© The McGraw-Hill Companies, Inc., 2005 McGraw-Hill/Irwin 20-1 COST-VOLUME-PROFIT ANALYSIS Chapter...

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

20-1

COST-VOLUME-PROFIT ANALYSIS

Chapter

20


20-2

CVP analysis is used to answer questionssuch as:How much must I sell to earn my desired income?How will income be affected

if I reduce selling prices toincrease sales volume?

What will happen toprofitability if I expandcapacity?

CVP analysis is used to answer questionssuch as:How much must I sell to earn my desired income?How will income be affected

if I reduce selling prices toincrease sales volume?

What will happen toprofitability if I expandcapacity?

Questions Addressed byCost-Volume-Profit Analysis

Questions Addressed byCost-Volume-Profit Analysis


20-3

Number of Local Calls

Mon

thly

Bas

ic

Tel

epho

ne B

ill

Total fixed costs remain unchangedwhen activity changes.

Your monthly basictelephone bill probablydoes not change when

you make more local calls.

Your monthly basictelephone bill probablydoes not change when

you make more local calls.

Total Fixed CostTotal Fixed Cost


20-4

Number of Local Calls

Mon

thly

Bas

ic T

elep

hone

B

ill p

er L

ocal

Cal

l

Fixed costs per unit decline as activity increases.

Your average cost perlocal call decreases as

more local calls are made.

Your average cost perlocal call decreases as

more local calls are made.

Fixed Cost Per UnitFixed Cost Per Unit


20-5

Minutes Talked

Tot

al L

ong

Dis

tanc

eT

elep

hone

Bill

Total variable costs change when activity changes.

Your total long distancetelephone bill is basedon how many minutes

you talk.

Your total long distancetelephone bill is basedon how many minutes

you talk.

Total Variable CostTotal Variable Cost


20-6

Minutes Talked

Per

Min

ute

Tel

epho

ne C

harg

e

Variable costs per unit do not changeas activity increases.

The cost per long distanceminute talked is constant.

For example, 10cents per minute.

The cost per long distanceminute talked is constant.

For example, 10cents per minute.

Variable Cost Per UnitVariable Cost Per Unit


20-7

Summary of Variable and Fixed Cost Behavior

Cost In Total Per Unit

Variable Changes as activity level

changes.Remains the same over wide

ranges of activity.

FixedRemains the same even

when activity level changes.Dereases as activity level

increases.

Cost Behavior SummaryCost Behavior Summary


20-8

Mixed costs contain a fixed portion that is incurred even when facility is unused, and a variable portion

that increases with usage.

Example: monthly electric utility chargeFixed service feeVariable charge per

kilowatt hour used

Mixed CostsMixed Costs


20-9

Variable

Utility Charge

Activity (Kilowatt Hours)

To

tal

Uti

lity

Co

st

Total mixed cost

Fixed Monthly

Utility Charge

Slope isvariable cost

per unitof activity.

Slope isvariable cost

per unitof activity.

Mixed CostsMixed Costs


20-10

Activity

Co

st

Total cost remainsconstant within anarrow range of

activity.

Total cost remainsconstant within anarrow range of

activity.

Stair-Step CostsStair-Step Costs


20-11

Activity

Co

st

Total cost increases to a new higher cost for the

next higher range of activity.

Stair-Step CostsStair-Step Costs


20-12

To

tal

Co

st

Relevant Range

A straight line closely (constant unit variable cost)approximates a

curvilinear variablecost line within

the relevant range.

A straight line closely (constant unit variable cost)approximates a

curvilinear variablecost line within

the relevant range.

Volume of Output

CurvilinearCost Function

Curvilinear CostsCurvilinear Costs


20-13

Let’s extend our

knowledge of

cost behavior to

CVP analysis.

Cost-Volume-Profit(CVP) Analysis

Cost-Volume-Profit(CVP) Analysis


20-14

The break-even point (expressed in units of product or dollars of sales) is the

unique sales level at which a company neither earns a profit nor incurs a loss.

Computing Break-Even PointComputing Break-Even Point


20-15

Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.

Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.

Total Unit

Sales Revenue (2,000 units) 100,000$ 50$

Less: Variable costs 60,000 30

Contribution margin 40,000$ 20$

Less: Fixed costs 30,000

Operating income 10,000$

Total Unit

Sales Revenue (2,000 units) 100,000$ 50$

Less: Variable costs 60,000 30

Contribution margin 40,000$ 20$

Less: Fixed costs 30,000

Operating income 10,000$

Computing Break-Even PointComputing Break-Even Point

How much contribution margin must this company have to cover its fixed costs (break even)?



Answer: $30,000


Answer: $30,000

How many units must this company sell to cover its fixed costs

(break even)?

How many units must this company sell to cover its fixed costs

(break even)?

How many units must this company sell to cover its fixed costs (break even)?

