objectives classify costs by their behavior as variable costs, fixed costs, or mixed costs

ObjectivesObjectives1. Classify costs by their behavior as variable

costs, fixed costs, or mixed costs.2. Compute the contribution margin, the

contribution margin ratio, and the unit contribution margin, and explain how they may be useful to management.

3. Using the unit contribution margin, determine the break-even point and the volume necessary to achieve a target profit.

Chapter Chapter 1818Cost Behavior and Cost-Volume-Profit AnalysisCost Behavior and Cost-Volume-Profit Analysis

4. Using a cost-volume profit chart and a profit-volume chart, determine the break-even point and the volume necessary to achieve a target profit.

ObjectivesObjectivesObjectivesObjectives

5. Calculate the break-even point for a business selling more than one product.

6. Compute the margin of safety and the operating leverage, and explain how managers use this concept.

7. List the assumptions underlying cost-volume-profit analysis.

Jason Inc. produces stereo sound systems under the brand name of J-Sound. The parts for the stereo are purchased from an outside supplier for $10 per unit (a variable cost).

Variable CostVariable CostVariable CostVariable Cost

Cost BehaviorCost BehaviorCost BehaviorCost Behavior

Total Variable Cost Graph

Tot

al C

osts

$300,000$250,000$200,000$150,000$100,000 $50,000

10 20 300Units Produced (in thousands)


Unit Variable Cost Graph

$20

$15

$10

$5

0C

ost

per

Un

it10 20 30

Units Produced (000)

Tot

al C

osts

Tot

al C

osts

$300,000$250,000$200,000$150,000$100,000 $50,000

10 20 300

$20$15$10

$5

0

Cos

t per

Uni

t

10 20 30

Number ofUnits

Produced



Direct Materials

Cost per Unit

Total Direct Materials

Cost

5,000 units $10 $ 50,00010,000 10 l00,00015,000 10 150,00020,000 10 200,00025,000 10 250,00030,000 10 300,000


The production supervisor for Minton

Inc.’s Los Angeles plant is Jane Sovissi. She is paid $75,000 per year.

The plant produces from 50,000 to 300,000 bottles of perfume.

La Fleur

Fixed CostsFixed CostsFixed CostsFixed Costs

Number ofBottles

Produced

Total Salary for Jane Sovissi

50,000 bottles $75,000 $1.500100,000 75,000 0.750150,000 75,000 0.500200,000 75,000 0.375250,000 75,000 0.300300,000 75,000 0.250

Salary per Bottle

Produced

Fixed CostsFixed CostsFixed CostsFixed Costs

Fixed CostsFixed Costs

Total Fixed Cost GraphTotal Fixed Cost GraphT

otal

Cos

tsT

otal

Cos

ts

$150,000$125,000$100,000$75,000$50,000

$25,000

100 200 3000

Unit Fixed Cost GraphUnit Fixed Cost Graph

Bottles Produced (000)

Number ofBottles

Produced

Cos

t per

Uni

t $1.50$1.25$1.00

$.75$.50

$.25

100 200 3000


Total Salary for Jane Sovissi

50,000 bottles $75,000 $1.500100,000 75,000 0.75015,000 75,000 0.50020,000 75,000 0.37525,000 75,000 0.30030,000 75,000 0.250

Salary per Bottle

Produced

Simpson Inc. manufactures sails using rented equipment.

The rental charges are $15,000 per year, plus $1 for each machine hour used over

10,000 hours.

Mixed CostsMixed CostsMixed CostsMixed Costs

Total Mixed Cost GraphTotal Mixed Cost Graph

Tot

al C

osts

Tot

al C

osts

0

Total Machine Hours (000)

$45,000$40,000 $35,000$30,000$25,000$20,000$15,000$10,000 $5,000

10 20 30 40

Mixed costs are usually separated into

their fixed and variable components

for management analysis.

Mixed costs are usually separated into

their fixed and variable components

for management analysis.

Mixed costs are sometimes called semivariable or semifixed costs.

Mixed costs are sometimes called semivariable or semifixed costs.

The high-low method is a simple way to separate mixed costs into their fixed and variable components.

