Principles of Accounting/ Financial and Managerial Accounting Chapter 19

© The McGraw-Hill Companies, Inc., 2002McGraw-Hill/Irwin

Cost-Volume-Profit Analysis

Chapter

19


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


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.

Total Fixed CostTotal Fixed Cost


Number of Local Calls

Mon

thly

Bas

ic T

elep

hone

B

ill p

er L

ocal

Cal

l

Fixed costs per unit declineas activity increases.

Your average cost perlocal call decreases as

more local calls are made.

Fixed Cost Per UnitFixed Cost Per Unit


Minutes Talked

Tot

al L

ong

Dis

tanc

eT

elep

hone

Bill

Total variable costs changewhen activity changes.

Your total long distancetelephone bill is basedon how many minutes

you talk.

Total Variable CostTotal Variable Cost


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.

Variable Cost Per UnitVariable Cost Per Unit


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


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 charge Fixed service fee Variable charge per

kilowatt hour used

Mixed CostsMixed Costs


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.

Mixed CostsMixed Costs


Activity

Co

st

Total cost remainsconstant within anarrow range of

activity.

Stair-Step CostsStair-Step Costs


Activity

Co

st

Total cost increases to a new higher cost for the

next higher range of activity.

Stair-Step CostsStair-Step Costs


To

tal

Co

st

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


Let’s extend our

knowledge of

cost behavior to

CVP analysis.

Cost-Volume-Profit(CVP) Analysis

Cost-Volume-Profit(CVP) Analysis


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


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$



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


Total Unit









Answer: $30,000


Answer: $30,000

Total Unit








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


Total Unit









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


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

Total Unit








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 Point

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

Formula for ComputingBreak-Even Sales (in Units)

Formula for ComputingBreak-Even Sales (in Units)


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)


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


break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units

Computing Break-Even SalesQuestion 1




break even?

a. 100,000 units

b. 40,000 units

c. 200,000 units

d. 66,667 units


break even?

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




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







a. $200,000

b. $300,000

c. $400,000

d. $500,000




a. $200,000

b. $300,000

c. $400,000

d. $500,000


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

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




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


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


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



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





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




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= ×

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


Oxco’s 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 ratio= ×

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

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


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

Oxco expects sales to increase by $15,000. 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= ×

What Change in Operating Income Do We Anticipate?

What Change in Operating Income Do We Anticipate?


Business Applications of CVPBusiness Applications of CVP


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 CyclCo, a

bicycle retailer:



Should CyclCo 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$



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


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, CyclCo is considering a 10 percent price reduction that willincrease sales by 25 percent. What is the income effect?



500 625Bikes Bikes


625 × $300

$80K + $12K

Income is decreased even more.

625 × $450

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

1.25 × 500



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, CyclCo

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?


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, CyclCo

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


Different products with different contribution margins.

Determining semivariablecost elements.

Complying with theassumptions of CVP analysis.

Additional Considerations in CVPAdditional Considerations in CVP


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

CVP Analysis When a Company Sells Many Products



CyclCo 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$




The overall contribution margin ratio is:

$265,000 $550,000

= 48% (rounded)


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




Break-even in sales dollars is:

$170,000 .48

= $354,167 (rounded)


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




OwlCo 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$Low activity level 5,000 6,100 Change 4,000 3,600$

The High-Low MethodThe High-Low Method


Units Cost


Unit variable cost = = = $0.90 per unitin cost

in units$3,600 4,000



Units Cost


Unit variable cost = = = $0.90 per unit

Fixed cost = Total cost – Total variable cost

in costin units

$3,600 4,000



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



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



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 unit

b. $.10 per unit

c. $.12 per unit

d. $.125 per unit


unit sold?

a. $.08 per unit

b. $.10 per unit

c. $.12 per unit

d. $.125 per unit

The High-Low MethodQuestion 1




unit sold?

a. $.08 per unit

b. $.10 per unit

c. $.12 per unit

d. $.125 per unit


unit sold?

a. $.08 per unit

b. $.10 per unit

c. $.12 per unit

d. $.125 per unit $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 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. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000


a. $ 2,000

b. $ 4,000

c. $10,000

d. $12,000





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

$14,000 = Total fixed cost +($.10 × 120,000 units)

Total fixed cost = $14,000 - $12,000

Total fixed cost = $2,000




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


End of Chapter 19End of Chapter 19

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Principles of Accounting/ Financial and Managerial Accounting Chapter 19