This document discusses cost-volume-profit (CVP) analysis and break-even points. It contains several examples and explanations of how to calculate break-even points using both the contribution margin approach and equation approach. It also discusses how to calculate break-even points for companies with multiple products using weighted average contribution margins. Additionally, it explains how to graph CVP relationships using cost-volume-profit and profit-volume graphs and how managers can use these graphs. Key assumptions of CVP analysis and how CVP relationships are reflected in traditional vs contribution format income statements are also summarized.

1. Chapter 7
Cost-Volume-
Profit Analysis
Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

2. Learning
Objective
1
Compute a break-
even point using the
contribution-margin
approach and the
equation approach
7-2

3. The Break-Even Point
The break-even point is the point in the
volume of activity where the organization’s
revenues and expenses are equal.
Sales 250,000$
Less: variable expenses 150,000
Contribution margin 100,000
Less: fixed expenses 100,000
Net income -$
7-3

4. Equation Approach
Sales revenue – Variable expenses – Fixed expenses = Profit
Unit
sales
price
Sales
volume
in units
×
Unit
variable
expense
Sales
volume
in units
×
($500 × X) ($300 × X)– – $80,000 = $0
($200X) – $80,000 = $0
X = 400 surf boards
7-4

5. Cost-Volume-Profit Analysis
 Break-Even Point
• Number of units sold that allow the company to
neither earn a profit nor incur a loss
• $0 = SP(x) – VC(x) – Fixed Costs
 CodeConnect has the following cost
structure
• Selling price $200.00 per unit
• Variable cost $90.83 per unit
• Total fixed cost $160,285
 Find CodeConnect’s break-even point (in units)
Slide 7-5

6. Cost-Volume-Profit Analysis
 Break-Even Point
$0 = SP(x) – VC(x) – TFC
$0 = [$200.00 (x)] – [$90.83(x)] – $160,285
$0 = [($200.00 – $90.83)(x)] – $160,285
$0 = $109.17(x) – $160,285
$109.17(x) = $160,285
x = $160,285 / $109.17 (Fixed Costs/CM per unit)
x = 1,468.21 units
Break-even point is 1,469 units (always round up)
Slide 7-6

7. Contribution-Margin Approach
For each additional surf board sold, Curl
generates $200 in contribution margin.
Total Per Unit Percent
Sales (500 surf boards) 250,000$ 500$ 100%
Less: variable expenses 150,000 300 60%
Contribution margin 100,000$ 200$ 40%
Less: fixed expenses 80,000
Net income 20,000$
Consider the following information
developed by the accountant at Curl, Inc.:
7-7

8. Contribution-Margin Approach
Fixed expenses
Unit contribution margin
=
Break-even point
(in units)
Total Per Unit Percent
Sales (500 surf boards) 250,000$ 500$ 100%
Less: variable expenses 150,000 300 60%
Contribution margin 100,000$ 200$ 40%
Less: fixed expenses 80,000
Net income 20,000$
$80,000
$200
= 400 surf boards
7-8

9. Contribution-Margin Approach
Here is the proof!
Total Per Unit Percent
Sales (400 surf boards) 200,000$ 500$ 100%
Less: variable expenses 120,000 300 60%
Contribution margin 80,000$ 200$ 40%
Less: fixed expenses 80,000
Net income -$
400 × $500 = $200,000 400 × $300 = $120,000
7-9

10. Learning
Objective
2 Compute the
contribution-
margin ratio and
use it to find the
break-even point
in sales dollars
7-10

11. Contribution Margin Ratio
Calculate the break-even point in sales dollars
rather than units by using the contribution margin
ratio.
Contribution margin
Sales
= CM Ratio
Fixed expense
CM Ratio
Break-even point
(in sales dollars)
=
7-11

12. Total Per Unit Percent
Sales (400 surf boards) 200,000$ 500$ 100%
Less: variable expenses 120,000 300 60%
Contribution margin 80,000$ 200$ 40%
Less: fixed expenses 80,000
Net income -$
Contribution Margin Ratio
$80,000
40%
$200,000 sales=
7-12

