20-1 Cost-Volume Profit Analysis Prepared by Douglas Cloud Pepperdine University Prepared by Douglas Cloud Pepperdine University

20-1

Cost-Cost-Volume Volume Profit Profit

AnalysisAnalysisPrepared by

Douglas Cloud Pepperdine University

Prepared by Douglas Cloud

Pepperdine University

20-2

1. Determine the number of units that must be sold to break even or to earn a targeted profit.

2. Calculate the amount of revenue required to break even or to earn a targeted profit.

3. Apply cost-volume-profit analysis in a multiple-product setting.

4. Prepare a profit-volume graph and a cost-volume-profit graph, and explain the meaning of each.

ObjectivesObjectivesObjectivesObjectives

After studying this After studying this chapter, you should chapter, you should

be able to:be able to:

After studying this After studying this chapter, you should chapter, you should

be able to:be able to:

ContinuedContinuedContinuedContinued

20-3

5. Explain the impact of the risk, uncertainty, and changing variables on cost-volume-profit analysis.

6. Discuss the impact of activity-based costing on cost-volume-profit analysis.

ObjectivesObjectivesObjectivesObjectives

20-4

Operating-Income ApproachOperating-Income ApproachOperating-Income ApproachOperating-Income Approach

Narrative Equation

Sales revenues

– Variable expenses

– Fixed expenses

= Operating income

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Sales (72,500 units @ $40)

$2,900,000

Less: Variable expenses

1,740,000

Contribution margin

$1,160,000

Less: Fixed expenses

800,000

Operating income

$ 360,000


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0 = ($40 x Units) – ($24 x Units) – $800,000

Break Even in Units

0 = ($16 x Units) – $800,000

($16 x Units) = $800,000

Units = 50,000 $1,740,000 ÷

72,500 ProofSales (50,000 units @ $40) $2,000,000Less: Variable expenses 1,200,000Contribution margin $ 800,000Less: Fixed expenses 800,000 Operating income $ 0

ProofSales (50,000 units @ $40) $2,000,000Less: Variable expenses 1,200,000Contribution margin $ 800,000Less: Fixed expenses 800,000 Operating income $ 0

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Contribution-Margin ApproachContribution-Margin ApproachContribution-Margin ApproachContribution-Margin Approach

Number of units =

$800,000

$40 – $24

Number of units =

Number of units = 50,000 units

Fixed costs

Unit contribution margin

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Target Income as a Dollar AmountTarget Income as a Dollar AmountTarget Income as a Dollar AmountTarget Income as a Dollar Amount

$424,000 = ($40 x Units) – ($24 x Units) – $800,000

$1,224,000 = $16 x Units

Units = 76,500

ProofSales (76,500 units @ $40) $3,060,000Less: Variable expenses 1,836,000Contribution margin $1,224,000Less: Fixed expenses 800,000 Operating income $ 424,000

ProofSales (76,500 units @ $40) $3,060,000Less: Variable expenses 1,836,000Contribution margin $1,224,000Less: Fixed expenses 800,000 Operating income $ 424,000

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Target Income as a Percentage Target Income as a Percentage of Sales Revenueof Sales Revenue

Target Income as a Percentage Target Income as a Percentage of Sales Revenueof Sales Revenue

0.15($40)(Units) = ($40 x Units) – ($24 x Units) – $800,000

$6 x Units = ($40 x Units) – ($24 x Units) – $800,000

$6 x Units = ($16 x Units) – $800,000

$10 x Units = $800,000

Units = 80,000

More-Power Company wants to know the number of sanders that must be sold in order to earn a profit

equal to 15 percent of sales revenue.

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Net income = Operating income – Income taxes

= Operating income – (Tax rate x Operating income)

After-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax Profit TargetsAfter-Tax Profit Targets

= Operating income (1 – Tax rate)

Or

Operating income =Net income

(1 – Tax rate)

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$487,500 = Operating income – 0.35(Operating income)

$487,500 = 0.65(Operating income)


$750,000 = Operating income

More-Power Company wants to achieve net income of $487,500 and its income tax rate is 35 percent.

