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CHAPTER 5 COST-VOLUME-PROFIT ANALYSIS TRUE/FALSE 1. Unit contribution margin equals price less unit variable cost. LO1 – True 2. Contribution margin is not an appropriate measure for evaluating short-term decisions. LO1 – False Contribution margin is an appropriate measure for evaluating short-term decisions. 3. Both revenues and variable costs are proportional to sales volume. LO1 – True 4. For every unit sold, profit increases by an amount equal to the unit gross margin. LO1 – False For every unit sold, profit increases by an amount equal to the unit contribution margin. 5. Over the short-term, fixed costs do not change with the number of units sold. LO1 – True 6. Even when there are no sales, total costs include only variable costs. LO2 – False When there are no sales, revenues are zero and total costs equal fixed costs. 7. To have any chance of making a profit, a firm must have a positive unit contribution margin. LO2 – True 8. For every unit sold, both contribution margin and profit increase at the same rate, by an amount equal to the unit contribution margin. LO2 – True 9. The contribution margin ratio is simply the unit contribution margin divided by variable costs. LO2 – False The contribution margin ratio is simply the unit contribution margin divided by price. 10. The contribution margin ratio is the portion of every sales dollar that contributes toward covering fixed costs and, ultimately, to profit. LO2 – True 11. In addition to planning profits, the CVP relation helps organizations make short-term decisions. LO3 – True 12. When all other factors remain the same, if a firm decides to decrease the selling price of its product, its unit contribution margin also decreases. LO3 – True

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Balakrishnan Managerial Accounting 13. If a firm decides to decrease the selling price of its product, the only way to increase overall profit is to offset the reduction in unit contribution margin by decreasing variable costs. LO3 – False If a firm decides to decrease the selling price of its product, its overall profit will increase only if the reduction in unit contribution margin is more than offset by the additional sales volume that price cuts typically generate. 14. Reducing price always increases demand of a product. LO3 – False Reducing the price too much could hurt profit. 15. CVP analysis allows firms to evaluate the tradeoff between price and quantity, and their effect on profit. LO3 – True 16. Breakeven volume = Unit Fixed costs ÷ Total contribution margin. LO4 – False Breakeven volume = Fixed costs ÷ Unit contribution margin. 17. Firms generally are reluctant to add fixed costs to their cost structure because fixed costs represent a sure outflow. LO4 – True 18. Two common measures of operating risk are contribution margin and margin of safety. LO4 – False Two common measures of operating risk are margin of safety and operating leverage. 19. The margin of safety allows firms to evaluate risk by considering the amount by which expected sales exceeds breakeven sales. LO4 – True 20. If the breakeven point is reduced, the margin of safety is also reduced. LO4 – False By reducing the breakeven point, margin of safety is increased. 21. When a firm makes multiple products or many versions of the same product, it is not advisable to perform CVP analysis on a product-by-product basis. LO5 – False When a firm makes multiple products or many versions of the same product, it is not advisable to perform CVP analysis on a product-by-product basis. Rather it is necessary to perform CVP analysis by taking into consideration all products at once as a group. 22. CVP analysis with many products is essentially the same as for a single product. LO5 – True 23. There are two equivalent methods for performing multi-product CVP analysis: the contribution margin method and the margin of safety method. LO5 – False There are two equivalent methods for performing multi-product CVP analysis: the weighted unit contribution margin method and the weighted contribution margin ratio method. 24. The weighted unit contribution margin is defined as the unit contribution margin averaged across multiple products with each product’s unit contribution margin being weighted by the product mix. LO5 – True 5-2

Cost-volume-Profit Analysis 25. We can compute the weighted contribution margin ratio either from the segment contribution margin statement or from unit level data. LO5 – True 26. CVP analysis enables decision makers to assess how much volume they need to avoid a loss or to maintain a certain margin of safety. LO6 – True 27. An advantage of CVP analysis is that it takes into account the time value of money. LO6 – False CVP analysis does not take into account the time value of money. 28. CVP analysis is a tool that helps managers improve profit by answering “what if” questions. LO6 – True 29. CVP analysis is well suited for a setting in which available capacity is not sufficient to meet all demand. LO6 – False CVP analysis is not well suited for a setting in which available capacity is not sufficient to meet all demand. 30. It can be difficult to use CVP analysis when decisions deal with individual products, resources, or customers. LO6 – True

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Balakrishnan Managerial Accounting MULTIPLE CHOICE 31. Which of the following equations highlights the cost-volume-profit relation? A. Profit before taxes = [(Price x Unit variable cost) ÷ Sales volume in units] – Fixed costs. B. Profit before taxes = [(Price – Unit fixed cost) x Sales volume in units] – Variable costs. C. Profit before taxes = [(Price – Total variable cost) x Sales volume in units] – Fixed costs. D. Profit before taxes = [(Price – Unit variable cost) x Sales volume in units] – Fixed costs. E. Profit before taxes = [Price – (Unit variable cost – Unit fixed cost) ] x sales volume in units. LO1 – D 32. If selling price is $25, unit contribution margin is $10, sales volume is 1,000 units, and fixed costs are $8,000, the profit is: A. $2,000 B. $15,000 C. $10,000 D. $7,000 E. None of the above. LO1 – A 33. Which of the following statements is not true? A. Over the short run, unit variable costs remain constant. B. Over the short run, fixed costs decrease as sales volume decreases. C. Variable costs are proportional to sales volume. D. Contribution margin is calculated by subtracting variable costs from revenue. E. None of the above. LO1 – B 34. Because fixed costs generally do not change in the short term: A. CVP is not appropriate if fixed costs are low. B. They are generally not included as a component in CVP analysis. C. Decreasing contribution margin increases profit by an identical amount. D. Increasing contribution margin increases profit by an identical amount. E. None of the above. LO1 – D 35. Gann Enterprises sells one product for $125. Unit variable cost is $85 and unit fixed cost is $20. Net income increases by what amount if one more unit is sold? A. $20 B. $105 C. $40 D. $125 E. None of the above. LO1 – C

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Cost-volume-Profit Analysis 36. Bill’s Tires produces specialty tires for the lawn mower industry. Bill is trying to evaluate his current month’s profit for his 6-inch tire. The tire’s unit selling price is $5.00, the variable cost per unit is $3, sales volume is 260 units, and fixed costs are $120 for the period. Which of the following is the amount of profit before taxes on the 6-inch tire product line? a. $1,180 b. $900 c. $400 d. $520 LO1 – Post-test - C 37. The controller of Samson Electronics is evaluating the unit contribution margin for the GPS receivers for the first quarter of the year. If 20 GPS receivers are produced and sold during June at a unit selling price of $100, with a fixed cost per unit of $5, and variable costs totaling $800, how much is the unit contribution margin for the each GPS receiver? a. $60 b. $100 c. $55 d. $40 LO1 – Pre-test – A 38. Contribution margin is: a. Sales revenue less variable expenses b. Sales revenue less fixed and variable expenses c. Fixed expenses less variable expenses d. Sales revenue less cost of goods sold LO1 – Self-test – A 39. Which of the following is not a use of the CVP relation? A. To plan profit. B. To evaluate a change in mix of fixed and variable costs. C. To evaluate the time value of money on a business decision. D. To evaluate the change in short-term prices. E. All of the above are uses of the CVP relation. LO2 – C 40. If selling price per unit and unit variable cost increase by 5% and fixed cost remain the same, which CVP relation is correct?

