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

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

3. 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

4. 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

5. 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 $

6. 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

7. 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
Proof
Sales (3,000 units) $1.200,000
Less: Variable exp ,000
Contribution margin $225,000
Less: Fixed expenses ,000
Operating income $ 180,000
(15% of Sales)
$15 x Units = $45,000
Units = 3,000

8. 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)

9. 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

10. 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

11. 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

12. 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

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

14. 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

15. 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

16. 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

17. 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

18. 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 $

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

20. 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

21. 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)

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

23. 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)

24. 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.