1. Cost-Volume-Profit Analysis
Chapter 10
Cost-Volume-Profit Analysis

2. Learning Objectives
Determine the number of units that must be sold to break even or to earn a targeted profit.
Determine the amount of revenue required to break even or to earn a targeted profit.

3. Learning Objectives (continued)
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.

4. Learning Objectives (continued)
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.

5. Sample Questions Raised and Answered by CVP Analysis
1. How many units must be sold (or how much sales revenue must be generated) in order to break even?
2. How many units must be sold to earn a before-tax profit equal to $60,000? A before-tax profit equal to 15 percent of revenues? An after-tax profit of $48,750?
3. Will total profits increase if the unit price is increased by $2 and units sold decrease 15 percent?
4. What is the effect on total profit if advertising expenditures increase by $8,000 and sales increase from 1,600 to 1,750 units?

6. Sample Questions Raised and Answered by CVP Analysis (continued)
5. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit and sales increase from 1,600 units to 1,900 units?
6. What is the effect on total profit if the selling price is decreased from $400 to $375 per unit, advertising expenditures are increased by $8,000, and sales increased from 1,600 units to 2,300 units?
7. What is the effect on total profit if the sales mix is changed?

7. CVP: A Short-Term Planning and Analysis Tool
Benefits of CVP:
Assists in establishing prices of products.
Assists in analyzing the impact that volume has on short-term profits.
Assists in focusing on the impact that changes in costs (variable and fixed) have on profits.
Assists in analyzing how the mix of products affects profits. 4

8. The Basics of Cost-Volume-Profit (CVP) Analysis
Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

9. The Basics of Cost-Volume-Profit (CVP) Analysis
CM goes to cover fixed expenses.

10. The Basics of Cost-Volume-Profit (CVP) Analysis
After covering fixed costs, any remaining CM contributes to income.

11. The Contribution Approach
For each additional unit Wind sells, $200 more in contribution margin will help to cover fixed expenses and profit.

12. The Contribution Approach
Each month Wind must generate at least $80,000 in total CM to break even.

13. The Contribution Approach
If Wind sells 400 units in a month, it will be operating at the break-even point.

14. The Contribution Approach
If Wind sells one more bike (401 bikes), net
operating income will increase by $200.

15. CVP Relationships in Graphic Form
Viewing CVP relationships in a graph is often helpful. Consider the following information for Wind Co.:

16. CVP Graph
Total Sales
Total Expenses
Dollars
Fixed expenses
Units

17. CVP Graph
Profit Area
Dollars
Break-even point
Loss Area
Units

18. Cost-Volume-Profit Graph
Total Revenue
Revenue
Profit
Total Cost Y
Loss X
Units sold
X = Break-even point in units
Y = Break-even point in revenue

19. Contribution Margin Ratio
The contribution margin ratio is: For Wind Bicycle Co. the ratio is:
Total CM
Total sales
CM Ratio =
$ 80,000
$200,000
= 40%

20. Contribution Margin Ratio
Or, in terms of units, the contribution margin ratio is: For Wind Bicycle Co. the ratio is:
Unit CM
Unit selling price
CM Ratio =
$200
$500
= 40%

21. Contribution Margin Ratio
At Wind, each $1.00 increase in sales revenue results in a total contribution margin increase of 40¢.
If sales increase by $50,000, what will be the increase in total contribution margin?

22. Contribution Margin Ratio
A $50,000 increase in sales revenue

23. Contribution Margin Ratio
A $50,000 increase in sales revenue results in a $20,000 increase in CM.
($50,000 × 40% = $20,000)

24. Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a b c d

25. Unit contribution margin
Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a b c d
Unit contribution margin
Unit selling price
CM Ratio = =
($1.49-$0.36)
$1.49
$1.13
= 0.758

26. Changes in Fixed Costs and Sales Volume
Wind is currently selling 500 bikes per month. The company’s sales manager believes that an increase of $10,000 in the monthly advertising budget would increase bike sales to 540 units.
Should we authorize the requested increase in the advertising budget?

27. Changes in Fixed Costs and Sales Volume
$80,000 + $10,000 advertising = $90,000
Sales increased by $20,000, but net operating income decreased by $2,000.

28. Changes in Fixed Costs and Sales Volume
The Shortcut Solution

29. Break-Even Analysis
Break-even analysis can be approached in three ways:
Graphical analysis.
Equation method.
Contribution margin method.

30. At the break-even point
Equation Method
Profits = Sales – (Variable expenses + Fixed expenses) OR
Sales = Variable expenses + Fixed expenses + Profits
At the break-even point
profits equal zero.