Units = ($800,000 + $750,000)/$16Units = $1,550,000/$16Units = 96,875

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ProofSales (96,875 units @ $40) $3,875,000Less: Variable expenses 2,325,000Contribution margin $1,550,000Less: Fixed expenses 800,000Income before income taxes $ 750,000Less: Income taxes (35%) 262,500 Net income $ 487,500

ProofSales (96,875 units @ $40) $3,875,000Less: Variable expenses 2,325,000Contribution margin $1,550,000Less: Fixed expenses 800,000Income before income taxes $ 750,000Less: Income taxes (35%) 262,500 Net income $ 487,500

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Break-Even Point in Sales DollarsBreak-Even Point in Sales DollarsBreak-Even Point in Sales DollarsBreak-Even Point in Sales Dollars

Revenue Equal to Variable Cost Plus Contribution Margin

Contribution Contribution MarginMargin

$10

$6

$0

Variable CostVariable Cost

Revenue

10 Units

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The following More-Power Company contribution margin income statement is

shown for sales of 72,500 sanders.

The following More-Power Company contribution margin income statement is

shown for sales of 72,500 sanders.

Sales $2,900,000 100%Less: Variable expenses 1,740,000 60%Contribution margin $1,160,000 40%Less: Fixed expenses 800,000Operating income $ 360,000

Sales $2,900,000 100%Less: Variable expenses 1,740,000 60%Contribution margin $1,160,000 40%Less: Fixed expenses 800,000Operating income $ 360,000

To determine the break-even in sales dollars, the contribution margin ratio must be determined ($1,160,000 ÷

$2,900,000).

To determine the break-even in sales dollars, the contribution margin ratio must be determined ($1,160,000 ÷

$2,900,000).

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Operating income = Sales – Variable costs – Fixed Costs

0 = Sales – (Variable cost ratio x Sales) – Fixed costs

0 = Sales (1 – Variable cost ratio) – Fixed costs

0 = Sales (1 – .60) – $800,000

Sales(0.40) = $800,000

Sales = $2,000,000

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Impact of Fixed Costs on ProfitsImpact of Fixed Costs on ProfitsImpact of Fixed Costs on ProfitsImpact of Fixed Costs on Profits

Fixed CostFixed Cost

Fixed Costs = Contribution Margin; Profit = 0

Contribution MarginContribution Margin

Total Variable CostTotal Variable Cost

Revenue

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Revenue


Fixed Costs < Contribution Margin; Profit > 0

ProfitProfit

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Revenue


Fixed Costs > Contribution Margin; Profit < 0

LossLoss

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Profit TargetsProfit TargetsProfit TargetsProfit Targets

How much sales revenue must More-Power generate to earn a before-tax profit of $424,000?

Sales = ($800,000) + $424,000/0.40

= $1,224,000/0.40

= $3,060,000

20-20

Multiple-Product AnalysisMultiple-Product AnalysisMultiple-Product AnalysisMultiple-Product Analysis

Regular Mini- Sander Sander Total

Sales $3,000,000 $1,800,000 $4,800,000Less: Variable expenses 1,800,000 900,000 2,700,000

Contribution margin $1,200,000 $ 900,000 $2,100,000Less: Direct fixed expenses 250,000 450,000 700,000

Product margin $ 950,000 $ 450,000 $1,400,000Less: Common fixed exp. 600,000

Operating income $ 800,000

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Regular sander break-even units

= Fixed costs/(Price – Unit variable cost)

= $250,000/$16

= 15,625 units

Mini-sander break-even units

= Fixed costs/(Price – Unit variable cost)

= $450,000/$30

= 15,000 units

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Regular Mini- Sander Sander Total

Sales $1,857,160 $1,114,260 $2,971,420Less: Variable expenses 1,114,296 557,130 1,671,426

Contribution margin $ 742,864 $ 557,130 $1,299,994Less: Direct fixed expenses 250,000 450,000 700,000