Answer: $30,000 ÷ $20 per unit = 1,500 units

How many units must this company sell to cover its fixed costs (break even)?

Answer: $30,000 ÷ $20 per unit = 1,500 units


20-16

We have just seen one of the basic CVP relationships – the break-even computation.

Break-even point in units = Fixed costs

Contribution margin per unit

Finding the Break-Even PointFormula for Computing

Break-Even Sales (in Units)Formula for Computing

Break-Even Sales (in Units)

Unit sales price less unit variable cost($20 in previous example)

Unit sales price less unit variable cost($20 in previous example)


20-17

The break-even formula may also be expressed in sales dollars.

Break-even point in dollars = Fixed costs

Contribution margin ratio

Unit sales price Unit variable cost

Formula for ComputingBreak-Even Sales (in Dollars)

Formula for ComputingBreak-Even Sales (in Dollars)


20-18

Computing Break-Even SalesComputing Break-Even Sales

ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per

unit, how many units must be sold to break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units



a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units


20-19



a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units



a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units Unit contribution = $5.00 - $3.00 = $2.00

Fixed costsUnit contribution =

$200,000$2.00 per unit

= 100,000 units



20-20

Use the contribution margin ratio formula to determine the amount of sales revenue ABC must

have to break even. All information remains unchanged: fixed costs are $200,000; unit sales

price is $5.00; and unit variable cost is $3.00.

a. $200,000

b. $300,000

c. $400,000

d. $500,000




a. $200,000

b. $300,000

c. $400,000

d. $500,000



20-21




a. $200,000

b. $300,000

c. $400,000

d. $500,000




a. $200,000

b. $300,000

c. $400,000

d. $500,000

Unit contribution = $5.00 - $3.00 = $2.00

Contribution margin ratio = $2.00 ÷ $5.00 = .40

Break-even revenue = $200,000 ÷ .4 = $500,000


Contribution margin ratio = $2.00 ÷ $5.00 = .40

Break-even revenue = $200,000 ÷ .4 = $500,000



20-22

Volume in Units

Co

sts

and

Rev

enu

ein

Do

llar

sRevenue

Starting at the origin, draw the total revenueline with a slope equal to the unit sales price.

Total fixed cost

Total fixed costextends horizontallyfrom the vertical axis.

Preparing a CVP GraphPreparing a CVP Graph


20-23

Total cost

Volume in Units

Co

sts

and

Rev

enu

ein

Do

llar

s

Total fixed cost

Break-even Point

Profit

Loss

Draw the total cost line with a slopeequal to the unit variable cost.

Revenue

Preparing a CVP GraphPreparing a CVP Graph


20-24

Break-even formulas may be adjusted to show the sales volume needed to earn

any amount of operating income.

Break-even formulas may be adjusted to show the sales volume needed to earn

any amount of operating income.

Unit sales = Fixed costs + Target incomeContribution margin per unit

Dollar sales = Fixed costs + Target income

Contribution margin ratio

Computing Sales Needed to Achieve Target Operating Income



20-25

ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn operating income of $40,000?

a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units


a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units




20-26


a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units


a. 100,000 units

b. 120,000 units

c. 80,000 units

d. 200,000 units = 120,000 units


Fixed costs + Target income Unit contribution

$200,000 + $40,000 $2.00 per unit




20-27

What is our Margin of Safety?What is our Margin of Safety?

Margin of safety is the amount by which sales may decline before reaching break-even sales:

Margin of safety provides a quick means of estimating operating income at any level of sales:

Margin of safety = Actual sales - Break-even sales

Operating Margin Contribution Income of safety margin ratio= ×


20-28

What is our Margin of Safety?What is our Margin of Safety?

ADM contribution margin ratio is 40 percent. If sales are $100,000 and break-even sales are

$80,000, what is operating income?

Operating Margin Contribution Income of safety margin ratioOperating Margin Contribution Income of safety margin ratio== ××

Operating IncomeOperating Income = $20,000 × .40 = $8,000= $20,000 × .40 = $8,000


20-29

What Change in Operating Income Do We Anticipate?

What Change in Operating Income Do We Anticipate?

Once break-even is reached, every additional dollar of contribution margin becomes operating income:

ADM expects sales to increase by $15,000 and has a contribution margin ratio of 40%. How much will operating

income increase?

Change in operating income = $15,000 × .40 = $6,000

Change in Change in Contributionoperating income sales volume margin ratio= ×


20-30

Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%

Less: fixed expenses 80,000 Operating income 20,000$

Consider the following information developed by the accountant at Speedo, a bicycle retailer:

Business Applications of CVPBusiness Applications of CVP


20-31

Should Speedo spend $12,000 on advertising to increase sales by 10 percent?

Total Per Unit PercentSales (500 bikes) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%

Less: fixed expenses 80,000 Operating income 20,000$



20-32

500 550Bikes Bikes

Sales 250,000$ 275,000$ Less: variable expenses 150,000 165,000 Contribution margin 100,000$ 110,000$ Less: fixed expenses 80,000 92,000 Operating income 20,000$ 18,000$

550 × $300

$80K + $12K

No, income is decreased.