31. Here is the information from Wind Bicycle Co.:
Break-Even Analysis
Here is the information from Wind Bicycle Co.:

32. We calculate the break-even point as follows:
Equation Method
We calculate the break-even point as follows:
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $0
Where:
Q = Number of bikes sold
$500 = Unit selling price
$300 = Unit variable expense
$80,000 = Total fixed expense

33. We calculate the break-even point as follows:
Equation Method
We calculate the break-even point as follows:
Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80,000 + $0
$200Q = $80,000
Q = $80,000 ÷ $200 per bike
Q = 400 bikes

34. Equation Method X = 0.60X + $80,000 + $0
We can also use the following equation to compute the break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80, $0
Where:
X = Total sales dollars
0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses

35. Equation Method X = 0.60X + $80,000 + $0 0.40X = $80,000
We can also use the following equation to compute the break-even point in sales dollars.
Sales = Variable expenses + Fixed expenses + Profits
X = 0.60X + $80, $0
0.40X = $80,000
X = $80,000 ÷ 0.40
X = $200,000

36. Contribution Margin Method
The contribution margin method is a variation of the equation method.
Fixed expenses
Unit contribution margin =
Break-even point
in units sold
Break-even point in
total sales dollars
Fixed expenses
CM ratio =

37. Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units?
a cups
b. 3,611 cups
c. 1,200 cups
d. 1,150 cups

38. Unit contribution margin
Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in units?
a cups
b. 3,611 cups
c. 1,200 cups
d. 1,150 cups
Fixed expenses
Unit contribution margin
Break-even =
$1,300
$1.49 per cup - $0.36 per cup =
$1.13 per cup
= 1,150 cups

39. Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars?
a. $1,300
b. $1,715
c. $1,788
d. $3,129

40. Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the break-even sales in dollars?
a. $1,300
b. $1,715
c. $1,788
d. $3,129
Fixed expenses
CM Ratio
Break-even sales =
$1,300
0.758
= $1,715 =

41. Target Profit Analysis
Suppose Wind Co. wants to know how many bikes must be sold to earn a profit of $100,000.
We can use our CVP formula to determine the sales volume needed to achieve a target net profit figure.

42. The CVP Equation Sales = Variable expenses + Fixed expenses + Profits
$500Q = $300Q + $80, $100,000
$200Q = $180,000
Q = 900 bikes

43. The Contribution Margin Approach
We can determine the number of bikes that must be sold to earn a profit of $100,000 using the contribution margin approach.
Fixed expenses + Target profit
Unit contribution margin =
Unit sales to attain
the target profit
$80, $100,000
$200 per bike
= 900 bikes

44. Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month?
a. 3,363 cups
b. 2,212 cups
c. 1,150 cups
d. 4,200 cups

45. Quick Check 
Fixed expenses + Target profit
Unit contribution margin
Unit sales to attain target profit
$1,300 + $2,500
$ $0.36 =
$3,800
$1.13
= 3,363 cups =
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. How many cups of coffee would have to be sold to attain target profits of $2,500 per month?
a. 3,363 cups
b. 2,212 cups
c. 1,150 cups
d. 4,200 cups

46. Variable-Costing Income Statement
Sales (10,000 x $10) $100,000
Less: Variable costs (10,000 x $6) ,000
Contribution margin $ 40,000
Less: Fixed costs ,000
Profit before taxes $0
Less: Income taxes
Profit after taxes $
=====

47. CVP Analysis: Targeted After-Tax Income
What sales in units and dollars are needed to obtain a
targeted profit after taxes of $24,000?
Let X = break-even point in units
Sales $ = $10X
Less: Variable costs$ = X
Contribution margin$ = $ 4X
Less: Fixed costs ,000
Profit before taxes $
Less income taxes
Profit after taxes $24,000
======

48. CVP Analysis: Targeted After-Tax Income (continued)
The Approach:
AFTER = Profit after taxes
BEFORE = Profit before taxes
AFTER = (1 - tax rate) x BEFORE
$24,000 = (1 - .4) x BEFORE
$24,000/.6 = BEFORE
$40,000 = BEFORE

49. Sales 10X CV (6X) CM 4 X FC (40,000) EBT ? Income Tax (?) EAT 24,000
EAT = (1-Tax) EBT
24,000 = (1-0.4) EBT
EBT = 40,000
EBT - Income Tax = EAT
40,000 – IT = 24,000
IT = 16,000
4X - 40,000 = 40,000
X = 20,000

50. CVP Analysis: Targeted After-Tax Income (continued)
The income statement below illustrates that $200,000 in sales will give you an after-tax profit of $24,000.
Sales $200,000
Less: Variable costs 120,000
Contribution margin $ 80,000
Less: Fixed costs ,000
Profit before taxes $ 40,000
Less: Income taxes ,000
Profit after taxes $ 24,000
======

51. The Margin of Safety
Excess of budgeted (or actual) sales over the break-even volume of sales. The amount by which sales can drop before losses begin to be incurred.
Margin of safety = Total sales - Break-even sales
Let’s calculate the margin of safety for Wind.

52. The Margin of Safety
Wind has a break-even point of $200,000. If actual sales are $250,000, the margin of safety is $50,000 or 100 bikes.

