1. 1

2. Cost-Volume-Profit Analysis
Chapter 7 2

3. Learning Objective 1
Calculate the unit contribution margin and the contribution margin ratio 3

4. Cost-Volume-Profit (CVP) Analysis
Is a powerful tool that helps managers make important business decisions
Is a relationship among costs, volume, and profit or loss
Determines how much the company must sell each month just to cover costs or to break even
Helps managers decide how sales volume would need to change to achieve the same profit level 4

5. Components of CVP Analysis
CVP analysis relies on the interdependency of five components or pieces of information
Sales price per unit
Volume sold
Variable costs per unit
Fixed costs
Operating income
If you know or can estimate four of these five components, you can compute the remaining unknown amount 5

6. CVP Assumptions Change in volume is only factor that affects costs
Managers can classify each cost as either variable or fixed
These costs are linear throughout relevant range
Revenues are linear throughout relevant range
Inventory levels will not change
The sales mix of products will not change 6

7. CVP Example Facts: Kay’s Posters
Kay has an e-tail poster business. She currently sells each poster for $35, while each poster has a variable cost of $21. Kay has fixed costs of $7,000. Kay is currently selling 550 posters. 7

8. Contribution Margin Income Statement
Kay’s e-tail poster example from prior slide
Sales revenue (550 posters) $ 19,250
Less: Variable expenses (11,550)
Contribution margin ,700
Less: Fixed expenses (7,000)
Operating income $ 8

9. Unit Contribution Margin
Kay’s e-tail poster example from previous slides Sales price per unit $ 35 - Variable costs per unit (21) Contribution margin per unit $ 14 Now assume sales are 650 units: Contribution margin ( 650 sales X $14) $ 9,100 - Fixed cost (7,000) Operating Income $ 2,100 9

10. Contribution Margin Ratio
Contribution margin ratio = percentage of each sales dollar that is available for covering fixed expenses and generating a profit.
Contribution
margin ratio
Unit contribution margin = $14
Sales price per unit $35
= 40%
Contribution margin ratio
Contribution margin = $ 7,700
Sales revenue $19,250
= 40%
Numbers above are from the Kay’s e-tail poster example on previous slides. 10

11. S7-1
Bay Cruiseline offers nightly dinner cruises off the coast of Miami, San Francisco, and Seattle. Dinner cruise tickets sell for $50 per passenger. Bay Cruiseline’s variable cost of providing the dinner is $20 per passenger, and the fixed cost of operating the vessels (depreciation, salaries, docking fees, and other expenses) is $210,000 per month. The company’s relevant range extends to 15,000 monthly passengers.
a. What is the contribution margin per passenger?
Sales revenue (1 passenger)
Less: Variable expenses
Contribution margin 11

12. S7-1 (continued)
b. What is the contribution margin ratio? c. Use the unit contribution margin to project operating income if monthly sales total 10,000 passengers. d. Use the contribution margin ratio to project operating income if monthly sales revenue totals $400,000. Contribution margin ( $400,000 sales X 60%) Fixed cost Operating Income
Contribution
margin ratio =
Unit contribution margin = $ 30
Sales price per unit = $ 50
= ? ? 12

13. S7-2
Bay Cruiseline offers nightly dinner cruises off the coast of Miami, San Francisco, and Seattle. Dinner cruise tickets sell for $50 per passenger. Bay Cruiseline’s variable cost of providing the dinner is $20 per passenger, and the fixed cost of operating the vessels (depreciation, salaries, docking fees, and other expenses) is $210,000 per month. The company’s relevant range extends to 15,000 monthly passengers.
If Bay Cruiseline sells an additional 500 tickets, by what amount will its operating income increase (or operating loss decrease)?
Contribution Margin per unit x additional tickets 13

14. Use CVP analysis to find breakeven points and target profit volumes
Learning Objective 2
Use CVP analysis to find breakeven points and target profit volumes 14

15. Breakeven Point Breakeven point:
Sales level at which operating income is zero
Fixed expenses = total contribution margin
Total sales = total expenses 15

16. Calculating Breakeven Point
Three approaches to calculating breakeven:
Income statement approach
Shortcut approach using unit contribution margin
Shortcut approach using contribution margin ratio 16

17. Income Statement Approach
Contribution Margin Income Statement
Sales
- Variable Expenses
Contribution Margin
- Fixed Expenses
Operating Income 17

18. Short-Cut Approach to Calculating Breakeven Using the Unit Contribution Margin
Fixed expenses + Operating income
Contribution margin per unit
Units sold =
$7,000 + $0
$14
Units sold =
= 500 posters 18

