1. Questions Addressed by Cost-Volume-Profit Analysis
CVP analysis is used to answer questions such as:
How many coffees must Starbucks sell in a store to break even?
How many coffees must Starbucks sell in order to make $10,000 at a store?
What is the change in income if selling prices decline and sales volume increases?
How much does income increase if we install a new machine to reduce labor costs?
What is the income effect if we change the sales mix of our products or services?
18-1

2. C1
Cost Behavior Summary
18-2

3. C1
Mixed Costs
Mixed costs contain a fixed portion that is incurred even when the facility is unused, and a variable portion that increases with usage.
Example: monthly electric utility charge
Fixed service fee
Variable charge per kilowatt hour used
18-3

4. Step-Wise Costs Cost Activity C1
Total cost remains constant within a narrow range of activity.
Example: Adding a supervisor for each 10 new workers.
Another type of cost is referred to as a step cost. Step costs remain constant in total within a relatively narrow range of activity.
Cost
Activity

5. Curvilinear Costs
Also called a nonlinear cost, it increases at a NON-constant rate as volume increases.
A linear cost increases at a constant rate (variable costs)
Example: adding hourly workers. The first few increase output because they can specialize more, but too many starts to slow communications and crowd a work space.

6. Total Variable Cost Graph Unit Variable Cost Graph
Variable Costs
Total Variable Cost Graph
Unit Variable Cost Graph
$300,000
$250,000
$200,000
$150,000
$100,000
$50,000
$20
$15
$10 $5
Total Costs
Cost per Unit
Units Produced (000)
Units Produced (000)
Units Total Cost
Produced Cost per Unit
5, $ 50,000 $10
10, ,
15, ,
20, ,
25, ,
30, ,

7. Total Variable Cost Graph Unit Variable Cost Graph
Variable Costs
Total Variable Cost Graph
Unit Variable Cost Graph
$300,000
$250,000
$200,000
$150,000
$100,000
$50,000
$20
$15
$10 $5
Total Costs
Cost per Unit
Units Produced (000)
Units Produced (000)
Units Total Cost
Produced Cost per Unit
5, $ 50,000 $10
10, ,
15, ,
20, ,
25, ,
30, ,

8. Total Variable Cost Graph Unit Variable Cost Graph
Variable Costs
Total Variable Cost Graph
Unit Variable Cost Graph
$300,000
$250,000
$200,000
$150,000
$100,000
$50,000
$20
$15
$10 $5
Total Costs
Cost per Unit
Units Produced (000)
Units Produced (000)
Units Total Cost
Produced Cost per Unit
5, $ 50,000 $10
10, ,
15, ,
20, ,
25, ,
30, ,

9. Fixed Costs Total Fixed Cost Graph Unit Fixed Cost Graph $150,000
$125,000
$100,000
$75,000
$50,000
$25,000
$1.50
$1.25
$1.00
$.75
$.50
$.25
Total Costs
Cost per Unit
Units Produced (000)
Units Produced (000)
Units Total Cost
Produced Cost per Unit
50, $75,000 $1.500
100, ,
150, ,
200, ,
250, ,
300, ,

10. Fixed Costs Total Fixed Cost Graph Unit Fixed Cost Graph $150,000
$125,000
$100,000
$75,000
$50,000
$25,000
$1.50
$1.25
$1.00
$.75
$.50
$.25
Total Costs
Cost per Unit
Units Produced (000)
Units Produced (000)
Units Total Cost
Produced Cost per Unit
50, $75,000 $1.500
100, ,
150, ,
200, ,
250, ,
300, ,

11. Fixed Costs Total Fixed Cost Graph Unit Fixed Cost Graph $150,000
$125,000
$100,000
$75,000
$50,000
$25,000
$1.50
$1.25
$1.00
$.75
$.50
$.25
Total Costs
Cost per Unit
Units Produced (000)
Units Produced (000)
Units Total Cost
Produced Cost per Unit
50, $75,000 $1.500
100, ,
150, ,
200, ,
250, ,
300, ,

