1. Cost-Volume-Profit Analysis: A Managerial Planning Tool
CHAPTER

2. After studying this chapter, you should be able to:
Objectives
1. Determine the number of units that must be sold to break even or earn a target 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.
After studying this chapter, you should be able to:

3. Objectives
5. Explain the impact of risk, uncertainty, and changing variables on cost-volume-profit analysis.
6. Discuss the impact of activity-based costing on cost-volume-profit analysis

4. Using Operating Income in CVP Analysis
Narrative Equation
Sales revenue
– Variable expenses
– Fixed expenses
= Operating income

5. Using Operating Income in CVP Analysis
Sales (1,000 $400) $400,000
Less: Variable expenses ,000
Contribution margin $ 75,000
Less: Fixed expenses ,000
Operating income $ 30,000

6. Using Operating Income in CVP Analysis
Break Even in Units
0 = ($400 x Units) – ($325 x Units) – $45,000
$400,000 ÷ 1,000
$325,000 ÷ 1,000

7. Using Operating Income in CVP Analysis
Break Even in Units
0 = ($400 x Units) – ($325 x Units) – $45,000
0 = ($75 x Units) – $45,000
$75 x Units = $45,000
Units = 600
Proof
Sales (600 units) $240,000
Less: Variable exp ,000
Contribution margin $ 45,000
Less: Fixed expenses ,000
Operating income $

8. Desired Operating Income of $60,000
Achieving a Targeted Profit
Desired Operating Income of $60,000
$60,000 = ($400 x Units) – ($325 x Units) – $45,000
$105,000 = $75 x Units
Units = 1,400
Proof
Sales (1,400 units) $560,000
Less: Variable exp ,000
Contribution margin $105,000
Less: Fixed expenses ,000
Operating income $ 60,000

9. Desired Operating Income of 15% of Sales Revenue
Targeted Income as a Percent of Sales Revenue
Desired Operating Income of 15% of Sales Revenue
0.15($400)(Units) = ($400 x Units) – ($325 x Units) – $45,000
$60 x Units = ($400 x Units) – $325 x Units) – $45,000
$60 x Units = ($75 x Units) – $45,000
$15 x Units = $45,000
Units = 3,000

10. After-Tax Profit Targets
Net income = Operating income – Income taxes
= Operating income – (Tax rate x Operating income)
= Operating income (1 – Tax rate) Or
Operating income =
Net income
(1 – Tax rate)

11. After-Tax Profit Targets
If the tax rate is 35 percent and a firm wants to achieve a profit of $48,750. How much is the necessary operating income?
$48,750 = Operating income – (0.35 x Operating income)
$48,750 = 0.65 (Operating income)
$75,000 = Operating income

12. After-Tax Profit Targets
How many units would have to be sold to earn an operating income of $48,750?
Units = ($45,000 + $75,000)/$75
Units = $120,000/$75
Units = 1,600
Proof
Sales (1,600 units) $640,000
Less: Variable exp ,000
Contribution margin $120,000
Less: Fixed expenses ,000
Operating income $ 75,000
Less: Income tax (35%) ,250
Net income $ 48,750

13. Break-Even Point in Sales Dollars
First, the contribution margin ratio must be calculated.
Sales $400, %
Less: Variable
expenses 325, %
Contribution
margin $ 75, %
Less: Fixed exp ,000
Operating income $ 30,000

14. Break-Even Point in Sales Dollars
Given a contribution margin ratio of 18.75%, how much sales revenue is required to break even?
Operating income = Sales – Variable costs – Fixed costs
$0 = Sales – (Variable costs ratio x Sales)
– $45,000
$0 = Sales (1 – ) – $45,000
Sales (0.1875) = $45,000
Sales = $240,000

15. Fixed Cost = Contribution Margin
Relationships Among Contribution Margin, Fixed Cost, and Profit
Fixed Cost = Contribution Margin
Fixed Cost
Contribution Margin
Total Variable Cost
Revenue

16. Fixed Cost < Contribution Margin
Relationships Among Contribution Margin, Fixed Cost, and Profit
Fixed Cost < Contribution Margin
Fixed Cost
Profit
Contribution Margin
Total Variable Cost
Revenue

17. Fixed Cost > Contribution Margin
Relationships Among Contribution Margin, Fixed Cost, and Profit
Fixed Cost > Contribution Margin
Fixed Cost
Loss
Contribution Margin
Total Variable Cost
Revenue

18. Profit Targets and Sales Revenue
How much sales revenue must a firm generate to earn a before-tax profit of $60,000. Recall that fixed costs total $45,000 and the contribution margin ratio is
Sales = ($45,000 + $60,000)/0.1875
= $105,000/0.1875
= $560,000

19. Multiple-Product Analysis
Mulching Riding
Mower Mower Total
Sales $480,000 $640,000 $1,120,000
Less: Variable expenses 390, , ,000
Contribution margin $ 90,000 $160,000 $ 250,000
Less: Direct fixed expenses , , ,000
Product margin $ 60,000 $120,000 $ 180,000
Less: Common fixed expenses ,250
Operating income $ 153,750