13. Learning
Objective
3
Prepare a cost-
volume-profit
(CVP) graph and
explain how it is
used
7-13

14. Graphing Cost-Volume-Profit
Relationships
Viewing CVP relationships in a graph gives
managers a perspective that can be obtained in
no other way.
Consider the following information for Curl, Inc.:
300 units 400 units 500 units
Sales 150,000$ 200,000$ 250,000$
Less: variable expenses 90,000 120,000 150,000
Contribution margin 60,000$ 80,000$ 100,000$
Less: fixed expenses 80,000 80,000 80,000
Net income (loss) (20,000)$ -$ 20,000$
7-14

15. Cost-Volume-Profit Graph
Dollars
600 700 800
Units
200 300 400 500
450,000
100
200,000
150,000
100,000
50,000
400,000
350,000
300,000
250,000
Fixed expenses
7-15

16. Cost-Volume-Profit Graph
Dollars
600 700 800
Units
200 300 400 500
450,000
100
200,000
150,000
100,000
50,000
400,000
350,000
300,000
250,000
Fixed expenses
7-16

17. Cost-Volume-Profit Graph
Dollars
600 700 800
Units
200 300 400 500
450,000
100
200,000
150,000
100,000
50,000
400,000
350,000
300,000
250,000
Fixed expenses
7-17

18. Cost-Volume-Profit Graph
Dollars
600 700 800
Units
200 300 400 500
450,000
100
200,000
150,000
100,000
50,000
400,000
350,000
300,000
250,000
Fixed expenses
7-18

19. Cost-Volume-Profit Graph
Dollars
600 700 800
Units
200 300 400 500
450,000
100
200,000
150,000
100,000
50,000
400,000
350,000
300,000
250,000
Fixed expenses
Break-even
point
7-19

20. Profit-Volume Graph
Some managers like the profit-volume
graph because it focuses on profits and volume.
`
100 200 300 400 500 600 700
Units
Profit
0
100,000
(20,000)
(40,000)
(60,000)
80,000
60,000
40,000
20,000
Break-even
point
7-20

21. Learning
Objective
4
Apply CVP analysis to
determine the effect on
profit from changes in
fixed expenses,
variable expenses,
sales prices, and sales
volume
7-21

22. Radford University - M. Chatham - Managerial Accounting
22
Contribution Margin Method
The contribution margin method is a
variation of the equation method.
Break-even point
in units sold
=
Fixed expenses
Contribution Margin per Unit
Break-even point
in total sales
dollars
=
Fixed expenses
Contribution Margin Ratio
But is any entrepreneur interested
in just breaking even?
+ Target Income
+ Target Income
Before-tax net profits

23. Target Net Profit
We can determine the number of surfboards
that Curl must sell to earn a profit of $100,000
using the contribution margin approach.
Fixed expenses + Target profit
Unit contribution margin
=
Units sold to earn
the target profit
$80,000 + $100,000
$200
= 900 surf boards
7-23

24. Equation Approach
Sales revenue – Variable expenses – Fixed expenses = Profit
($500 × X) ($300 × X)– – $80,000 = $100,000
($200X) = $180,000
X = 900 surf boards
7-24

25. Applying CVP Analysis
Safety Margin (or Margin of Safety)
• The difference between budgeted sales
revenue and break-even sales revenue.
• The amount by which sales can drop before
losses begin to be incurred.
7-25

26. Safety Margin
Curl, Inc. has a break-even point of $200,000.
If actual sales are $250,000, the safety margin is
$50,000 or 100 surf boards.
Break-even
sales
400 units
Actual sales
500 units
Sales 200,000$ 250,000$
Less: variable expenses 120,000 150,000
Contribution margin 80,000 100,000
Less: fixed expenses 80,000 80,000
Net income -$ 20,000$
7-26