12. Mixed Costs Total Mixed Cost Graph
$40,000
$35,000
$30,000
$25,000
$20,000
$15,000
$10,000
$5,000
Mixed costs are sometimes called semivariable or semifixed costs.
Total Costs
Mixed costs are usually separated into their fixed and variable components for management analysis.
Total Machine Hours (000)

13. Variable Costs Fixed Costs
Total Variable Costs
Total Fixed Costs
Total Costs
Total Costs
Total Units Produced
Total Units Produced
Unit Fixed Costs
Unit Variable Costs
Per Unit Cost
Per Unit Cost
Total Units Produced
Total Units Produced

14. regardless of activity level.
Variable Costs
Fixed Costs
Total Variable Costs
Total Fixed Costs
Used for planning.
Remains the same
regardless of activity level.
Total Costs
Total Costs
$75,000
total
Total Units Produced
Total Units Produced
Unit Fixed Costs
Unit Variable Costs
Per Unit Cost
Per Unit Cost
$10 per unit
Total Units Produced
Total Units Produced

15. Step-Wise Costs Cost Activity C1
Total cost remains constant within a narrow range of activity.
Example: Adding a supervisor for each 10 new workers.
Another type of cost is referred to as a step cost. Step costs remain constant in total within a relatively narrow range of activity.
Cost
Activity

16. Curvilinear Costs
Also called a nonlinear cost, it increases at a NON-constant rate as volume increases.
A linear cost increases at a constant rate (variable costs)
Example: adding hourly workers. The first few increase output because they can specialize more, but too many starts to slow communications and crowd a work space.

17. Contribution Margin helps us figure out:
How many coffees must Starbucks sell in a store to break even?
How many coffees must Starbucks sell in order to make $10,000 at a store?
What is the change in income if selling prices decline and sales volume increases?
How much does income increase if we install a new machine to reduce labor costs?
What is the income effect if we change the sales mix of our products or services?
18-17

18. Contribution Margin Income Statement
The contribution margin is available to cover the fixed costs and income from operations.
Total
Sales (50,000 units) $1,000,000
Variable costs ,000
Contribution margin $400,000
Fixed costs ,000
Income from operations$100,000
Variable costs
Sales
Fixed costs
Income from operations

19. Contribution Margin Income Statement
Total Per Unit Percent/Ratio
Sales (50,000 units) $1,000,000 $ %
Variable costs , %
Contribution margin $400,000 $ %
Fixed costs ,000
Income from operations $100,000
The statement can be extended to include per unit dollars and percentage numbers.

20. Contribution Margin Income Statement
Total Per Unit Percent/Ratio
Sales (50,000 units) $1,000,000 $ %
Variable costs , %
Contribution margin $400,000 $ %
Fixed costs ,000
Income from operations $100,000
The statement can be extended to include per unit dollars and percentage numbers.

21. Contribution Margin Income Statement
Total Per Unit Percent/Ratio
Sales (50,000 units) $1,000,000 $ %
Variable costs , %
Contribution margin $400,000 $ %
Fixed costs ,000
Income from operations $100,000
Income
from
operations
Variable
costs
Fixed
costs
Sales = + +
Variable
costs
Contribution
margin
Sales – =

22. Contribution Margin Income Statement
Total Per Unit Percent/Ratio
Sales (50,000 units) $1,000, $ %
Variable costs , %
Contribution margin $400,000 $ %
Fixed costs ,000
Income from operations $100,000
Unit Contribution Margin
Contribution Margin Ratio
The contribution margin can be expressed three ways:
1. Total contribution margin in dollars.
2. Unit contribution margin (dollars per unit).
3. Contribution margin ratio (percentage).

23. Calculating the Break-Even Point
Total Per Unit Percent
Sales (???? units) ? $ %
Variable costs ? %
Contribution margin $300,000 $ %
Fixed costs ,000
Income from operations $
At the break-even point, fixed costs and the contribution margin are equal.

24. Calculating the Break-Even Point Divide by either: $8 per unit or 40%
Total Per Unit Percent
Sales (???? units) ? $ %
Variable costs ? %
Contribution margin $ 300,000 $ %
Fixed costs ,000
Income from operations $ / or
Divide by either: $8 per unit or 40%
Break-even
sales
Fixed
costs
Contribution
margin = /

25. Calculating the Break-Even Point
Total Per Unit Percent
Sales (???? units) ? $ %
Variable costs ? %
Contribution margin $ 300,000 $ %
Fixed costs ,000
Income from operations $  or
Break-even
sales
Fixed
costs
Contribution
Margin per unit = /
What is the break-even sales in units?