20. Income Statement: B/E Solution
Mulching Riding
Mower Mower Total
Sales $184,800 $246,400 $431,200
Less: Variable expenses 150, , ,950
Contribution margin $ 34,650 $ 61,600 $ 96,250
Less: Direct fixed expenses , , ,000
Segment margin $ 4,650 $ 23,600 $ 26,250
Less: Common fixed expenses ,250
Operating income $

21. The profit-volume graph portrays the relationship between profits and sales volume.

22. Example
The Tyson Company produces a single product with the following cost and price data:
Total fixed costs $100
Variable costs per unit 5
Selling price per unit 10

23. Profit-Volume Graph (40, $100) I = $5X - $100 $100— 80— 60— 40— 20— 0—
- 20—
- 40—
-60—
100—
Profit or Loss
Break-Even Point
(20, $0)
| | | | | | | | | |
Units Sold
Loss
(0, -$100)

24. The cost-volume-profit graph depicts the relationship among costs, volume, and profits.

25. Cost-Volume-Profit Graph
Revenue
Units Sold $ --
50 --
0 --
| | | | | | | | | | | |
Total Revenue
Profit ($100)
Total Cost
Variable Expenses ($5 per unit)
Loss
Break-Even Point (20, $200)
Fixed Expenses ($100)

26. Assumptions 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.

27. Relevant Range $
Total Revenue
Total Cost
Relevant Range
Units

28. Alternative 1: If advertising expenditures increase by $8,000, sales will increase from 1,600 units to 1,725 units.
BEFORE THE WITH THE
INCREASED INCREASED
ADVERTISING ADVERTISING
Units sold 1,600 1,725
Unit contribution margin x $75 x $75
Total contribution margin $120,000 $129,375
Less: Fixed expenses , ,000
Profit $ 75,000 $ 76,375
DIFFERENCE IN PROFIT
Change in sales volume 125
Unit contribution margin x $75
Change in contribution margin $9,375
Less: Change in fixed expenses 8,000
Increase in profits $1,375

29. Alternative 2: A price decrease from $400 to $375 per lawn mower will increase sales from 1,600 units to 1,900 units.
BEFORE THE WITH THE
PROPOSED PROPOSED CHANGES CHANGES
Units sold 1,600 1,900
Unit contribution margin x $75 x $50
Total contribution margin $120,000 $95,000
Less: Fixed expenses , ,000
Profit $ 75,000 $50,000
DIFFERENCE IN PROFIT
Change in contribution margin $ -25,000
Less: Change in fixed expenses
Decrease in profits $ -25,000

30. Alternative 3: Decreasing price to $375and increasing advertising expenditures by $8,000 will increase sales from 1,600 units to 2,600 units.
BEFORE THE WITH THE
PROPOSED PROPOSED
CHANGES CHANGES
Units sold 1,600 2,600
Unit contribution margin x $75 x $50
Total contribution margin $120,000 $130,000
Less: Fixed expenses , ,000
Profit $ 75,000 $ 77,000
DIFFERENCE IN PROFIT
Change in contribution margin $10,000
Less: Change in fixed expenses 8,000
Increase in profit $ 2,000

31. Margin of Safety
Assume that a company has the following projected income statement:
Sales $100,000
Less: Variable expenses ,000
Contribution margin $ 40,000
Less: Fixed expenses ,000
Income before taxes $ 10,000
Break-even point in dollars (R):
R = $30,000 ÷ .4 = $75,000
Safety margin = $100,000 - $75,000 = $25,000

32. Degree of Operating Leverage (DOL)
Now suppose that sales are 25% higher than projected. What is the percentage change in profits?
Percentage change in profits = DOL x percentage change in sales
Percentage change in profits = 4.0 x 25% = 100%

33. Degree of Operating Leverage (DOL)
Proof:
Sales $125,000
Less: Variable expenses ,000
Contribution margin $ 50,000
Less: Fixed expenses ,000
Income before taxes $ 20,000

34. CVP and ABC Assume the following: Sales price per unit $15
Variable cost
Fixed costs (conventional) $180,000
Fixed costs (ABC) $100,000 with $80,000 subject to ABC analysis
Other Data:
Unit Level of
Variable Activity
Activity Driver Costs Driver
Setups $
Inspections 18

35. CVP and ABC 1. What is the BEP under conventional analysis?
= 18,000 units 19

36. CVP and ABC 2. What is the BEP under ABC analysis?
BEP = [$100, (100 x $500) + (600 x $50)]/$10
= 18,000 units

37. CVP and ABC
3. What is the BEP if setup cost could be reduced to $450 and inspection cost reduced to $40?
BEP = [$100,000 + (100 x $450) + (600 x $40)]/$10
= 16,900 units

38. Chapter Sixteen
The End