A. B. C. D. E.

Contribution Margin Per Unit Decrease Decrease Increase Increase Decrease

Break-Even Units Increase Decrease Increase Decrease Increase

Overall Profit Increase Decrease Increase Increase Decrease

LO2 – D

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Balakrishnan Managerial Accounting 41. If selling price is $25, unit contribution margin equals $15 and fixed costs are $12,000, then breakeven volume is: A. 300 units. B. 1,200 units. C. 800 units. D. 2,500 units. E. 1,500 units. LO2 – C 42. If selling price is $25, unit contribution margin equals $15 and fixed costs are $12,000, then breakeven revenues total: a. $27,000 b. $22,000 c. $30,000 d. $20,000 e. $7,500 LO2 – D 43. Palmer’s Custom Saddlery reported sales of $700,000 for the current year, fixed costs of $130,000 and a contribution margin ratio of 30%. Profit before taxes equals: a. $80,000 b. $210,000 c. $360,000 d. $570,000 e. $171,000 LO2 – A 44. The CEO of RV USA is trying to estimate sales based on a budgeted target profit before taxes of $150,000. If unit contribution margin is $5,000, total sales in June are estimated at $900,000 and fixed costs are $500,000, how many RVs must be sold to attain the target profit before taxes? a. 130 b. 80 c. 210 d. 30 LO1 – Post-test – A 45. Which one of the following correctly indicates how to calculate breakeven volume? a. Variable costs divided by unit contribution margin. b. Profit divided by sales volume. c. Fixed costs divided by unit contribution margin. d. Variable costs divided by fixed costs. LO2 – Pre-test – C

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Cost-volume-Profit Analysis 46. How is the break-even point in units calculated? A. Fixed costs divided by contribution margin ratio B. net operating income divided by contribution margin per unit C. fixed costs divided by contribution margin per unit D. Net operating income divided by contribution margin ratio LO2 – Self-test – C 47. The Hamilton Company has provided the following income statement for 2008: Sales (24,000 units) $440,000 Variable expenses 275,000 Contribution margin 165,000 Fixed expenses 98,000 Net Income $67,000 The company’s contribution margin ratio (rounded) is: A. 37.5% B. 40.6% C. 59.4% D. 35.6% LO2 – Self-test – A 48. Glaus Company’s break-even point in sales is $690,000 and its variable expenses are 60% of sales. If the company had a profit of $10,000 in 2008, its sales must have been: A. $762,000 B. $665,000 C. $700,000 D. $715,000 LO2 – Self-test – D 49. The Wingo Company sells a single product for $21 per unit. If variable expenses are 70% of sales and fixed costs are $4,200, the break-even point in dollars will be: A. $6,300 B. $14,000 C. $4,200 D. $6,000 LO2 – Self-test – B 50. The Worxs Company wants to achieve a profit of $126,000. They currently sell 5,000 units at a price of $72 per unit with variable costs of $32 per unit. Fixed costs total $84,000. In order to achieve their target profit without increasing the selling price, the company will need to: A. Increase sales by 250 units B. Increase sales by 600 units C. Keep sales at their current levels D. Increase sales by $84,000 LO2 – Self-test – A

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Balakrishnan Managerial Accounting 51. If Company A is heavily labor-intensive and Company B is heavily capital-intensive which of the following is most likely to be true relative to the other company? A. Company A’s contribution margin per unit will be higher B. Company B’s contribution margin per unit will be higher C. Company A’s break-even point will be higher D. Company B’s contribution margin ratio will be lower LO2 – Self-test – B 52. A company can achieve an increase in contribution margin (given no other changes) if: A. Fixed costs decrease B. Selling price decreases C. Fixed costs increase D. Variable costs decrease LO2 – Self-test – D 53. Greenbrier Company had sales of $400,000, variable costs of $240,000, and fixed costs of $90,000. In order to break-even necessary sales would be: A. $240,000 B. $225,000 C. $70,000 D. $250,000 LO2 – Self-test – B 54. If selling price per unit and sales volume remain the same while variable costs per unit decrease and total fixed costs decrease, which of the following is false: A. Contribution margin ratio will increase. B. Contribution margin per unit will increase. C. Net operating income will increase. D. Net operating income will decrease. LO2 – Self-test – D 55. The following information is being provided for the two products produced by the Stay-Dri Deodorant Company. For every 5 units sold, 3 of those units are from the men’s line of product while 2 units are from the women’s line of product. Men Women Total Expected product mix 3 2 Selling price per unit $2.20 2.80 Variable cost per unit 1.50 1.10 Fixed Costs (total) $88,000 How many units of each product need to be sold in order to break-even in total? Men Women A. 48,000 32,000 B. 40,000 40,000 C. 80,000 80,000 D. 32,000 48,000 LO2 – Self-test – A

