1. Cost Behavior and Cost-Volume-Profit Analysis
Chapter 19
Student Version
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2. Classify costs as variable costs, fixed costs, or mixed costs.
Learning Objective 1
Classify costs as variable costs, fixed costs, or mixed costs.

3. LO 1
Cost Behavior
Cost behavior is the manner in which a cost changes as a related activity changes. Understanding the behavior of a cost depends on:
Identifying the activities that cause the cost to change, called activity bases (or activity drivers).
Specifying the range of activity over which the changes in the cost are of interest. This range of activity is called the relevant range.

4. LO 1
Variable Costs
Variable costs are costs that vary in proportion to changes in the level of activity.

5. LO 1
Variable Costs
Jason Sound
Jason Sound Inc. produces stereo systems. The parts for the stereo systems are purchased from suppliers for $10 per unit (a variable cost) and are assembled by Jason Sound Inc. For Model JS-12, the direct materials costs for the relevant range of 5,000 to 30,000 units of production are shown on the next slide.

6. LO 1
Variable Costs
Jason Sound

7. LO 1
Variable Costs
As shown in the previous slides, the variable costs have the following characteristics:
Cost per unit remains the same regardless of changes in the activity base.
Total cost changes in proportion to changes in the activity base.

8. LO 1
Fixed Costs
Fixed costs are costs that remain the same in total dollar amount as the activity base changes.

9. LO 1
Milton
Fixed Costs
Minton Inc. manufactures, bottles, and distributes perfume. The production supervisor is Jane Sovissi. She is paid $75,000 per year. The plant produces from 50,000 to 300,000 bottles of perfume.

10. The more units produced, the lower the fixed cost per unit.
Milton
Fixed Costs
The more units produced, the lower the fixed cost per unit.

11. Fixed Costs Fixed costs have the following characteristics:
Cost per unit changes inversely to changes in the activity base.
Total cost remains the same regardless of changes in the activity base.

12. LO 1
Mixed Costs
Mixed costs have characteristics of both a variable and a fixed cost. Mixed costs are sometimes called semivariable or semifixed costs.
Over one range of activity, the total mixed cost may remain the same. Over another range of activity, the mixed cost may change in proportion to changes in the level of activity.

13. LO 1
Mixed Costs
Simpson Inc. manufactures sails, using rented equipment. The rental charges are $15,000 per year, plus $1 for each machine hour used over 10,000 hours.

14. LO 1
Mixed Costs
The rental charges for various hours used within the relevant range of 8,000 hours to 40,000 hours are as follows:

15. LO 1
Mixed Costs
The high-low method is a cost estimation method that may be used to separate mixed costs into their fixed and variable components.

16. LO 1
Mixed Costs
kason
The Equipment Maintenance Department of Kason Inc. incurred the following costs during the past five months:

17. LO 1
Mixed Costs
kason
The number of units produced is the activity base, and the relevant range is the units produced between June and October. The next series of slides for Kason Inc. illustrate how the high-low method is used to determine the fixed and variable costs.

18. Mixed Costs LO 1 kason Production Total (Units) Cost
June 1,000 $45,550
July 1,500 52,000
August 2,100 61,500
September 1,800 57,500
October ,250
$61,500 – $41,250
Variable Cost per Unit =
= $15
2,100 – 750

19. LO 1
Mixed Costs
kason
The fixed cost is estimated by subtracting the total variable costs from the total costs for the units produced as shown below:
Fixed Cost = Total Costs – (Variable Cost per Unit x Units Produced)
Fixed Cost = $61,500 – ($15 x 2,100 units)
Fixed Cost = $61,500 – $31,500
Fixed Cost = $30,000

20. LO 1
Mixed Costs
kason
With fixed costs and variable costs estimated at $30,000 plus $15 per unit, a formula is in place to estimate production at any level. If the company is expected to produce 2,000 units in November, the estimated total cost would be calculated as follows:
Total Cost = ($15 x Units Produced) + $30,000
Total Cost = ($15 x 2,000) + $30,000
Total Cost = $30,000 + $30,000
Total Cost = $60,000

21. Learning Objective 2
Compute the contribution margin, the contribution margin ratio, and the unit contribution margin.

22. Cost-Volume-Profit Relationships
LO 2
Cost-Volume-Profit Relationships
Cost-volume-profit analysis is the examination of the relationships among selling prices, sales and production volume, costs, expenses, and profits.

