Cost Behaviour, Operating Leverage, and Profitability Analysis Chapter 2

Cost Behaviour, Operating Leverage, and Profitability Analysis

Chapter 2

Copyright © 2003 McGraw-Hill Ryerson Limited, Canada2-2

Fixed Cost Behaviour

Increases Decreases

Total Fixed Cost Remains constant Remains Constant

Fixed Cost Per Unit Decreases Increases

Consider the followingconcert example where theband will be paid $48,000

regardless of the number of tickets sold.

When activity . . . .


Fixed Cost Behaviour

Tickets sold 2,700 3,000 3,300

Total Cost of Band 48,000$ 48,000$ 48,000$

Per Unit Cost of Band 17.78$ 16.00$ 14.55$

$48,000 ÷ 3,000 Tickets = $16.00 per Ticket


Operating Leverage

A measure of the extent to which fixedcosts are being used in an organization.

Operating leverage is greatest in companies that have a high proportion of fixed costs in

relation to variable costs.

Consider the followingconcert example where

all costs are fixed.


Operating Leverage

When all costs are fixed, every additional sales dollar contributes one dollar to gross profit.

10% RevenueIncrease

90% GrossProfit Increase


Risk and Reward Assessment

Risk refers to the possibility thatsacrifices may exceed benefits.

Risk may be reduced byconverting fixed costs

into variable costs.

Let’s see what happens to the concert example if the band receives $16 per

ticket instead of $48,000.


Tickets sold 2,700 3,000 3,300

Band Cost per Ticket Sold 16$ 16$ 16$

Total Cost of Band 43,200$ 48,000$ 52,800$

The total variable cost increases in direct proportion to the number of tickets sold.

Variable unit cost per ticket remains at$16 regardless of the number of tickets sold.

Risk and Reward Assessment


Variable Cost Behaviour

Increases Decreases

Total Variable Cost

Increases Proportionately

Decreases Proportionately

Variable Cost Per Unit

Remains Constant Remains Constant

When activity . . .


Shifting the cost structure from fixed to variable notonly reduces risk but also the potential for profits.

Risk and RewardAssessment

10% RevenueIncrease

10% GrossProfit Increase


Relationship Between CostBehaviour and Revenue

Fixed Cost Structure

$

Units

Revenue

Fixed CostProfit

Loss


Relationship Between CostBehaviour and Revenue

Variable Cost Structure

Variable Cost

Revenue

Profit

$

Units


The Effect of Cost Structureon Profit Stability

VariableCosts

FixedCosts

Do companieswith higher levels of

fixed costs experiencemore earnings

volatility?



Now Let’s see what happens whenthe number of units sold increases.



The income increase is greaterin the All Fixed Company.



VariableCosts

FixedCosts

If sales decrease,will the income

decrease be greaterin the All Fixed

Company?



Yes, the income decrease is greaterin the All Fixed Company.



VariableCosts

FixedCosts

Level of Fixed Cost

Earnings Volatility

High High

Low Low


Determining the Contribution Margin

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 behaviour. Contribution margin covers fixed costs

and provides for income.


Measuring Operating leverage Using the Contribution Margin

Contribution margin

Net income

Operating

Leverage=

Show mean example.



$20,000

$5,000

Operating

Leverage= = 4

A measure of how a percentagechange in sales will effect profits.



A 10 percent increase in sales results in a 40 percent increase in net income.


Using Fixed Cost to Provide a Competitive Operating Advantage

Consider the following two companies:

What happens if each company cuts the service revenueto $7 per hour in order to double the amount of business?



Advantage to the All Fixed Company.



What happens toincome if demand

falls to 1,000 hoursfor each company?



Advantage to the All Variable Company.



I suppose fixed costs arebetter if volume is increasing,but variable costs are better

if business is declining.


Cost Behaviour Summarized

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

Total Fixed Cost


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.



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


Total V

aria

ble C

ost


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.


Variable Cost Per Unit


Total Cost Cost Per Unit

Fixed CostsRemains Constant

Changes Inversely

Variable CostsChanges in

Direct ProportionRemains Constant

Cost Behaviour SummarizedWhen activity level changes . . .