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Cost-volume-Profit Analysis 56. Debbie’s Donut Shop has been the only donut shop in town. However, after Barry’s Breakfast Treats opened up last month, Debbie’s sales have dropped. Debbie decides to cut the selling price of her delicious donuts. The decrease in selling price will result in: a. A reduction in the unit contribution margin. b. An increase in the unit contribution margin. c. A reduction in the unit variable costs. d. An increase in the unit variable costs. e. A reduction in fixed costs. LO3 – A 57. Assume University T-Shirt Shop has a selling price of $25 and unit variable cost of $10 for its longsleeve cotton shirts. Fixed costs total $1,000. University believes increasing its price to $27 will not cause a reduction in the number of shirts it will sell. If University’s sales volume for the month is 300 shirts, how will net profit be affected by the change in selling price? a. $1,600 increase. b. $250 increase. c. $600 increase. d. $270 increase. e. $1,600 decrease. LO3 – C 58. Barry’s Breakfast Treats has been selling only plain and cream-filled donuts. Barry believes he can increase his sales by adding a healthy-choice muffin to his menu. He will incur some additional costs such as ingredients, muffin pans and advertisement on the local TV station. Which of the following statements is false? a. Barry’s fixed costs will probably increase. b. Barry’s total variable costs will probably increase c. Barry should add the muffin only if the increased contribution margin exceeds the increase in revenues. d. Barry should add the muffin only if the increased contribution margin exceeds the increase in fixed costs. e. All of the above statements are false. LO3 – C 59. Assume University T-Shirt Shop has a selling price of $25 and unit variable cost of $10 for its longsleeve cotton shirts. Fixed costs total $1,000. University believes increasing its price to $27 its sales volume will drop by 5 percent. If University’s sales volume for the month was estimated to be 300 shirts before the price increase, how will net profit be affected by the change in selling price? a. $395 increase. b. $345 increase. c. $345 decrease. d. $150 increase. e. $150 decrease. LO3 – B

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Balakrishnan Managerial Accounting 60. If unit variable cost is reduced and selling price and fixed cost remain the same, then: a. Contribution margin will decrease. b. Contribution margin will remain the same. c. Sales volume will increase d. Sales volume will decrease. e. Overall profit will increase. LO3 – E 61. Which of the following statements is correct about the relationship of the CVP factors? a. Variable costs will always be more than fixed costs. b. Demand will always be weaker at lower prices. c. Sales volume contributes to more profit at higher volumes. d. Sales price at lower volumes always contributes to higher contribution margins. LO3 – Post-test – C 62. Which of the following products should be produced to maximize profit? a. Product A: Sales volume of 10,000 units, unit contribution margin of $20, fixed costs of $120,000. b. Product B: Sales volume of 9,000, unit contribution margin of $22, fixed costs of $150,000. c. Product C: Sales volume of 8,000, unit contribution margin of $21, fixed costs of $110,000. d. Product D: Sales volume of 11,000, unit contribution margin of $23, fixed costs of $170,000. LO3 – Pre-test – D 63. Rocky Company sells a single product. If both the selling price and variable cost per unit increase by 5% and fixed costs remain steady then: Contribution Margin Break Even Per Unit in Units A. Decrease Increase B. Increase No change C. Decrease No change D. Increase Decrease LO3 – Self-test – D 64. The Norman Company recorded net operating income of $51,000 on sales of $280,000. If the company’s variable costs were 60% of sales, fixed costs must have been: A. $117,000 B. $112,000 C. $61,000 D. $137,400 LO3 – Self-test – C

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Cost-volume-Profit Analysis 65. The Hernandez Brothers Company wants to earn an AFTER-tax profit of $180,000. The company sells each unit for $100 and variable costs represent 60% of sales. If fixed costs total $62,000 and the company’s tax rate is 40%, how many units does the company need to sell in order to meet their goal? A. 9,050 units B. 12,800 units C. 11,250 units D. 7,500 units LO3 – Self-test – A 66. Williams Company has a selling price of $2.50 and a break-even sales volume of 8,000 units. Current revenue is $25,000. What is Williams’ margin of safety? a. 20%. b. $2.00 c. 62.5% d. $6.25 e. .03% LO4 – A 67. Operating leverage is used as: a. A measure of risk arising from having a sales volume which differs from breakeven volume. b. A measure of risk arising from having less margin of safety than anticipated. c. A measure of risk arising from having more fixed costs. d. A measure of risk arising from having more variable costs. e. None of the above. LO4 – C 68. Which of the following statements is true? a. The lower the margin of safety, the lower the risk of a loss if actual sales do not meet expectations. b. A good rule of thumb is that the margin of safety should be approximately 20%. c. The higher the margin of safety, the lower the risk of a loss if actual sales do not meet expectations. d. Firms that face highly variable demand conditions desire a lower margin of safety. e. None of the above statements are true. LO4 – C 69. Assume current sales are 10,000 units, selling price is $2.50 and margin of safety is 20%. If sales increase by 5%, what is the percent change in profits before taxes? a. 40% b. 25% c. 250% d. 12.5% e. 50% LO4 – B

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Balakrishnan Managerial Accounting 70. Assume sales volume of 3,000 units, unit variable cost of $3, fixed costs of $15,000. What is operating leverage? a. 60% b. 37.5% c. 20% d. 62.5% e. 1.6% LO4 – D 71. The controller of Nationwide Bicycle Parts is evaluating the sensitivity of changes in profit as it relates to proposed adjustments to sales volume and margin of safety. If sales volume is estimated to decrease by 10%, the contribution margin ratio is 35%, and the margin of safety is 25%, by how much will profit before taxes decrease? a. 40% b. 250% c. 28.5% d. 2.5% LO4 – Post-test – A 72. Which of the following is true of operating leverage? a. Operating leverage increases as profit increases. b. Companies with higher operating leverage experience higher increases in profit when sales increase. c. Operating leverage decreases as total variable costs decrease. d. New technology generally decreases operating leverage. LO4 – Post-test – B 73. If fixed costs for Watts Corporation for the current year total $800,000, widgets are sold at $25 per unit, total variable costs are $1,200,000, how much is operating leverage? a. 40.0% b. 66.7% c. 25.0% d. 60.0% LO4 – Pre-test – A 74. RAM Auto Parts’ CEO wants to obtain additional financing from the company’s bank. The banker wants to know the company’s margin of safety. If revenues of the company for the current year total $4 million, widgets are sold at $20 per unit, the variable cost per unit is $16, fixed costs are $500,000, how much is the margin of safety? a. 12.5% b. 80.0% c. 96.9% d. 37.5% LO4 – Pre-test – D

