CHAPTER 6

DECISION-MAKING: COST-VOLUME-PROFIT

SUMMARY OF QUESTION TYPES BY LEARNING OBJECTIVE, BLOOM’S TAXONOMY, LEVEL OF DIFFICULTY, AACSB CODES, AND CPA CODES

Bloom’s: AN = Analysis AP = Application C = Comprehension E = Evaluation

K = Knowledge

LOD: E = Easy M = Medium H = Hard

AACSB: AN = Analytic

CPA: F = Financial Reporting MA = Management Accounting

^*This topic is dealt with in an Appendix to the chapter.

SUMMARY OF QUESTION TYPES BY LEARNING OBJECTIVE,

CPA CODES (CONT’D)

Bloom’s: AN = Analysis AP = Application C = Comprehension E = Evaluation

K = Knowledge

LOD: E = Easy M = Medium H = Hard

AACSB: AN = Analytic

CPA: F = Financial Reporting MA = Management Accounting

^*This topic is dealt with in an Appendix to the chapter.

SUMMARY OF LEARNING OBJECTIVES BY QUESTION TYPE

Note: TF = True-False C = Completion BE = Brief Exercise

MC = Multiple Choice Ex = Exercise SAE = Short-Answer Essay

Ma = Matching MP = Multi-Part

^*This topic is dealt with in an Appendix to the chapter.

CHAPTER LEARNING OBJECTIVES

1. Prepare a cost-volume-profit income statement to determine contribution margin.

The five components of CVP analysis are (1) volume or level of activity, (2) unit selling prices, (3) variable cost per unit, (4) total fixed costs, and (5) sales mix. The CVP income statement classifies costs as variable or fixed and calculates a contribution margin.

Contribution margin is the amount of revenue remaining after deducting variable costs. It is identified in a CVP income statement, which classifies costs as variable or fixed. It can be expressed as a per-unit amount or as a ratio.

2. Calculate the break-even point using three approaches.

The break-even point can be (1) calculated with a mathematical equation, (2) calculated by using a contribution margin technique, or (3) derived from a CVP graph.

3. Determine the sales required to earn the target operating income and define the margin of safety.

Target NI before tax: One formula is required sales = variable costs + fixed costs + target operating income. Another formula is (fixed costs + target operating income) ÷ contribution margin ratio = required sales.

Target NI after tax: One formula is required sales = variable costs + fixed costs + target operating income before tax. Another formula is (fixed costs + target operating income before tax) ÷ contribution margin ratio = required sales.

Margin of safety is the difference between actual or expected sales and sales at the break-even point. The formulas for margin of safety are actual (expected) sales − break-even sales = margin of safety in dollars, and margin of safety in dollars ÷ actual (expected) sales = margin of safety ratio.

4. Understand how to apply basic cost-volume-profit concepts in a changing business environment.

CVP can be used to respond to business changes by calculating the break-even sales point, such as when deciding whether to match a competitor’s discount, when deciding whether to invest in new equipment, and when determining how many units must be sold in order to achieve a target operating income.

5. Explain the term sales mix and its effect on break-even sales.

The sales mix is the relative proportion in which each product is sold when a company sells more than one product. For a multi-product company, break-even sales in units is determined by using the weighted-average unit contribution margin of all the products. If the company sells many different products, calculating the break-even point using unit information is not practical. Instead, the company calculates the break-even sales in dollars using the weighted-average contribution margin ratio.

6. Understand how cost structure and operating leverage affect profitability (Appendix 6A).

Operating leverage is how much a company’s operating income reacts to a change in sales. Operating leverage is determined by a company’s relative use of fixed versus variable costs. Companies with high fixed costs relative to variable costs have a high operating leverage. A company with a high operating leverage will experience a sharp increase (decrease) in operating income with an increase (decrease) in sales. A company can measure the degree of operating leverage by dividing the contribution margin by operating income.

TRUE-FALSE STATEMENTS

1. Contribution margin is the amount of profit remaining after deducting cost of goods sold.

2. The margin of safety is the difference between sales at break even and sales at a determined activity level.

3. If O’Brien Company has a margin of safety ratio of .60, it could sustain a 60 percent decline in sales before it would be operating at a loss.

4. Using the assumptions of CVP analysis, if a company thought its sales may increase by 50% in the upcoming year over last year, the variable costs in total will change by a similar percentage.

5. For a company with multiple products, the break-even point in dollars is variable costs divided by the weighted-average contribution margin ratio.

*6. If a company installs an automated factory that increases its fixed costs and lowers its variable costs, one might say it has decreased its operating leverage.

*7. Cost structure refers to the relative proportion of fixed versus variable costs that a company incurs.

*8. Operating leverage refers to the extent to which a company’s net income reacts to a given change in fixed costs.

ANSWERS TO TRUE-FALSE STATEMENTS

MULTIPLE CHOICE QUESTIONS

9. In CVP analysis,

a) it is assumed that all costs can be classified as either variable or fixed.

b) it is assumed the term ‘cost’ includes only manufacturing costs.

c) it is assumed that costs must be classified as either fixed, mixed, or variable.

d) it is assumed that when more than one type of product is sold the sales mix will vary.

10. A CVP income statement

a) shows contribution margin and gross profit.

b) classifies costs into three sections based on behaviour.

c) separates costs based on behaviour.

d) shows revenue less fixed costs as contribution margin.

Use the following information for questions 11–13.

In September, Smith Company had the following financial statement amounts related to producing 500 units:

Direct materials $27,000

Depreciation expense 11,000

Sales revenue 95,000

Direct labour 23,000

Rent expense 25,000

11. How much is total contribution margin for September?

a) $45,000

b) $9,000

c) $68,000

d) $20,000

12. How much is the net operating income, (loss), for September?

a) $45,000

b) $9,000

c) $68,000

d) $20,000

13. How much is the unit contribution margin?

a) $45,000

b) $9,000

c) $90

d) $18

14. NEKP Inc. sells two versions of its product: Standard and Deluxe. The Standard model has a 15 percent profit margin and the Deluxe model has a 17 percent profit margin. The Standard model has a 30 percent contribution margin and the Deluxe has a 23 percent contribution margin. If other factors are equal, which product should NEKP promote to its customers?

a) the Standard model

b) the Deluxe model

c) Selling either results in the same additional income for the company.

d) Not enough information is given.

15. Hartley, Inc. has one product with a selling price per unit of $250, the unit variable cost is $150, and the total monthly fixed costs are $750,000. How much is Hartley’s contribution margin ratio?

a) 40%

b) 60%

c) 66.7%

d) 75%

16. Gift Gallery sold 2,000 Zooglars during 2022. The following information is provided regarding the Zooglar product:

Sales $ 60,000

Variable costs 24,000

Fixed costs 10,000

Net income $ 26,000

If Gift Gallery sells 30 more units, by how much will its operating income increase?

a) $18

b) $540

c) $390

d) $900

17. In CVP analysis, what does the term "cost" mean?

a) It includes all fixed and variable costs of products.

b) It includes all costs that are part of cost of goods sold.

c) It includes manufacturing costs plus selling and administrative expenses.

d) It includes all manufacturing costs.

18. Which one of the following is an assumption of CVP analysis?

a) Sales in units remain constant.

b) All costs are variable.

c) The change in beginning and ending inventories is reflected in the analysis.

d) The behaviour of costs and revenues are linear within the relevant range.

19. Which one of the following is a consideration of CVP analysis?

a) The level of activity must remain constant over the relevant range.

b) Total fixed costs remain constant over the relevant range.

c) Total variable costs remain constant over the relevant range.

d) Cost behaviour can change provided total costs remain the same at all activity levels.

20. Which of the following is an underlying assumption of CVP analysis?

a) Factors other than changes in activity may affect costs.

b) Cost classifications are reasonably accurate.

c) Increases in inventories cause an increase in total fixed costs.

d) Unit costs remain the same over the relevant range.

21. In which one of the following calculations would CVP analysis be most important?

a) calculating depreciation expense

b) determining the selling price

c) determining how many employees to hire

d) estimating units to be produced at capacity

22. CVP analysis is most applicable to which function of management?

a) directing

b) controlling

c) planning

d) organizing

23. The variable cost ratio is:

a) the contribution margin expressed as a percentage of variable costs.

b) the variable costs expressed as a percentage of contribution margin.

c) the sales expressed as a percentage of variable costs.

d) the variable costs expressed as a percentage of sales.

24. Sarks Company has a contribution margin of $150,000 and a contribution margin ratio of 30%. How much are total variable costs?

a) $45,000

b) $350,000

c) $105,000

d) $500,000

25. Which of the following is the correct formula for the contribution margin ratio?

a) sales – total variable cost

b) (unit selling price – unit variable cost) ÷ unit selling price

c) unit selling price – unit variable cost

d) (unit selling price – unit variable cost) ÷ unit variable cost

26. Hardage Company has a unit contribution margin of $15 and a contribution margin ratio of 60%. How much is the selling price of each unit?

a) $25

b) $37.50

c) $9

d) Cannot be determined without more information.

27. Sales are $60,000 and variable costs are $45,000. What is the contribution margin ratio?

a) 75%

b) 50%

c) 25%

d) Cannot be determined without more information.

28. Which one of the following is true concerning a CVP income statement?

a) Costs and expenses are classified only by function.

b) It is prepared for both internal and external use.

c) It shows contribution margin instead of gross profit.

d) Costs and expenses are classified as product or period.

