39147 Cost Behaviour

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©The McGraw-Hill Companies, 2002

Cost behaviour: Analysis and

Use

Chapter 5




Types of Cost behaviourPatterns

Summary of Variable and Fixed Cost Behavior Cost In Total Per Unit

Variable Total variable cost is Variable cost per unit remains

proportional to the activity the same over wide ranges

level within the relevant range. of activity.

Fixed Total fixed cost remains the Fixed cost per unit goes

same even when the activity down as activity level goes up.

level changes within the

relevant range.

Recall the summary of our cost behaviour

discussion from Chapter 2.




Total Variable Cost Example

Your total long distance telephone bill isbased on how many minutes you talk.

Minutes Talked

T o t a l L o n g D i s t a n c e

T e l e

p h o n e B i l l




Variable Cost Per UnitExample

Minutes Talked

P e r M i n u t e

T e l e p h

o n e C h a r g e

The cost per minute talked is constant. Forexample, 10 pence per minute.




Total Fixed Cost Example

Your monthly basic telephone bill isprobably fixed and does not change when

you make more local calls.

Number of Local Calls

M o n t h l y B a s i c

T e l e p h o n e B i l l




Fixed Cost Per Unit Example

Number of Local Calls M o n t h l y B

a s i c T e l e p h

o n e

B i l l p e r L o c a l C a l l

The fixed cost per local call decreases asmore local calls are made.




Cost behaviour

Merchandisers

Cost of Goods Sold

Manufacturers Direct Material, Directlabour, and Variable

Manufacturing Overhead

Merchandisers andManufacturers

Sales commissions andshipping costs

Service Organizations

Supplies and travel

Examples of normally variable costs

Examples of normally fixed costsMerchandisers, manufacturers, and

service organizations

Real estate taxes, Insurance, Sales salariesDepreciation, Advertising




The Activity Base

Machinehours

Labour hours

Unitsproduced

Milesdriven

A measure of the event

causing the incurrence of a

variable cost – a cost driver




Step-Variable Costs

Activity

C o

s t

Total cost remains

constant within a

narrow range of

activity.




Step-Variable Costs

Activity

C o

s t

Total cost increases to anew higher cost for the

next higher range of

activity.




The Linearity Assumption and

the Relevant Range

Activity

T o t a l C o s t

Economist’s

Curvilinear Cost

Function



©The McGraw-Hill Companies, 2002Activity

T o t a l C o s t

Economist’s

Curvilinear Cost

Function

Accountant’s Straight-Line

Approximation (constant

unit variable cost)

The Linearity Assumption andthe Relevant Range



©The McGraw-Hill Companies, 2002Activity

T o t a l C o s t Relevant

Range

The Linearity Assumption andthe Relevant Range

Accountant’s Straight-Line Approximation (constant

unit variable cost)

Economist’s

Curvilinear Cost

Function

A straight line

closely

approximates

a curvilinear

variable costline within the

relevant

range.




Types of Fixed Costs

Fixed Costs

Discretionary

May be altered in theshort-term by currentmanagerial decisions

Committed

Long-term, cannot bereduced in the short

term.

Examples

Depreciation onBuildings and

Equipment

Examples

Advertising andResearch andDevelopment




Trend Toward Fixed Costs

Increased automation.

Increase in salaried knowledge workers

who are difficult to train and replace.Implications

Managers are more “locked-in” with fewer decision

alternatives.

Planning becomes more crucial because fixed costs are

difficult to change with current operating decisions.




Example: Office space

is available at a rental

rate of £30,000 per

year in increments of

1,000 square metres.

As the business grows

more space is rented,increasing the total

cost.

Fixed Costs and RelevantRange

Continue




R e n t C o s t i n

T h o u

s a n d s o f p

o u n d s

0 1,000 2,000 3,000

Rented Area (Square metres)

0

30

60

Fixed Costs and Relevant

Range90

RelevantRange

Total cost doesn’t

change for a wide

range of activity,

and then jumps to a

new higher cost for

the next higher

range of activity.




How does this type

of fixed cost differ from a step-variable

cost?

Step-variable costscan be adjusted more

quickly and . . .

The width of theactivity steps is much

wider for the fixedcost.

Fixed Costs and RelevantRange




A mixed cost

has both fixedand variable

components.

Mixed Costs

Consider thefollowing electric

utility example.




Fixed Monthly

Utility Charge

Variable

Utility Charge

Activity (Kilowatt Hours)

T o t a l U t i l i t y C o s t

Mixed Costs

X

Y




Fixed Monthly

Utility Charge

Variable

Utility Charge



Mixed Costs

X

Y

The total mixed cost line can be expressedas an equation: Y = a + bX

Where: Y = the total mixed cost

a = the total fixed cost (the

vertical intercept of the line)

b = the variable cost per unit of

activity (the slope of the line)

X = the level of activity




Fixed Monthly

Utility Charge

Variable

Utility Charge



Mixed Costs

bX

a

X

Y




The Analysis of Mixed Costs

Engineering Approach

Account Analysis

Scattergraph Method

Least-Square Regression Method

High-Low Method




Account Analysis

Each account is classified as either

variable or fixed based on the analyst’s

knowledge of how the account behaves.