Product margin $ 492,864 $ 107,130 $ 599,994Less: Common fixed exp. 600,000

Operating income $ -6

Not zero due to rounding

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Profit-Volume Graph

Profit or Loss

Loss

(40, $100)I = $5X - $100

Break-Even Point(20, $0)

$100—

80—

60—

40—

20—

0—

- 20—

- 40—

-60—

-80—

-100—

5 10 15 20 25 30 35 40 45 50 | | | | | | | | | |

Units Sold

(0, -$100)

20-24

Cost-Volume-Profit GraphRevenue

Units Sold

$500 --

450 --

400 --

350 --

300 --

250 --

200 --

150 --

100 --

50 --

0 -- 5 10 15 20 25 30 35 40 45 50 55 60 | | | | | | | | | | | |

Total Revenue

Total Cost

Profit ($100)

Profit ($100)

LossLoss

Break-Even Point (20, $200)

Fixed Expenses ($100)

Variable Expenses ($5 per unit)

20-25

Assumptions of C-V-P AnalysisAssumptions of C-V-P AnalysisAssumptions of C-V-P AnalysisAssumptions of C-V-P Analysis

1. The analysis assumes a linear revenue function and a linear cost function.

2. The analysis assumes that price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range.

3. The analysis assumes that what is produced is sold.

4. For multiple-product analysis, the sales mix is assumed to be known.

5. The selling price and costs are assumed to be known with certainty.

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$

Units

Total Cost

Total Revenue

Relevant Range

Relevant Range

20-27

Alternative 1: If advertising expenditures increase by $48,000, sales will increase from 72,500 units to 75,000 units.

Before theBefore the With theWith the IncreasedIncreased IncreasedIncreased

AdvertisingAdvertising AdvertisingAdvertising

Units sold 72,500 75,000Unit contribution margin x $16 x $16Total contribution margin $1,160,000 $1,200,000Less: Fixed expenses 800,000 848,000 Profit $ 360,000 $ 352,000

Difference in ProfitsDifference in Profits

Change in sales volume 2,500Unit contribution margin x $16

Change in contribution margin $40,000Less: Increase in fixed expense 48,000 Decrease in profit $ -8,000

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Before the Before the With theWith theProposed Proposed ProposedProposed

Price IncreasePrice Increase Price IncreasePrice IncreaseUnits sold 72,500 80,000Unit contribution margin x $16 x $16

Total contribution margin $1,160,000 $1,120,000Less: Fixed expenses 800,000 800,000 Profit $ 360,000 $ 320,000

Alternative 2: A price decrease from $40 per sander to $38 would increase sales from 72,500 units to 80,000 units.

Difference in Difference in ProfitProfit

Change in contribution margin $-40,000Less: Change in fixed expenses ----- Decrease in profit $-40,000

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Before theBefore the With the ProposedWith the ProposedProposed Price andProposed Price and Price DecreasePrice Decrease

Advertising ChangeAdvertising Change Advertising Advertising IncreaseIncreaseUnits sold 72,500 90,000

Unit contribution margin x $16 x $14Total contribution margin $1,160,000 $1,260,000

Less: Fixed expenses 800,000 848,000 Profit $ 360,000 $ 412,000

Alternative 3: Decreasing price to $38 and increasing advertising expenditures by $48,000 will increase sales from 72,500 units to 90,000 units.

Difference in ProfitDifference in Profit

Change in contribution margin $100,000Less: Change in fixed expenses 48,000 Increase in profit $ 52,000

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Margin of SafetyMargin of SafetyMargin of SafetyMargin of Safety

Assume that a company has a break-even volume of 200 units and the company is currently selling 500 units.

Current sales 500Break-even volume 200Margin of safety (in units) 300

Break-even point in dollars: Current revenue

$350,000Break-even volume

200,000Margin of safety (in dollars)

$150,000

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Operating LeverageOperating LeverageAutomated Manual

System SystemSales (10,000 units) $1,000,000 $1,000,000Less: Variable expenses 500,000 800,000

Contribution margin $ 500,000 $ 200,000Less: Fixed expenses 375,000 100,000

Operating income $ 125,000 $ 100,000

Unit selling price $100 $100Unit variable cost 50 80Unit contribution margin 50 20

$500,000 ÷ $125,000 = DOL of 4

$500,000 ÷ $125,000 = DOL of 4

$200,000 ÷ $200,000 = DOL of 2

$200,000 ÷ $200,000 = DOL of 2

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Operating LeverageOperating Leverage

What happens to profit in each system if sales increase by 40 percent?

