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Cost-Volume-ProfitAnalysis

Chapter Eight

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The Break-Even PointThe break-even point is the point in the volume of

activity where the organization’s revenues andexpenses are equal.

Sales 200,000$Less: variable expenses 120,000Contribution margin 80,000Less: fixed expenses 80,000Net income -$

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Contribution-Margin Approach

Consider the following information developedby the accountant at Curl, Inc.:

Total Per Unit PercentSales (500 surf boards) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%Less: fixed expenses 80,000Net income 20,000$

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Total Per Unit PercentSales (500 surf boards) 250,000$ 500$ 100%Less: variable expenses 150,000 300 60%Contribution margin 100,000$ 200$ 40%Less: fixed expenses 80,000Net income 20,000$

Contribution-Margin Approach

For each additional surf board sold, Curlgenerates $200 in contribution margin.

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Contribution-Margin Approach

Fixed expensesUnit contribution margin

= Break-even point(in units)

Total P er U n it Percen tSales (500 sur f boards) 250,000$ 500$ 100%Less: var iab le expenses 150,000 300 60%C ontr ibut ion m arg in 100,000$ 200$ 40%Less: fixed expenses 80,000N et income 20,000$

Tota l P er U n it Percen tSales (500 sur f boards) 250,000$ 500$ 100%Less: var iab le expenses 150,000 300 60%C ontr ibut ion m arg in 100,000$ 200$ 40%Less: fixed expenses 80,000N et income 20,000$

$80,000$200

= 400 surf boards

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Contribution-Margin Approach

Here is the proof!

Total Per Unit PercentSales (400 surf boards) 200,000$ 500$ 100%Less: variable expenses 120,000 300 60%Contribution margin 80,000$ 200$ 40%Less: fixed expenses 80,000Net income -$

Total Per Unit PercentSales (400 surf boards) 200,000$ 500$ 100%Less: variable expenses 120,000 300 60%Contribution margin 80,000$ 200$ 40%Less: fixed expenses 80,000Net income -$

400 × $500 = $200,000 400 × $300 = $120,000

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Contribution Margin Ratio

Calculate the break-even point in sales dollars ratherthan units by using the contribution margin ratio.

Contribution marginSales = CM Ratio

Fixed expenseCM Ratio

Break-even point(in sales dollars)

=

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Contribution Margin Ratio

Total Per Unit PercentSales (400 surf boards) 200,000$ 500$ 100%Less: variable expenses 120,000 300 60%Contribution margin 80,000$ 200$ 40%Less: fixed expenses 80,000Net income -$

$80,00040%

$200,000 sales=

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Equation ApproachSales revenue –Variable expenses –Fixed expenses = Profit

Unitsalesprice

Salesvolumein units

×Unit

variableexpense

Salesvolumein units

×

($500 × X) ($300 × X)– – $80,000 = $0

($200X) – $80,000 = $0

X = 400 surf boardsMcGraw-Hill/Irwin

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Graphing Cost-Volume-ProfitRelationships

Viewing CVP relationships in a graph givesmanagers a perspective that can be obtained in no

other way.Consider the following information for Curl, Inc.:

Income300 units

Income400 units

Income500 units

Sales 150,000$ 200,000$ 250,000$Less: variable expenses 90,000 120,000 150,000Contribution margin 60,000$ 80,000$ 100,000$Less: fixed expenses 80,000 80,000 80,000Net income (loss) (20,000)$ -$ 20,000$

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-

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

450,000

- 100 200 300 400 500 600 700 800

Cost-Volume-Profit Graph

Fixed expenses

Units Sold

Sal

e sin

Dol

lars

Total expenses

Total salesBreak-evenpoint

Profit area

Loss area

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$(100,000)

$(80,000)

$(60,000)

$(40,000)

$(20,000)

$-

$20,000

$40,000

$60,000

$80,000

$100,000

$- $50 $100 $150 $200 $250 $300 $350 $400

1 3 4 52 6 7 8

Pro

fi t

Units sold (00s)

Profit-Volume GraphSome managers like the profit-volume

graph because it focuses on profits and volume.

Break-evenpoint

Profitarea

Lossarea

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Target Net Profit

We can determine the number ofsurfboards that Curl must sell to earn aprofit of $100,000 using the contribution

margin approach.

Fixed expenses + Target profitUnit contribution margin = Units sold to earn

the target profit

$80,000 + $100,000$200 = 900 surf boards

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Equation ApproachSales revenue –Variable expenses –Fixed expenses = Profit

($500 × X) ($300 × X)– – $80,000 = $100,000

($200X) = $180,000

X = 900 surf boards

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Applying CVP Analysis

Safety MarginThe difference between budgeted sales

revenue and break-even sales revenue.The amount by which sales can drop

before losses begin to be incurred.

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Safety Margin

Curl, Inc. has a break-even point of $200,000. Ifactual sales are $250,000, the safety margin is

$50,000 or 100 surf boards.Break-even

sales400 units

Actual sales500 units

Sales 200,000$ 250,000$Less: variable expenses 120,000 150,000Contribution margin 80,000 100,000Less: fixed expenses 80,000 80,000Net income -$ 20,000$

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Changes in Fixed Costs

Curl is currently selling 500 surf boards permonth.

