs(£k)

Jan 20 82

Feb 16 70

Mar 24 90

Apr 22 85

May 18 73

a) Calculate the fixed cost and the variable cost per unitb) What would be total costs if output was 22,000 units

The following data is available for a factory

X Y XY Xsq000 hrs £'000

1 20 82 1640.00 400.002 16 70 1120.00 256.003 24 90 2160.00 576.004 22 85 1870.00 484.005 18 73 1314.00 324.00

100 400 8104.00 2040.00

Complex and difficult

Need to consider various factors

Sales of product A over the past 7 years were as follows:

Yr Sales (‘000 units) 1 22 2 25 3 24 4 26 5 29 6 28 7 30 Noting that X becomes the years,

identify the sales in Year 8 using regression analysis

Yr X Y XY X sq1 1 22 22 12 2 25 50 43 3 24 72 94 4 26 104 165 5 29 145 256 6 28 168 367 7 30 210 49

sum 28 184 771 140

Y = a + bX

b= ((7 x 771) -(28 x 184))((7 x 140) - (28 x 28)

b= 245 / 196 = 1.25

a = (184 ) - (1.25 x 28) = 21.37 7

Y= 21.3 + 1.25X