29. The following information is available for Chap Company:

Sales $350,000

Total fixed expenses $60,000

Cost of goods sold 120,000

Total variable expenses 100,000

What amount would you find on Chap’s CVP income statement?

a) contribution margin of $250,000

b) contribution margin of $190,000

c) gross profit of $230,000

d) gross profit of $190,000

30. Which one of the following is the format of a CVP income statement?

a) sales – variable costs = fixed costs + net income

b) sales – fixed costs – variable costs – operating expenses = net income

c) sales – cost of goods sold – operating expenses = net income

d) sales – variable costs – fixed costs = net income

31. Which one of the following is true of the CVP income statement?

a) It is part of the accounting information provided to all financial statement users.

b) It is used internally by management.

c) It provides the amount of gross profit of a company.

d) It separates manufacturing from non-manufacturing costs.

32. A division sold 280,000 calculators during 2022:

Sales $5,600,000

Variable costs:

Materials $1,400,000

Order processing 280,000

Billing labour 1,120,000

Delivery costs 840,000

Selling expenses 560,000

Total variable costs 4,200,000

Fixed costs 750,000

How much is the unit contribution margin, rounded to the nearest cent?

a) $17.32

b) $15.00

c) $7.00

d) $5.00

33. Saver Company produces only one product. Monthly fixed expenses are $20,000, monthly unit sales are 3,500, and the unit contribution margin is $7. How much is monthly net profit?

a) $44,500

b) $24,500

c) $0

d) $4,500

34. Croc Catchers calculates its contribution margin to be less than zero. Which statement is true?

a) Its fixed costs are less than the variable cost per unit.

b) Its operating income is greater than its total costs.

c) The company should sell more units.

d) Its selling price is less than its variable costs.

35. Old Canadian Company has sales of $500,000, variable costs of $425,000, and fixed costs of $25,000. New World Company has sales of $500,000, variable costs of $200,000, and fixed costs of $250,000. Old Canadian’s contribution margin ratio is

a) 15%.

b) 60%.

c) 85%.

d) 95%.

36. A major reason for using the CVP income statement is that

a) it separates variable and fixed cost components.

b) it increases information available to management.

c) it allows management to establish what sales level is necessary to cover fixed costs.

d) it indicates the sales mix of the company’s products or services.

37. A major benefit of using a contribution ratio format is that

a) it supports management’s decision on its sales mix.

b) it assists in determining the effect of sales on operating income.

c) it isolates the variable costs, so the costs can be easily reduced.

d) it shows the impact of fixed costs on the sales mix.

38. When using the CVP income statement, which of the following will result from an increase of one unit sold?

a) Variable costs will increase in direct relation to the contribution margin ratio.

b) Variable costs will decrease in direct relation to the contribution margin ratio.

c) Every unit of product sold will decrease income by the contribution margin.

d) Every unit of product sold will increase income by the contribution margin.

39. The break-even point

a) is the point at which total sales equals total contribution margin.

b) is the point at which total revenue equals total fixed costs plus total variable costs.

c) is the point at which total sales equal total fixed costs.

d) is the point at which total sales equal total variable costs.

40. In September, Smith Company had the following financial statement amounts related to producing 500 units:

Direct materials $27,000

Depreciation expense 11,000

Sales revenue 95,000

Direct labour 23,000

Rent expense 25,000

How much is the break-even point, rounded to the nearest whole number?

a) $18 units

b) $50 units

c) $122 units

d) 400 units

41. A company has total fixed costs of $180,000 and a contribution margin ratio of 30%. What level of sales are necessary to break even?

a) $540,000

b) $600,000

c) $54,000

d) $126,000

42. A company sells a product that has a unit sales price of $9, unit variable cost of $6 and total fixed costs of $60,000. How many units must the company sell to break even?

a) 180,000

b) 20,000

c) 6,667

d) 10,000

43. Which one of the following describes the break-even point?

a) It is the point where total sales equal total variable plus total fixed costs.

b) It is the point where the contribution margin equals zero.

c) It is the point where total variable costs equal total fixed costs.

d) It is the point where total sales equal total fixed costs.

44. If a firm is currently at the break-even point and it sells one more unit, what happens to its operating income?

a) It will increase by the unit selling price.

b) It will decrease by the unit variable cost.

c) It will increase by the unit contribution margin.

d) It will increase by the fixed cost divided by the unit contribution margin.

45. CopperZ Company has variable costs that are 40% of its unit selling price and fixed costs of $30,000. What level of sales dollars will CopperZ report at its break-even point?

a) $50,000

b) $75,000

c) $12,000

d) $18,000

46. Fixed costs are $400,000 and the unit contribution margin is $80. What is the break-even point?

a) $500,000

b) $2,000,000

c) 320,000 units

d) 5,000 units

47. Tykee Company has the following data:

Variable costs are 75% of the unit selling price.

The unit contribution margin is $400.

The fixed costs are $600,000.

Which of the following expresses the break-even point in dollars?

a).25 x 600,000 = X

b) 600,000 ÷.75 = X

c) ($600,000 ÷ $400) x.75 = X

d) $600,000 ÷.25 = X

48. Which one of the following lines is not drawn separately on a CVP graph?

a) total cost line

b) fixed cost line

c) sales line

d) variable cost line

49. Which one of the following calculates the break-even point in units?

a) Divide total fixed costs by the unit contribution margin.

b) Divide fixed cost per unit by the unit contribution margin.

c) Divide total contribution margin by the number of units sold.

d) Divide total fixed costs by the contribution margin ratio.

50. Where is the break-even point located in a CVP graph?

a) at the intersection of the sales line and the fixed cost line

b) at the intersection of the variable cost line and the fixed cost line

c) at the intersection of the total cost line and the sales line

d) at the intersection of the mixed cost line and the sales line

51. Sutton Company produces flash drives for computers, which it sells for $20 each. Each flash drive incurs $6 of variable costs during production. In April, 1,000 drives were sold. Fixed costs for April were $2 per unit for a total of $2,000 for the month. What is the contribution margin ratio?

a) 30%

b) 40%

c) 60%

d) 70%

52. Sutton Company produces flash drives for computers, which it sells for $20 each. The variable cost to make each flash drive is $6. During April, 700 drives were sold. Fixed costs for April were $2 per unit for a total of $1,400 for the month. What is the monthly break-even level of sales in dollars for Sutton Company?

a) $100

b) $2,000

c) $7,000

d) $4,200

53. Sutton Company produces flash drives for computers, which it sells for $20 each. Each flash drive incurs$6 of variable costs during production. In April, 1,000 drives were sold. Fixed costs for April were $4.20 per unit for a total of $4,200 for the month. If variable costs decrease by 10%, what happens to the break-even level of units per month for Sutton Company?

a) It is 10% higher than the original break-even point.

b) It decreases by approximately 12 units.

c) It decreases by approximately 30 units.

d) It depends on the number of units the company expects to produce and sell.

54. Niagara Winery has fixed costs of $10,000 per year. Its warehouse sells wine with a contribution margin of 20%. What level of sales does Sonoma need to break even per year if wine is its only product?

a) $8,000

b) $2,000

c) $12,500

d) $50,000

55. Select the correct statement concerning the cost-volume-profit graph below:

a) The point identified by ‘A’ is the break-even point.

b) Line F is the break-even line.

c) Line D is the variable cost line.

d) At point B, profits equal total costs.

56. Select the correct statement concerning the cost volume-profit graph below:

a) The point identified by ‘B’ is the break-even point.

b) Line F is the break-even line.

c) Line F is the variable cost line.

d) Line E is the total cost line.

57. Martin Worldwide sells a single product with a contribution margin of $12 per unit and fixed costs of $24,000. What is Martin’s break-even point?

a) 2,500 units

b) $12,000

c) $24,000

d) 2,000 units

58. At the break-even point of 2,000 units, variable costs are $55,000, and fixed costs are $32,000. What is the selling price per unit?

a) $43.50

b) $11.50

c) $16

d) not enough information

59. Fallow-Hawke is a non-profit organization that captures stray deer from residential communities. Fixed costs are $10,000. The variable cost of capturing deer is $10.00 each. Fallow-Hawke is funded by local philanthropy in the amount of $32,000 for 2022. How many deer can Fallow-Hawke capture during 2022?

a) 2,200

b) 3,200

c) 4,200

d) 2,000

60. ABC Bread sells a box of bagels with a contribution margin of 62.5%. Its fixed costs are $150,000 per year. What level of sales dollars does ABC Bread need to break even per year if bagels are its only product?

a) $93,750

b) $150,000

c) $240,000

d) $90,000

61. Old Canadian Company has sales of $500,000, variable costs of $425,000, and fixed costs of $25,000. New World Company has sales of $500,000, variable costs of $200,000, and fixed costs of $250,000. Old Canadian break-even point in dollars is

a) $166,667.

b) $400,000.

c) $450,000.

d) $466,667.

62. Arbitrage Company had an operating loss of $36,000, sales of $420,000, a contribution margin of $90,000. What is the break-even point in sales dollars?

a) $27,000

b) $588,000

c) $11,571

d) $252,000

63. Companies generally set sales targets higher than break-even figures because

a) it indicates the sales needed to attain a certain level of profit.

b) assists in planning for new equipment if sales can be reached.

c) an income objective is set that can be communicated throughout the company.

d) break-even analysis may not be effective in all situations.