Mixed CostsMixed CostsMixed CostsMixed Costs

Low

High

Actual costs incurred

ProductionTotal(Units) Cost $

High-Low MethodHigh-Low Method

Variable cost per unit =

Highest level of activity ($) minus lowest level of activity ($)

Highest level of activity (units) minus lowest level of activity (units)

Activity relates to units of production

June 1,000 $45,550July 1,500 52,000August 2,100 61,500September 1,800 57,500October 750 41,250

$61,500 – $41,250

2,100 – 750


ProductionTotal(Units) Cost

Variable cost per unit =



= $15

$20,250

1,350=



Variable cost per unit = $15

What is the total fixed cost (using the

highest level)?

Total cost = (Variable cost per unit x Units of production) + Fixed cost


$61,500 = ($15 x 2,100) + Fixed cost

$61,500 = ($15 x 2,100) + $30,000




Variable cost per unit = $15

The fixed cost is the same at the lowest

level.

Total cost = (Variable cost per unit x Units of production) + Fixed cost


$41,250 = ($15 x 750) + Fixed cost

$41,250 = ($15 x 750) + $30,000


Variable CostsVariable Costs

Total Fixed Costs

Total Units Produced

Tot

al C

osts


Per

Uni

t Cos

t

Total Variable Costs


Unit Variable Costs


Tot

al C

osts

Per

Uni

t Cos

t


ReviewReviewUnit Fixed CostsUnit costs remain the same regardless of

activity.

Total costs increase and decreases with

activity level.Total costs increase and

decreases proportionately with activity level.

Unit costs remain the same per unit regardless

of activity.

Contribution Margin Income StatementContribution Margin Income Statement

Sales (50,000 units) $1,000,000Variable costs 600,000Contribution margin $ 400,000 Fixed costs 300,000Income from operations $ 100,000

The contribution margin is

available to cover the fixed costs

and income from operations.

The contribution margin is

available to cover the fixed costs

and income from operations.

FIXED FIXED COSTSCOSTS

Contribution margin

Income from Operations

Contribution Margin Income StatementContribution Margin Income Statement

Sales Sales VariableVariablecosts costs

ContributionContributionmarginmargin

– =


Contribution Margin RatioContribution Margin Ratio

100% 60%

40% 30%

10%

Contribution margin ratio =Sales – Variable costs

Sales

Contribution margin ratio =$1,000,000 – $600,000

$1,000,000

Contribution margin ratio = 40%


100% 60%

40% 30%

10%

The contribution margin can be expressed three ways:1. Total contribution margin in dollars.3. Contribution margin ratio (percentage).3. Unit contribution margin (dollars per unit).

The contribution margin can be expressed three ways:1. Total contribution margin in dollars.3. Contribution margin ratio (percentage).3. Unit contribution margin (dollars per unit).

$20 12$ 8


Contribution Margin RatioContribution Margin Ratio

What is the break-even

point?

What is the break-even

point?

Revenues Costs=

Break-even

Calculating the Break-Even PointCalculating the Break-Even PointCalculating the Break-Even PointCalculating the Break-Even Point

At the break-even point, fixed costs and the contribution

margin are equal.

At the break-even point, fixed costs and the contribution

margin are equal.

Sales (? units) $ ?Variable costs ?Contribution margin $ 90,000 Fixed costs 90,000Income from operations $ 0

$25 15$10

9,000 units

Sales ($25 x ? units) $ ?Variable costs ($15 x ? units) ?Contribution margin $ 90,000 Fixed costs 90,000Income from operations $ 0

$25 15$10

Break-even sales (units) =Unit contribution margin

Fixed costs

$90,000

$10

Sales ($25 x 9,000) $225,000Variable costs ($15 x 9,000) 135,000Contribution margin $ 90,000Fixed costs 90,000Income from operations $ 0

Calculating the Break-Even PointCalculating the Break-Even PointCalculating the Break-Even PointCalculating the Break-Even PointIn UnitsIn Units

=

=

Sales ($250 x ? units) $ ?Variable costs ($145 x ? units) ?Contribution margin $ ? Fixed costs 840,000Income from operations $ 0

$250 145$105


Fixed costs$840,000

$1058,000 units


The unit selling price is $250 and unit variable cost is $145. Fixed costs are $840,000.

