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Second level
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Cost Behavior and Cost-Volume-Profit Analysis
Student Version
9/12/2018 1

2. Classify costs as variable costs, fixed costs, or mixed costs.1
Classify costs as variable costs, fixed costs, or mixed costs.
4-2

3. 1
Variable Costs
Variable costs are costs that vary in proportion to changes in the level of activity.

4. 1
Jason Sound Inc.
Jason Sound Inc. produces stereo systems. The parts for the stereo system are purchased from suppliers for $10 per unit (a variable cost) and assembled by Jason Sound Inc.

5. 1
For Model JS-12, the direct materials for the relevant range of 5,000 to 30,000 units of production are shown below.

6. 1
Fixed Costs
Fixed costs are costs that remain the same in total dollar amount as the activity base changes.

7. 1
Minton Inc.
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 La Fleur Perfume.

8. 1
Fixed Versus Variable Cost of Jane Sovissi’s Salary per Bottle of Perfume
Number of
Bottles of Perfume Produced
Salary per Bottle of Perfume Produced
Total Salary for Jane Sovissi
50,000 bottles $75,000 $1.500
100, ,
150, ,
200, ,
250, ,
300, ,

9. 1
Mixed Costs
Mixed costs (sometimes called semivariable or semifixed costs) have characteristics of both a variable and a fixed cost. 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 level of activity.

10. 1
Simpson Inc.
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.

11. 1
High-Low Method
The high-low method is a cost estimation method that may be used for separating mixed costs into their fixed and variable components.

12. Estimating Variable Cost Using High-Low1
Estimating Variable Cost Using High-Low
Production Total
(Units) Cost
Fill in the formula for difference in 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
$20,250
Difference in Total cost
$20,250
Variable Cost per Unit =
Difference in Production

13. Estimating Variable Cost Using High-Low Difference in total cost1
Estimating Variable Cost Using High-Low
Production Total
(Units) Cost
Then, fill in the formula for difference in production.
June 1,000 $45,550
July 1,500 52,000
August 2,100 61,500
September 1,800 57,500
October ,250
2,100
750
1,350
Difference in total cost
$20,250
Variable Cost per Unit =
Difference in Production
1,350

14. Estimating Variable Cost Using High-Low1
Estimating Variable Cost Using High-Low
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
Variable cost per unit is $15
$20,250
= $15
Variable Cost per Unit =
1,350

15. Estimating Fixed Cost Using High-Low1
Estimating Fixed Cost Using High-Low
The first step in determining fixed cost is to insert the variable cost of $15 into the following formula:
Total Cost = (Variable Cost per Unit × Units of Production) + Fixed Cost
Total Cost = ($15 × Units of Production) + Fixed Cost

16. 1
Production Total
(Units) Cost
Using the highest level of production, we insert the total cost and units produced in the formula.
June 1,000 $45,550
July 1,500 52,000
August 2,100 61,500
September 1,800 57,500
October ,250
Total Cost = (Variable Cost per Unit × Units of Production) + Fixed Cost
$61,500
Total cost = ($15 × Units of Production) + Fixed Cost
2,100 units)

17. 1 $61,500 = ($15 × 2,100 units) + Fixed cost
If the lowest level had been chosen, the results of the formula would provide the same fixed cost of $30,000.

18. 1
With fixed costs and variable costs estimated at $30,000 and $15 per unit, a formula is in place to estimate production at any level. If the company is expected to produce 950 units in November, the estimated total overhead would be calculated as follows:
Total Cost = (Variable Cost per Unit × Units of Production) Fixed cost
Total Cost = $15 (950) + $30,000
Total Cost = $44,250

19. 2
Compute the contribution margin, the contribution margin ratio, and the unit contribution margin.
4-19

20. Cost-Volume-Profit Relationships2
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.

21. 2
Contribution Margin
The contribution margin is the excess of sales revenues over variable costs. It is especially useful because it provides insight into the profit potential of a company.