27. i>clicker question
All other things (e.g., sales) remaining
constant, what will happen to the
margin of safety if fixed costs decrease?
a) it will grow larger
b) it will get smaller
c) it will remain unchanged
d) it depends…there is not enough
information to answer the question

28. Changes in Fixed Costs
• Curl is currently selling 500 surfboards per
year.
• The owner believes that an increase of
$10,000 in the annual advertising budget,
would increase sales to 540 units.
Should the company increase
the advertising budget?
7-28

29. Current
Sales
(500 Boards)
Proposed
Sales
(540 Boards)
Sales 250,000$ 270,000$
Less: variable expenses 150,000 162,000
Contribution margin 100,000$ 108,000$
Less: fixed expenses 80,000 90,000
Net income 20,000$ 18,000$
Changes in Fixed Costs
$80,000 + $10,000 advertising = $90,000
540 units × $500 per unit = $270,000
7-29

30. Current
Sales
(500 Boards)
Proposed
Sales
(540 Boards)
Sales 250,000$ 270,000$
Less: variable expenses 150,000 162,000
Contribution margin 100,000$ 108,000$
Less: fixed expenses 80,000 90,000
Net income 20,000$ 18,000$
Changes in Fixed Costs
Sales will increase by
$20,000, but net income
decreased by $2,000.
7-30

31. Changes in Unit
Contribution Margin
Because of increases in cost of raw materials,
Curl’s variable cost per unit has increased
from $300 to $310 per surfboard. With no
change in selling price per unit, what will be
the new break-even point?
($500 × X) ($310 × X)– – $80,000 = $0
X = 422 units (rounded)
7-31

32. Changes in Unit
Contribution Margin
Suppose Curl, Inc. increases the price of
each surfboard to $550. With no change
in variable cost per unit, what will be the
new break-even point?
($550 × X) ($300 × X)– – $80,000 = $0
X = 320 units
7-32

33. Predicting Profit Given Expected
Volume
Fixed expenses
Unit contribution margin
Target net profit
Find: {req’d sales volume}Given:
Fixed expenses
Unit contribution margin
Expected sales volume
Find: {expected profit}Given:
7-33

34. Predicting Profit Given
Expected Volume
In the coming year, Curl’s owner expects to sell
525 surfboards. The unit contribution margin is
expected to be $190, and fixed costs are
expected to increase to $90,000.
($190 × 525) – $90,000 = X
X = $9,750 profit
X = $99,750 – $90,000
Total contribution - Fixed cost = Profit
7-34

35. Learning
Objective
5 Compute the
break-even point
and prepare a
profit-volume
graph for a
multiproduct
enterprise
7-35

36. CVP Analysis with Multiple
Products
For a company with more than one product,
sales mix is the relative combination in which a
company’s products are sold.
Different products have different selling prices,
cost structures, and contribution margins.
Let’s assume Curl sells surfboards and sail
boards and see how we deal with break-
even analysis.
7-36

37. CVP Analysis with Multiple
Products
Curl provides us with the following
information:
Description
Selling
Price
Unit
Variable
Cost
Unit
Contribution
Margin
Number
of
Boards
Surfboards 500$ 300$ 200$ 500
Sailboards 1,000 450 550 300
Total sold 800
Description
Number
of Boards
% of
Total
Surfboards 500 62.5% (500 ÷ 800)
Sailboards 300 37.5% (300 ÷ 800)
Total sold 800 100.0%
7-37

38. CVP Analysis with Multiple
Products
Weighted-average unit contribution margin
Description
Contribution
Margin % of Total
Weighted
Contribution
Surfboards 200$ 62.5% 125.00$
Sailboards 550 37.5% 206.25
Weighted-average contribution margin 331.25$
$200 × 62.5%
$550 × 37.5%
7-38
Description
Number
of Boards
% of
Total
Surfboards 500 62.5% (500 ÷ 800)
Sailboards 300 37.5% (300 ÷ 800)
Total sold 800 100.0%