64. When using the contribution margin technique

a) a target operating income is added to variable costs.

b) a target operating income is added to fixed costs.

c) fixed costs must always be shown separate from other costs and the target.

d) the target operating income should be shown after the break-even analysis indicates zero profit or loss.

65. What does the margin of safety measure?

a) how much prices can be changed before the CVP analysis is no longer valid

b) how much sales can drop before the firm has an operating loss

c) how much fixed costs can drop before the firm has an operating loss

d) how much variable costs can rise before the firm has an operating loss

66. Tiny Tots Toys has actual sales of $400,000 and a break-even point of $260,000. What is its margin of safety ratio?

a) 35%

b) 65%

c) 286%

d) 53.8%

67. Needles, Inc. is evaluating its margin of safety. Which one of the following is true?

a) The break-even point is not relevant.

b) The higher the ratio, the greater the margin of safety.

c) The higher the dollar amount, the lower the margin of safety.

d) The higher the ratio, the lower the fixed costs.

68. If M&H Ltd. has a margin of safety of $100,000, which of the following statements is correct?

a) Sales can increase by $100,000 before M&H has an operating loss.

b) Fixed costs can increase by $100,000 before M&H has an operating loss.

c) Sales can decrease by $50,000 and fixed costs can increase by $40,000 before M&H has an operating loss.

d) Sales can increase by $50,000, and fixed costs can decrease by $50,000 before M&H has an operating loss.

69. Forms, Inc. wants to sell enough product to earn an after-tax net income of $40,000. If the unit sales price is $10, unit variable cost is $8, and total fixed costs are $80,000, how many units must be sold to earn income of $40,000? Forms, Inc. has a tax rate of 40%.

a) 73,334 units

b) 18,334 units

c) 40,000 units

d) 90,000 units

70. What level of sales are required to earn a target after-tax net income of $80,000 if total fixed costs are $100,000, the contribution margin ratio is 40%, and the tax rate is 25%?

a) $6,000,000

b) $250,000

c) $516,667

d) $1,050,000

71. Goose Bay Sync’s management established its target net income for the year. What did the company do?

a) It estimated its break-even income level for the year.

b) It calculated its contribution margin.

c) It determined the behaviour of its costs.

d) It established its desired annual income for its product lines.

72. Sulingo, Inc. calculated how many units it needed in order to earn net income totalling $67,750 for the month. What calculation did Sulingo perform?

a) [Variable costs + ($67,750 / 1 - tax rate)] ÷ contribution margin ratio

b) [Fixed costs + ($67,750 / 1 + tax rate)] ÷ contribution margin ratio

c) [Fixed costs + ($67,750 / 1 - tax rate)] ÷ unit contribution margin

d) [Variable costs + ($67,750 / tax rate)] ÷ unit contribution margin

73. A company requires $600,000 in sales to meet its target net income after tax. Its contribution margin is 40%, and fixed costs are $80,000. How much is the target net income, given that its after-tax rate is 70%?

a) $400,000

b) $160,000

c) $48,000

d) $112,000

74. Organizer Company has fixed costs of $200,000 and variable costs are 60% of sales. What is Organizer Company’s sales when its net income equals $20,000?

a) $550,000

b) $366,667

c) $520,000

d) $132,000

75. Stacker requires sales of $500,000 to cover its fixed costs of $100,000 and to earn net income of $80,000. What percentage is variable cost of sales?

a) 36%

b) 2.77%

c) 20%

d) 64%

76. Sutton Company produces flash drives for computers, which it sells for $20 each. The variable cost for each flash drive is $6. During April, 700 drives were sold. Fixed costs for April were $4 per unit for a total of $2,800 for the month. How much does Sutton’s operating income increase for each $1,000 increase in revenue per month?

a) $700

b) $500

c) $14,000

d) Not enough information to determine the answer.

77. Which concept answers the following question: ‘If budgeted revenues are above break even and decline, how far can they fall before the break-even point is reached?’

a) contribution margin

b) relevant range of operations

c) operating leverage

d) margin of safety

78. The following monthly data are available for Wackadoos, Inc. It produces only one product: Selling price per unit: $42; Unit variable expenses: $14; Total fixed expenses: $42,000; Actual sales for the month of June: 4,000 units. What is the margin of safety for the company for June?

a) $70,000

b) $105,000

c) $63,000

d) $2,500

79. Swashbuckler, Inc. produces buckets. The selling price is $20 per unit and the variable costs are $8 per bucket. Fixed costs per month are $4,800. If Swashbuckler sells 10 more units beyond break even, how much does operating income increase as a result?

a) $120

b) $400

c) $600

d) $12,000

80. Old Canadian Company has sales of $500,000, variable costs of $425,000, and fixed costs of $25,000. New World Company has sales of $500,000, variable costs of $200,000, and fixed costs of $250,000. New World’s margin of safety ratio is

a).17.

b).33.

c).67.

d).83.

81. The margin of safety ratio

a) is calculated as actual sales divided by break-even sales.

b) indicates what percentage decline in sales could be sustained before the company would operate at a loss.

c) measures the ratio of fixed costs to variable costs.

d) is used to determine the break-even point.

82. A key reason for management to build in a margin of safety in its projections is

a) management can assess if its targets are reasonable and will cover fixed costs.

b) if sales do not reach the targeted number, management will not suffer the consequences.

c) variable costs may fluctuate, and this will affect the break-even calculation.

d) it will show the operating profit if sales are not as expected.

83. Franklin Company sells its leading product for $30 per unit and has a contribution margin ratio of 30%. Total fixed costs are $183,000 per year and Franklin has a 40% tax rate. How many units does the company need to sell to generate an after-tax operating profit of $45,000?

a) 9,850

b) 28,667

c) 12,000

d) 32,833

84. Connor Company sells its product for $280 per unit, the variable cost is $240 per unit and the company fixed costs are $250,000. The company is considering the purchase of some new equipment that will increase fixed costs by 25% and reduce variable costs by 25%. The company’s sales price per unit will remain unchanged. Calculate the company’s new break even point in units if it purchases the equipment.

a) 7,813

b) 2,500

c) 3,125

d) 6,250

85. Sample, Inc. determined its unit variable cost increased by 15%. Which one of the following will NOT increase as a direct result?

a) total costs

b) total variable costs

c) contribution margin

d) the break-even point

86. Wardley Corporation sells its product for $40. The variable costs are $18 per unit. Fixed costs are $16,000. The company is considering the purchase of an automated machine that will result in a $2 reduction in unit variable costs and an increase of $5,000 in fixed costs. Which of the following is true about the break-even point in units?

a) It will remain unchanged.

b) It will decrease.

c) It will increase.

d) It cannot be determined from the information provided.

87. NoWeeds, Inc. has variable costs equal to 25% of sales. Its selling price is $95 per unit. If NoWeeds sells one unit more than the number of break-even units, how much will operating income increase?

a) $71.25

b) $23.75

c) $32.50

d) $380.00

88. Company A and Company B sell their products for exactly the same sales price. Both have the same annual total costs. Company A’s variable and fixed costs at break-even total $60,000 and $30,000 respectively. Company B’s variable and fixed costs at break-even total $30,000 and $60,000 respectively. Both companies have the same net income. If both companies experience an increase in sales, which company will have the higher net income?

a) Company A

b) Company B

c) Both companies will report the same profits since total costs are the same.

d) More information is needed to determine the answer.

89. Phi Kappa is planning to hold a seminar for students at the University Centre. It has two options:

OPTION 1: Fixed rental cost of $1,000 and $12 per person for books

or

OPTION 2: Fixed rental cost of $3,000 and $8 per person for books

Tickets will be $5 per student. Other items will be donated by recruiters wishing to network with students. Which option will cause the biggest loss if very few students attend?

a) Option 1

b) Option 2

c) Both options provide the same amount of risk.

d) Neither option has risks.

90. T’pol Corporation is considering a plan that will increase total units sold. The plan will cause a shift from high- to low-margin sales. The plan will

a) increase net income.

b) decrease net income.

c) not effect net income.

d) can’t be determined, more information is needed.

91. In a competitive business environment, using break-even analysis would be least effective

a) for negotiating new agreements with its unions at contract time.

b) in adjusting the company’s prices on its products or services.

c) changing the mix of its products offered.

d) when changing its advertising program to emphasize its new product line.

92. What aspect of business would have the greatest impact on a break-even analysis calculation?

a) highly fluctuating costs from suppliers

b) annual increases in fixed costs such as power

c) annual decreases due to overall corporate cost savings

d) changes in sales estimates from management

93. Barcelona Bagpipes produces two models: Model 24 has sales of 200 units with a contribution margin of $35 each; Model 26 has sales of 75 units with a contribution margin of $37 each. If sales of Model 26 increase by 50 units, how much will operating income change?

a) $1,850 increase

b) $1,750 increase

c) $3,600 increase

d) $7,400 increase

94. Proops Company has a weighted-average unit contribution margin of $30 for its two products: Drew and Carey. Expected sales for Proops are 40,000 Drews and 60,000 Careys. Fixed expenses are $1,800,000. At the expected sales level, Proops’ net income will be

a) $(300,000).

b) $0.

c) $1,200,000.

d) $3,000,000.

95. Mix-It-Up Company sells two products called Shake and Stir and the company sales mix is 60% and 40%, respectively. The unit contribution for the Shake product is $18, while the unit contribution for Stir is $15. The company’s fixed costs are $184,800.

