Cost Behaviour: Analysis and Use - · PDF fileCost Behaviour: Analysis and Use Chapter5 ... Use a cost formula to predict costs at a new level of activity. 4. Analyze a mixed cost

Cost Behaviour:Analysis and Use

Chapter

5

© McGraw-Hill Ryerson Limited., 2001

5-2

LEARNING OBJECTIVES

1. Explain the effect of a change in activity onboth total variable costs and per unit variablecosts.

2. Explain the effect of a change in activity onboth total fixed costs and fixed costsexpressed on a per unit.

3. Use a cost formula to predict costs at a newlevel of activity.

4. Analyze a mixed cost using the high-lowmethod.

After studying this chapter, you should be able to:


5-3

LEARNING OBJECTIVES

5. Analyze a mixed cost using the scattergraphmethod.

6. Explain the least-squares regression method ofanalyzing a mixed cost.

7. Prepare an income statement using thecontribution format.

8. (Appendix 5A) Analyze a mixed cost using theleast-squares regression method.

After studying this chapter, you should be able to:


5-4

Types of Cost Behaviour Patterns

Summary of Variable and Fixed Cost Behaviour

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 behaviourdiscussion from Chapter 2.


5-5

Total Variable Cost Example

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

Minutes Talked

To

tal L

on

g D

ista

nc

eT

elep

ho

ne

Bil

l


5-6

Variable Cost Per Unit Example

Minutes Talked

Per

Min

ute

Tel

eph

on

e C

har

ge

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


5-7

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

Mo

nth

ly B

asic

Tel

eph

on

e B

ill


5-8

Fixed Cost Per Unit Example

Number of Local Calls

Mo

nth

ly B

asic

Tel

eph

on

eB

ill p

er L

oca

l C

all

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


5-9

Cost Behaviour

MerchandisersCost of Goods Sold

ManufacturersDirect 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 costs

Merchandisers, manufacturers, andservice organizations

Real estate taxes, Insurance, Sales salariesAmortization, Advertising


5-10

The Activity Base

Machinehours

Labourhours

Unitsproduced

Milesdriven

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


5-11

Step-Variable Costs

Activity

Co

st

Total cost remainsconstant within anarrow range of

activity.


5-12

Step-Variable Costs

Activity

Co

st

Total cost increases to a new higher cost for the

next higher range ofactivity.


5-13

The Linearity Assumption and theRelevant Range

Activity

To

tal C

ost

Economist’sCurvilinear Cost

Function


5-14

Activity

To

tal C

ost


Function

Accountant’s Straight-LineApproximation (constant

unit variable cost)



5-15

Activity

To

tal C

ost

RelevantRange


Accountant’s Straight-LineApproximation (constant

unit variable cost)


Function

A straight lineclosely

approximatesa curvilinearvariable costline within the

relevantrange.

A straight lineclosely

approximatesa curvilinearvariable costline within the

relevantrange.


5-16

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

Amortization onBuildings and

Equipment

Examples

Advertising andResearch andDevelopment


5-17

Trend Toward Fixed Costs

Increased automation.

Increase in salaried “knowledge” workerswho are difficult to train and replace.

Implications

Managers are more “locked-in” with fewer decisionalternatives.

Planning becomes more crucial because fixed costs aredifficult to change with current operating decisions.

Implications

Managers are more “locked-in” with fewer decisionalternatives.

Planning becomes more crucial because fixed costs aredifficult to change with current operating decisions.


5-18

Example: Office spaceis available at a rental

rate of $30,000 peryear in increments of1,000 square feet. As

the business growsmore space is rented,

increasing the totalcost.

Fixed Costs and Relevant Range

Continue


5-19

Re

nt

Co

st i

nT

ho

usa

nd

s o

f D

olla

rs

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

0

30

60


90

Relevant

Range

Total cost doesn’tchange for a widerange of activity,

and then jumps to anew higher cost for

the next higherrange of activity.


5-20

How does this typeof fixed cost differ

from a step-variablecost?

Step-variable costscan be adjusted more

quickly and . . .

The width of theactivity steps is much

wider for the fixedcost.



5-21

A mixed costhas both fixedand variablecomponents.

Mixed Costs

Consider thefollowing electricutility example.