39. CVP Analysis with Multiple
Products
Break-even point
Break-even
point
=
Fixed expenses
Weighted-average unit contribution margin
Break-even
point
=
$170,000
$331.25
Break-even
point
= 514 combined unit sales
7-39

40. CVP Analysis with Multiple
Products
Break-even point
Break-even
point
= 514 combined unit sales
Description
Breakeven
Sales
% of
Total
Individual
Sales
Surfboards 514 62.5% 321
Sailboards 514 37.5% 193
Total units 514
7-40

41. Multiproduct Analysis
Rohr Watch Company
Model A Model B Total
Selling price $2,000 $3,000
Variable cost 800 1,200
Contribution margin $1,200 $1,800
Units produced and sold 4,000 2,000 6,000
Weight 4,000 / 6,000 2,000 / 6,000
Weighted average contribution margin is
[(2 × $1,200) + (1 × $1,800)]/3 = $1,400 per unit
Break-even is $3,500,000 / $1,400 = 2,500 units
Break-even is 2,500 × (4,000 / 6,000) = 1,667 Model A units (Whole units.)
Break-even is 2,500 × (2,000 / 6,000) = 834 Model B units (Whole units.)
Slide 7-41

42. i>clicker question
If, everything else being equal
(including sales), the sales mix changes
so that relatively less of a product with a
lesser contribution margin is sold?
a) net profits will increase
b) net profits will decrease
c) sales will increase and net profits will
remain unchanged
d) sales will decrease and net profits
will remain unchanged
e) not enough information provided!

43. Learning
Objective
6
List and discuss
the key
assumptions of
CVP analysis
7-43

44. Assumptions Underlying
CVP Analysis
1. Selling price is constant throughout
the entire relevant range.
2. Costs are linear over the relevant
range.
3. In multi-product companies, the
sales mix is constant.
4. In manufacturing firms, inventories
do not change (units produced =
units sold).
7-44

45. Learning
Objective
7
Prepare and
interpret a
contribution
income
statement
7-45

46. CVP Relationships and
the Income Statement
A. Traditional Format
Sales $500,000
Less: COGS 380,000
Gross margin $120,000
Less: Operating expenses:
Selling expenses $35,000
Administrative expenses 35,000 70,000
Net income $50,000
ACCUTIME COMPANY
Income Statement
For the Year Ended December 31, 20x1
7-46

47. CVP Relationships and the Income Statement
B. Contribution Format
Sales $500,000
Less: Variable expenses:
Variable manufacturing $280,000
Variable selling 15,000
Variable administrative 5,000 300,000
Contribution margin $200,000
Less: Fixed expenses:
Fixed manufacturing $100,000
Fixed selling 20,000
Fixed administrative 30,000 150,000
Net income $50,000
Income Statement
For the Year Ended December 31, 20x1
ACCUTIME COMPANY
7-47

48. Learning
Objective
8
Explain the role
of cost structure
and operating
leverage in CVP
relationships
7-48

49. Cost Structure and Operating
Leverage
• The cost structure of an organization is the
relative proportion of its fixed and variable
costs.
• Operating leverage is . . .
– the extent to which an organization uses fixed
costs in its cost structure.
– greatest in companies that have a high
proportion of fixed costs in relation to variable
costs.
7-49

50. Measuring Operating Leverage
Contribution margin
Net income
Operating leverage
factor =
Actual sales
500 Board
Sales 250,000$
Less: variable expenses 150,000
Contribution margin 100,000
Less: fixed expenses 80,000
Net income 20,000$
$100,000
$20,000
= 5
7-50

51. Measuring Operating Leverage
A measure of how a percentage change in
sales will affect profits. If Curl increases its
sales by 10%, what will be the percentage
increase in net income?
Percent increase in sales 10%
Operating leverage factor × 5
Percent increase in profits 50%
7-51

52. Measuring Operating Leverage
A firm with proportionately high fixed costs has
relatively high operating leverage. On the other
hand, a firm with high operating leverage has a
relatively high break-even point.
7-52

53. Radford University - M. Chatham - Managerial Accounting 53
CVP in Choosing a Cost
Structure
Cost structure refers to the relative proportion of
fixed and variable costs in an organization.
Bogside Farm and Sterling Farm are both in the
blueberry business. Bogside depends on migrant
workers to pick its berries, while Sterling uses
expensive picking machinery. Bogside has
higher variable costs, while Sterling has higher
fixed costs. Let’s look at the impact of cost
structures on the two companies.