22. Contribution Margin Ratio (in dollars)2
Contribution Margin Ratio (in dollars)
The contribution margin ratio is most useful when the increase or decrease in sales volume is measured in sales dollars. In this case, the following formula is used to determine change in income from operations.
Change in Sales Dollars × Contribution Margin Ratio
Change in Income from Operations =

23. Contribution Margin Ratio2
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%

24. Using Contribution Margin per Unit as a Shortcut2
Using Contribution Margin per Unit as a Shortcut
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 × $8) as shown below.
Change in Income from Operations
Changes in Sales Units × Unit Contribution Margin =
Change in Income from Operations
15,000 × $8 =
Change in Income from Operations
$120,000 =

25. 3
Determine the break-even point and sales necessary to achieve a target profit.
4-25

26. 3
Baker Corporation’s fixed costs are estimated to be $90,000. The unit contribution margin is calculated as follows:
Unit selling price $25
Unit variable cost 15
Unit contribution margin $10

27. Unit Contribution Margin3
The break-even point (in 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

28. 3
The break-even point (in dollars) is calculated using the following equation:
Break-Even Sales (dollars) =
Fixed Costs
Contribution Margin Ratio
Unit Contribution Margin
Unit Selling Price
$90,000
.40
Break-Even Sales (dollars) =
$10
$25
Break-Even Sales (dollars) = $225,000

29. 3
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 unit contribution margin before the additional 2% commission is determined below.
Unit selling price $250
Unit variable cost 145
Unit contribution margin $105

30. Unit Contribution Margin3
Without additional 2% commission:
Break-Even in Sales (units) =
Fixed Costs
Unit Contribution Margin
Break-Even in Sales (units) =
$840,000
$105 =
8,000 units
With additional 2% commission:
Break-Even in Sales (units) =
$840,000
$100 =
8,400 units
$250 – [$145 + ($250 × 2%)] = $100

31. 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

32. Units Required for Target Profit3
Units Required for Target Profit
Fixed costs are estimated at $200,000, and the desired profit is $100,000. Unit contribution margin is $30.
Unit selling price $75
Unit variable cost 45
Unit contribution margin $30
Sales (units) =
Fixed Costs + Target Profit
Unit Contribution Margin
$200,000
$100,000
$30
Sales (units) = 10,000 units

33. Necessary sales to have a $100,000 target profit3
Target Profit
Unit Contribution Margin
Unit Selling Price
Contribution Margin Ratio =
Contribution Margin Ratio =
$30
$75
from Slide 32
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 have a $100,000 target profit

34. 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.
4-34

35. Unit contribution margin $ 20 Total fixed costs $100,0004
The cost-volume-profit chart in Slides 36 to 48 is based on Exhibit 5. Exhibit 5 was constructed using the following data:
Unit selling price $ 50
Unit variable cost 30
Unit contribution margin $ 20
Total fixed costs $100,000

36. Units of Sales (in thousands)4
Exhibit 5
Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Dollar amounts are indicated along the vertical axis.
Sales and Costs (in thousands)
Units of Sales (in thousands)
Volume is shown on the horizontal axis.
(continued)

37. 4
Using maximum sales of $500,000 and knowing that each unit sells for $50, we can find the values of the two axis. Where the horizontal sales and costs line intersects the vertical 10,000 unit of sales line is Point A in Slide 38.

38. Units of Sales (in thousands)4
Exhibit 5
Cost-Volume-Profit Chart (continued)
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Point A
Sales and Costs (in thousands)
Units of Sales (in thousands)
Point A could have been plotted at any sales level because linearity is assumed.

39. Units of Sales (in thousands)4
Exhibit 5
Cost-Volume-Profit Chart (continued)
Point A
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Sales and Costs (in thousands)
Units of Sales (in thousands)
Beginning at zero on the left corner of the graph, connect a straight line to the dot (Point A).

40. 4 Exhibit 5 Cost-Volume-Profit Chart (continued)
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Sales and Costs (in thousands)
Units of Sales (in thousands)
Fixed cost of $100,000 is a horizontal line.

41. 4
A point on the chart is needed to establish the revenue line. An arbitrary sales amount is picked of 10,000 units. At this sales level, the cost should be $400,000, calculated as follows: [(10,000 × $30) + $100,000] = $400,000.