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Cost-volume-Profit Analysis 75. If sales volume increases and everything else remains constant, the: A. Break-even point will decrease B. Margin of safety will increase C. Net operating income will decrease D. Contribution margin ratio will increase LO4 – Self-test – B 76. The proportion, expressed in units, in which products are expected to be sold is referred to as: a. Product mix. b. Weighted contribution. c. Operating leverage. d. Unit margin. e. Proportionate contribution. LO5 – A 77. Hill Toppers sells two types of hiking boots, the Voyager and the Traveler. The Voyager sells for $150 and has a contribution margin of $60. The Traveler sells for $100 and has a contribution margin of $60. Total revenue for the period is $300,000 and total fixed costs are $125,000. Each product contributes 50% to total revenue. Using the weighted contribution margin ratio, calculate profit before taxes. a. $25,000 b. ($53,000) c. $89,000 d. $175,000 e. $150,000 LO5 – A 78. Water Sports, Inc. sells two types of canoes, the Deluxe model and the Super model. The following segmented contribution margin statement shows the results of the most recent period. Water Sports, Inc. Segmented Contribution Margin Statement Current Period Deluxe Super Total Sales volume 10,000 6,030 16,030 Revenues $153,000 $147,000 $ 300,000 Variable costs 91,800 58,800 150,600 Contribution margin $ 61,200 $ 88,200 $149,400 Common Fixed Costs 125,000 Profit before Taxes $ 24,400 What is the weighted unit contribution margin? a. 49.8% b. $9.32 c. 10,7% d. 83.6% e. $2.00 LO5 – B 5-13

Balakrishnan Managerial Accounting 79. Water Sports, Inc. sells two types of canoes, the Deluxe model and the Super model. The following segmented contribution margin statement shows the results of the most recent period. Water Sports, Inc. Segmented Contribution Margin Statement Current Period Deluxe Super Total Sales volume 10,000 6,030 16,030 Revenues $153,000 $147,000 $ 300,000 Variable costs 91,800 58,800 150,600 Contribution margin $ 61,200 $ 88,200 $149,400 Common Fixed Costs 125,000 Profit before Taxes $ 24,400 What is Water Sport’s breakeven volume? a. 6,024 units. b. 16,030 units. c. 16,159 units. d. 13,412 units. e. None of the above. LO5 – D 80. Hill Toppers sells two types of hiking boots, the Voyager and the Traveler. The Voyager sells for $150 and has a contribution margin of $60. The Traveler sells for $100 and has a contribution margin of $60. Total revenue for the period is $300,000 and total fixed costs are $125,000. Each product contributes 50% to total revenue. Using the weighted contribution margin ratio, calculate break-even sales volume. a. $300,000 b. $25,000 c. $175,000 d. $250,000 e. $150,000 LO5 – D 81. If the weighted contribution margin ratio for a multi-product manufacturing company is 45%, the weighted contribution margin per unit is $5, fixed costs are $100,000, and total revenues are $650,000, how much is profit before taxes? a. $392,500 b. $292,500 c. $192,500 d. $247,500 LO5 – Post-test – C

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Cost-volume-Profit Analysis 82. Ben’s Landscaping sells two types of mulch for residential use. Cypress mulch constitutes 35% of all sales and pine mulch the other 65%. What is the weighted unit contribution margin for Ben’s inventory if cypress mulch sells for $2.00 per pound and pine mulch sells for $1.50 per pound? a. $1.83 b. $1.68 c. $1.75 d. $3.50 LO5 – Pre-test – B 83. CVP analysis is useful for short-term decisions relating to all of the following except: a. Break-even volume. b. Cost structure. c. Pricing. d. Advertising. e. All of the above. LO6– E 84. Which of the following is not an assumption used in CVP analysis? a. Revenues increase proportionally with sales volume. b. A flexible product mix. c. Selling prices, unit variable costs, and fixed costs are known with certainty. d. Single-period analysis. e. All of the above are assumptions used in CVP analysis. LO6 – B 85. The typical CVP analysis assumes a single-period analysis. Which of the following statements does not relate to this assumption? a. This assumption does not allow for complex tax provisions. b. This assumption does not account for the time value of money. c. This assumption does not allow for incurring the cost of production in one period but realizing the associated sales revenue in the next period. d. This assumption does not allow for flexible pricing policies. e. All of the above statements are true. LO6 – D 86. Which of the following statements relating to CVP assumptions is not true? a. CVP analysis is not well suited for a setting in which available capacity is not sufficient to meet al demand. b. CVP analysis does not always provide the best solution to short term decisions. c. Fixed costs increase proportionately with sales volume. d. Selling prices and costs are known with certainty. e. All of the above statements are true. LO6 – C

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Balakrishnan Managerial Accounting 87. The sales volume in units at which profit equals zero is referred to as: a. Breakeven volume. b. Margin of safety. c. Contribution margin. d. Segment margin. e. None of the above. LO6-A 88. Considering issues surrounding product-mix assumptions, which of the following answers is correct assuming the principles of CVP? a. CVP analysis assumes a known and constant product mix. b. CVP assumes that only one product can be analyzed at one time. c. CVP assumes that there must be a maximum weighted contribution ratio when evaluating multiple products together. d. CVP assumes that management must assume no fixed costs when evaluating multiple products. LO6 – Post-test – A 89. Which of the following is not a key assumption using CVP analysis? a. Capacity is available with no limitations on the supply of raw materials. b. Selling prices, unit variable costs, and fixed costs are known with certainty. c. Variable costs and revenue increase proportionately with sales volume. d. CVP will always provide the best answer for short-term decisions. LO6 – Pre-test – D

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Cost-volume-Profit Analysis Problems 1. River Toys manufactures Angler’s Choice kayaks. River Toys believes that the demand during the current year’s fishing season will be 4,000 units. Additional cost data follows: Item Selling Price Variable manufacturing costs Fixed manufacturing overhead Gross margin Variable selling costs Fixed selling and administrative costs Profit margin

Value per unit $800 300 25 $475 20 125 $330

Required: a. What is River Toys’ breakeven point in units?

b. What is River Toys’ breakeven point in revenue?

2. Bubba’s Bait Shop sells spinner, top water, diving and tube baits. Bubba estimates that his variable costs are $0.20 per sales dollar and fixed costs total $4,500 per month. Required: a. How much revenue does Bubba need to break even each month?

b. How much revenue does Bubba need to generate in order to realize a profit of $3,000 each month?

c. If Bubba expects his vendors to increase the price of baits by 40%, what will be his break-even revenue per month?

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Balakrishnan Managerial Accounting 3. Casting Company manufactures ultra-lite fishing rods called Catch’ums. The rods are sold exclusively via Internet. Each Catch’um sells for $18 ($15 plus $3 shipping and handling.) Casting’s contribution margin ratio is 60%. Casting calculates breakeven units to be 5,000 per month. Required: a. What is the unit variable cost of a Catch’um rod?

b. What is Casting’s monthly fixed cost?

c. Suppose Casting introduces an offer for “free” shipping and handling. How many additional rods will Casting have to sell each month to break even?.