What is the weighted-average contribution margin?

a) $10.80

b) $16.20

c) $6.00

d) $16.80

96. How many units of each product must Mix-It-Up sell in order to break-even?

a) Shake break-even= 6,600; Stir break-even = 4,400

b) Shake break-even = 10,266; Stir break-even = 12,320.

c) Shake break-even= 4,400; Stir break-even = 6,600

d) Shake break-even = 5,500; Stir break-even = 5,500.

97. Data analytics does not

a) involve collecting data.

b) ensure increased profits.

c) involve analyzing data.

d) assist in making predictions.

98. Sales mix

a) is a measure of the percentage increase in sales from period to period.

b) is not important to managers when different products have substantially different contribution margins.

c) is a measure of the percentage increase in sales by product from period to period.

d) is the relative proportion in which each product is sold when a company sells more than one product.

99. Which of the following is false?

a) The weighted-average contribution margin of all the products is calculated when determining the break-even sales for a multi-product firm.

b) If Conan Corporation sells two products with a sales mix of 75%–25%, and the respective contribution margins are $100 and $300, then weighted-average unit contribution margin is $150.

c) If fixed costs are $100,000 and weighted-average unit contribution margin is $50, then the break-even point in units is 2,000 units.

d) The weighted-average contribution margin cannot be used to calculate break-even sales for a mix of two or more products.

100. Which is not true concerning sales mix?

a) Sales mix is the relative percentage in which each product is sold when a company sells more than one product.

b) Sales mix is important to managers because different products often have substantially different contribution margins.

c) Sales mix does not affect break-even analysis.

d) The computation of weighted-average unit contribution margin is useful in sales mix analysis.

Use the following information for items 101–104.

Brad Sherwood Corporation sells two types of computers; one is designed for audio applications and the other for video applications. Sherwood incurs $300,125 in fixed costs.

Per-unit data on the two products is presented blow:

Unit data Audio computer Video computer

Selling price $1,500 $1,750

Variable costs 1,100 1,200

Contribution margin $ 400 $550

Sales mix 75% 25%

101. The weighted-average contribution margin is

a) $437.50.

b) $475.00.

c) $1,125.00.

d) $375.00.

102. The break-even point in units is

a) 267.

b) 632.

c) 686.

d) 800.

103. How many audio computers are sold at the break-even point?

a) 477

b) 172

c) 515

d) 158

104. What is the total contribution margin at the break-even point?

a) $225,000

b) $276,000

c) $300,125

d) $372,250

105. In a sales mix situation, at any level of units sold, net income is higher if

a) there are more higher contribution margin units are sold than lower contribution margin units.

b) there are more lower contribution margin units are sold than higher contribution margin units.

c) there are more fixed expenses incurred.

d) there is a decrease in the weighted-average unit contribution margin.

106. Estes Company sells two types of computer chips. The sales mix is 30% (Chip A) and 70% (Chip B). Chip A has variable costs per unit of $20 and a selling price of $40. Chip B has variable costs per unit of $25 and a selling price of $55. The weighted-average unit contribution margin for Estes is

a) $23.00.

b) $25.00.

c) $27.00.

d) $50.50.

107. Proops Company has a weighted-average unit contribution margin of $30 for its two products: Drew and Carey. Expected sales for Proops are 40,000 Drews and 60,000 Careys. Fixed expenses are $1,800,000. How many Drews would Proops sell at the break-even point?

a) 24,000

b) 36,000

c) 40,000

d) 60,000

108. The weighted-average contribution margin ratio is

a) 44%.

b) 45%.

c) 46%.

d) 50%.

109. The break-even point in dollars is

a) $985,600.

b) $4,869,565.

c) $4,977,777.

d) $5,500,000.

110. What are sales for the Outdoor Sports Division at the break-even point?

a) $2,200,000

b) $2,750,000

c) $2,921,739

d) $3,300,000

111. What is the total contribution margin at the break-even point?

a) $ 960,000

b) $1,600,000

c) $2,420,000

d) $4,960,000

112. It is critical for management to understand its overall sales mix when using CVP income statements because

a) variable cost allocations between products may be difficult to determine.

b) fixed cost allocations between products may be difficult to determine.

c) overhead allocation must be spread evenly across all product lines.

d) different products can have widely differing contribution margins even with the same level of sales.

*113. Montrose Company has a degree of operating leverage of 3. If the company’s sales increase from $200,000 to $225,000, by what percentage should its operating income increase?

a) 33.3%

b) 100%

c) 83.3%

d) 37.5%

Brief Exercises

Brief Exercise 120

Holiday Company produces two models: Red and Green. Information regarding the products is summarized for the month of April in the following table:

a) If Holiday sells 4 more red units, by how much will profit increase?

b) If Holiday sells 9 more green units, by how much will profit increase?

Solution 120

a) CM per red units: ($7,000 – $5,600) / 700 = $2 per unit

For 4 units: $2 x 4 units = $8. No change in fixed costs.

b) CM per green units: ($4,500 – $3,600) / 300 = $3 per unit

For 9 units: $3 x 9 units = $27. No change in fixed costs.

Brief Exercise 121

Deighan Company has the following income statement:

How much is Deighan's contribution margin?

Solution 121

Sales – variable costs = contribution margin

$25,000 – $17,000 – $2,000 = $6,000

Brief Exercise 122

Sam Company makes two products: footballs and baseballs. Additional information follows:

If Sam has unlimited demand for both products, which product should Sam tell his salespeople to emphasize?

Solution 122

Unit contribution margin:

Footballs = [$60,000 – $36,000] / 4,000 = $6

Baseballs = [$25,000 – $7,000] / 2,500 = $7.20

Sam should tell the salespeople to sell more baseballs due to the higher unit contribution margin.

Brief Exercise 123

Determine the missing amounts.

Solution 123

a) $300 – $200 = $100

b) $100 / $300 = 33.3%

c) $600 – $100 = $500

d) $100 / $600 = 16.7%

e) $400 / 40% = $1,000

f) If 40% = CM ratio, then 60% = variable cost percentage; $1,000 x 60% = $600

Or $1,000 – $400 = $600

Brief Exercise 124

MCL Inc. has fixed costs totalling $75,000. Its unit contribution margin is $2.50, and the selling price is $7.00 per unit. What is the break-even point in units and in dollars?

Solution 124

Break even in units = Fixed costs ÷ Unit contribution margin

= $75,000 ÷ $2.50

= 30,000 units

Break even in dollars = Break even in units x Selling price per unit

= 30,000 units x $7.00

= $210,000

Brief Exercise 125

Diaz Doughnuts sells boxes of doughnuts each with a variable cost percentage of 45%. Its fixed costs are $60,500 per year. What level of sales dollars does Diaz need in order to break even per year if doughnuts are its only product?

Solution 125

Contribution margin ratio = 100% – 45% = 55%

55X – $60,500 = 0

X = $$110,000 sales dollars

Brief Exercise 126

Kettle Goods Company has a unit selling price of $500, variable cost per unit $300, and fixed costs of $170,000. Calculate the break-even point in units and in sales dollars.

Solution 126

$500X − $300X − $170,000 = 0

BEP in units = X = 850 units

BEP in dollars = 850 units x $500 = $425,000

Brief Exercise 127

The following monthly data is available for Marketplace, Inc., which produces only one product that it sells for $22 per unit. The unit variable costs are $9, and its total fixed expenses are $9,100. Actual sales for the month of May totalled 4,000 units. How much is the margin of safety for the company for May?

Solution 127

BEP in units: $22 – $9X – $9,100 = 0

BEP in units = 700 units

Units at current sales level = 4,000

Margin of safety = (4,000 – 700) x $22 = $72,600

Sales can drop, or fixed costs can rise, by $72,600 before the company incurs a loss.

Brief Exercise 128

At the break-even point a company sells 2,400 widgets. Its selling price is $8 per widget, variable cost is $5 per widget, and its fixed cost is $3 per widget. If it sells 50 additional widgets, how much is incremental operating income?

Solution 128

$8(2,400) – $5(2,400) – X = 0

Total fixed costs = $7,200

Incremental profit = 50 x ($8 – $5) = $150

Brief Exercise 129

Whitey’s Fish Camp has sales of $1,500,000 for the first quarter of 2022. In making the sales, the company incurred the following costs and expenses:

Calculate net income using a contribution approach for 2022.

Solution 129

$500,000 − [$400,000 + $100,000 + $80,000] − [$550,000 + $75,000 + $67,000] = $228,000

Brief Exercise 130

Strom Widget Company reported sales of $1,800,000, and fixed costs of $400,000. The contribution margin ratio is 25%. Calculate the margin of safety in dollars and the margin of safety ratio.

Solution 130

BEP in dollars: $400,000 / 25% = $1,600,000

Margin of safety in dollars: $1,800,000 − $1,600,000 = $200,000

Margin of safety ratio: $200,000 / $1,800,000 = 11.1%

Brief Exercise 131

Erin’s Tires had sales of $775,000 last year. Total fixed costs were $300,000, and the contribution margin ratio was 40%. If rent is increased by $1,000 per month, will Erin’s Tires still make a profit?

Solution 131

BEP in dollars: $300,000 / 40% = $750,000

Margin of safety in dollars: $775,000 – $750,000 = $25,000

Increase in rent: $1,000 x 12 months = $12,000

Therefore, because the $12,000 increase in fixed costs is within the margin of safety, Erin’s Tires will still be profitable.