Engineering Estimates

Cost estimates are based on an evaluationof production methods, and material, labour

and overhead requirements.




WiseCo recorded the following production activityand maintenance costs for two months:

Using these two levels of activity, compute: the variable cost per unit; the fixed cost; and then express the costs in equation form Y = a + bX.

The High-Low Method

Units Cost

High activity level 9,000 9,700£Low activity level 5,000 6,100

Change 4,000 3,600£




Unit variable cost =Changein cost

Change in units

Units Cost

High activity level 9,000 9,700£

Low activity level 5,000 6,100

Change 4,000 3,600£

The High-Low Method




Units Cost



Change 4,000 3,600£

The High-Low Method

Unit variable cost = £3,600 ÷ 4,000 units = £0.90 per unit




Units Cost



Change 4,000 3,600£

The High-Low Method


Fixed cost = Total cost – Total variable cost

Fixed cost = £9,700 – (£0.90 per unit × 9,000 units)Fixed cost = £9,700 – £8,100 = £1,600





Fixed cost = Total cost – Total variable cost

Fixed cost = £9,700 – (£0.90 per unit × 9,000 units)Fixed cost = £9,700 – £8,100 = £1,600

Total cost = Fixed cost + Variable cost (Y = a + bX)

Y = £1,600 + £0.90X

Units Cost



Change 4,000 3,600£

The High-Low Method




If sales salaries and commissions are £10,000when 80,000 units are sold and £14,000 when

120,000 units are sold, what is the variable portion of sales salaries and commission?

a. £0.08 per unit

b. £0.10 per unitc. £0.12 per unit

d. £0.125 per unit

The High-Low Method




If sales salaries and commissions are £10,000when 80,000 units are sold and £14,000 when120,000 units are sold, what is the variable

portion of sales salaries and commission?a. £0.08 per unit

b. £0.10 per unit

c. £0.12 per unitd. £0.125 per unit

The High-Low Method

£4,000 ÷ 40,000 units

= £0.10 per unit

Units Cost

High level 120,000 14,000£

Low level 80,000 10,000 Change 40,000 4,000£




If sales salaries and commissions are £10,000when 80,000 units are sold and £14,000 when120,000 units are sold, what is the fixed portionof sales salaries and commissions?

a. £ 2,000

b. £ 4,000

c. £10,000

d. £12,000

The High-Low Method




If sales salaries and commissions are £10,000when 80,000 units are sold and £14,000 when120,000 units are sold, what is the fixed portionof sales salaries and commissions?

a. £ 2,000

b. £ 4,000

c. £10,000

d. £12,000

The High-Low Method

Total cost = Total fixed cost +

Total variable cost

14,000£ = Total fixed cost +

(£0.10 × 120,000 units)

Total fixed cost = £14,000 - £12,000

Total fixed cost = 2,000£




The Scattergraph Method

Plot the data points on agraph (total cost vs. activity).

0 1 2 3 4

*

T o t a l C o s t i n

1 , 0

0 0 ’ s

o f p o u

n d s

10

20

0

***

* ** **

*

Activity, 1,000’s of Units Produced

X

Y





Draw a line through the data points with about an

equal numbers of points above and below the line.

0 1 2 3 4

*


1 , 0

0 0 ’ s

o f p o u

n d s

10

20

0

***

* ** **

*


X

Y





Estimated fixed cost = £10,000

0 1 2 3 4

*


1 , 0

0 0 ’ s

o f p o u

n d s

10

20

0

***

* ** **

*


X

Y

The slope of this line is the variable unitcost. (Slope is the change in total cost for

a one unit change in activity).





Slope = Change in costChange in units

Horizontal distance is

the change in activity.

0 1 2 3 4

*


1 , 0 0 0 ’ s

o f p o u

n d s

10

20

0

***

* ** **

*


X

Y

Vertical

distanceis the

change

in cost.

S




• Accountants and managersmay use computer softwareto fit a regression line

through the data points.• The cost analysis objective

is the same: Y = a + bx

Least-Squares RegressionMethod

Least-squares regression also provides a statistic, called

the adjusted R2, that is a measure of the goodness

of fit of the regression line to the data points.

L S R i




0 1 2 3 4

T o t a l C o s t

10

20

0

Activity

*

***

**

****

Least-Squares RegressionMethod

R2 is the percentage of the variation

in total cost explained by the activity.

R2 for this relationship is near 100% since the data points are

very close to the regression line.

X

Y




Let’s put our knowledge of cost

behaviour to work

by preparing acontribution format

profit statement.

The Contribution Format





Total UnitSales Revenue 100,000£ 50£

Less: Variable costs 60,000 30

Contribution margin 40,000£ 20£

Less: Fixed costs 30,000

Net profit 10,000£

The contribution margin format emphasizes cost

behaviour. Contribution margin covers fixed costs

and provides for profit.





Used primarily for

external reporting.

Used primarily by

management.



End of Chapter 5

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39147 Cost Behaviour

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