19. Short-Cut Using the Unit Contribution Margin Ratio
Fixed expenses + Operating income
Contribution margin ratio
Sales in $ =
$7,000 + $0
0.40
Sales in $ =
= $17,500 19

20. Finding the Volume Needed for a Target Profit Using Unit CM
CVP analysis helps managers determine what they need to sell to earn a target amount of profit.
Fixed expenses + Operating income
Contribution margin per unit
Units sold =
$7,000 + $4,900
$14
$11,900
$14
Units sold = =
= 850 posters
= 850 posters x $35 = $29,750 20

21. Finding the Volume Needed for a Target Profit Using Ratio
CVP analysis helps managers determine what they
need to sell to earn a target amount of profit.
Fixed exp + Target operating income
Contribution margin ratio
Units sold =
$7,000 + $4,900
0.40
$11,900
0.40
Units sold = =
= 29,750 posters 21

22. S7-3
Use the information from the Bay Cruiseline Data Set to compute the number of dinner cruise tickets it must sell to break even.
a. Use the income statement equation approach.
($50 x units) – ($20 x units) $210,000 = $0
($50 – $20 ) x units $210,000 = $0 22

23. S7-3 (continued)
Use the information from the Bay Cruiseline Data Set to compute the number of dinner cruise tickets it must sell to break even. b. Using the shortcut unit contribution margin approach, perform a numerical proof to ensure that your answer is correct.
Fixed expenses + Operating income
Contribution margin per unit
Units sold = ?
Units sold = ?
Units sold =
= ? 23

24. S7-3 (continued)
Use the information from the Bay Cruiseline Data Set to compute the number of dinner cruise tickets it must sell to break even.
c. Use your answers from a and b to determine the sales revenue needed to break even.
7,000 units to break even X $50 sales price = ? 24

25. S7-3 (continued)
Use the information from the Bay Cruiseline Data Set to compute the number of dinner cruise tickets it must sell to break even. d. Use the shortcut contribution margin ratio approach to verify the sales revenue needed to break even.
Fixed expenses + Operating income
Contribution margin ratio
Sales in $ = ?
Sales in $ = ?
Sales in $ =
= ? 25

26. Graphing the CVP Relationships
Step 1:
Choose a sales volume (Units x $Price)
Plot point for total sales revenue
Draw sales revenue line from origin through the plotted point 26

27. Preparing a CVP Chart 27

28. Preparing a CVP Chart
Step 2: Draw the fixed cost line
$4,000 28

29. Preparing a CVP Chart
Step 3: Draw the total cost line (fixed plus variable) 29

30. Preparing a CVP Chart
Step 4: Identify the breakeven point and the areas of
operating income and loss
Breakeven point 30

31. Preparing a CVP Chart
Step 5: Mark operating income and operating loss areas
on graph
Breakeven point
Operating Income
Operating Loss 31

32. S7-5
Revenues 32

33. S7-5 (continued)
Fixed Cost 33

34. S7-5 (continued)
Breakeven Point
Income Area
Total Cost
Loss Area 34

35. Learning Objective 3
Perform sensitivity analysis in response to changing business conditions 35

36. Sensitivity Analysis
Managers need to be prepared for increasing costs, pricing pressure from competitors, and other changing business conditions.
Sensitivity Analysis:
Conducts “What if” analysis 36

37. What if the Sales Price Changes?
Calculate a new unit contribution margin using the new sales price
Use the new unit contribution margin to compute breakeven sales in units
Use the new unit contribution margin to compute breakeven sales to maintain target profit
Using the new breakeven numbers, decide if a change should be made 37

38. What if Costs Change?
Calculate a new unit contribution margin using the new cost
Use the new unit contribution margin to compute breakeven sales in units
Use the new unit contribution margin to compute breakeven sales to maintain target profit
Using the new breakeven numbers, decide if a change should be made 38

39. What if Fixed Costs Change?
Changes in fixed costs do not affect the contribution margin
Breakeven point changes because fixed costs change
Use the unit contribution margin to compute the new breakeven sales in units
Use the unit contribution margin to compute breakeven sales to maintain target profit
Using the new breakeven numbers, decide if a change should be made 39

40. Find breakeven and target profit volumes for multiproduct companies
Learning Objective 4
Find breakeven and target profit volumes for multiproduct companies 40

41. Breakeven in Sales Revenue: Multiproduct Firm
Total expected contribution margin: Regular posters (500 x $14) $ 7,000 Large posters (300 x $30) $ 9,000 Total expected contribution margin $16,000 Divided by total expected sales revenue: Regular posters (500 x $35) $17,500 Large posters (300 x $70) ,000 Total expected sales ÷ $38,500 Contribution margin ratio = % 41