550 × $500


Should Speedo spend $12,000 on advertising to increase sales by 10 percent?


20-33

500Bikes

Sales 250,000$ Less: variable expenses 150,000 Contribution margin 100,000$ Less: fixed expenses 80,000 Operating income 20,000$

Now, in combination with the advertising, Speedo is considering a 10 percent price reduction that willincrease sales by 25 percent. What is the income effect?



20-34

500 625Bikes Bikes


625 × $300

$80K + $12K

Income is decreased even more.

625 × $450

Now, in combination with the advertising, Speedo is considering a 10 percent price reduction that willincrease sales by 25 percent. What is the income effect?

1.25 × 500



20-35

500Bikes

Sales 250,000$ Less: variable expenses 150,000 Contribution margin 100,000$ Less: fixed expenses 80,000 Operating income 20,000$

Business Applications of CVPBusiness Applications of CVPNow, in combination with advertising and a price cut, Speedo

will replace $50,000 in sales salaries with a $25 per bike commission, increasing sales by 50 percent above the

original 500 bikes. What is the effect on income?


20-36

500 750Bikes Bikes


The combination of advertising, a price cut,and change in compensation increases income.

750 × $325

$92K - $50K

750 × $450

Business Applications of CVPBusiness Applications of CVPNow, in combination with advertising and a price cut, Speedo

will replace $50,000 in sales salaries with a $25 per bike commission, increasing sales by 50 percent above the

original 500 bikes. What is the effect on income?

1.5 × 500


20-37

Different products with different contribution margins.

Determining semivariablecost elements.

Complying with theassumptions of CVP analysis.

Additional Considerations in CVPAdditional Considerations in CVP


20-38

Sales mix is the relative combination in whicha company’s different products are sold.

Different products have different selling prices, costs, and contribution margins.

If Speedo sells bikes and carts, howwill we deal with break-even analysis?

Sales mix is the relative combination in whicha company’s different products are sold.

Different products have different selling prices, costs, and contribution margins.

If Speedo sells bikes and carts, howwill we deal with break-even analysis?

CVP Analysis When a Company Sells Many Products



20-39

Speedo provides us with the following information:

Bikes Carts TotalSales 250,000$ 100% 300,000$ 100% 550,000$ 100%Var. exp. 150,000 60% 135,000 45% 285,000 52%Contrib. margin 100,000$ 40% 165,000$ 55% 265,000$ 48%

Fixed exp. 170,000 Net income 95,000$




20-40

The overall contribution margin ratio is:

= 48% (rounded)


Fixed exp. 170,000 Net income 95,000$



$265,000 $550,000


20-41

Break-even in sales dollars is:

= $354,167 (rounded)


Fixed exp. 170,000 Operating income 95,000$



$170,000 .48


20-42

Matrix, Inc. recorded the following production activity and maintenance costs for two months:

Using these two levels of activity, compute: the variable cost per unit. the total fixed cost. total cost formula.

Units Cost

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

Units Cost


The High-Low MethodThe High-Low Method


20-43

Units Cost


Unit variable cost = = = $0.90 per unitin cost

in units$3,600 4,000



20-44

Units Cost


Unit variable cost = = = $0.90 per unit

Fixed cost = Total cost – Total variable cost

in costin units

$3,600 4,000



20-45

Units Cost




Fixed cost = $9,700 – ($0.90 per unit × 9,000 units)

Fixed cost = $9,700 – $8,100 = $1,600

in costin units

$3,600 4,000



20-46

Units Cost




Fixed cost = $9,700 – ($0.90 per unit × 9,000 units)

Fixed cost = $9,700 – $8,100 = $1,600 Total cost = $1,600 + $.90 per unit

in costin units

$3,600 4,000



20-47


If sales 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 commission per unit sold?

a. $.08 per unitb. $.10 per unit c. $.12 per unitd. $.125 per unit





20-48








$4,000 ÷ 40,000 units = $.10 per unit

Units Cost

High level 120,000 14,000$Low level 80,000 10,000 Change 40,000 4,000$


20-49


If sales 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 the sales commission?a. $ 2,000b. $ 4,000 c. $10,000d. $12,000




20-50





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

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



20-51

A limited range of activity, called the relevant range, where CVP relationships are linear. Unit selling price remains constant.Unit variable costs remain constant.Total fixed costs remain constant.

Sales mix remains constant.

Production = sales (no inventory changes).

Assumptions Underlying CVP Analysis

Assumptions Underlying CVP Analysis


20-52

End of Chapter 20End of Chapter 20

© The McGraw-Hill Companies, Inc., 2005 McGraw-Hill/Irwin 20-1 COST-VOLUME-PROFIT ANALYSIS Chapter...

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