53. The Margin of Safety
The margin of safety can be expressed as 20% of sales. ($50,000 ÷ $250,000)

54. Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety?
a. 3,250 cups
b cups
c. 1,150 cups
d. 2,100 cups

55. Margin of safety percentage
Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the margin of safety?
a. 3,250 cups
b cups
c. 1,150 cups
d. 2,100 cups
Margin of safety = Total sales – Break-even sales
= 950 cups
= 2,100 cups – 1,150 cups or
950 cups
2,100 cups
Margin of safety percentage =
= 45%

56. Operating Leverage
A measure of how sensitive net operating income is to percentage changes in sales.
With high leverage, a small percentage increase in sales can produce a much larger percentage increase in net operating income.
Contribution margin
Net operating income
Degree of
operating leverage =

57. Operating Leverage
$100,000
$20,000
= 5

58. Here’s the verification!
Operating Leverage
With a operating leverage of 5, if Wind increases its sales by 10%, net operating income would increase by 50%.
Here’s the verification!

59. 10% increase in sales from . . . results in a 50% increase in
Operating Leverage
10% increase in sales from
$250,000 to $275,
. . . results in a 50% increase in
income from $20,000 to $30,000.

60. Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage?
a. 2.21
b. 0.45
c. 0.34
d. 2.92

61. Quick Check 
Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the operating leverage?
a. 2.21
b. 0.45
c. 0.34
d. 2.92
Contribution margin
Net operating income
Operating leverage =
$2,373
$1,073
= 2.21

62. Quick Check 
At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, and the average fixed expense per month is $1,300. 2,100 cups are sold each month on average.
If sales increase by 20%, by how much should net operating income increase?
a. 30.0%
b. 20.0%
c. 22.1%
d. 44.2%

63. Quick Check 
At Coffee Klatch the average selling price of a cup of coffee is $1.49, the average variable expense per cup is $0.36, and the average fixed expense per month is $1,300. 2,100 cups are sold each month on average.
If sales increase by 20%, by how much should net operating income increase?
a. 30.0%
b. 20.0%
c. 22.1%
d. 44.2%

64. Verify increase in profit

65. The Concept of Sales Mix
Sales mix is the relative proportions in which a company’s products are sold.
Different products have different selling prices, cost structures, and contribution margins.
Let’s assume Wind sells bikes and carts and see how we deal with break-even analysis.

66. Multiple-Product Example
Product P - V = CM x Mix = Total CM
A $10 - $6 = $4 x 3 = $12
B = x 2 =
Total CM per package $18
===
Total fixed expenses = $180,000

67. Multiple-Product Example (continued)
Break-even point:
X = Fixed cost / Unit contribution margin
= $180,000 / $18
= 10,000 packages to break even
Each package contains 3 units of A and 2 units of B. Therefore, to break even, we need to sell the following units of A and B:
A: 3 x 10,000 = 30,000 units
B: 2 x 10,000 = 20,000 units

68. Multi-product break-even analysis
Wind Bicycle Co. provides the following information:
$265,000
$550,000
= 48.2% (rounded)

69. Multi-product break-even analysis
Fixed expenses
CM Ratio
Break-even sales =
$170,000
0.482
= $352,697 =
Rounding error

70. Another Multiple-Product Example
Assume the following:
Regular Deluxe Total Percent
Units sold
Sales price per unit $ $
Sales $200,000 $150,000 $350, %
Less: Variable expenses , , ,
Contribution margin $ 80,000 $ 90,000 $170, %
Less: Fixed expenses ,000
Net income $ 40,000
=======
1. What is the break-even point?
2. How much sales-revenue of each product must be generated to earn a before tax profit of $50,000? 13

71. Another Multiple-Product Example: BEP
BEP = Fixed cost / CM ratio for sales mix
= $130,000 / 0.486
= $267,490 for the firm
BEP for Regular Model:
(400/600) x $267,490 = $178,327
BEP for Deluxe Model:
(200/600) x $267,490 = $89,163 14

72. Another Multiple-Product Example: Targeted Revenue
BEP = (Fixed Costs + Targeted income) / CM ratio per sales mix
= ($130,000 + $50,000) / 0.486
= $370,370 for the firm
BEP for Regular Model:
(400/600) x $370,370 = $246,913
BEP for Deluxe Model:
(200/600) x 370,370 = $123,457 15

73. CVP and ABC Assume the following: Sales price per unit $15
Variable cost
Fixed costs (conventional) $180,000
Fixed costs (ABC) ,000 with $80,000 subject to ABC analysis
Other Data:
Unit Level of
Variable Activity
Activity Driver Costs Driver
Setups $
Inspections
1. What is the BEP under conventional analysis?
2. What is the BEP under ABC analysis?
3. What is the BEP if setup cost could be reduced to $450 and inspection cost reduced to $40? 18

74. CVP and ABC (continued)
1. Break-even units (conventional analysis)
BEP = $180,000/$10
= 18,000 units
2. Break-even units (ABC analysis)
BEP = [$100, (100 x $500) + (600 x $50)]/$10
3. BEP = [$100,000 + (100 x $450) + (600 x $40)]/$10
= 16,900 units
What implications does ABC have for improving performance? 19

75. Assumptions of CVP Analysis
Selling price is constant.
Costs are linear.
In multi-product companies, the sales mix is constant.
In manufacturing companies, inventories do not change (units produced = units sold).