Sales ($25 x ? units) $ ?Variable costs ($15 x ? units) ?Contribution margin $ ? Fixed costs 840,000Income from operations $ 0

$250 145$105


Fixed costs$840,000

$1008,400 units

$250 150$100

Next, assume Next, assume variable costs is variable costs is increased by $5.increased by $5.

Next, assume Next, assume variable costs is variable costs is increased by $5.increased by $5.


The unit selling price is $250 and unit variable cost is $145. Fixed costs are $840,000.

Sales $ ?Variable costs ?Contribution margin $ ? Fixed costs $600,000Income from operations $ 0


Fixed costs$600,000

$2030,000 units

$50 30

$20


A firm currently sells their product at $50 per unit and it has a related unit variable cost of

$30. The fixed costs are $600,000.

Sales $ ?Variable costs ?Contribution margin $ ? Fixed costs $600,000Income from operations $ 0


Fixed costs$600,000

$3020,000 units

$50 30

$20

$60 30$30


Management increases Management increases the selling price from the selling price from

$50 to $60.$50 to $60.

Management increases Management increases the selling price from the selling price from

$50 to $60.$50 to $60.

Summary of Effects of Changes on Summary of Effects of Changes on Break-Even PointBreak-Even Point

Summary of Effects of Changes on Summary of Effects of Changes on Break-Even PointBreak-Even Point

Target ProfitTarget ProfitTarget ProfitTarget Profit

Fixed costs are estimated at $200,000, and the desired profit is $100,000. The unit selling

price is $75 and the unit variable cost is $45. The firm wishes to make a $100,000 profit.

Sales (? units) $ ?Variable costs ?Contribution margin $ ? Fixed costs 200,000Income from operations $ 0

$75 45$35

In Units

In Units

Sales (? units) $ ?Variable costs ?Contribution margin $ ? Fixed costs 200,000Income from operations $ 0

Sales (units) =Unit contribution margin

Fixed costs + target profit$200,000 + $100,000

$3010,000 units

Target ProfitTarget ProfitTarget ProfitTarget Profit In Units

In Units

$75 45$30

$75 45$30

Sales (10,000 units x $75) $750,000Variable costs (10,000 x $45) 450,000Contribution margin $300,000Fixed costs 200,000Income from operations $100,000

Proof that sales of 10,000 units Proof that sales of 10,000 units will provide a profit of $100,000.will provide a profit of $100,000.Proof that sales of 10,000 units Proof that sales of 10,000 units

will provide a profit of $100,000.will provide a profit of $100,000.

Target ProfitTarget ProfitTarget ProfitTarget Profit

Graphic Approach to Cost-Volume-Profit

Analysis

Cost-Volume-Profit ChartCost-Volume-Profit ChartSa

les

and

Cos

ts (

$000

)Sa

les

and

Cos

ts (

$000

)

0

Units of Sales (000)

$500$450$400$350$300$250$200$150$100$ 50

Unit selling price $ 50Unit variable cost 30Unit contribution margin $ 20

Total fixed costs $100,000



60%60%

Total Sales

Variable Costs

1 2 3 4 5 6 7 8 9 10


les

and

Cos

ts (

$000

)Sa

les

and

Cos

ts (

$000

)

0


$500$450$400$350$300$250$200$150$100$ 50





60%60%

40%

Contribution Margin

100% 60%

40%

1 2 3 4 5 6 7 8 9 10


les

and

Cos

ts (

$000

)Sa

les

and

Cos

ts (

$000

)

0


$500$450$400$350$300$250$200$150$100$ 50






100% 60%

40%

TotalTotalCostsCosts

1 2 3 4 5 6 7 8 9 10


les

and

Cos

ts (

$000

)Sa

les

and

Cos

ts (

$000

)

0

$500$450$400$350$300$250$200$150$100$ 50

1 2 3 4 5 6 7 8 9 10

Break-Even Point






100% 60%

40%$100,000

$20= 5,000 units


les

and

Cos

ts (

$000

)Sa

les

and

Cos

ts (

$000

)

0


$500$450$400$350$300$250$200$150$100$ 50





100% 60%

40%

Operating Profit Area

Operating Loss Area

$100$75$50$25$ 0

$(25)$(50)$(75)

$(100)

Sales (10,000 units x $50) $500,000 Variable costs (10,000 units x $30) 300,000

Contribution margin (10,000 units x $20) $200,000 Fixed costs 100,000

Operating profit $100,000




Units of Sales (000’s)

1 2 3 4 5 6 7 8 9 10

Relevant range is

10,000 units

Relevant range is

10,000 units

Op

erat

ing

Pro

fit

(Los

s) $

000’

s


1 2 3 4 5 6 7 8 9 10

Maximum loss is equal to the

total fixed costs.

