cost behavior analysis

©The McGraw-Hill Companies, 2002

Cost behaviour:

Analysis and Use


Types of Cost behaviour Patterns

Summary of Variable and Fixed Cost Behavior

Cost In Total Per Unit

Variable Total variable cost is Variable cost per unit remainsproportional 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 goessame even when the activity down as activity level goes up.

level changes within therelevant range.


Total Variable Cost Example

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

Minutes Talked

To

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on

g D

ista

nce

Tel

eph

on

e B

ill


Variable Cost Per Unit Example

Minutes Talked

Per

Min

ute

Tel

eph

on

e C

har

ge

The cost per minute talked is constant. For example, 10 pence per minute.


Total Fixed Cost Example

Your monthly basic telephone bill is probably fixed and does not change when you make more local calls.

Number of Local Calls

Mo

nth

ly B

asic

T

elep

ho

ne

Bill


Fixed Cost Per Unit Example

Number of Local Calls

Mo

nth

ly B

asic

Tel

eph

on

e B

ill p

er L

oca

l Cal

l

The fixed cost per local call decreases as more local calls are made.


Cost behaviour

MerchandisersCost of Goods Sold

ManufacturersDirect Material, Direct labour, and Variable

Manufacturing Overhead

Merchandisers and Manufacturers

Sales commissions and shipping costs

Service Organizations Supplies and travel

Examples of normally variable costs

Examples of normally fixed costs

Merchandisers, manufacturers, and service organizations

Real estate taxes, Insurance, Sales salariesDepreciation, Advertising


The Activity Base

Machinehours

Labourhours

Unitsproduced

Milesdriven

A measure of the event causing the incurrence of a variable cost – a cost driver


Step-Variable Costs

Activity

Co

st

Total cost remainsconstant within anarrow range of

activity.


Step Costs

Activity

Co

st

Total cost increases to a new higher cost for the

next higher range of activity.


The Linearity Assumption and the Relevant Range

Activity

To

tal

Co

st

Economist’sCurvilinear Cost

Function

©The McGraw-Hill Companies, 2002Activity

To

tal

Co

st


Function

Accountant’s Straight-Line Approximation (constant

unit variable cost)


©The McGraw-Hill Companies, 2002Activity

To

tal

Co

st

RelevantRange


Accountant’s Straight-Line Approximation (constant

unit variable cost)


Function

A straight line closely

approximates a curvilinear variable cost line within the

relevant range.

A straight line closely

approximates a curvilinear variable cost line within the

relevant range.


Types of Fixed Costs

Fixed Costs

DiscretionaryMay be altered in the short-term by current managerial decisions

CommittedLong-term, cannot be reduced in the short

term.

ExamplesDepreciation on Buildings and

Equipment

ExamplesAdvertising and Research and Development


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.

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 Relevant Range

Continue


Ren

t C

ost

in

T

ho

usa

nd

s o

f p

ou

nd

s

0 1,000 2,000 3,000 Rented Area (Square metres)

0

30

60

Fixed Costs and Relevant Range

90

Relevant

Range

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.


A semi-variable cost

has both fixed and variablecomponents.

Semi-variable Costs (also called mixed cost)

Consider thefollowing electric utility example.


Fixed Monthly

Utility Charge

Variable

Utility Charge

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

stMixed Costs

X

Y

Total mixed cost


Total mixed cost Y

= a + bX

Fixed Monthly

Utility Charge

Variable

Utility Charge


To

tal

Uti

lity

Co

stMixed Costs

X

Y

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

Where: Y = the total mixed cost

a = the total fixed cost (thevertical intercept of the line)

b = the variable cost per unit ofactivity (the slope of the line)

X = the level of activity


Fixed Monthly

Utility Charge

Variable

Utility Charge


To

tal

Uti

lity

Co

st

Total mixed cost Y

= a + bX

Mixed Costs

bX

aX

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 eithervariable or fixed based on the analyst’s

knowledge of how the account behaves.


Engineering Estimates

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

and overhead requirements.


WiseCo recorded the following production activity and 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 costChange in units

Units Cost


The High-Low Method


Units Cost


The High-Low Method

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


Units Cost


The High-Low Method

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


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


The High-Low Method


If sales salaries and commissions are £10,000 when 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 unitb. £0.10 per unit c. £0.12 per unitd. £0.125 per unit


The High-Low Method




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 £10,000 when 80,000 units are sold and £14,000 when 120,000 units are sold, what is the fixed portion of sales salaries and commissions?a. £ 2,000b. £ 4,000 c. £10,000d. £12,000


The High-Low Method




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 a graph (total cost vs. activity).

0 1 2 3 4

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000’

s o

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s

10

20

0

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Activity, 1,000’s of Units Produced

X

Y


The Scattergraph MethodDraw a line through the data points with about an

equal numbers of points above and below the line.

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X

Y



Estimated fixed cost = £10,000

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20

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X

Y

The slope of this line is the variable unit cost. (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

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X

Y

Vertical distance

is the change in cost.


• Accountants and managers may use computer software to fit a regression line through the data points.

• The cost analysis objective is the same: Y = a + bx

Least-Squares Regression Method

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.

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.


0 1 2 3 4

To

tal

Co

st

10

20

0

Activity

****

**

****

Least-Squares Regression Method

R2 is the percentage of the variationin total cost explained by the activity.

R2 for this relationship is near100% 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 a

contribution format

profit statement.

The Contribution Format


The Contribution FormatTotal Unit

Sales 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.


The Contribution Format

Used primarily forexternal reporting.

Used primarily bymanagement.

cost behavior analysis

Education

variable variable cost

fixedtotal fixed cost

local callthe fixed

new higher cost

total mixed cost line

cost behaviour examples

unit of activity

semivariable costs