Cost Behavior:Analysis and Use

Chapter

5

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Types of Cost Behavior 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.

Recall the summary of our cost behavior discussion from Chapter 1.

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Total Variable Cost Example

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

Minutes Talked

To

tal L

on

g D

ista

nce

Tel

eph

on

e B

ill

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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 cents per minute.

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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

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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.

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Cost Behavior

MerchandisersCost of Goods Sold

ManufacturersDirect Material, Direct Labor, 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

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The Activity Base

Machinehours

Laborhours

Milesdriven

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

Unitsproduced

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Step-Variable Costs

Activity

Co

st

Total cost remainsconstant within anarrow range of

activity.

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Step-Variable Costs

Activity

Co

st

Total cost increases to a new higher cost for the

next higher range of activity.

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Activity

To

tal

Co

st

Economist’sCurvilinear Cost

Function

The Linearity Assumption and the Relevant Range

Accountant’s Straight-Line Approximation (constant

unit variable cost)

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Activity

To

tal

Co

st

RelevantRange

The Linearity Assumption and the Relevant Range

Accountant’s Straight-Line Approximation (constant

unit variable cost)

Economist’sCurvilinear 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.

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ExamplesAdvertising and Research and Development

ExamplesDepreciation on Buildings and

Equipment

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.

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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.

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Example: Office space is available at a rental

rate of $30,000 per year in increments of 1,000 square feet. As

the business grows more space is rented,

increasing the total cost.

Fixed Costs and Relevant Range

Continue

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Ren

t C

ost

in

T

ho

usa

nd

s o

f D

oll

ars

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

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.

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Quick Check Which of the following statements about cost

behavior are true?

a. Fixed costs per unit vary with the level of activity.

b. Variable costs per unit are constant within the relevant range.

c. Total fixed costs are constant within the relevant range.

d. Total variable costs are constant within the relevant range.

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How does this type of fixed cost differ

from a step-variable cost?

Step-variable costs can be adjusted more

quickly and . . .

The width of the activity steps is much

wider for the fixed cost.

Fixed Costs and Relevant Range

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A mixed costhas both fixed and variablecomponents.

Mixed Costs

Consider thefollowing electric utility example.

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Fixed Monthly

Utility Charge

Variable

Utility Charge

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

stMixed Costs

X

Y

Total mixed cost

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Total mixed cost Y

= a + bX

Fixed Monthly

Utility Charge

Variable

Utility Charge

Activity (Kilowatt Hours)

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

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Fixed Monthly

Utility Charge

Variable

Utility Charge

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

st

Total mixed cost Y

= a + bX

Mixed Costs

bX

aX

Y

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The Analysis of Mixed Costs

Engineering Approach

Account Analysis

Scattergraph Method

Least-Square Regression Method

High-Low Method

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Account Analysis

Each account is classified as eithervariable or fixed based on the analyst’s

knowledge of how the account behaves.

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Engineering Estimates

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

and overhead requirements.

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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$

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Unit variable cost =Changein costChange 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

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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

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

© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 30

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

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

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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

High activity level 9,000 9,700$ Low activity level 5,000 6,100 Change 4,000 3,600$

The High-Low Method

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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 unit

b. $0.10 per unit

c. $0.12 per unit

d. $0.125 per unit

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 unit

b. $0.10 per unit

c. $0.12 per unit

d. $0.125 per unit

Quick Check

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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. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000

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. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000

Quick Check

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Note

How does the high-low method work when you have data for more than two periods?

Select the two periods with the lowest and highest level of activity.

Patients Admitted

Costs of Admitting

March 2,510 15,204$ April 2,550 14,976$ May 2,480 14,680$ June 2,590 15,108$ July 2,670 15,060$

Low

High

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Quick Check Using the high-low method, estimate the cost

formula Y = a +bX for the patient admitting costs on the previous page.

a. Y = $9,720 + $2.00X

b. Y = $7,050 + $3.00X

c. Y = $8,385 + $2.50X

d. Y = $8,480 + $2.50X

© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 39

The Scattergraph MethodPlot the data points on a

graph (total cost vs. activity).

0 1 2 3 4

*

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tal

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n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*

Activity, 1,000’s of Units Produced

X

Y

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

equal numbers of points above and below the line.

0 1 2 3 4

*

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tal

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st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*

Activity, 1,000’s of Units Produced

X

Y

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The Scattergraph Method

Estimated fixed cost = $10,000

0 1 2 3 4

*

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*

Activity, 1,000’s of Units Produced

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).

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The Scattergraph Method

Slope = Change in costChange in units

Horizontal distance is the change in activity.

0 1 2 3 4

*

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*

Activity, 1,000’s of Units Produced

X

Y

Vertical distance

is the change in cost.

© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 43

Software can be used 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.

© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 44

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

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Note

Let’s plot the data for patient admitting costs.

$14,000

$14,200

$14,400

$14,600

$14,800

$15,000

$15,200

$15,400

2,450 2,500 2,550 2,600 2,650 2,700

Patients Admitted

Pat

ient

Adm

itti

ng C

osts

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Note

Problems with the high-low method:Throws away information contained in all of the data

other than the low and the high points.The low and high levels of activity tend to be

unusual.

You should always plot the data if you have more than two points to make sure it even makes sense to be using the high-low method.

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Let’s put our

knowledge of cost

behavior to work by

preparing a

contribution format

income statement.

The Contribution Format

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The Contribution Format

Total Unit

Sales Revenue 100,000$ 50$

Less: Variable costs 60,000 30

Contribution margin 40,000$ 20$

Less: Fixed costs 30,000

Net income 10,000$

The contribution margin format emphasizes cost behavior. Contribution margin covers fixed costs

and provides for income.

© The McGraw-Hill Companies, Inc., 2002Irwin/McGraw-Hill 49

The Contribution Format

Used primarily forexternal reporting.

Used primarily bymanagement.