What happens to profit in each system if sales increase by 40 percent?

20-33

Operating LeverageOperating LeverageAutomated Manual

System SystemSales (14,000 units) $1,400,000 $1,400,000Less: Variable expenses 700,000 1,120,000

Contribution margin $ 700,000 $ 280,000Less: Fixed expenses 375,000 100,000

Operating income $ 325,000 $ 180,000

Automated system—40% x 4 = 160%$125,000 x 160% =

$200,000 increase$125,000 + $200,000 =

$325,000

Manual system—40% x 2 = 80%$100,000 x 80% = $80,000 $100,000 + $80,000 =

$180,000

20-34

CVP Analysis and ABCCVP Analysis and ABCCVP Analysis and ABCCVP Analysis and ABC

Total cost = Fixed costs + (Unit variable cost x Number of units) + (Setup cost x Number of setups) + (Engineering cost x Number of engineering hours)

The ABC Cost Equation

Operating income = Total revenue – [Fixed costs + (Unit variable cost x Number of units) + (Setup cost x Number of setups) + (Engineering cost x Number of engineering hours)]

Operating Income

20-35

CVP Analysis and ABCCVP Analysis and ABCCVP Analysis and ABCCVP Analysis and ABC

Break-even units = [Fixed costs + (Setup cost x Number of setups) + (Engineering cost x Number of engineering hours)]/(Price – Unit variable cost)

Break-Even in Units

Differences Between ABC Break-Even and Convention Break-Even

The fixed costs differ

The numerator of the ABC break-even equation has two nonunit-variable cost terms

20-36

CVP Analysis and ABC—ExampleCVP Analysis and ABC—ExampleCVP Analysis and ABC—ExampleCVP Analysis and ABC—Example

Data about Variables

Cost Driver Unit Variable Cost Level of Cost DriverUnits sold $ 10 --

Setups 1,000 20

Engineering hours 30 1,000

Other data:

Total fixed costs (conventional)$100,000

Total fixed costs (ABC) 50,000

Unit selling price 20

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Units to be sold to earn a before-tax profit of $20,000:

Units = (Targeted income + Fixed costs)/(Price – Unit variable cost)

= ($20,000 + $100,000)/($20 – $10)

= $120,000/$10

= 12,000 units

20-38


Same data using the ABC:

Units = ($20,000 + $50,000 + $20,000 + $30,000/($20 – $10)

= $120,000/$10

= 12,000 units

20-39


Suppose that marketing indicates that only 10,000 units can be sold. A new design reduces direct labor by $2 (thus, the new variable cost is $8). The new break-even is calculated as follows:

Units = Fixed costs/(Price – Unit variable cost)

= $100,000/($20 – $8)

= 8,333 units

20-40


The projected income if 10,000 units are sold is computed as follows:

Sales ($20 x 10,000) $200,000

Less: Variable expenses ($8 x10,000) 80,000

Contribution margin $120,000

Less: Fixed expenses 100,000

Operating income $ 20,000

20-41


Suppose that the new design requires a more complex setup, increasing the cost per setup from $1,000 to $1,600. Also, suppose that the new design requires a 40 percent increase in engineering support. The new cost equation is given below:

Total cost = $50,000 + ($8 x Units) + ($1,600 x Setups) + ($30 x Engineering hours)

20-42


The break-even point using the ABC equation is calculated as follows:

Units = [$50,000 + ($1,600 x 20) + ($30 x 1,400)]/($20 – $8)

= $124,000/$12

= 10,333

This is more than the firm can sell!

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End ofEnd of

ChapterChapter

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20-1 Cost-Volume Profit Analysis Prepared by Douglas Cloud Pepperdine University Prepared by Douglas Cloud Pepperdine University