26. Calculating the Break-Even Point
Total Per Unit Percent
Sales (????? units) ? $ %
Variable costs ? %
Contribution margin $ 300,000 $ %
Fixed costs ,000
Income from operations $ / or
Break-even
sales
Fixed
costs
Contribution
margin = /
Break-even sales = $300,000 / $8 = 37,500 units
What is the break-even sales in dollars?

27. Calculating the Break-Even Point
Total Per Unit Percent
Sales (????? units) ? $ %
Variable costs ? %
Contribution margin $ 300, $ %
Fixed costs ,000
Income from operations $ / or
Break-even
sales
Fixed
costs
Contribution
margin = /
Break-even sales = $300,000 / $8 = 37,500 units
Break-even sales = $300,000 / 40% = $750,000

28. Computing Sales for a Target Income
Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income.
Fixed costs + Target income
Unit sales =
Contribution margin per unit
Fixed costs + Target income
Dollar sales =
Contribution margin ratio
18-28

29. Calculating a Planned Sales Level
Total Per Unit Percent
Sales (50,000 units) ? $ %
Variable costs ? %
Contribution margin $ 400,000 $ %
Fixed costs ,000
Income from operations $ 100,000 / or
Planned
sales
Contribution
margin
Fixed Target costs profit + = /
Fixed costs plus the target profit equals the required total contribution margin.

30. Calculating a Planned Sales Level
Total Per Unit Percent
Sales (50,000 units) ? $ %
Variable costs ? %
Contribution margin $ 400,000 $ %
Fixed costs ,000
Income from operations $ 100,000 / or
Planned
sales
Fixed Target
costs profit
Contribution
margin + = /
$8 per unit or 40%

31. Calculating a Planned Sales Level
Sales (????? units) ? $ %
Variable costs ? %
Contribution margin $ 400, $ %
Fixed costs ,000
Income from operations $ 100,000
Total Per Unit Percent / or
Planned
sales
Fixed Target
costs profit
Contribution
margin + = /
What is the planned sales level in units?

32. Calculating a Planned Sales Level
Sales (????? units) ? $ %
Variable costs ? %
Contribution margin $ 400, $ %
Fixed costs ,000
Income from operations $ 100,000
Total Per Unit Percent / or
Planned
sales
Fixed Target
costs profit
Contribution
margin + = /
Planned sales = ($300,000 + $100,000) / $8 = 50,000 units
What is the planned sales level in dollars?

33. Calculating a Planned Sales Level
Total Per Unit Percent
Sales (50,000 units) $1,000, $ %
Variable costs , %
Contribution margin $ 400, $ %
Fixed costs ,000
Income from operations $ 100,000 / or
Planned
sales
Fixed Target
costs profit
Contribution
margin = + /
Planned sales = ($300,000 + $100,000) / $8 = 50,000 units
Planned sales = ($300,000 + $100,000) / 40% = $1,000,000
$1,000,000

34. How do taxes impact our analysis?
THINK:
Taxes come out of profits, reducing our profits.
Taxes are typically stated as a percent of our profits/income.
Must listen carefully and read carefully, are we asked for a target income or a target “pre-tax” income or a target “after-tax” income ?
Which requires higher sales: 1)a target income of $100,000 or 2) a target “pre-tax” income of $100,000 or a target “after-tax” income of $100,000? Assume a 40% tax rate. Explain, show calculations:

35. How do taxes impact our analysis?
Which is a larger number: 1)a target income of $100,000 or 2) a target “pre-tax” income of $100,000 or a target “after-tax” income of $100,000? Assume a 40% tax rate. Explain, show calculations.
A target income and “pre-tax” income are the same thing, we don’t factor in taxes.
A target “after-tax” income of $100,000 means we have to earn more than $100,000 because that is what we want after we have paid our taxes.
Pre-tax income = After-tax income/(100% - tax rate)
Pre-tax income = $100,000 / (100% - 40%)
Pre-tax income = $100,000 / 60%
Pre-tax income = $166,666
Proof: = $166,666 X 40% = gives us taxes due
Taxes due = $ 66,666
Income after tax = $100,000

36. Sales Mix – Weighted Average
Contribution margin
Products
A B
Sales $ 90 $140
Variable costs
Contribution margin $ 20 $ 45
Sales mix % 20%
What is the average contribution for each product?

