1. Chapter 17 Cost-Volume-Profit Analysis
COPYRIGHT © 2009 South-Western Publishing, a division of Cengage Learning. Cengage Learning and South-Western are trademarks used herein under license.

2. Study Objectives
Determine the number of units that must be sold to break even or to earn a targeted profit.
Calculate the amount of revenue required to break even or to earn a targeted profit.
Apply cost-volume-profit analysis in a multiple-product setting.
Prepare a profit-volume graph and a cost-volume-profit graph, and explain the meaning of each.
Explain the impact of risk, uncertainty, and changing variables on cost-volume-profit analysis.
Discuss the impact of activity-based costing on cost-volume-profit analysis.

3. The Break-Even Point in Units1.
The controller of More-Power Company has prepared the following projected income statement:
Sales (72,500 $40) $2,900,000
Less: Variable expenses ,740,000
Contribution margin $1,160,000
Less: Fixed expenses ,000
Operating income $ 360,000

4. The Break-Even Point in Units1.
Operating Income Approach
0 = ($40 x Units) – ($24 x Units) – $800,000
0 = ($16 x Units) – $800,000
$1,740,000 ÷ 72,500
($16 x Units) = $800,000
Units = 50,000
Proof
Sales (50,000 $40) $2,000,000
Less: Variable expenses 1,200,000
Contribution margin $ 800,000
Less: Fixed expenses ,000
Operating income $

5. The Break-Even Point in Units1.
Contribution Margin Approach
Number of units
= $800,000 ÷ ($40 - $24)
= $800,000 ÷ $16 contribution margin per unit
= 50,000

6. The Break-Even Point in Units1.
Target Income as a Dollar Amount
$424,000
= ($40 x Units) – ($24 x Units) – $800,000
$1,224,000
= $16 x Units
Units
= $1,224,000 ÷ $16
= 76,500
Proof
Sales (76,500 $40) $3,060,000
Less: Variable expenses 1,836,000
Contribution margin $1,224,000
Less: Fixed expenses ,000
Operating income $ 424,000

7. The Break-Even Point in Units1.
Target Income as a Percentage of Sales Revenue
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.
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

8. The Break-Even Point in Units1.
After-Tax Profit Targets
Net income
= Operating income – Income taxes
= Operating income – (Tax rate × Operating income)
= Operating income × (1 – Tax rate) Or

9. The Break-Even Point in Units1.
After-Tax Profit Targets
More-Power Company wants to achieve net income of $487,500 and its income tax rate is 35 percent.
$487,500 = Operating income – 0.35(Operating income)
$487,500 = 0.65(Operating income)
$750,000 = Operating income
Units = ($800,000 + $750,000) ÷ $16
= $1,550,000 ÷ $16
= $96,875

10. Break-Even Point in Sales Dollars2.

11. Break-Even Point in Sales Dollars2.
The following More-Power Company contribution margin income statement is shown for sales of 72,500 sanders.
Sales $2,900,000
Less: Variable expenses 1,740,000
Contribution margin $1,160,000
Less: Fixed expenses ,000
Operating income $ 360,000

12. Break-Even Point in Sales Dollars2.
To determine the break-even in sales dollars, the contribution margin ratio must be determined ($1,160,000 ÷ $2,900,000)
Sales $2,900, %
Less: Variable expenses 1,740, %
Contribution margin $1,160, %
Less: Fixed expenses ,000
Operating income $ 360,000
Sales $2,900,000
Less: Variable expenses 1,740,000
Contribution margin $1,160,000
Less: Fixed expenses ,000
Operating income $ 360,000

13. Break-Even Point in Sales Dollars2.
Operating income = Sales – Variable costs – Fixed Costs
0 = Sales – (Variable cost ratio × 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

14. Break-Even Point in Sales Dollars2.

15. Break-Even Point in Sales Dollars2.

16. Break-Even Point in Sales Dollars2.

17. Break-Even Point in Sales Dollars2.
Profit 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

18. Multiple-Product Analysis3.
More-Power plans on selling 75,000 regular sanders and 30,000 mini-sanders. The sales mix is 5:2
Regular Mini-
Sander Sander Total
Sales $3,000,000 $1,800,000 $4,800,000
Less: Variable expenses 1,800, , ,700,000
Contribution margin $1,200,000 $ 900,000 $2,100,000
Less: Direct fixed expenses , , ,000
Product margin $ 950,000 $ 450,000 $1,400,000
Less: Common fixed exp ,000
Operating income $ 800,000

19. Multiple-Product Analysis3.
Break-Even Point in Units
Regular sander break-even units
= Fixed costs ÷ (Price – Unit variable)
= $250,000 ÷ $16
= 15,625 units
Mini-sander break-even units
= Fixed costs ÷ (Price – Unit variable)
= $450,000 ÷ $30
= 15,000 units

20. Multiple-Product Analysis3.
Sales Mix and CVP Analysis
Package break-even units
= Fixed costs ÷ Package contribution margin
= $1,300,000 ÷ $140
= 9, units
Sales volume for break-even
Regular sander: 46,429 units
Mini sander: 18,571 units