4. Buck’s Camo Shop sells a variety of camo-patterned outdoor garments. Buck has built up a loyal customer base because of the quality of his garments and the customer service he provides. In a typical month Buck’s revenue is $150,000 and he earns a net profit of $9,300. Buck’s contribution ratio is 60%. Required: a. Determine Buck’s margin of safety at his current sales level.

b. What is Buck’s operating leverage?

c. What is the revenue required for Buck to break even on a cash basis? Assume that 25% of Buck’s fixed costs represent non-cash items such as depreciation. All other expenses are paid in cash and all revenues are received in cash.

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Cost-volume-Profit Analysis 5. The Doggy Palace is an upscale grooming salon for dogs. Doggy Palace sells two types of doggy shampoo. Shiny Coat sells for $20 per bottle and Flea-B-Gone sells for $10 per bottle. Fixed costs total $20,000. Additional cost data is as follows: Price per bottle Unit variable cost Unit contribution margin Sales volume

Shiny Coat $20 $10 $10 1,600

Flea-B-Gone $10 $ 5 5 3,200

Required: a. How many bottles of Shiny Coat and Flea-B-Gone must The Doggy Palace sell in a year to break even?

b. At the current product mix, how many bottles of Shiny Coat and Flea-B-Gone must The Doggy Palace sell in a year in order to earn a profit of $25,000?

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Balakrishnan Managerial Accounting 6. The CVP relation captures how revenues, costs, and profit vary as the volume of business varies. It is important to understand the assumptions underlying CVP analysis and the extent to which they are likely to be valid. Required: Identify the following statements regarding the assumptions underlying CVP analysis that are valid. Place an “X” in the appropriate response column. Valid

Invalid

Statement CVP analysis assumes a known and constant product mix. CVP is a tool that helps managers improve profit by answering “what if” questions. CVP analysis assumes that unit variable cost changes proportionally as volume changes. Companies generally base assumptions about product mix on a history of past sales data and from the marketing department. CVP analysis assumes that all revenues and costs occur in a single period. Managers evaluate alternative product-mix assumptions to assess their confidence in estimated profit as change in product mix can significantly affect profit. CVP analysis assumes that total sales remain constant from period to period. CVP analysis is not well suited for a setting in which available capacity is not sufficient to meet all demand, meaning that companies have to decide which products to cut back on. CVP analysis takes into account the time value of money. Managers can predict with relative certainty when machines will break down.

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Cost-volume-Profit Analysis Problem Solutions 1. Contribution Margin, Unit level costs (LO1) a. Breakeven units: Total fixed costs = (4,000 x $25) + (4,000 x $125) = $600,000 Unit contribution margin = $800 - $300 - $20 = $480 Breakeven = $600,000 ÷ $480 = 1,250 units b. Breakeven revenue Breakeven units x selling price 1,250 x $800 = $1,000,000

2. CVP Relation and solving for unknown (LO1, LO2) a. Breakeven revenue: (Revenue - .2 Revenue) - $4,500 Fixed Cost = 0 .8 Revenue = $4,500 Revenue = $4,500 ÷.8 Revenue = $5,625 b. Profit (Revenue - .2 Revenue) - $4,500 Fixed Cost = $3,000 Profit .8 Revenue = $4,500 + $3,000 Revenue = $7,500 ÷.8 Revenue = $9,375 c. Breakeven revenue: (Revenue - .28 Revenue) - $4,500 Fixed Cost = 0 .72 Revenue = $4,500 Revenue = $4,500 ÷.72 Revenue = $6,250

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Balakrishnan Managerial Accounting 3. CVP Relation, Inferring Cost Structure, Extension to Decision Making (LO2, LO3) a. Unit Variable Cost = $7.20 Unit variable cost = $18 (selling price) – (.60 x $18) Unit variable cost = $18 - $10.80 Unit variable cost = $7.20

b. Fixed cost = $54,000 $18(5,000) =($7.20 x 5,000) – FC FC = $90,000 – 36,000 FC = $54,000

c. Breakeven units = 6,923 $15x - $7.20x - $54,000 = 0 $7.80x = $54,000 x = 6,923

4. CVP Relation and Decision Making, margin of Safety, Operating Leverage, Cash-Basis Breakeven Analysis (LO 3, LO4) a. Margin of Safety = 10.33%: Revenue Variable Costs (40%) Contribution Margin (60%) Fixed Cost Profit

At Current Level $150,000 60,000 90,000 80,700 $ 9,300

Breakeven Level $134,500 53,800 80,700 80,700 $ 0

Margin of Safety: ($150,000 - $134,000) ÷$150,000 = 10.33% b. Operating Leverage = 57.36% Fixed Costs ÷ Total Costs $80,700 ÷ ($80,700 + $60,000) = 57.36% c. Cash-Basis Breakeven = $100,875 Fixed Costs Contribution margin% $60,525 ÷ 60% = $100,875

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Cost-volume-Profit Analysis 5. Multiple Products (LO5) a. Price per bottle Unit variable cost Unit contribution margin Sales volume

Shiny Coat $20 $10 $10 1,600

Flea-B-Gone $10 $ 5 5 3,200

Total $30 $15 $15

Weighted average contribution = (1/3 x $10) + (2/3 x $5) = $6.667 Break even = $6.667x + $20,000 $20,000/$6.667 = 3,000 units 1,600 units 1/3 3,200 units 2/3 4,800 units 3,000 units x 1/3 = 1,000 units of Shiny Coat 3,000 units x 2/3 = 2,000 units of Flea-B-Gone b. ($20,000 + $25,000) ÷ $6.667 = 6,750 units 6,750 units x 1/3 = 2,500 units of Shiny Coat 6,750 units x 2/3 = 4,500 units of Flea-B-Gone

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Balakrishnan Managerial Accounting 6. CVP Assumptions (LO6) Valid x x

Invalid

X

x x x X x X X

Statement CVP analysis assumes a known and constant product mix. CVP is a tool that helps managers improve profit by answering “what if” questions. CVP analysis assumes that unit variable cost changes proportionally as volume changes. CVP analysis assumes that unit variable cost is constant and does not vary with sales volume. Companies generally base assumptions about product mix on a history of past sales data and from the marketing department. CVP analysis assumes that all revenues and costs occur in a single period. Managers evaluate alternative product-mix assumptions to assess their confidence in estimated profit as change in product mix can significantly affect profit. CVP analysis assumes that total sales remain constant from period to period. CVP analysis assumes that the selling price per unit is constant does not vary with sales volume. CVP analysis is not well suited for a setting in which available capacity is not sufficient to meet all demand, meaning that companies have to decide which products to cut back on. CVP analysis takes into account the time value of money. CVP analysis does not take into account the time value of money. Managers can predict with relative certainty when machines will break down. Managers cannot be sure when a machine a machine will break down.