54. Radford University - M. Chatham - Managerial Accounting 54
CVP in Choosing a Cost
Structure
Amount % Amount %
Sales 100,000$ 100% 100,000$ 100%
Less: Variable expenses 60,000 60% 30,000 30%
Contribution margin 40,000 40% 70,000 70%
Less: Fixed costs 30,000 60,000
Net operating income 10,000$ 10,000$
Bogside Farm Sterling Farm
Presented above is the current period’s financial
information for the two companies. Let’s see what
happens to income if each company experiences a
10% increase in sales revenue.

55. Radford University - M. Chatham - Managerial Accounting 55
CVP in Choosing a Cost
Structure
Amount % Amount %
Sales 110,000$ 100% 110,000$ 100%
Less: Variable expenses 66,000 60% 33,000 30%
Contribution margin 44,000 40% 77,000 70%
Less: Fixed costs 30,000 60,000
Net operating income 14,000$ 17,000$
Bogside Farm Sterling Farm
Sterling’s higher contribution margin leads to a
larger increase in net operating income.
Let’s look at the breakeven sales dollars for each
company.

56. Radford University - M. Chatham - Managerial Accounting
56
CVP in Choosing a Cost
Structure
Bogside has lower fixed expenses and is more
protected from a downturn in sales.
Bogside Sterling
Amount Amount
Fixed expenses 30,000$ 60,000$
Divided by: CM Ratio 40% 70%
Breakeven sales 75,000$ 85,714$

57. Radford University - M. Chatham - Managerial Accounting 57
Operating Leverage
Operating leverage is a measure of how sensitive net
operating income is to percentage changes in sales.
(Degree of)
Operating
Leverage
=
Contribution Margin
Net Operating Income

58. Learning
Objective
9
Understand the
implications of
activity-based
costing for CVP
analysis
7-58

59. CVP Analysis, Activity-Based Costing,
and Advanced Manufacturing Systems
An activity-based costing system can provide
a much more complete picture of cost-
volume-profit relationships and thus provide
better information to managers.
Break-even
point
= Fixed costs
Unit contribution margin
7-59

60. Learning
Objective
10
Be aware of the
effects of
advanced
manufacturing
technology on
CVP analysis
7-60

61. Overhead costs like setup, inspection, and
material handling are fixed with respect to
sales volume, but they are not fixed with
respect to other cost drivers.
This is the fundamental distinction between
a traditional CVP analysis and an activity-
based costing CVP analysis.
A Move Toward JIT and
Flexible Manufacturing
7-61

62. Learning
Objective
11
Understand the
effect of income
taxes on CVP
analysis
(appendix).
7-62

63. Radford University - M. Chatham - Managerial Accounting
Contribution Margin Method
The contribution margin method is a
variation of the equation method.
Break-even point
in units sold
=
Fixed expenses
Contribution Margin per Unit
Break-even point
in total sales
dollars
=
Fixed expenses
Contribution Margin Ratio
But is any entrepreneur interested
in just breaking even?
+ Target Income
+ Target Income
Before-tax net profits

64. Effect of Income Taxes
Target after-tax net income
1 - t
=
Before-tax
net income
Income taxes affect a company’s
CVP relationships. To earn a
particular after-tax net income, a
greater before-tax income will be
required.
7-64

65. Slide 4-65

66. End of Chapter 7
We made
it!
7-66
Congrats!!!
And good
luck with
the
homework!