Example: Office space is available at a fixed 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.

The Relevant Range

Continue


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

The Relevant Range

90

Relevant

Range

Total fixed cost doesn’t change for a range of activity,

and then jumps to a new higher cost for

the next higher range of activity.


Activity

To

tal

Co

st

RelevantRange

The Relevant RangeOur variable cost

assumption (constant unit variable cost)

applies within the relevant range.

Our variable cost assumption

(constant unit variable cost)

applies within the relevant range.

Possible VariableCost Behaviour

Our VariableCost Assumption


Definitions of Fixed and Variable are Context Sensitive

Recall the earlier concert example, where the band waspaid $48,000 regardless of the number of tickets sold.

The cost of the band is fixed relative to the number of tickets sold for a specific concert.

The cost of the band is variable relativeto the number of concerts produced.


Cost Averaging

Lake Resorts provides water-skiing lessons for itsguests with the following costs:

Equipment rental $80 per dayInstructor pay $15 per hourFuel $ 2 per hour

What is the average cost per one-hour lesson for2 lessons per day? 5 lessons per day? 10 lessons

per day?


Cost Averaging

Number of Lessons 2 5 10

Cost of Equipment Rental 80$ 80$ 80$ Cost of Instruction 30 75 150 Cost of Fuel 4 10 20 Total Cost 114$ 165$ 250$

Cost Per Lesson 57$ 33$ 25$

Average costs decline as activity increases whenfixed costs such as equipment rental are involved.

Managers must use these average costs withcaution as they differ at every level of activity.


A mixed costhas both fixed and variablecomponents.

Mixed Costs

Consider thefollowing electric utility example.


Fixed Monthly

Utility Charge

Variable

Utility Charge

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

stMixed Costs

Total mixed cost


Estimating Fixed and Variable Costs

High-Low Method

Scattergraph Method

Regression Method


Grizzly Co. 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. the total cost.

The High-Low Method


Unit variable cost =Changein costChange in units

The High-Low Method


Unit variable cost = $3,600 ÷ 4,000 units = $.90 per unit

The High-Low Method


The High-Low Method

Unit variable cost = $3,600 ÷ 4,000 units = $.90 per unit Fixed cost = Total cost – Total variable cost

Fixed cost = $9,700 – ($.90 per unit × 9,000 units)

Fixed cost = $9,700 – $8,100 = $1,600


Unit variable cost = $3,600 ÷ 4,000 units = $.90 per unit Fixed cost = Total cost – Total variable cost

Fixed cost = $9,700 – ($.90 per unit × 9,000 units)

Fixed cost = $9,700 – $8,100 = $1,600 Total cost = Fixed cost + Variable cost Total cost = $1,600 + $0.90X

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. $.08 per unit

b. $.10 per unit

c. $.12 per unit

d. $.125 per unit


a. $.08 per unit

b. $.10 per unit

c. $.12 per unit

d. $.125 per unit

The High-Low Method



a. $.08 per unit

b. $.10 per unit

c. $.12 per unit

d. $.125 per unit


a. $.08 per unit

b. $.10 per unit

c. $.12 per unit

d. $.125 per unit

The High-Low Method

$4,000 ÷ 40,000 units = $.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. $ 2,000

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



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

Total cost = Total fixed cost + Total variable cost

$14,000 = Total fixed cost +($.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

*

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


Draw a line through the data points with about anequal 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



0 1 2 3 4

*

To

tal

Co

st i

n1,

000’

s o

f D

oll

ars

10

20

0

***

**

**

*

*


X

Y

Estimated fixedis $10,000

Vertical distance is total cost,

approximately $16,000.


Variable cost per unit is represented by the slope of 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 fixedis $10,000

Vertical distance is total cost,

approximately $16,000.

Total variable cost = Total cost – Total fixed costTotal variable cost = $16,000 – $10,000 = $6,000Unit variable cost = $6,000 ÷ 3,000 units = $2



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.

I can use spreadsheet software to fit a

regression line throughthe data points.


End of Chapter 2

Documents

Cost Behaviour, Operating Leverage, and Profitability Analysis Chapter 2