Brief Exercise 132

Lo-Calorie Doughnuts operates a chain of coffee shops in Southern Alberta. Its budgeted sales for the next year are $10,000,000 and its fixed and variable costs are $1,650,000 and $8,200,000, respectively. Management of the company wants to see what impact changes in activity and costs could have on its operating income.

In each of the following scenarios, calculate the effect on budgeted operating income:

a) a 10% reduction in variable costs

b) a 10% increase in fixed costs

c) a 5% increase in sales

d) a 5% increase in fixed costs and a 5% increase in sales

e) a 5% increase in fixed costs and a 5% decrease in variable costs

Solution 132 (4–6 min.)

Current Budget: Sales $10,000,000

Variable costs 8,200,000

Contribution margin 1,800,000

Fixed Costs 1,650,000

Operating income $150,000

a) Increase in CM: $8,200,000 x 10% = $820,000

New OI $150,000 + $820,000 = $970,000

b) Increase in fixed costs: $1,650,000 x 10% = $165,000

New OI $150,000 – $165,000 = ($15,000)

c) Increase in CM: $1,800,000 x 5% = $90,000

New OI $150,000 + $90,000 = $240,000

d) Increase in CM: $1,800,000 x 5% = $90,000

Increase in fixed costs: $1,650,000 x 5% = $82,500

New OI $150,000 + $90,000 – $82,500 = $157,500

e) New variable costs: $8,200,000 x 95% = $7,790,000

New CM = $10,000,000 – $7,790,000 = $2,210,000

Increase in CM: $2,210,000 – $1,800,000 = $410,000

Increase in fixed costs: $1,650,000 x 5% = $82,500

New OI $150,000 + $410,000 – $82,500 = $477,500

Brief Exercise 133

Haldi Corporation sells three different sets of sportswear. Sleek sells for $30 and has variable costs of $18; Smooth sells for $50 and has variable costs of $28; Potent sells for $90 and has variable costs of $45. The sales mix of the three sets is: Sleek, 50%; Smooth, 30%, and Potent, 20%. What is the weighted-average unit contribution margin?

Solution 133 (6–8 min.)

Sleek: 50% x ($30 – $18) = $6.00

Smooth 30% x ($50 – $28) = 6.60

Potent 20% x ($90 – $45) = 9.00

Weighted-average unit contribution margin $21.60

Brief Exercise 134

Garrett Corporation sells two product lines. The sales mix of the product lines is: Standard, 70%; and Deluxe, 30%. The contribution margin ratio of each line is: Standard, 35%; and Deluxe, 45%. Garrett’s fixed costs are $2,280,000. What is the dollar amount of Deluxe sales at the break-even point?

Solution 134 (6–8 min.)

Standard: 70% x 35% = 24.5%

Deluxe 30% x 45% = 13.5%

Weighted-average contribution margin ratio 38.0%

$2,280,000 / 38% = $6,000,000 break-even point in dollars.

Dollar amount of Deluxe sales at the break-even point: $6,000,000 x 30% = $1,800,000.

*Brief Exercise 135

Sheldon Corporation is considering buying new equipment for its factory. The new equipment will reduce variable labour costs but increases depreciation expense. The contribution margin is expected to increase from $200,000 to $300,000. Net income is expected to remain the same at $100,000. Calculate the degree of operating leverage before and after the purchase of the new equipment. What is your interpretation of these results?

Solution 135 (4–6 min.)

Contribution margin / Net income = Degree of operating leverage

Before: $200,000 / $100,000 = 2

After: $300,000 / $100,000 = 3

After the new equipment is purchased, Sheldon’s earnings would go up (or down) by 1.5 times (3/2) as much as it would have before the purchase, with an equal increase (or decrease) in sales.

*Brief Exercise 136

Ipso Company and Facto Company have degrees of operating leverage of 2.0 and 3.5 respectively and each has operating income of $5,000. Determine the fixed costs of each company.

Solution 136 (4–6 min.)

Ipso Facto

Contribution margin $5,000 x 2 = $10,000

$5,000 x 3.5 = $17,500

Operating income 5,000 5,000

Fixed costs $5,000 $12,500

*Brief Exercise 137

Tidy Cleaners sold 25,000 units during the month of April. The company’s CVP income statement for the month is reflected below:

Sales $1,800,000

Variable expenses 1,200,000

Contribution margin 600,000

Fixed expenses 450,000

Operating Income $ 150,000

Calculate the following for Tidy Cleaners:

a) Break-even units

b) Break-even sales

c) Margin of safety

Solution 137

a) Break-even units: $450,000 / ($600,000 / 25,000) = 18,750 units

b) Break-even sales: $1,800,000 / 25,000 x 18,750 = $1,350,000

c) Margin of safety: $1,800,000 – $1,350,000 = $450,000

EXERCISES

Exercise 138

Oak Hammock Company compiled the following information for its bucket sales:

Sales price $6.50 per unit

Variable cost of goods sold $1.50 per unit

Fixed cost of goods sold $26,000

Variable selling expense 10% of sales price

Variable administrative expense $0.25 per unit

Fixed selling expense $4,000

Fixed administrative expense $3,000

For the year ended December 31, 2022, Oak Hammock Company produced and sold 15,000 buckets.

Instructions

a) Prepare a CVP income statement using the contribution margin format for Oak Hammock Company for 2022.

b) Briefly explain how this statement differs from the traditional GAAP income statement.

Solution 138 (9–12 min.)

a)

OAK HAMMOCK COMPANY

CVP Income Statement

For the Year Ended December 31, 2022

——————————————————————————————————————————

Sales $97,500

Variable expenses

Cost of goods sold $22,500

Administrative 3,750

Selling expenses 9,750

Total variable expenses 36,000

Contribution margin 61,500

Fixed expenses

Cost of goods sold 26,000

Selling 4,000

Administrative 3,000

Total fixed expenses 33,000

Net income $28,500

b) The CVP income statement format separates costs into fixed and variable components. The traditional GAAP income statement separates costs into product and period costs. Both report the same net income assuming ending and beginning inventories do not change during the period.

Exercise 139

Ripple Company bottles and distributes Ripple Fizz, a flavoured wine beverage. The beverage is sold for $1.50 per 8-ounce bottle to retailers. Management estimates the following revenues and costs at 100% of capacity.

Instructions

a) How much is net income for the year using the CVP approach? Present your answer in CVP income statement format.

b) Calculate the break-even point units and dollars.

c) How much is the contribution margin ratio?

Solution 139 (6–8 min.)

a) Sales $3,000,000

Less:

Direct Materials $700,000

Direct Labour 1,000,000

Variable MOH 400,000

Variable Selling 35,000

Variable Admin 15,000

Total Variable Costs 2,150,000

CM 850,000

Less:

Fixed MOH 170,000

Fixed Selling 14,000

Fixed Admin 30,000

Total Fixed Costs 214,000

Net Income $636,000

b) Number of units sold = $3,000,000 / $1.50 = 2,000,000

Variable cost/unit = $2,150,000 / 2,000,000 = $1.075

BEP in units: $1.50X − $1.075X − $214,000 = 0

Units = 503,529.41 or 503,530 units

BEP in dollars: 503,530 x $1.50 = $755,295

c) $850,000 / $3,000,000 = 28.3%

Exercise 140

In the month of June, Doe Company sold 400 widgets. The average sales price was $24. During the month, fixed costs were $4,320 and variable costs were 40% of sales.

Instructions

a) Determine the contribution margin in dollars, per unit, and as a ratio.

b) Calculate the break-even point in units and dollars.

c) How much are total variable costs at break even?

Solution 140 (7–9 min.)

a) Contribution margin in dollars

Sales (400 × $24) $9,600

Less: Variable costs ($9,600 × 40%) 3,840

Contribution margin $5,760

Unit contribution margin

Unit sales price $24.00

Less: Variable cost per unit ($24 × 40%) 9.60

Unit contribution margin $14.40

or Unit contribution margin ÷ Widgets sold = $5,760 ÷ 400 = $14.40

Contribution margin ratio: $14.40 ÷ $24 = 60%

b) BEP in units: $24X − $9.6X − $4,320 = $0

X = 300 units

BEP in dollars: 300 x $24 = $7,200

c) 300 x $9.60 = $2,880

Exercise 141

Graphly Company has prepared the following cost-volume-profit graph:

Instructions

For the items listed below, enter to the left of the item, the letter in the graph that best corresponds to the item.

____ 1. Operating Income ____ 6. Break-even point

____ 2. Revenues ____ 7. Dollars

____ 3. Total costs ____ 8. Fixed costs

____ 4. Variable costs ____ 9. Loss

____ 5. Activity base

Solution 141 (4–7 min.)

1. B Operating Income

2. I Revenues

3. H Total costs

4. F Variable costs

5. D Activity base

6. A Break-even point

7. E Dollars

8. C Fixed costs

9. G Loss

Exercise 142

In 2021 Karly Company had a break-even point of $800,000 based on a selling price of $10 per unit and fixed costs of $320,000. In 2022 the selling price and variable costs per unit did not change, but the break-even point increased to $920,000.

Instructions

a) Calculate the variable cost per unit for 2021 and 2022.

b) Calculate the contribution margin ratio for 2021 and 2022.

c) Calculate the amount of total fixed costs for 2022.