42. Units of Sales (in thousands)4
Exhibit 5
Cost-Volume-Profit Chart (continued)
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Sales and Costs (in thousands)
Units of Sales (in thousands)
A line is drawn between fixed cost ($100,000) and the point.

43. 4
The line would be the same if another point had been picked. For example, assume that 8,000 units had been chosen. At this sales level, the cost should be $400,000 [(8,000 × $30) + $100,000 = $340,000].

44. Units of Sales (in thousands)4
Exhibit 5
Cost-Volume-Profit Chart (continued)
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Break-Even Point
Sales and Costs (in thousands)
Units of Sales (in thousands)

45. 4 Exhibit 5 Cost-Volume-Profit Chart (continued) Break-Even Point
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Break-Even Point
Sales and Costs (in thousands)
Units of Sales (in thousands)
Break-even is sales of 5,000 units or $250,000.

46. Units of Sales (in thousands)4
Exhibit 5
Cost-Volume-Profit Chart (continued)
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Operating Loss Area
Sales and Costs (in thousands)
Units of Sales (in thousands)

47. Units of Sales (in thousands)4
Exhibit 5
Cost-Volume-Profit Chart (continued)
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
Sales and Costs (in thousands)
Operating Profit Area
Units of Sales (in thousands)

48. 4
Exhibit 5
Cost-Volume-Profit Chart (concluded)

49. 4 Exhibit 6 Revised Cost-Volume-Profit Chart
Break-even in sales would be reduced from $250,000 to $200,000 (5,000 to 4,000 in units).

50. 4
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, computed as follows:
Sales (10,000 units × $50) $500,000
Variable costs (10,000 units × $30) 300,000
Contribution margin (10,000 units × $20) $200,000
Fixed costs 100,000
Operating profit $100,000
Maximum Profit

51. 5
Compute the break-even point for a company selling more than one product, the operating leverage, and the margin of safety.
4-51

52. Cascade Company Example5
Cascade Company Example
Cascade Company sold 8,000 units of Product A and 2,000 units of Product B during the past year. Cascade Company’s fixed costs are $200,000. Other relevant data are as follows:
Unit Unit Unit Sales
Selling Variable Contribution Mix
Product Price Cost Margin %
A $ 90 $70 $20 80%
B %

53. 5
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.
Unit selling price of E: ($90 × 0.8) + ($140 × 0.2) = $100
Unit variable cost of E: ($70 × 0.8) + ($95 × 0.2) =
Unit contribution margin of E: $ 25

54. Break-Even Point of 8,000 Units of E5
Break-Even Point of 8,000 Units of E
Fixed Costs
Unit Contribution Margin
Break-Even Sales (units) =
Break-Even Sales (units) =
$200,000
$25
Break-Even Sales (units) = 8,000 units

55. Operating Leverage Example5
Operating Leverage Example
Jones Inc Wilson Inc.
Sales $400,000 $400,000
Variable costs 300, ,000
Contribution margin $100,000 $100,000
Fixed costs , ,000
Income from operations $ 20,000 $ 50,000
Operating leverage ? ?
Both companies have the same contribution margin.

56. Operating Leverage Example Income from Operations5
Operating Leverage Example
Jones Inc Wilson Inc.
Sales $400,000 $400,000
Variable costs 300, ,000
Contribution margin $100,000 $100,000
Fixed costs , ,000
Income from operations $ 20,000 $ 50,000
Operating leverage ? ? 5
Contribution Margin
Income from Operations
$100,000
Jones Inc.:
= 5
$20,000

57. Operating Leverage Example Income from Operations5
Operating Leverage Example
Jones Inc Wilson Inc.
Sales $400,000 $400,000
Variable costs 300, ,000
Contribution margin $100,000 $100,000
Fixed costs , ,000
Income from operations $ 20,000 $ 50,000
Operating leverage ? ? 5 2
Contribution Margin
Income from Operations
$100,000
Wilson Inc.:
= 2
$50,000

58. 5
Margin of Safety
The margin of safety indicates the possible decrease in sales that may occur before an operating loss results.