Chapter 5 Cost Behavior: Analysis and Use. © The McGraw-Hill Companies, Inc., 2005 McGraw-Hill /Irwin Types of Cost Behavior Patterns Recall the summary

Chapter 5

Cost Behavior:

Analysis and Use

© The McGraw-Hill Companies, Inc., 2005McGraw-Hill /Irwin

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.


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


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.


Total Fixed Cost Example

Your monthly basic telephone bill is probably fixed and does not changewhen 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 decreasesas more local calls are made.


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 organizationsReal estate taxes, Insurance, Sales salaries

Depreciation, Advertising


The Activity Base

Machinehours

Laborhours

Milesdriven

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

Unitsproduced


Step-Variable Costs

Activity

Co

st

Total cost remainsconstant within anarrow range of

activity.


Step-Variable Costs

Total cost increases to a new higher cost for the

next higher range of activity.

Activity

Co

st


RelevantRange

The Linearity Assumption and the Relevant Range

Accountant’s Straight-Line Approximation (constant

unit variable cost)

Activity

To

tal

Co

st

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.


Types of Fixed Costs

Discretionary

•One-year planning horizon

•Can be cut for short periods of time

Discretionary

•One-year planning horizon

•Can be cut for short periods of time

Committed

•Multi-year planning horizon

•Cannot be cut for short periods of time

Committed

•Multi-year planning horizon

•Cannot be cut for short periods of time

ExamplesDepreciation on Buildings and

Equipment

ExamplesDepreciation on Buildings and

Equipment

ExamplesAdvertising and Research and Development

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.


Fixed if work force is stable because managementis reluctant to increase/decrease the number of

employees in response to short-term fluctuationsin business activity.

Fixed if work force is stable because managementis reluctant to increase/decrease the number of

employees in response to short-term fluctuationsin business activity.

Variable if size of work force is easily adjusted forshort-term fluctuations in business activity.

Variable if size of work force is easily adjusted forshort-term fluctuations in business activity.

Labor Costs: Fixed or Variable?

May be both fixed and variable if temporary workers are employed to accommodate short-term

fluctuations in business activity.

May be both fixed and variable if temporary workers are employed to accommodate short-term

fluctuations in business activity.


Fixed Costs and Relevant Range

Continue

Example: Office spaceis available at a rental rate

of $30,000 per year inincrements of 1,000 square

feet. As the business grows, more space is rented,

increasing the total cost.

Example: Office spaceis available at a rental rate

of $30,000 per year inincrements of 1,000 square

feet. As the business grows, more space is rented,

increasing the total cost.


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


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.

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.


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.





relevant range.






relevant range.





relevant range.

Quick Check


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.



A mixed costhas both fixed and variablecomponents.

Mixed Costs

Consider thefollowing electric utility example.


Fixed Monthly

Utility Charge

Variable

Utility Charge

Mixed Costs

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

st

X

Y

Total mixed cost


Fixed Monthly

Utility Charge

Variable

Utility Charge


To

tal

Uti

lity

Co

st

X

Y

Total mixed cost

Mixed Costs 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


Mixed Costs

bX

a

Variable

Utility Charge


To

tal

Uti

lity

Co

st

X

Y

Total mixed cost = Y = a + bX

Fixed Monthly

Utility Charge


The Analysis of Mixed Costs

Engineering Approach

Account Analysis

Scattergraph Plot

Least-Squares 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, labor

and overhead requirements.


Plot the data points on a graph (total cost vs. 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

The Scattergraph Plot


Draw a line through the data pointswith about an equal numbers of

points above and below the line.

0 1 2 3 4

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*


X

Y



Estimated fixed cost = $10,000

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

for a one unit change in activity).

0 1 2 3 4

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*


X

Y



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

***

**

**

*

*


X

Y

Vertical distance

is the change in cost.



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

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

Units Cost



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 unit

b. $0.10 per unit

c. $0.12 per unit

d. $0.125 per unit


a. $0.08 per unit

b. $0.10 per unit

c. $0.12 per unit

d. $0.125 per unit

Quick Check



a. $0.08 per unit

b. $0.10 per unit

c. $0.12 per unit

d. $0.125 per unit


a. $0.08 per unit

b. $0.10 per unit

c. $0.12 per unit

d. $0.125 per unit$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$

Quick Check


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


a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000

Quick Check



a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000


a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000

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

Quick Check


• 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.

• 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.

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 month

High month

Note


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

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

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

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

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

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

Using the high-low method, estimate the cost formula Y = a + bX for the patient admitting costs.

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

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

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

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


Low month

High month



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

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

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

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


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

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

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

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


Low month

High month

Quick Check

b = = = $2

a = $15,060 – $2 × 2,670 = $15,060 – $5,340 = $9,720

b = = = $2

a = $15,060 – $2 × 2,670 = $15,060 – $5,340 = $9,720

$15,060 – $14,680 2,670 – 2,480

$380 190


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

Note


Problems with the high-low method:• Disregards 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.

Always plot the data if you have more than two points to make sure it even makes sense to use the high-low method.

Problems with the high-low method:• Disregards 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.

Always plot the data if you have more than two points to make sure it even makes sense to use the high-low method.

Note


• Software can be used to fit a regression line through the data points.

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

• 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 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.

Least Squares Regression


0 1 2 3 4

To

tal

Co

st

10

20

0

Activity

****

**

****

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

Least Squares Regression


Let’s put our

knowledge of cost

behavior to work by

preparing a

contribution format

income statement.

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.



Used primarily forexternal reporting.

Used primarily bymanagement.



End of Chapter 5

Documents

Chapter 5 Cost Behavior: Analysis and Use. © The McGraw-Hill Companies, Inc., 2005 McGraw-Hill /Irwin Types of Cost Behavior Patterns Recall the summary