Solution 142 (7–9 min.)

a) Units sold = $800,000 / $10 = 80,000 units

$800,000 – (80,000) (X) − $320,000 = $0

VC = $6 per unit

b) ($10 − $6) / $10 = 40%

c) Fixed costs = Break-even Sales × CM Ratio

= $920,000 × 40% = $368,000

Exercise 143

Homer Company produces two models: Bart and Lisa. Information regarding these models is summarized for the month of March in the following table:

Fixed costs of Bart will be avoided if only the Lisa model is produced.

Instructions

a) Show how the unit contribution margin of the Bart model was calculated.

b) If Homer produces ONLY the Lisa model, how many units must it sell to earn operating income of $33,000?

Solution 143 (5–7 min.)

a) Contribution margin/units =

($90,000 – $60,000) / 6,000 units = $5/unit

b) Selling price – variable costs – fixed costs = $33,000

$12X – *$9X – $27,000 = $33,000

X = 20,000 units

*$12 – $3 = $9

Exercise 144

Slow Movers compiled the following unit amounts for a division that manufactures one product:

Per Unit

Sales price $90

Variable cost 54

Contribution margin $36

Total fixed costs $432,000

Instructions

Answer the following independent questions and show computations to support your answers.

a) How many units must be sold to break even?

b) What are the total sales in dollars that must be generated for the company to earn an operating income of $50,400?

c) If the company is presently selling 14,000 units, but plans to spend an additional $135,000 on an advertising program, how many additional units must the company sell to earn the same net income it is now making?

Solution 144 (7–9 min.)

a) $90X − $54X − $432,000 = $0

X = 12,000 units

b) $90X − $54X − $432,000 = $50,400

X = 13,400 units

Sales = 13,400 x $90 = $1,206,000

c) Current income = 14,000 ($36) − $432,000 = $72,000

$90X − $54X – ($432,000 + $135,000) = $72,000

Units needed = 17,750

Additional units = 17,750 – 14,000 = 3,750

Exercise 145

Speakerboxx Music, Inc. produces a hip-hop CD that is sold for $15. The contribution margin ratio is 30%. Fixed expenses total $6,750.

Instructions

a) Calculate the variable cost per unit.

b) Calculate how many CDs that Speakerboxx will have to sell to break even.

c) Calculate how many CDs that Speakerboxx will have to sell to make a target operating income of $16,200.

d) Fill in the dollar amounts for the summary CVP income statement below based on your answer to part C.

Solution 145 (7–10 min.)

a) Variable cost per CD: $15 × (1 –.30) = $10.50/unit

b) $15X – $10.50X – $6,750 = $0

X = 1,500 units

c) $15X – $10.50X – $6,750 = $16,200

X = 5,100 units

d) Sales revenue $76,500

Variable costs 53,550

Contribution margin 22,950

Fixed costs 6,750

Net income $16,200

Exercise 146

Gloria Meehan is considering opening a window tinting business. She estimates that the following costs will be incurred during the first year of operations: Rent, $6,500; depreciation on equipment, $7,250; Wages, $4,250 (wages vary with production, estimate is based on 625 windows tinted in the previous year); tinting, $4 per square foot. Each window tinted takes 5 square feet of tint. Gloria anticipates that she will tint each window for a retail price of $63 each.

Instructions

a) Determine variable costs per unit and total fixed costs.

b) Determine the break-even point in number of windows to be tinted.

c) How many windows need to be tinted to earn income of $21,000?

Solution 146 (6–8 min.)

a) Variable cost:

Wages, $4,250 / 625 = $6.80 per window

+ Materials: (5sf x $4/sf) = 20.00

Total variable cost = $26.80 per window

Fixed costs: $6,500 + $7,250 = $13,750

b) $63X − $26.80X − $13,750 = $0

BEP in units = 380 units

c) $63X − $26.80X − $13,750 = 21,000

Units to earn $21,000 = 960 units

Exercise 147

Tractor Power, Inc. estimates that variable costs will be 55% of sales and fixed costs will total $297,000. The selling price of each gear is $120, and 5,600 units will be sold.

Instructions

a) Calculate the break-even point in units and dollars.

b) How much can sales decline before the company experiences a loss?

Solution 147 (4–5 min.)

a) Variable cost per unit = $120 x 55% = $66

$120X − $66X − $297,000 = $0

Units = 5,500

Sales = 5,500 x $120 = $660,000

b) Margin of safety in dollars:

($120 x 5,600) – $660,000 = $12,000

Exercise 148

Varona Company makes student book bags that sell for $12 each. For the coming year, management expects fixed costs to be $43,000. Variable costs are $7 per unit.

Instructions

a) Calculate break-even sales in dollars.

b) Calculate the sales in dollars required to earn net income of $30,000.

Solution 148 (4–5 min.)

a) $12X − $7X − $43,000 = $0

X = 8,600 units; 8,600 × $12/unit = $103,200

b) $12X − $7X − $43,000 = $30,000

X = 14,600 units; 14,600 x $12/unit = $175,200

Exercise 149

Jay Manufacturing’s sales decreased significantly in 2021 due to increased online purchasing. The company’s income statement showed the following results from selling 375,000 units of product: Net sales, $1,781,250; total costs and expenses, $2,480,000; and net loss of $698,750. Costs and expenses consisted of the following:

Management is considering the following alternative for 2022:

Purchase new automated equipment that will change the proportion between variable and fixed costs to 23% variable and 77% fixed.

Instructions

a) Determine the selling price per unit.

b) Calculate the break-even point in dollars for 2021.

c) Calculate the break-even point in dollars under the alternative course of action for 2022.

d) Which course of action do you recommend? Justify your answer.

Solution 149 (8–10 min.)

a) Selling price = $1,781,250 / 375,000 = $4.75 per unit

b) Variable cost per unit = $975,000 / 375,000 = $2.60 per unit

Sales – VC – FC = 0

$4.75X − $2.60X − $1,505,000 = 0

BEP in units = 700,000 units

BEP in dollars = 700,000 x $4.75 = $3,325,000

c) Current variable proportion = $975,000 / $2,480,000 = 39%

New variable cost per unit = (23% x $2,480,000) / 375,000 = $1.52 per unit

$4.75X – $1.52X – ($2,480,000 x 77%) = 0

New BEP in units = 591,207 units

New BEP in dollars = 591,207 x $4.75 = $2,808,235

d) Since the break-even point declines, the company should select the alternate option.

Exercise 150

Alice Davies operates a day spa in Jacksonville, Florida. She estimates the following costs during the year:

Depreciation on the building and equipment = $21,000

Maintenance person’s annual salary = $34,000

Spa Technicians’ annual salaries = $87,000

Miscellaneous operating costs = $15 per customer per service

The average revenue of services is $65.

Instructions

a) How much is the contribution margin per service?

b) Calculate the number of services Alice must provide in order to break even.

c) Alice is considering upgrading the shower area to attract more business and increase prices. This will cost an additional $4.00 per service, with an annual increase in depreciation of $10,880, and will allow the average price of services to be increased to $75. How many services will Alice need to provide to break even under these changes?

d) Should Alice upgrade the shower area? Why or why not?

Solution 150 (8–10 min.)

a) $65 – $15 = $50

b) Fixed costs = $21,000 + $34,000 + $87,000 = $142,000

65X – 15X – 142,000 = 0

X = 2,840

c) 75X – (15X + 4X) – (142,000 + 10,880) = 0

X = 2,730 services

d) Yes. The number of services to be provided to break even will decline.

Exercise 151

Treasure Island Bullion Chests Ltd. is looking at adding a new treasure chest to its lineup, called the Jake Sparrow model. This model has the following budgeted sales and costs data:

Budgeted sales 10,000 chests

Selling price per chest $225

Variable costs per chest $120

Fixed costs for the year

Manufacturing $350,000

Head office administration $175,000

The company knows that the new chest will reduce sales of current models and the contribution margin of these models will decrease by $260,000. The manufacturing fixed costs are considered to be avoidable; however, the head office administration costs are not.

Instructions

a) If the new chest is produced and sold, calculate the change in operating income.

b) Calculate the lowest selling price per chest that could be charged for the company to break even.

Solution 151 (8–10 min.)

a) 10,000 x ($225 – $120) = $1,050,000 – $350,000 – $260,000 = $440,000

(Note that the HO administration fixed costs are unavoidable and therefore, do not enter the calculation)

b) 10,000 * (X – 120) – $350,000 – $260,000 = $0

10,000X = $1,810,000

X = $181 is the lowest price that can be charged in order for the company to break even.

Exercise 152

Jagswear, Inc. earned net income of $250,000 during 2021. The company wants to earn an operating income of $275,000 during 2022. The company’s fixed costs are expected to be $75,000, and variable costs are expected to be 40% of sales.

Instructions

a) Determine the required sales to meet the target net income during 2022.

b) Fill in the dollar amounts for the summary CVP income statement for 2022 below based on your answer to part a).

Solution 152 (4–5 min.)

a) 60%X – 75,000 = 275,000

Required sales = $583,333

b) Sales revenue $583,333

Variable costs 233,333

Contribution margin 350,000

Fixed costs 75,000

Net income $275,000

Exercise 153

Fred is thinking of entering the soft drinks market in the area surrounding his cottage. He is going to call his company “Pop’s Pop.” He realizes that the soft drink industry is dominated by only three companies that keep the competition out by spending a great deal on advertising. Nonetheless, Fred is tempted by the high profit margin. He plans to sell his cola for a dollar per bottle. Variable costs are $0.20 per bottle. His fixed costs are estimated at $100,000. He currently has the capacity to make and sell 200,000 bottles in a summer. In order to justify spending his time on this venture, rather than sitting on his dock, Fred needs to have an operating income of $15,000.