5-22

Fixed Monthly

Utility Charge

Variable

Utility Charge

Activity (Kilowatt Hours)

To

tal U

tilit

y C

os

tMixed Costs

X

Y

Total mixed cost


5-23

Total mixed cost Y

= a + bX

Fixed Monthly

Utility Charge

Variable

Utility Charge


To

tal U

tilit

y C

os

tMixed 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


5-24

Fixed Monthly

Utility Charge

Variable

Utility Charge


To

tal U

tilit

y C

os

t

Total mixed cost Y

= a + bX

Mixed Costs

bX

aX

Y


5-25

The Analysis of Mixed Costs

Engineering Approach

Account Analysis

Scattergraph Method

Least-Square Regression Method

High-Low Method


5-26

Account Analysis

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

knowledge of how the account behaves.


5-27

Engineering Estimates

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

and overhead requirements.


5-28

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

Using these two levels of activity, compute:υ the variable cost per unit;ϖ the fixed cost; and thenω 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$


5-29

υ Unit variable cost =Change in costChange in units

Units Cost


Change 4,000 3,600$

The High-Low Method


5-30

Units Cost


Change 4,000 3,600$

The High-Low Method

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


5-31

Units Cost


Change 4,000 3,600$

The High-Low Method


ϖ 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


5-32


ϖ 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

ω 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


5-33

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

The High-Low Method


5-34


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

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$


5-35

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


a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000

The High-Low Method


5-36


a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000


a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000

The High-Low Method

Tota l cost = Tota l fixed cost + Tota l variable cost

$14,000 = Tota l fixed cost +($0.10 × 120,000 units)

Tota l fixed cost = $14,000 - $12,000

Tota l fixed cost = $2,000


5-37

The Scattergraph MethodPlot the data points on a

graph (total cost vs. activity).

0 1 2 3 4

*

To

tal C

ost

(00

0’s

of

Do

llars

)

10

20

0

***

**

**

*

*

Activity (000’s of Units Produced)

X

Y


5-38

The Scattergraph MethodDraw a line through the data points with about anequal numbers of points above and below the line.

0 1 2 3 4

*

To

tal C

ost

(00

0’s

of

Do

llars

)

10

20

0

***

**

**

*

*


X

Y


5-39

The Scattergraph Method

Estimated fixed cost = $10,000

0 1 2 3 4

*

To

tal C

ost

(00

0’s

of

Do

llars

)

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).


5-40

The Scattergraph Method

Slope = Change in costChange in units

Horizontal distance isthe change in activity.

0 1 2 3 4

*

To

tal C

ost

(00

0’s

of

Do

llars

)

10

20

0

***

**

**

*

*


X

Y

Verticaldistance

is thechangein cost.


5-41

! Accountants and managersmay use computer softwareto fit a regression linethrough the data points.

! The cost analysis objectiveis 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.


5-42

0 1 2 3 4

To

tal C

ost

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


5-43

Let’s put our

knowledge of cost

behaviour to work

by preparing a

contribution format

income statement.

The Contribution Format


5-44


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 costbehaviour. Contribution margin covers fixed costs

and provides for income.


5-45


Comparison of the Contribution Income Statement with the Traditional Income Statement

Traditional Approach Contribution Approach (costs organized by function) (costs organized by behavior)

Sales 100,000$ Sales 100,000$ Less cost of goods sold 70,000 Less variable expenses 60,000 Gross margin 30,000$ Contribution margin 40,000$ Less operating expenses 20,000 Less fixed expenses 30,000 Net income 10,000$ Net income 10,000$

Used primarily forexternal reporting.

Used primarily bymanagement.

Least-Squares RegressionCalculations

Appendix

5A


5-47

Least-Squares Regression

This method provides the most objective and precisebreakdown of mixed costs into variable and fixedcomponents.

This method also uses the most complex calculations.However, most business calculators and severalcomputer software programs can quickly complete thecalculations required.

This method mathematically places the line in the mostfavourable location by ensuring that the total of thesquares of all points off the line is minimized.


5-48

Least-Squares RegressionCalculations:

b = n(∑XY-(∑X)(∑Y)

n(∑X2) - (∑X)2

a = (∑Y) - b(∑X)

n

where X= the level of activity (Independent variable)

Y= the total mixed cost (dependent variable)

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

b = the variable cost per unit of activity (slope ofline)

n = number of observations

∑ = sum across all n observations


5-49

End of Chapter 5

Documents

Cost Behaviour: Analysis and Use - · PDF fileCost Behaviour: Analysis and Use Chapter5 ... Use a cost formula to predict costs at a new level of activity. 4. Analyze a mixed cost