42. Breakeven in Sales Revenue: Multiproduct Firm (continued)
Fixed expenses + Operating income
Contribution margin ratio
Units sold =
$7,
$7,000
Units sold = =
= $16,844 (rounded) 42

43. Information Technology and Sensitivity Analysis
Allows managers to perform a wide array of sensitivity analyses before committing to decisions.
Uses Excel spreadsheets to perform sensitivity analyses
Allows managers to estimate how one change (or several simultaneous changes) affects business operations
Uses spreadsheet software to create CVP graphs 43

44. S7-9 Regular Cruise Executive Cruise Sales price per ticket $50 $130
Variable expense per passenger
$20
$40
Assuming that Bay Cruiseline expects to sell four regular cruises for every executive cruise, compute the weighted-average contribution margin per unit.
Sales Mix Calculation Regular Executive Total
Sales price per unit $ 50 $130
Less: Variable cost per unit (20) (40)
Contribution margin per unit
Sales mix
Contribution margin
Weighted-average contribution
margin per unit ($210/5) 44

45. S7-9 (continued) Sales Mix Calculation Regular Executive Total
Sales price per unit $ 50 $130
Less: Variable cost per unit (20) (40)
Contribution margin per unit
Sales mix
Contribution margin
Weighted-average contribution
margin per unit ($210/5)
Is it higher or lower than a simple average contribution margin?
Why? 45

46. S7-9 (continued) Fixed expenses + Operating income Sales in $ =
Sales Mix Calculation Regular Executive Total
Sales price per unit $ 50 $130
Less: Variable cost per unit (20) (40)
Contribution margin per unit
Sales mix
Contribution margin
Weighted-average contribution
margin per unit ($210/5)
Will this new sales mix cause Bay Cruiseline’s breakeven point to increase or decrease from what it was when it sold only regular cruises?
Fixed expenses + Operating income
Weighted Average Contribution margin per unit
Sales in $ = ?
Sales in $ = = 46

47. What if the Sales Mix Changes?
Use the same CVP formula for multiple products.
Use the weighted-average contribution margin per unit of all products.
Can find the breakeven or the target profit volume in terms of units, or in terms of sales revenue.
Sales Mix Calculation Regular Large
Product Product Total
Sales price per unit $ 35 $ 70
Less: Variable cost per unit (21) (40)
Contribution margin per unit
Sales mix
Contribution margin
Weighted-average contribution
margin per unit ($160/8) 47

48. Determine a firm’s margin of safety and operating leverage
Learning Objective 5
Determine a firm’s margin of safety and operating leverage 48

49. Common Indicators of Risk
Margin of Safety
The excess of expected sales over breakeven sales
Operating Leverage
The relative amount of fixed and variable costs that make up a company’s total costs 49

50. Margin of Safety Excess of expected sales over breakeven sales
Drop in sales that the company can absorb before incurring a loss
Used to evaluate the risk of current operations as well as the risk of new plans 50

51. Margin of Safety Breakeven sales in units Margin of safety in units
Expected sales = −
= units − units
450 units
Breakeven sales
Margin of safety
in dollars
Expected sales = −
= $33, – $17,500
= $15,750 51

52. Margin of Safety as a Percentage
Margin of safety in units
Expected sales in units =
450 Units
950 Units =
47.4% (rounded) =
Margin of safety
as a percentage
Margin of safety in dollars
Expected sales in dollars =
$15,750
$33,250 =
47.4% (rounded) = 52

53. Operating Leverage Factor
How responsive a company’s operating income is to changes in volume
Lowest possible value for this factor is 1, if the company has no fixed costs
Operating leverage factor =
Contribution margin
Operating income
Operating leverage factor =
$13,300
$6,300 =
2.11 (rounded) 53

54. High Operating Leverage
High operating leverage companies have:
Higher levels of fixed costs and lower levels of variable costs
Higher contribution margin ratios
For high operating leverage companies, changes in volume significantly affect operating income, so they face:
Higher risk
Higher potential for reward
Examples include golf courses, hotels, rental car agencies, theme parks, airlines, cruise lines 54

55. Low Operating Leverage
Low operating leverage companies have:
Higher levels of variable costs and lower levels of fixed costs
Lower contribution margin ratios
For low operating leverage companies, changes in volume do NOT have as significant an effect on operating income, so they face:
Lower risk
Lower potential for reward
Examples include merchandising companies. 55

56. End of Chapter 7 56