The owner believes that an increase of $10,000in the monthly advertising budget, wouldincrease bike sales to 540 units.

Should we authorize the requested increase inthe advertising budget?

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CurrentSales

(500 Boards)

ProposedSales

(540 Borads)Sales 250,000$ 270,000$Less: variable expenses 150,000 162,000Contribution margin 100,000$ 108,000$Less: fixed expenses 80,000 90,000Net income 20,000$ 18,000$

CurrentSales

(500 Boards)

ProposedSales

(540 Borads)Sales 250,000$ 270,000$Less: variable expenses 150,000 162,000Contribution margin 100,000$ 108,000$Less: fixed expenses 80,000 90,000Net income 20,000$ 18,000$

Changes in Fixed Costs

$80,000 + $10,000 advertising = $90,000

540 units × $500 per unit = $270,000

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CurrentSales

(500 Boards)

ProposedSales

(540 Borads)Sales 250,000$ 270,000$Less: variable expenses 150,000 162,000Contribution margin 100,000$ 108,000$Less: fixed expenses 80,000 90,000Net income 20,000$ 18,000$

CurrentSales

(500 Boards)

ProposedSales

(540 Borads)Sales 250,000$ 270,000$Less: variable expenses 150,000 162,000Contribution margin 100,000$ 108,000$Less: fixed expenses 80,000 90,000Net income 20,000$ 18,000$

Changes in Fixed Costs

Sales will increase by$20,000, but net income

decreased by $2,000.

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Changes in UnitContribution Margin

Because of increases in cost of raw materials,Curl’s variable cost per unit has increasedfrom $300 to $310 per surf board. With no

change in selling price per unit, what will bethe new break-even point?

($500 × X) ($310 × X)– – $80,000 = $0

X = 422 units (rounded)

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Predicting Profit Given ExpectedVolume

Fixed expensesUnit contribution marginTarget net profit

Find: {required sales volume}Given:

Fixed expensesUnit contribution marginExpected sales volume

Find: {expected profit}Given:

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Predicting Profit GivenExpected Volume

In the coming year, Curl’s owner expects to sell525 surfboards. The unit contribution marginis expected to be $190, and fixed costs are

expected to increase to $90,000.

($190 × 525) – $90,000 = X

X = $9,750 profit

X = $99,750 –$90,000

Total contribution - Fixed cost = Profit

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CVP Analysis with MultipleProducts

For a company with more than one product,sales mix is the relative combination in which

a company’s products are sold.Different products have different selling prices,

cost structures, and contribution margins.

Let’s assume Curl sells surf boards and sailboards and see how we deal with break-

even analysis.

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CVP Analysis with MultipleProducts

Curl provides us with the following information:

DescriptionSellingPrice

UnitVariable

Cost

UnitContribution

Margin

Numberof

BoardsSurfboards 500$ 300$ 200$ 500Sailborads 1,000 450 550 300Total sold 800

DescriptionNumber

of Boards% of

TotalSurfboards 500 62.5% (500 ÷ 800)Sailborads 300 37.5% (300 ÷ 800)Total sold 800 100.0%

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CVP Analysis with MultipleProducts

Weighted-average unit contribution margin

DescriptionContribution

Margin % of TotalWeighted

ContributionSurfboards 200$ 62.5% 125.00$Sailborads 550 37.5% 206.25Weighted-average contribution margin 331.25$

$200 × 62.5%

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CVP Analysis with MultipleProducts

Break-even pointBreak-evenpoint = Fixed expenses

Weighted-average unit contribution margin

Break-evenpoint = $170,000

$331.25

Break-evenpoint = 514 combined unit sales

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CVP Analysis with MultipleProducts

Break-even pointBreak-evenpoint = 514 combined unit sales

DescriptionBreakeven

Sales% ofTotal

IndividualSales

Surfboards 514 62.5% 321Sailborads 514 37.5% 193Total units 514

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Assumptions UnderlyingCVP Analysis

Selling price is constant throughoutthe entire relevant range.

Costs are linear over the relevantrange.

In multi-product companies, thesales mix is constant.

In manufacturing firms, inventoriesdo not change (units produced =units sold).

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Cost Structure and OperatingLeverage

The cost structure of an organization is therelative proportion of its fixed and variablecosts.

Operating leverage is . . . the extent to which an organization uses

fixed costs in its cost structure. greatest in companies that have a high

proportion of fixed costs in relation to variablecosts.

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Measuring Operating Leverage

Contribution marginNet income

Operating leveragefactor =

Actual sales500 Board

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

Actual sales500 Board

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

$100,000$20,000

= 5

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Measuring Operating Leverage

A measure of how a percentage change insales will affect profits. If Curl increases itssales by 10%, what will be the percentage

increase in net income?

Percent increase in sales 10%Operating leverage factor × 5Percent increase in profits 50%

Percent increase in sales 10%Operating leverage factor × 5Percent increase in profits 50%

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End of Chapter 8We made

it!