37. Sales Mix – Weighted Average
Contribution margin
Products
A B
Sales $ 90 $140
Variable costs
Contribution margin $ 20 $ 45
Sales mix x 80% x 20%
Product contribution $ 16 $ 9
STEP ONE: What is the total product contribution?

38. Sales Mix – Weighted Average
Contribution margin
Products
A B
Sales $ $140
Variable costs
Contribution margin $ $ 45
Sales mix x 80% x 20%
Product contribution $ $ 9
Total product contribution $ 25
(weighted average)
The pure average is: $32.50 ($20+$45) / 2
We don’t use this because we aren’t selling products on a 1:1 basis.

39. Sales Mix – Weighted Average
Contribution margin
Products
A B
Sales $ $140
Variable costs
Contribution margin $ $ 45
Sales mix x 80% x 20%
Product contribution $ $ 9
Total product contribution $ 25
Step Two: Treat the “total product contribution” as if it were the CONTRIBUTION margin of a single product and CALCULATE BREAK EVEN

40. Sales Mix – Weighted Average
Contribution margin
Products
A B
Sales $ $140
Variable costs
Contribution margin $ $ 45
Sales mix x 80% x 20%
Product contribution $ $ 9
Total product contribution $ 25
Beak-even sales units
Total fixed costs $200,000
Product contribution $25
What is the break-even sales units?

41. Sales Mix – Weighted Average
Contribution margin
Products
A B
Sales $ 90 $140
Variable costs
Contribution margin $ 20 $ 45
Sales mix x 80% x 20%
Product contribution $ 16 $ 9
Total product contribution $ 25
Break-even sales units
Total fixed costs $200,000
Product contribution $25
STEP 3: this is the total units of A and B combined. Need to calculate how many of A & B need to be sold, based on original sales mix of 80% & 20%.
= 8,000 units

42. Sales Mix – Weighted Average
Contribution margin
Products
A B
Sales $ 90 $140
Variable costs
Contribution margin $ 20 $ 45
Sales mix x 80% x 20%
Product contribution $ 16 $ 9
Total product contribution $ 25
Break-even sales units
Total fixed costs $200,000
Product contribution $25
Break-even sales units ,000
Product A units (80%) ,400
Product B units (20%) ,600
= 8,000 units

43. Operating Leverage Contribution margin Operating income
Operating leverage is a measure of the relative mix of variable costs and fixed costs and tells us how sensitive operating income is to changes in sales. High leverage = higher increase in income from increased sales.
Jones Inc Wilson Inc.
Sales $400, $400,000
Variable costs , ,000
Contribution margin $100, $100,000
Fixed costs , ,000
Income from operations $20,000 $ 50,000

44. Both companies have the same contribution margin.
Operating Leverage
Contribution margin
Operating income
Operating leverage is a measure of the relative mix of variable costs and fixed costs.
Jones Inc Wilson Inc.
Sales $400, $400,000
Variable costs , ,000
Contribution margin $100, $100,000
Fixed costs , ,000
Income from operations $20,000 $ 50,000 A
Both companies have the same contribution margin.

45. What is the operating leverage?
Contribution margin
Operating income
Operating leverage is a measure of the relative mix of variable costs and fixed costs.
Jones Inc Wilson Inc.
Sales $400, $400,000
Variable costs , ,000
Contribution margin $100, $100,000
Fixed costs , ,000
Income from operations $20,000 $ 50,000
Operating leverage (A/B) A B
What is the operating leverage?