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Cost-volume-Profit Analysis END OF CHAPTER HOMEWORK CONTENT Short Answer 1. What is the CVP relation? 2. What does the CVP relation follow directly from? 3. What is breakeven volume? 4. What are breakeven revenues? 5. What is the contribution margin ratio? 6. How do taxes affect the CVP relation? 7. How can we use the CVP relation to analyze the profit effect of price changes? 8. What is the margin of safety? 9. How could we use the margin of safety to calculate the percent change in profit given a percent change in sales? 10. What is operating leverage? 11. What is a product mix? 12. What is a weighted unit contribution margin? 13. What is a weighted contribution margin ratio? 14. Why do managers often prefer to calculate CVP relations using the weighted contribution margin ratio approach? 15. What are the assumptions underlying CVP analysis?

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Balakrishnan Managerial Accounting Solutions to Short Answer 1. (LO-1) Profit before taxes = [(Price – Unit variable cost) × Sales volume in units] – Fixed costs = Unit contribution margin × Sales volume in units – Fixed costs. 2. (LO-1)

The contribution margin statement.

3. (LO-2)

The sales volume at which profit equals zero.

4. (LO-2)

The sales dollars at which profit equals zero.

5. (LO-2)

The unit contribution margin divided by price.

6. (LO-2) Taxes reduce profit by a certain percentage beyond the breakeven point. Above the breakeven point, the slope of the profit line decreases by taxes paid. 7. (LO-3)

Use the CVP relation to estimate profit at each price, quantity combination.

8. (LO-4) The amount by which sales exceed breakeven sales. It equals (Sales in units – Breakeven volume)/Sales in Units or, equivalently, (Revenues – Breakeven revenues)/Revenues. 9. (LO-4) The percentage change in profit = the percentage change in sales volume (or revenues) × (1/Margin of safety). 10. (LO-4) Operating leverage is a measure of risk from having more fixed costs. It equals Fixed costs/Total costs. 11. (LO-5) The relative proportion in which a company expects to sell products – e.g., two units of product A for every unit of product B. 12. (LO-5)

The contribution margin per average unit.

13. (LO-5)

The contribution margin per average sales dollar.

14. (LO-5) It is easier to work with revenues directly and comparing contribution margin ratios across products makes more sense than comparing unit contribution margins. 15. (LO-6) (1) Revenues increase proportionally with sales volume, (2) variable costs increase proportionally with sales volume, (3) selling prices, unit variable costs, and fixed costs are known with certainty, (4) a single-period analysis, (5) a known and constant product mix, (6) CVP analysis does not always provide the “best” solution to a short-term decision, and (7) the availability of capacity.

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Cost-volume-Profit Analysis Short Essay 1. Which action has a greater effect on the unit contribution margin: (1) increasing the unit selling price by 10% or (2) reducing the unit variable cost by 10%? 2. A firm reported a contribution margin equal to 40% of revenues and profit before taxes equal to 15% of revenues. If fixed costs were $200,000, what were the firm’s revenues? 3. We could readily extend CVP analysis to consider cash breakeven by considering cash fixed costs only (exclude noncash items such as depreciation). Which kinds of firms would value this approach? 4. If fixed costs increase, but the unit contribution margin stays the same, can we calculate the additional volume needed to break even by dividing the change in fixed costs by the unit contribution margin? Why or why not? 5. In the text, we refined the CVP relation to incorporate taxes that are proportional to pretax profit. How could we further refine the CVP relation to include multiple tax brackets, where the tax rate depends on the magnitude of the profit? 6. Could we modify the CVP relation to include step costs? What complications might arise in the context of CVP analysis with step costs? 7. Is the contribution margin ratio of a Microsoft likely to be higher or lower than the contribution margin ratio of Ford? What does this imply about the sensitivity of profit to sales? 8. What do you think of the business practice of charging customers different prices for essentially the same good? List some examples where you see this practice? 9. How might managers use the margin of safety concept in decision making? 10. Why does operating leverage decrease as sales volume increases? 11. Why is operating leverage viewed as a measure of risk? 12. Consider a large multidivisional firm such as John Deere. Does it make sense to perform CVP analysis for such a firm as a whole? How could such firms use CVP insights effectively? 13. The text suggests that comparing the unit contribution margin of a sports car with an entry-level vehicle is like comparing apples and oranges, but that comparing the contribution margin ratios is a fair comparison. Do you agree? Why? Can you think of an example where it may be more appropriate to compare unit contribution margins but not contribution margin ratios? 14. Think about each of the assumptions underlying CVP analysis. Do you believe each assumption accurately depicts reality? Can you think of a setting where each assumption is likely to be violated?

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Balakrishnan Managerial Accounting Solutions to Short Essay

1. (LO-1) Unit contribution margin equals unit selling price less unit variable cost. If unit contribution margin is positive, unit selling price is a bigger number than unit variable cost, and so a 10% increase in unit selling price will increase unit contribution margin more than a 10% decrease in unit variable cost. To illustrate, unit selling price is$50 and unit variable cost is $30. Unit contribution margin will be $20. A 10% increase in unit selling price will increase the unit contribution margin to $25 ($55-$20), but a 10% reduction in unit variable cost will increase the unit contribution margin to only $23 ($50-$27). 2. (LO-1)

Profit before taxes = .15 * Revenues (fact 1) Profit before taxes = .40*Revenues – $200,000 (fact 2) Setting these equations equal to each other… Revenues = $200,000/.25 = $800,000.