21. Multiple-Product Analysis3.

22. Multiple-Product Analysis3.
Sales Dollar Approach
Projected Income:
Sales $4,800,000
Less: Variable expenses 2,700,000
Contribution margin $2,100,
Less: Fixed expenses 1,300,000
Operating income $ 800,000
Break-even sales = Fixed costs ÷ contribution margin ratio
= 1,300,000 ÷
= $2,971,429

23. Graphical Representation of CVP Relationships4.

24. Graphical Representation of CVP Relationships4.

25. Graphical Representation of CVP Relationships4.
Assumptions of C-V-P Analysis
The analysis assumes a linear revenue function and a linear cost function.
The analysis assumes that price, total fixed costs, and unit variable costs can be accurately identified and remain constant over the relevant range.
The analysis assumes that what is produced is sold.
For multiple-product analysis, the sales mix is assumed to be known.
The selling price and costs are assumed to be known with certainty.

26. Changes in the CVP Variables5.
Alternative 1: If advertising expenditures increase by $48,000, sales will increase from 72,500 units to 75,000 units.

27. Changes in the CVP Variables5.
Alternative 2: A price decrease from $40 per sander to $38 would increase sales from 72,500 units to 80,000 units.

28. Changes in the CVP Variables5.
Alternative 3: Decreasing price to $38 and increasing advertising expenditures by $48,000 will increase sales from 72,500 units to 90,000 units.

29. Changes in the CVP Variables5.
Margin of safety
The excess of units sold over break-even units
The excess of revenue earned over break-even sales
Current sales 500
Break-even volume 200
Margin of safety (in units) 300
Current revenue $350,000
Break-even volume 200,000
Margin of safety (in dollars) $150,000

30. Changes in the CVP Variables5.
Operating Leverage
Automated Manual
System System
Sales (10,000 units) $1,000,000 $1,000,000
Less: Variable expenses , ,000
Contribution margin $ 500,000 $ 200,000
Less: Fixed expenses , ,000
Operating income $ 125,000 $ 100,000
Unit selling price $100 $100
Unit variable cost 50 80
Unit contribution margin 50 20
DOL of 4 $500,000 ÷ $125,000
DOL of 2 $200,000 ÷ $100,000

31. Changes in the CVP Variables5.
Operating Leverage
Automated Manual
System System
Assume a 40% increase in sales
Increase in sales 40% 40%
Degree of operating leverage × × 2
Increase in operating income 160% 80%
Sales (14,000 units) $1,400,000 $1,400,000
Less: Variable expenses , ,120,000
Contribution margin $ 700,000 $ 280,000
Less: Fixed expenses , ,000
Operating income $ 325,000 $ 180,000

32. CVP Analysis and Activity-Based Costing6.
The ABC Cost Equation:
Total revenue
– Total Cost
= Operating income
Operating Income:
Fixed costs
+ Unit variable cost × number of units
+ Setup cost × number of setups
+ Engineering cost × number of engineering hours
= Total cost
Break-Even in Units:

33. CVP Analysis and Activity-Based Costing6.
Differences between ABC break-even and conventional break-even
Fixed costs differ
Costs by vary with non-unit cost drivers
The numerator of the ABC break-even equation has two nonunit-variable cost terms
Batch-related activities
Product-sustaining activities

34. CVP Analysis and Activity-Based Costing6.
Example Comparing Conventional and ABC Analysis
Cost Driver Unit Variable Cost Level of Cost Driver
Units sold $
Setups 1,
Engineering hours 30 1,000
Other data:
Total fixed costs (conventional) $100,000
Total fixed costs (ABC) 50,000
Unit selling price 20

35. CVP Analysis and Activity-Based Costing6.
Example Comparing Conventional and ABC Analysis
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
Same data using the ABC
Units = ($20,000 + $50,000 + $20,000 + $30,000) ÷ ($20 – $10)
= $120,000 ÷ $10
= 12,000

36. CVP Analysis and Activity-Based Costing6.
Example Comparing Conventional and ABC Analysis
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 :
Units = Fixed costs ÷ (Price – Unit variable cost)
= $100,000 ÷ ($20 – $8)
= 8,333

37. CVP Analysis and Activity-Based Costing6.
Example Comparing Conventional and ABC Analysis
Projected income if 10,000 units are sold:
Sales ($20 × 10,000) $200,000
Less: Variable expenses ($8 × 10,000) 80,000
Contribution margin $120,000
Less: Fixed expenses 100,000
Operating income $ 20,000

38. CVP Analysis and Activity-Based Costing6.
Example Comparing Conventional and ABC Analysis
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.
New cost equation:
$50,000 (fixed costs)
+ ($8 × units)
+ ($1,600 × setups)
+ ($30 × engineering hours)

39. CVP Analysis and Activity-Based Costing6.
Example Comparing Conventional and ABC Analysis
Break-even point using the ABC equation:
This exceeds the firm’s sales capacity!

40. End Chapter 17
COPYRIGHT © 2009 South-Western Publishing, a division of Cengage Learning. Cengage Learning and South-Western are trademarks used herein under license.