23. Cost-Volume-Profit Relationships
LO 2
Cost-Volume-Profit Relationships
Some of the ways cost-volume-profit analysis may be used include:
Analyzing the effects of changes in selling prices on profits
Analyzing the effects of changes in costs on profits
(continued)

24. Cost-Volume-Profit Relationships
LO 2
Cost-Volume-Profit Relationships
Analyzing the effects of changes in volume on profits
Setting selling prices
Selecting the mix of products to sell
Choosing among marketing strategies

25. LO 2
Contribution Margin
Contribution margin is the excess of sales over variable costs, as shown in the formula below.
Contribution Margin = Sales – Variable Costs

26. Contribution Margin Assume the following data for Lambert, Inc.: LO 2

27. LO 2
Contribution Margin
Lambert

28. Contribution Margin Ratio
LO 2
Contribution Margin Ratio
The contribution margin ratio, sometimes called the profit-volume ratio, indicates the percentage of each sales dollar available to cover fixed costs and to provide income from operations. It is computed as follows:
Contribution Margin Ratio =
Contribution Margin
Sales

29. Contribution Margin Ratio
LO 2
Contribution Margin Ratio
Lambert
The contribution margin ratio is 40% for Lambert Inc., computed as follows:
Contribution Margin Ratio =
Contribution Margin
Sales
Contribution Margin Ratio =
$400,000
$1,000,000
Contribution Margin Ratio = 40%

30. Contribution Margin Ratio
LO 2
Contribution Margin Ratio
Lambert
If Lambert Inc. adds $80,000 in sales from the sale of an additional 4,000 units, its income will increase by $32,000, as computed below.
Change in Income from Operations
Change in Sales Dollars x Contribution Margin Ratio =
Change in Income from Operations
$80,000 x 40% = $32,000 =

31. Unit Contribution Margin
LO 2
Unit Contribution Margin
The unit contribution margin is useful for analyzing the profit potential of proposed decisions. The unit contribution margin is computed as follows:
Unit Contribution Margin =
Sales Price per Unit
Variable Cost per Unit –

32. Change in Income from Operations
LO 2
Unit Contribution Margin
The unit contribution margin is most useful when the increase or decrease in sales volume is measured in sales units (quantities).
The change in income from operations can be determined using the following formula:
Change in Income from Operations
Change in Sales Units = x
Unit Contribution Margin

33. Unit Contribution Margin
LO 2
Unit Contribution Margin
Lambert
Lambert Inc.’s sales could be increased by 15,000 units, from 50,000 to 65,000 units. Lambert’s income from operations would increase by $120,000 (15,000 x $8), as shown below.
Change in Income from Operations
Change in Sales Units = x
Unit Contribution Margin
Change in Income from Operations =
15,000 units x $8 = $120,000

34. Learning Objective 3
Determine the break-even point and sales necessary to achieve a target profit.

35. LO 3
Break-Even Point
The break-even point is the level of operations at which a company’s revenues and expenses are equal.

36. Break-Even Point Baker
LO 3
Break-Even Point
Baker
Assume the following data for Baker Corporation:
Fixed costs $90,000
Unit selling price $25
Unit variable cost 15
Unit contribution margin $10

37. Unit Contribution Margin
LO 3
Break-Even Point
Baker
The break-even point (in sales units) is calculated using the following equation:
Break-Even Sales (units) =
Fixed Costs
Unit Contribution Margin
Break-Even Sales (units) =
$90,000
$10
Break-Even Sales (units) = 9,000 units

38. Contribution Margin Ratio
LO 3
Break-Even Point
Baker
The break-even point (in sales dollars) is calculated using the following equation:
Break-Even Sales (dollars) =
Fixed Costs
Contribution Margin Ratio
$90,000
.40
Break-Even Sales (dollars) =
$10
$25
Break-Even Sales (dollars) = $225,000

39. Effect of Changes in Fixed Costs
LO 3
Effect of Changes in Fixed Costs
Bishop Co. is evaluating a proposal to budget an additional $100,000 for advertising. The data for Bishop Co. are as follows:

40. Unit Contribution Margin
LO 3
Effect of Changes in Fixed Costs
Break-Even Sales (units) =
Fixed Costs
Unit Contribution Margin
Without additional advertising:
Break-Even Sales (units) =
$600,000
$20 =
30,000 units
With additional advertising:
Break-Even Sales (units) =
$700,000
$20 =
35,000 units