3. (LO-2) It is generally advisable to conduct CVP analysis on a cash basis. Non-cash items such as depreciation are not relevant. However, it is not uncommon to see CVP analysis being used in conjunction with accounting profits---which would include depreciation as an expense---rather than net cash flow. Such an analysis can be particularly erroneous for startups and growth firms because the magnitude of non-cash items or accruals is likely to be large. 4. (LO-2) Yes. Let us consider an example. Suppose the unit contribution margin is $5 and the fixed costs are $200,000. The breakeven quantity then is 40,000 units (=$200,000/$5). Let us say that the fixed costs increase by $100,000 to $300,000 but the unit contribution margin stays at $5. The new breakeven quantity is 60,000 (=$300,000/$5). That is we need an additional volume of 20,000 units to breakeven. We can also calculate this additional volume needed to breakeven by dividing the change in fixed costs by the unit contribution margin (=$100,000/$5). 5. (LO-2) Many countries use a progressive tax structure. That is, the tax rate increases for higher income brackets. However, the CVP analysis is fundamentally the same except that the profit equation is more elaborate. Consider an example where the tax rate is 30% up to $300,000, but increases to 40% beyond $300,000. In this case, we have to modify the computation of profit after taxes as: If profit before taxes is less than or equal to $300,000 then [EQ]Profit after taxes = Profit before taxes × (1 – 30%) If profit before taxes is greater than $300,000 then [EQ]Profit after taxes = $300,000 × (1 – 30%) + (Profit before taxes - $300,000) × (1 – 40%) Thus, for the first $300,000 of profit, the company would pay tax at the rate of 30%; beyond $300,000 the applicable tax rate would be 40%. Keep in mind, however, that having multiple tax brackets has no consequence for the calculation of the breakeven point because, at the breakeven point, the profit is zero and there are no taxes. 5-28

Cost-volume-Profit Analysis

6. (LO-2) Yes, we can modify the CVP relation to include step costs. With step costs, fixed costs do not stay fixed for all volumes. It stays fixed for a volume range beyond which it increases to the next level. Consider, for example, a company that leases a copier for its needs and pays a monthly rent. The copier has a certain fixed capacity to make copies. Till this capacity is reached, the rent does not vary with the volume of copies made. However, once the company’s copying needs exceeds its capacity, another copier may have to be rented and the rent payment increases by a step to include the rent of the next copier. When fixed cost increases in steps, the CVP analysis may have to be repeated a few times to converge to the answer. Think about computing the breakeven point. First, assume that the breakeven point would fall within the first step. With this assumption, we can calculate the breakeven point in the usual manner described in the text. If this calculation yields a breakeven point that is within the volume range over which the fixed cost does not increase to the next step, we are done. Otherwise, we change the fixed cost to the next step value and repeat our breakeven calculation. We repeat this process until we reach a point where the breakeven volume falls within the range of the assumed step fixed cost! 7. (LO-3) Software companies typically have a high proportion of fixed costs in their cost structure (i.e., high operating leverage) because their primary resource is trained software professionals. Most of these professionals are paid fixed salaries and wages that do not vary with the volume of software programs they generate, or the number of software programs a company like Microsoft sells. Relatively speaking, an automobile company such as Ford would have a greater proportion of variable costs in its cost structure, although over time this proportion has decreased because of increased automation. 8. (LO-3) The practice of selling the same good at different prices to different customers is called discriminatory pricing. In general the Robinson-Patman Act of 1936 prohibits discriminatory pricing in certain situations. However, in other situations, such differential pricing may well be necessary depending on the nature of the customer or the specific.. We will discuss this aspect later in Chapter 10, when we discuss Customer Profitability Analysis. 9. (LO-4) Margin of safety is a “cushion” that the existing level of operations allows managers in dealing with operating risk. The smaller this cushion, the closer is the manager to making a loss. Thus, when demand uncertainty increases unexpectedly, this cushion “protects” managers from incurring losses. In such situations, it gives them some room to offer discounts or promotions to keep up the volume in the short-term in order to preserve profitability. 10. (LO-4) As the sales volume increases, the total variable costs increase but fixed costs stay the same. Recall that operating leverage is the ratio of fixed costs to total costs. Because fixed costs stay the same and the total costs increase (because of the increase in variable costs), the operating leverage decreases.

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Balakrishnan Managerial Accounting

11. (LO-4) As demand conditions fluctuate, short-term profits are more sensitive to consequent changes in sales volume for firms with higher operating leverage. This is why operating leverage is viewed as measure of risk. Referring to Exhibit 5.14, the operating leverage of Sierra Plastics increases with the new technology. Notice that its profits fluctuate more with the sales volume with the new technology than without the technology. 12. (LO-5) In general, divisions of large firms often have very different cost structures and serve different markets. Because the CVP analysis is essentially a tool for short-term decision making that helps managers in deciding the level of operations, it makes more sense for individual divisional heads to perform CVP analysis at their respective divisions. At the firm level, the effects of these short-term decisions can then be aggregated to determine the overall state of the firm in the short run, and which divisions are contributing in what measure in this respect. 13. (LO-5) Yes. In general the unit of one product is not comparable to a unit of another dissimilar product because they require different amounts of resources---such as raw material, labor, machining time---to produce. Therefore, we cannot say that the sports car is more profitable to produce because its unit contribution margin is higher than the contribution margin of an entry-level vehicle. However, with the contribution margin ratio, we can express relative profitability in terms of sales dollars. We can say that for every sales dollar, the sports car contributes twenty cents toward profit (i.e., CMR of 20%), and the entry-level vehicle contributes ten cents toward profit (i.e., CMR of 10%). 14. (LO-6) CVP analysis should be considered as a convenient tool to understand the relations between cost, volume and profit. It makes many assumptions as discussed in the text. Let us consider a few assumptions assumption and identify a setting in which it would be violated. 







Assumption 1: Revenues increase proportionally with sales volume. This assumption essentially means that price per unit is constant and does not vary with volume. However, it is well known that as you decrease price per unit, you can sell more and vice versa. In other words, price per unit and sales volume are inversely related. When we allow for this possibility, this assumption is violated. Assumption 2: Variable costs increase proportionally with sales volume. In other words, unit variable cost stays the same over the relevant range of operations so that variable costs increase linearly with volume. This assumption will be violated whenever the sales volume goes beyond relevant range (e.g., when firms stretch existing capacity to meet demand). In such cases, variable costs can increase more than proportionately. Assumption 3: Selling prices, unit variable costs, and fixed costs are known with certainty. In the real world, we have to deal with uncertainty all the time. The assumed selling price, and variable/fixed costs may turn out be different from the actual price and costs because of changes in demand conditions or resource availability. Assumption 4: Single-period analysis. Most business relationships extend beyond a single period, and most short-term decisions have longer-term implications. Please refer 5-30

Cost-volume-Profit Analysis



to a discussion of such implications in Chapter 2. Such implications would result in a violation of this assumption. Assumption 5: Product-mix assumption. With many products, CVP analysis assumes a known and constant product mix. However, in most instance, the product-mix itself has to be decided. Changing the product-mix may be best the way to react to changes in demand for the different products in the mix.