Instructions

a) What is Fred’s break even in units?

b) How many bottles must Fred sell to achieve his target income of $15,000?

c) Is Fred’s plan feasible?

Solution 153 (7–9 min.)

a) Break even in units = Fixed costs ÷ Unit contribution margin

= $100,000 ÷ ($1.00 – $0.20)

= 125,000 bottles.

b) Units needed for target income = ($100,000 + $15,000) ÷ ($1.00 – $0.20)

= 143,750 bottles

c) If Fred can sell 200,000 bottles, his plan is feasible. He only needs to sell 125,000 bottles to break even, and 143,750 to reach his target income of $15,000. If he does sell 200,000 bottles, he will have income of (200,000 x $0.80) – $100,000, or $60,000.

Exercise 154

The CVP income statement for Raple Stark Company for 2022 appears below:

RAPLE STARK COMPANY

CVP Income Statement

For the Year Ended December 31, 2022

——————————————————————————————————————————

Sales (25,000 units) $650,000

Variable expenses 227,500

Contribution margin 422,500

Fixed expenses 439,400

Net income (loss) $(16,900)

Instructions

Answer the following independent questions and show computations to support your answers:

a) How much additional sales revenue does the company need to break even in 2022?

b) If the company is able to reduce variable costs by $1.25 per unit in 2023 and other costs and unit revenues remain unchanged, how many units will the company have to sell in order to earn a net income of $50,650?

Solution 154 (7–9 min.)

a) Selling price per unit = $650,000 / 25,000 = $26

Variable cost per unit = $227,500 / 25,000 = $9.10

$26X − $9.10X − $439,400 = $0

Total units to break even = 26,000

Total sales revenue to break even = 26,000 x $26 = $676,000

Additional sales revenue to break even = $676,000 − $650,000 = $26,000

b) $26X – [($9.10 − $1.25)X] − $439,400 = $ 50,650

Units needed to break even = 27,000

Exercise 155

Daryl’s Anything for a Buck is a dollar store. It reported the following results for the month of August:

Sales (100,000 units) $100,000

Variable costs 30,000

Contribution margin 70,000

Fixed costs 49,000

Operating income $21,000

Daryl is concerned the slowdown in the economy will have a negative impact on sales. To add to Daryl’s concerns, his landlord is looking to increase his monthly rent by $1,000.

Instructions

a) What was Daryl’s margin of safety for August?

b) What would Daryl’s operating income be if the rent increase does occur, and sales fall by 10%?

Solution 155 (6–8 min.)

a) Break even in dollars = Fixed costs ÷ Contribution margin ratio

Contribution margin ratio = Contribution margin ÷ Sales

= $70,000 / $100,000

= 70%

Break even in dollars = $49,000 / 0.7, or $70,000

Margin of safety = Actual sales – Break-even sales

= $100,000 – $70,000

= $30,000

b) Sales (100,000 x 0.9 units) $90,000

Variable costs 27,000

Contribution margin 63,000

Fixed costs 50,000

Operating income $13,000

Exercise 156

Trail King manufactures mountain bikes. Its sales mix and contribution margin information per unit is shown is follows:

Sales mix Contribution margin

Destroyer 15% $120

Voyager 60% $ 60

Rebel 25% $ 40

It has fixed costs of $5,440,000.

Instructions

Calculate the number of each type of bike that the company needs to sell to break even under this product mix.

Solution 156 (8–12 min.)

Sales Mix Margin Contribution Margin

Destroyer 15% $120 $ 18

Voyager 60% $ 60 $ 36

Rebel 25% $ 40 $ 10

64

Total break-even sales = $5,440,000 ÷ $64 = 85,000 bikes

Sales mix

Destroyer 15% x 85,000 = 12,750 bikes

Voyager 60% x 85,000 = 51,000 bikes

Rebel 25% x 85,000 = 21,250 bikes

Exercise 157

Account-Able provides two lines of service: accounting and tax. Accounting-related services represent 60% of its revenue and provide a contribution margin ratio of 30%. Tax services provide 40% of its revenue and provide a 45% contribution margin ratio. The company’s fixed costs are $8,100,000.

Instructions

a) Calculate the revenue from each type of service that the company must achieve to break even.

b) The company has a desired net income of $1,800,000. What amount of revenue would Account-Able earn from tax services if they achieve this goal with the current sales mix?

Solution 157 (10–15 min.)

a)

Contribution Weighted-Average

Sales Mix Margin Ratio Contribution Margin Ratio

Accounting 60% 30% 18%

Tax 40% 45% 18%

36%

Total break-even sales = $8,100,000 ÷.36 = $22,500,000

Sales mix

Accounting 60% x $22,500,000 = $13,500,000

Tax 40% x $22,500,000 = $ 9,000,000

b) Sales to achieve target net income = ($8,100,000 + $1,800,000) ÷.36 = $27,500,000

Sales mix

Tax 40% x $27,500,000 = $11,000,000

Exercise 158

Mad City Flash sells computers and video game systems. The business is divided into two divisions along product lines. CVP income statements for the current year are presented below:

Computers VG Systems Total

Sales $800,000 $200,000 $1,000,000

Variable costs 480,000 140,000 620,000

Contribution margin $320,000 $ 60,000 380,000

Fixed costs 228,000

Net income $ 152,000

Instructions

a) Determine the sales mix, and contribution margin ratio for each division.

b) Calculate the company’s weighted-average contribution margin ratio.

c) Calculate the company’s break-even point in dollars.

d) Determine the sales level, in dollars, for each division at the break-even point.

Solution 158 (15–20 min.)

a) Sales mix:

Computers: $800,000 ÷ ($800,000 + $200,000) = 80%

VG Systems: $200,000 ÷ ($800,000 + $200,000) = 20%

Contribution margin ratio:

Computers: $320,000 ÷ $800,000 = 40%

VG Systems: $ 60,000 ÷ $200,000 = 30%

b) Weighted-average contribution margin ratio = (80% x 40%) + (20% x 30%) = 38%

c) Break-even point in dollars = $228,000 ÷.38 = $600,000

d) Sales dollars at break-even point

Computers: $600,000 x.80 = $480,000

VG Systems: $600,000 x.20 = $120,000

*Exercise 159

Jenson Industries manufactures and sells a mouse pad for office environments. Information on this product is as follows:

Mouse pads sold 250,000 per year

Selling price $30

Variable costs $15

Fixed costs $1,200,000

Instructions

a) Determine the break-even point for this product in dollars and units.

b) Determine the degree of operating leverage.

Solution 159 (8–10 min.)

a) In dollars: Fixed Costs ÷ CM ratio: $1,200,000 ÷.50 = $2,400,000

In units:

Total revenue 250,000 x $30 = $7,500,000

Variable costs 250,000 x $15 = 3,750,000

Contribution margin $3,750,000

CM per unit: $3,750,000 ÷ 250,000 = $15

Fixed Costs ÷ Unit CM ratio: $1,200,000 ÷ 15 = 80,000 units

b) [250,000 (30 – 15)] / [250,000 (30 – 15) – 1,200,000] = 1.471

*Exercise 160

The following CVP income statements are available for Antique Company and Contemporary Company:

Antique Company Contemporary Company

Sales revenue $ 700,000 $700,000

Variable costs 350,000 140,000

Contribution margin 350,000 560,000

Fixed costs 200,000 410,000

Net income $150,000 $150,000

Instructions

a) Calculate the degree of operating leverage for each company.

b) Assume that sales revenue decreases by 20%. Prepare a CVP income statement for each company.

*Solution 160 (15–20 min.)

a)

Contribution ÷ Net = Degree of Operating

Margin Income Leverage

Antique $350,000 ÷ $150,000 = 2.333

Contemporary $560,000 ÷ $150,000 = 3.733

b)

Antique Company Contemporary Company

Sales revenue *$ 560,000 *$560,000

Variable costs **280,000 ***112,000

Contribution margin 280,000 448,000

Fixed costs 200,000 410,000

Net income $ 80,000 $ 38,000

*$700,000 x.8

** ($350,000 ÷ $700,000) x $560,000

*** ($140,000 ÷ $700,000) x $560,000

*Exercise 161

An investment banker is analyzing two companies that specialize in the production and sale of gourmet cappuccino and chai mixes. The first company, Fireside uses a labour-intensive approach, while Stirring Moments uses a mechanized system. CVP income statements for the two companies are shown below:

Fireside Stirring Moments

Sales $1,000,000 $1,000,000

Variable costs 600,000 250,000

Contribution margin 400,000 750,000

Fixed costs 200,000 550,000

Net income $ 200,000 $ 200,000

The investment banker is interested in purchasing one of these companies. However, she is concerned about the effect that each company’s cost structure might have on its profitability.

Instructions

a) Calculate each company’s degree of operating leverage.

b) Determine the effect on each company’s net income if sales decrease by 10% and if sales increase by 20%. Do not prepare income statements.

*Solution 161 (8–10 min.)

a) Degree of

Operating

Contribution Margin ÷ Net Income = Leverage

Fireside $400,000 ÷ $200,000 = 2.00

St. Moments $750,000 ÷ $200,000 = 3.75

b) Degree of % Change

Operating in

% Change in Sales x Leverage = Net Income

Fireside (10%) x 2.00 = (20.0%)

St. Moments (10%) x 3.75 = (37.5%)

Fireside 20% x 2.00 = 40.0%

St. Moments 20% x 3.75 = 75.0%

*Exercise 162

Some details regarding Golf Plus and New Golf are indicated below:

Determine the missing amounts.