46. What do these numbers mean?
Operating Leverage
Contribution margin
Operating income
Operating leverage is a measure of the relative mix of variable costs and fixed costs.
Jones Inc Wilson Inc.
Sales $400, $400,000
Variable costs , ,000
Contribution margin $100, $100,000
Fixed costs , ,000
Income from operations $20,000 $ 50,000
Operating leverage (A/B) A B
What do these numbers mean?

47. Operating Leverage Contribution margin Operating income
Operating leverage is a measure of the relative mix of variable costs and fixed costs and tells us how sensitive operating income is to changes in sales. High leverage = higher increase in income from increased sales.
Jones Inc Wilson Inc.
Sales $400, $400,000
Variable costs , ,000
Contribution margin $100, $100,000
Fixed costs , ,000
Income from operations $20,000 $ 50,000
Operating leverage (A/B)
This tells us that, if sales increase 10% for both companies, we can expect a 50% and 20% increase in operating income, respectively. A B

48. Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Sales and Costs ($000)
Units of Sales (000)
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

49. Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Sales and Costs ($000)
60%
Variable Costs
Units of Sales (000)
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

50. Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Contribution Margin
40%
Sales and Costs ($000)
60%
Variable Costs
Units of Sales (000)
100%
60%
40%
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

51. Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Total Costs
Sales and Costs ($000)
Fixed Costs
Variable Costs
Units of Sales (000)
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

52. Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Total Costs
Sales and Costs ($000)
Units of Sales (000)
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

53. Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Operating Profit Area
Total Costs
Sales and Costs ($000)
Operating Loss Area
Units of Sales (000)
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

54. Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Total Costs
Sales and Costs ($000)
Break-Even Point
Units of Sales (000)
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

55. Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Total Costs
Sales and Costs ($000)
Break-Even Point
Units of Sales (000)
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $20
Total fixed costs $100,000
$100,000
$20
= 5,000 units

56. Cost-Volume-Profit Chart (Break-Even)
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Operating Profit Area
Total Costs
Sales and Costs ($000)
Break-Even Point
Operating Loss Area
Units of Sales (000)
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000
$100,000
$20
= 5,000 units

57. Revised Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Total Sales
Operating Profit Area
Total Costs
Sales and Costs ($000)
Revised Break-Even Point
Operating Loss Area
Units of Sales (000)
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $80,000
$80,000
$20
= 4,000 units

58. Profit-Volume Chart Relevant range is 10,000 units.
$100
$75
$50
$25
$ 0
$(25)
$(50)
$(75)
$(100)
Operating Profit
(Loss) $000’s
Relevant range is 10,000 units.
Units of Sales (000’s)
Sales (10,000 units x $50) $500,000
Variable costs (10,000 units x $30) ,000
Contribution margin (10,000 units x $20) $200,000
Fixed costs ,000
Operating profit $100,000

59. Profit-Volume Chart Maximum profit within the relevant range.
$100
$75
$50
$25
$ 0
$(25)
$(50)
$(75)
$(100)
Operating Profit
(Loss) $000’s
Maximum profit within the relevant range.
Units of Sales (000’s)
Maximum loss is equal to the total fixed costs.
Sales (10,000 units x $50) $500,000
Variable costs (10,000 units x $30) ,000
Contribution margin (10,000 units x $20) $200,000
Fixed costs ,000
Operating profit $100,000

60. Profit-Volume Chart Sales (10,000 units x $50) $500,000
$100
$75
$50
$25
$ 0
$(25)
$(50)
$(75)
$(100)
Profit Line
Operating
Profit
Operating Profit
(Loss) $000’s
Operating
Loss
Units of Sales (000’s)
Sales (10,000 units x $50) $500,000
Variable costs (10,000 units x $30) ,000
Contribution margin (10,000 units x $20) $200,000
Fixed costs ,000
Operating profit $100,000

61. Profit-Volume Chart Sales (10,000 units x $50) $500,000
$100
$75
$50
$25
$ 0
$(25)
$(50)
$(75)
$(100)
Profit Line
Operating
Profit
Operating Profit
(Loss) $000’s
Operating
Loss
Break-Even Point
Units of Sales (000’s)
Sales (10,000 units x $50) $500,000
Variable costs (10,000 units x $30) ,000
Contribution margin (10,000 units x $20) $200,000
Fixed costs ,000
Operating profit $100,000