41. Effect of Changes in Unit Variable Costs
LO 3
Effect of Changes in Unit Variable Costs
Park Co. is evaluating a proposal to pay an additional 2% commission on sales to its salespeople (a variable cost) as an incentive to increase sales. Fixed costs are estimated at $840,000. The other data for Park Co. are as follows:

42. Unit Contribution Margin
LO 3
Effect of Changes in Unit Variable Costs
Break-Even Sales (units) =
Fixed Costs
Unit Contribution Margin
Without additional 2% commission:
Break-Even Sales (units) =
$840,000
$105 =
8,000 units
With additional 2% commission:
Break-Even Sales (units) =
$840,000
$100 =
8,400 units
$250 – [$145 + ($250 x 2%)] = $100

43. Effect of Changes in Unit Selling Price
LO 3
Effect of Changes in Unit Selling Price
Graham Co. is evaluating a proposal to increase the unit selling price of a product from $50 to $60. The estimated fixed costs are $600,000. The following additional data have been gathered:

44. Unit Contribution Margin
LO 3
Effect of Changes in Unit Selling Price
Fixed Costs
Unit Contribution Margin
Break-Even Sales (units) =
Without price increase:
Break-Even Sales (units) =
$600,000
$20 =
30,000 units
With price increase:
Break-Even Sales (units) =
$600,000
$30 =
20,000 units

45. Target Profit Assume the following data for Waltham Co.:
What would be the necessary sales to earn the target profit of $100,000?

46. Fixed Costs + Target Profit Unit Contribution Margin
LO 3
Target Profit
WALTHAM
Sales (units) =
Fixed Costs + Target Profit
Unit Contribution Margin
Sales (units) =
$200,000 + $100,000
$30
Sales (units) = 10,000 units

47. Unit Contribution Margin
LO 3
Target Profit
WALTHAM
Unit Contribution Margin
Unit Selling Price
Contribution Margin Ratio =
Contribution Margin Ratio =
$30
$75
Contribution Margin Ratio =
40%
Sales (dollars) =
Fixed Costs + Target Profit
Contribution Margin Ratio
Sales (dollars) =
$200,000 + $100,000
40%
= $750,000
Necessary sales to earn a $100,000 target profit

48. Learning Objective 4
Using a cost-volume-profit chart and a profit-volume chart, determine the break-even point and sales necessary to achieve a target profit.

49. Cost-Volume-Profit (Break-Even) Chart
LO 4
Cost-Volume-Profit (Break-Even) Chart
A cost-volume-profit chart, sometimes called a break-even chart, graphically shows sales, costs, and the related profit or loss for various levels of units sold.

50. Units of Sales (in thousands)
LO 4
LO 4
Cost-Volume-Profit (Break-Even) Chart
Cost-Volume-Profit (Break-Even) Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Break-even Point
Sales and Costs (in thousands)
Units of Sales (in thousands)
The point where the revenue (blue) line and the total costs (orange) line intersect is the break-even point.
(continued)

51. Units of Sales (in thousands)
LO 4
LO 4
Cost-Volume-Profit (Break-Even) Chart
Cost-Volume-Profit (Break-Even) Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Break-even Point
Sales and Costs (in thousands)
Units of Sales (in thousands)
For this chart, the break-even is sales of 5,000 units or $250,000.

52. Units of Sales (in thousands)
LO 4
LO 4
Cost-Volume-Profit (Break-Even) Chart
Cost-Volume-Profit (Break-Even) Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Operating Loss Area
Break-even Point
Sales and Costs (in thousands)
Operating Profit Area
Units of Sales (in thousands)

53. LO 4
LO 4
Profit-Volume Chart
Another graphic approach to cost-volume-profit analysis, the profit-volume chart, plots only the difference between total sales and total costs (or profits). The following data are used:
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

54. LO 4
LO 4
Profit-Volume Chart
The maximum operating loss is equal to the fixed costs of $100,000. Assuming that the maximum unit sales within the relevant range is 10,000 units, the maximum operating profit is $100,000, as shown below.
Maximum profit

55. LO 4
LO 4
Profit-Volume Chart

56. Revised Maximum profit
LO 4
LO 4
Profit-Volume Chart
Assume that an increase in fixed costs of $20,000 is to be evaluated. The maximum operating profit would be $80,000, as shown below:
Sales (10,000 units x $50) $500,000
Variable costs (10,000 units x $30) 300,000
Contribution margin (10,000 units x $20) $200,000
Fixed costs 120,000
Operating profit $ 80,000
Revised Maximum profit