Solution 162

COMPLETION STATEMENTS

163. The amount of revenue remaining after deducting total variable costs is called the ___.

164. A ___ income statement classifies costs and expenses as variable or fixed and reports contribution margin.

165. The ___ point is when total revenues equal total costs.

166. ___ divided by the contribution margin ratio calculates the amount of ___ to break even.

167. The difference between actual or expected sales and break-even sales is called the ___.

168. ___ is the relative percentage in which each product is sold when a company sells more than one product.

169. When more than one product is sold, break-even point can be determined by dividing fixed expenses by ___.

*170. The ___ provides a measure of a company’s earning’s volatility and can be used to compare operating leverage across two companies.

ANSWERS TO COMPLETION STATEMENTS

163. contribution margin

164. CVP

165. break-even

166. fixed costs, sales in dollars

167. margin of safety

168. sales mix

169. weighted-average unit contribution margin

170. degree of operating leverage

MATCHING

*171. Match the items in the two columns below by entering the appropriate code letter in the space provided.

A. Activity index F. Mixed costs

B. Variable costs G. Break-even point

C. Fixed costs H. Contribution margin

D. Degree of Operating Leverage I. Margin of safety

E. Relevant range J. Contribution margin ratio

___ 1. The level of activity at which total revenues equal total costs

___ 2. The operating level at which the company expects to operate during the year

___ 3. Costs that remain the same in total regardless of changes in the activity level

___ 4. A measure of a company’s earnings volatility

___ 5. The amount of revenue remaining after deducting variable costs

___ 6. Costs that contain both a variable and a fixed cost element

___ 7. The percentage of sales dollars available to cover fixed costs and produce income

___ 8. The difference between actual sales and sales required to break even

ANSWERS TO MATCHING

1. G

2. E

3. C

4. D

5. H

6. F

7. J

8. I

SHORT-ANSWER ESSAY QUESTIONS

SAE 172

A CVP income statement is frequently prepared for internal use by management. Describe the features of the CVP income statement that make it more useful for management decision making than the traditional GAAP income statement that is prepared for external users.

Solution 172

Several features of the CVP income statement make it more useful for internal decision making. The CVP income statement classifies costs as either fixed or variable, rather than by function. Being able to identify the behaviour of costs in this manner can aid management in controlling those costs.

Also, the CVP income statement shows the contribution margin, rather than a gross profit. This helps management establish the extent to which their sales are able to cover their fixed costs, and to analyze the impact on net income of changes in sales or costs.

SAE 173

A cost-volume-profit graph is frequently used in business meetings because it presents a picture of cost relationships within a company. Briefly describe the type of information and data that you would need in order to prepare a CVP graph. After a CVP graph is prepared, what are the major points that could be made from the graph that would be of interest to management?

Solution 173

To begin constructing a CVP graph, information is needed to determine the maximum estimated expected level of sales units and the unit sales price. This is necessary to create the axes and to plot the total revenue line from the origin. In addition, the costs must be broken down into fixed and variable components, in order to plot both the fixed cost line and the total cost line.

Using a CVP graph, management can readily identify the break-even point and can see how much operating income or loss would result from varying levels of sales. The graph also makes it easy to portray the effects of any changes such as fixed costs, variable costs or selling prices.

SAE 174

Spinel Company had the following information related to the sale of 8,000 units for the period:

Sales $56 per unit

Variable costs $28 per unit

Fixed costs $84,000

Operating income $0.25 per unit

Instructions

1. Calculate the margin of safety in dollars and the margin of safety ratio.
2. Explain the results from part (a) in terms of operating income and risk.

Solution 174

1. Margin of safety in dollars:

($56 x 8,000) – [$84,000 / ($56- $28)] x $56 = $280,000

Margin of safety ratio:

$280,000 / ($56 x 8,000) x 100 = 62.5%

1. The company’s sales would have to fall more than $280,000 or 62.5% before it would be operating at a loss. The higher the margin of safety dollars or margin of safety ratio, the lower the risk the company will operate at a loss.

SAE 175

For two years Alex Mackenzie has been the manager of the production department of a company manufacturing toys made of plastic-coated cardboard. One of the toys is a paper doll, whose "clothes" are made of acetate and stay on the doll with static electricity. The company's sales were mainly to large educational institutions until last year, when the dolls were sold for the first time to a large discount retailer. The dolls were sold out immediately, and enough orders received to keep the department at full capacity for the immediate future.

The fixed costs for the department are $45,000, with $0.75 per-unit variable costs. Each set consists of a doll and one set of clothes and sells for $2.75. The maximum volume is 80,000 units. With the increased volume, Mr. Mackenzie is considering two options to improve profitability. One would reduce variable costs to $0.50, and the other would reduce fixed costs to $30,000.

Instructions

Given the fact that sales are increasing, make a short (one paragraph) recommendation to Mr. Mackenzie about which option he should choose. Support your recommendation with a calculation showing him how profitability will change with each option.

Solution 175

The variable costs should be reduced to $0.50 per unit because profits are higher at this level.

Current Profit = ($2.75 × 80,000) – ($0.75 × 80,000) – $45,000

= $220,000 – $60,000 – $45,000

= $115,000

Plan #1: Reduce Variable Costs to $0.50

Profit = ($2.75 × 80,000) – ($0.50 × 80,000) – $45,000

= $220,000 – $40,000 – $45,000

= $135,000

Plan #2: Reduce Fixed Costs to $30,000

Profit = ($2.75 × 80,000) – ($0.75 × 80,000) – $30,000

= $220,000 – $60,000 – $30,000

= $130,000

SAE 176

As CVP analysis can be used when responding to change. Identify and explain whether or a not a change should be made given the following scenarios:

1. A decrease in contribution margin of $10,000; a decrease in fixed costs of $12,000.
2. An increase in contribution margin of $15,000; an increase in fixed costs of $18,000.

Solution 176

1. The change should be made, given that fixed costs will be reduced by a greater amount than the decrease in contribution margin resulting in improved operating income.
2. The change should not be made, given that contribution margin will be increased by a lower amount than the increase in fixed costs resulting in deteriorated operating income.

SAE 177

Describe three ways in which data analytics can play an important role in CVP analysis.

Solution 177

CVP analysis is used to study the effects that changes in costs and volume have on a company’s profit. The collection and analysis of data, referred to as data analytics, plays an important role in CVP analysis as it can assist managers in accurately distinguish fixed and variable costs and optimizing sales mix, making future predictions and improving profitability.

*SAE 178

Jacob Andrews, president of Video Adventure, has heard about operating leverage and asks you to explain this term. What is operating leverage? How does a company increase its operating leverage?

*Solution 178

Operating leverage refers to the change in net income that a company experiences when there is a change in net sales revenue. Companies that have higher fixed costs relative to variable costs have higher operating leverage. In that case, the company’s operating income will increase rapidly when sales revenue increases, but decrease rapidly when sales revenue decreases. A company can increase its operating leverage by increasing its reliance on fixed costs, with a corresponding decrease in variable costs.

MULTI-PART QUESTION

179. The following information for 2022 for Vinnie`s Cream Pie Fillings is available:

Baking capacity 3,000 tonnes of filling

Tonnage sold in year 1,800

Sales $900,000

Variable costs 495,000

Contribution margin $405,000

Fixed costs

Manufacturing 90,000

Selling 112,500

Administration 45,000

Income before taxes $157,500

Income taxes @ 40% 63,000

Net income $ 94,500

Instructions

Consider each of the following scenarios independently:

a) Calculate the break-even volume in tonnes for the year.

b) If Vinnie expects to sell 2,100 tonnes of filling next year, calculate the expected after-tax income, assuming costs and prices remain the same.

c) Vinnie`s cousin says he can sell pie filling to a new company in a nearby city but will require Vinnie to pay $61,500 to advertise the product. In addition, Vinnie will have to pay his cousin $25 for each tonne sold. Calculate the number of tones that will have to be sold to maintain the current after-tax net income.

d) Vinnie wants to ramp up production by investing in a new machine that will cost $58,500. The benefit will be that variable costs will decrease by $25 per tonne. Calculate the new break even if the new machine is purchased.

e) Assume instead that Vinnie does not purchase the machine or begin selling in the new city. He is worried that per-tonne selling prices will decline by 10% and variable costs will increase by $40 per tonne. Calculate the sales volume in dollars needed if Vinnie is to maintain his after-tax income of $94,500.

Solution 179

a) CM/Unit = $405,000 ÷ 1,800 = $225

B/E point = $247,500 ÷ 225 = 1,100 tonnes

b) [(2,100 x 225) – 247,500] x.6 = $135,000

c) B/E in new city: CM/Unit = $225 – 25 = $200

Incremental fixed costs = $61,500

B/E point = 61,500 ÷ 200 = 307.5 tonnes

d) CM/unit = $250

FC = 247,500 + 58,500 = $306,000

B/E Point = $306,000 / 250 = 1,224 tonnes

e) New Selling Price = 900,000 ÷ 1,800 x.9 = $450

New VC/unit = $275 + 40 = $315

CM/Unit = $135

CM ratio = 30%

Before tax income = 94,500 ÷.6 = 157,500

Sales = (247,500 + 157,500) ÷.30 = $1,350,000

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