Maximum loss is equal to the

total fixed costs.

Profit Line

Operating loss

Operating Operating profitprofit

$100$75$50$25$ 0

$(25)$(50)$(75)

$(100)







Maximum profit within the relevant

range.

Maximum profit within the relevant

range.

Op

erat

ing

Pro

fit

(Los

s) $

000’

s

Op

erat

ing

Pro

fit

(Los

s) $

000’

s


1 2 3 4 5 6 7 8 9 10

Operating loss

Operating Operating profitprofit

Break-Even Point







$100$75$50$25$ 0

$(25)$(50)$(75)

$(100)

Sales Mix Considerations

Cascade Company sold 8,000 units of Product A and 2,000 units of Product B during the past year. Cascade Company’s fixed costs are $200,000. Other relevant data are as follows:

Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix 80% 20%

Products A B

Sales $ 90 $140 Variable costs 70 95 Contribution margin $ 20 $ 45 Sales mix 80% 20%

Sales Mix ConsiderationsSales Mix Considerations Sales Mix ConsiderationsSales Mix Considerations

Products A B

Product contribution margin $16 $ 9

$25

Fixed costs, $200,000Fixed costs, $200,000


Products A BProduct contribution

margin $16 $ 9

$25

Break-even sales unitsBreak-even sales units

$200,000

$25




margin $16 $ 9

$25

Break-even sales unitsBreak-even sales units

$200,000

$25


= 8,000 units



margin $16 $ 9

$25

A:A: 8,000 units x Sales Mix (80%) = 6,400

B:B: 8,000 units x Sales Mix (20%) = 1,600

PROOFPROOF

Product A Product B Total

Sales:6,400 units x $90 $576,000 $576,0001,600 units x $140 $224,000 224,000Total sales $576,000 $224,000 $800,000

Variable costs:6,400 x $70 $448,000 $448,0001,600 x $95 $152,000 152,000Total variable costs $448,000 $152,000 $600,000

Contribution margin $128,000 $ 72,000 $200,000

Fixed costs 200,000Income from operations $ 0Break-even point

Margin of Safety

Margin of Safety =Sales – Sales at break-even point

Sales

The margin of safety indicates the possible decrease in sales that may occur

before an operating loss results.

Margin of Safety =$250,000 – $200,000

$250,000

Margin of Safety = 20%

Operating LeverageOperating Leverage

Both companies have the same contribution margin.Both companies have the same contribution margin.


Jones Inc. Wilson Inc.

Contribution margin

Income from operations

Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Contribution margin ? ?

Contribution margin



$100,000

$20,000= 5.0 Jones Inc.:


5.0

Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Contribution margin ?

Contribution margin



= 5.0

$100,000

$20,000Jones Inc.


Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Contribution margin 5.0 ?

Contribution margin



= 2.0$100,000Wilson Inc.:

Capitalintensive?

Laborintensive?

2.0


Sales $400,000 $400,000Variable costs 300,000 300,000Contribution margin $100,000 $100,000Fixed costs 80,000 50,000Income from operations $ 20,000 $ 50,000Contribution margin 5.0

$50,000

Assumptions of Cost-Volume-Profit AnalysisAssumptions of Cost-Volume-Profit AnalysisAssumptions of Cost-Volume-Profit AnalysisAssumptions of Cost-Volume-Profit Analysis

1. Total sales and total costs can be represented by straight lines.

2. Within the relevant range of operating activity, the efficiency of operations does not change.

3. Costs can be accurately divided into fixed and variable components.

4. The sales mix is constant.5. There is no change in the inventory quantities during the

period.

The reliability of cost-volume-profit analysis depends upon several assumptions.

The EndThe End

Chapter 18Chapter 18

objectives classify costs by their behavior as variable costs, fixed costs, or mixed costs

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