57. LO 4
LO 4
Profit-Volume Chart
(continued)
Units of Sales

58. LO 4
LO 4
Profit-Volume Chart

59. Assumptions of Cost-Volume-Profit Analysis
LO 4
Assumptions of Cost-Volume-Profit Analysis
The primary assumptions are as follows:
Total sales and total costs can be represented by straight lines.
Within the relevant range of operating activity, the efficiency of operations does not change.
Costs can be divided into fixed and variable components.
The sales mix is constant.
There is no change in the inventory quantities during the period.

60. Learning Objective 5
Compute the break-even point for a company selling more than one product, the operating leverage, and the margin of safety.

61. Sales Mix Considerations
LO 5
Sales Mix Considerations
Many companies sell more than one product at different selling prices. In addition, the products normally have different unit contribution margins.
The sales mix is the relative distribution of sales among the various products sold by a company.

62. Sales Mix Considerations CASCADE
LO 5
Sales Mix Considerations
CASCADE
Cascade Company sold Products A and B during the past year as follows:

63. Sales Mix Considerations CASCADE
LO 5
Sales Mix Considerations
CASCADE
It is useful to think of the individual products as components of one overall enterprise product. For Cascade Company, the overall enterprise product is called E. The unit selling price, unit variable cost, and unit contribution margin for E are computed as follows:

64. Unit Contribution Margin
LO 5
Sales Mix Considerations
CASCADE
Fixed Costs
Unit Contribution Margin
Break-Even Sales (units) =
Break-Even Sales (units) =
$200,000
$25
Break-Even Sales (units) = 8,000 units

65. Sales Mix Considerations CASCADE
LO 5
Sales Mix Considerations
CASCADE
Break-even point

66. Income from Operations
LO 5
Operating Leverage
The relationship of a company’s contribution margin to income from operations is measured by operating leverage. A company’s operating leverage is computed as follows:
Contribution Margin
Income from Operations
Operating Leverage =

67. LO 5
Operating Leverage
Both companies have the same contribution margin.

68. Income from Operations
LO 5
LO 5
Operating Leverage
Operating Leverage 5
Jones Inc.:
Contribution Margin
Income from Operations
$100,000
$20,000
= 5

69. Income from Operations
LO 5
LO 5
Operating Leverage
Operating Leverage 5 2
Wilson Inc.:
Contribution Margin
Income from Operations
$100,000
$50,000
= 2

70. Percent Change in Sales
LO 5
LO 5
Operating Leverage
Operating Leverage
Operating leverage can be used to measure the impact of changes in sales on income from operations. This measure can be computed as follows:
Percent Change in Income from Operations
Percent Change in Sales
Operating Leverage = x

71. Operating Leverage Operating Leverage Jones Inc.: Wilson Inc.:
LO 5
LO 5
Operating Leverage
Operating Leverage
Assume that sales increased 10%, or $40,000 ($400,000 x 10%), for Jones Inc. and Wilson Inc.
Percent Change in Income from Operations =
Jones Inc.:
10% x 5 = 50%
Percent Change in Income from Operations =
Wilson Inc.:
10% x 2 = 20%

72. Operating Leverage Operating Leverage LO 5 LO 5
50% increase ($10,000/$20,000)

73. Operating Leverage Operating Leverage LO 5 LO 5
20% increase ($10,000/$50,000)

74. Operating Leverage Operating Leverage
LO 5
LO 5
Operating Leverage
Operating Leverage
The impact of a change in sales on income from operations for companies with high and low operating leverage can be summarized as follows:

75. LO 5
LO 5
Margin of Safety
The margin of safety indicates the possible decrease in sales that may occur before an operating loss results.
The margin of safety may be expressed in the following ways:
Dollars of sales
Units of sales
Percent of current sales

76. Sales – Sales at Break-Even Point
LO 5
LO 5
Margin of Safety
If sales are $250,000, the unit selling price is $25, and the sales at the break-even point are $200,000, the margin of safety is 20%, computed as follows:
Margin of Safety =
Sales – Sales at Break-Even Point
Sales
Margin of Safety =
$250,000 – $200,000
$250,000
Margin of Safety = 20%

77. Cost Behavior and Cost-Volume-Profit Analysis
The End