1. Cost Behavior and Cost-Volume-Profit Analysis
Chapter 21
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2. 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.
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.

5. LO 1
Variable Costs

6. 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.

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

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

9. 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.

10. 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.

11. 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. The rental charges for various hours used within the relevant range of 8,000 hours to 40,000 hours are as follows:

12. 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.

13. LO 1
Mixed Costs
The Equipment Maintenance Department of Kason Inc. incurred the costs shown in the chart below during the past five months. We will demonstrate how to use the high-low method to determine variable cost per unit and total fixed cost.

14. Difference in Total Cost Difference in Production
LO 1
Mixed Costs
Production Total
(Units) Cost
Actual costs incurred
June 1,000 $45,550
July 1,500 52,000
August 2,100 61,500
September 1,800 57,500
October ,250
Variable Cost per Unit =
Difference in Total Cost
Difference in Production
First, select the highest and lowest levels of activity and note their related total cost.

15. Mixed Costs LO 1 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
Next, we fill in and solve the formula.
Variable Cost per Unit =
$61,500 – $41,250
2,100 – 750
Variable Cost per Unit = $15

16. LO 1
Mixed Costs
Finally, we calculate total fixed cost by using either the high end or low end of the formula. We will use the high end for this illustration. The company produced 2,100 units at a cost of $61,500 at the highest level of production.
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 = $30,000

17. Learning Objective 2
Classify costs as variable costs, fixed costs, or mixed costs.
Compute the contribution margin, the contribution margin ratio, and the unit contribution margin.

18. 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.

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

20. 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

21. 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

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

23. 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

24. Contribution Margin Ratio
LO 2
Contribution Margin Ratio
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%

25. Contribution Margin Ratio
LO 2
Contribution Margin Ratio
100%
60%
40%
30%
10%
Contribution Margin Ratio =
Sales – Variable Costs
Sales
$1,000,000 – $600,000
$1,000,000
Contribution Margin Ratio =
Contribution Margin Ratio =
40%

26. Contribution Margin Ratio
LO 2
Contribution Margin Ratio
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 =

27. 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 –

28. 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

29. Unit Contribution Margin
LO 2
Unit Contribution Margin
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

30. Unit Contribution Margin
LO 2
Unit Contribution Margin
Lambert Inc.’s contribution margin income statement, shown below, confirms that income increased to $220,000 when 65,000 units are sold.

31. Learning Objective 3
Classify costs as variable costs, fixed costs, or mixed costs.
Compute the contribution margin, the contribution margin ratio, and the unit contribution margin.
Determine the break-even point and sales necessary to achieve a target profit.

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

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

34. Unit Contribution Margin
LO 3
Break-Even Point
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

35. LO 3
Break-Even Point
Income from operations is zero when 9,000 units are sold—hence, the break-even point is 9,000 units.

36. Contribution Margin Ratio
LO 3
Break-Even Point
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

37. 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:

38. 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

39. 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:

40. 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

41. 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:

42. 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

43. LO 3
Target Profit
The sales volume required to earn a target profit is determined by modifying the break-even equation.
Sales (units) =
Fixed Costs + Target Profit
Unit Contribution Margin

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

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

46. Unit Contribution Margin
LO 3
Target Profit
Unit Contribution Margin
Unit Selling Price
Contribution Margin Ratio =
Contribution Margin Ratio =
$30
$75
From an earlier slide
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

47. Learning Objective 4
Classify costs as variable costs, fixed costs, or mixed costs.
Compute the contribution margin, the contribution margin ratio, and the unit contribution margin.
Determine the break-even point and sales necessary to achieve a target profit.
Using a cost-volume-profit chart and a profit-volume chart, determine the break-even point and sales necessary to achieve a target profit.

48. 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.

49. Cost-Volume-Profit (Break-Even) Chart
LO 4
LO 4
Cost-Volume-Profit (Break-Even) Chart
Cost-Volume-Profit (Break-Even) Chart

50. Cost-Volume-Profit (Break-Even) Chart
LO 4
LO 4
Cost-Volume-Profit (Break-Even) Chart
Cost-Volume-Profit (Break-Even) Chart
A proposal to reduce fixed costs by $20,000 is to be evaluated. The cost-volume-profit chart in Exhibit 6 (next slide) was designed to assist in this evaluation. Note that the total costs line has been drawn from fixed costs at zero sales of $80,000, reducing the break-even point to dollar sales of $200,000, or 4,000 units.

51. Cost-Volume-Profit (Break-Even) Chart
LO 4
LO 4
Cost-Volume-Profit (Break-Even) Chart
Cost-Volume-Profit (Break-Even) Chart

52. 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). Data from Exhibit 5 are used.
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

53. 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

54. 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

55. 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.

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

57. 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.

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

59. Sales Mix Considerations
LO 5
Sales Mix Considerations
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:

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

61. 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 =

62. 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

63. Operating Leverage Operating Leverage
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.
Jones Inc.:
Percent Change in Income from Operations =
10% x 5 = 50%
Wilson Inc.:
Percent Change in Income from Operations =
10% x 2 = 20%

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

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

66. 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

67. 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%

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