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Balakrishnan Managerial Accounting Exercises 1. Ajay Singh plans to offer gift-wrapping services at the local mall during the month of December. Ajay will wrap each package, regardless of size, in the customer’s choice of wrapping paper and bow for a price of $3. Ajay estimates that his variable costs will total $1 per package wrapped and that his fixed costs will total $600 for the month. Required: a. Express Ajay’s profit before taxes in terms of the number of packages sold. b. How many packages does Ajay need to wrap to break even? c. How many packages must Ajay wrap to earn a profit of $1,400?

2. Gina Matheson owns and operates a successful florist shop in Bloomington, Indiana. Gina estimates that her variable costs are $0.25 per sales dollar (i.e., variable costs represent 25% of revenue) and that her fixed costs amount to $6,000 per month. Required: a. How much revenue does Gina need to generate to earn a profit of $3,600 per month? b. Suppose Gina estimates that she will be able to generate revenue of $15,000 in a month. Assume also that she wishes to earn $4,000 in profit each month. What is the maximum amount that she can spend on fixed costs? c. Suppose Gina’s variable costs were to increase by 50%. What is Gina’s breakeven revenue per month?

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Cost-volume-Profit Analysis 3. Zap, Inc., manufactures an organic insecticide that is marketed and sold via television infomercials. Each “ZAP” kit sells for $22, which includes a base price of $20 per “ZAP” kit plus $2 in shipping and handling fees. Zap’s contribution margin ratio is 60%. In addition, Zap expects to break even if it sells 17,500 “ZAP” kits per month. Required: a. What is the unit variable cost of a “ZAP” kit? b. What are Zap’s monthly fixed costs? c. Suppose Zap introduces an offer for “free” shipping and handling. How many additional “ZAP” kits must be sold each month to break even?

4. The Cottage Bakery sells a variety of gourmet breads, cakes, pies, and pastries. Although its wares are considerably more expensive than those available at supermarkets and other bakeries, the Cottage Bakery has a loyal clientele willing to pay a premium price for premium quality. In a typical month, the Cottage Bakery generates revenue of $150,000 and earns a profit of $7,500. The Cottage Bakery’s contribution margin ratio is 40%. Required: a. What is the Cottage Bakery’s margin of safety at its current sales level? b. What is the Cottage Bakery’s operating leverage? c. What is the revenue required for Cottage Bakery to break even on a cash basis? Assume that 30% of the Cottage Bakery’s fixed costs represent noncash items (e.g., depreciation expense on the ovens, furniture, and fixtures). All other expenses are paid in cash and all revenues are received in cash.

5. Tom and Lynda operate Hercules Gym. The club currently has 900 individual members and 300 family memberships. The fee for individual memberships is $100 per month, and families pay $150 per month. Variable costs are $35 per month for individual and $60 per month for a family. Monthly fixed costs amount to $42,750. Required: a. Calculate Hercules’ weighted contribution margin. Use this answer to calculate the number of individual and family memberships at breakeven volume. b. Calculate Hercules’ weighted contribution margin ratio. Use this answer to calculate the total revenue to achieve breakeven.

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Balakrishnan Managerial Accounting Solutions to Exercises 1. (LO1 and LO2) a. Recall that: Profit before taxes = (unit contribution margin  sales volume in units) – fixed costs. Additionally, Unit contribution margin = Unit selling price – Unit variable cost. = $3.00 – $1.00 = $2.00 per package. The problem also informs us that Ajay’s fixed costs for the month = $600. Thus, Ajay’s profit is: Profit before taxes = ($2.00  number of packages sold) – $600. b. Breaking even implies a profit of zero. Thus, we have: $0 = ($2.00  Breakeven volume) – $600, $600 Or, breakeven volume in packages = = 300 packages. $2.00 c. Substituting Ajay’s target profit of $1,400 into the expression for profit we developed in part [a], we have: $1,400 = $2.00  Required number of packages – $600. $600  $1,400 OR, Required sales = .= 1,000 packages. $2.00

2. (LO1 and LO2) a. Substituting a target profit of $3,600 into the monthly profit equation, we have: $3,600 = (0.75  Required revenue) – $6,000. OR, Required revenue =

 $3,600 ($6,0000.75 )

= $12,800 per month.

b. Substituting the data into Gina’s profit equation, we have: $4,000 = (0.75  $15,000) – Fixed costs. Maximum expenditure on fixed costs = $11,250 – $4,000 = $7,250. c. Gina’s new variable cost is $0.25  (1 + 0.5) = $0.375 per $1.00 of sales. Thus, Gina’s new contribution margin ratio is:

- $.375 ($1.00$1.00 )

= 0.625.

Substituting this information into the profit calculation and setting profit equal to $0, we have: $0 = (0.625  Breakeven revenue)– $6,000. Breakeven revenue = $9,600.

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Cost-volume-Profit Analysis

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Balakrishnan Managerial Accounting 3. (LO2 and LO3)

a. The contribution margin ratio =

Price - Unit variable cost ( ). Price

With Zap’s information, we have the contribution margin ratio =

$22.00 - Unit variable cost ( ) $22.00 = 0.60. Unit variable cost = $8.80 for each “ZAP” kit. Or Contribution margin ratio = 1 – Variable cost ratio. 0.60 = 1 – Variable cost ratio, or Variable cost ratio = 40% of sales price That is, unit variable cost = 0.40 × $22 = $8.80 per unit. b. Let us use the profit expression: Profit before taxes = (Contribution margin ratio  Revenue) – Fixed costs. We know that Zap expects to break even at 17,500 “ZAP” kits – thus, revenue = 17,500 × $22.00 = $385,000. We know that profit = $0 at the breakeven point. Thus, we have: $0 = (0.60  $385,000) – Fixed costs. Solving, we find that fixed costs = $231,000. Or

$0 = (Unit contribution margin  Breakeven volume) – Fixed costs. From part [a], we know that the unit variable cost = $8.80. Because the selling price = $22.00, we know that the unit contribution margin = $22.00 – $8.80 = $13.20. Thus, we have: $0 = ($13.20  17,500) – Fixed costs. Again, we find that fixed costs = $231,000. c. The free shipping and handling offer reduces Zap’s revenue per “ZAP” kit to $20.00. With the knowledge acquired in parts [a] and [b] (i.e., the variable cost per “ZAP” kit and Zap’s monthly fixed costs, respectively), we can calculate Zap’s breakeven volume as: $0 = (Unit contribution margin  Breakeven volume) – Fixed costs. or, $0 = [($20.00 – $8.80)  Breakeven volume] – $231,000 Breakeven number of kits (Breakeven volume) = 20,625. Consequently, Zap must sell an additional 20,625 – 17,500 = 3,125 kits to break even if the company decides to offer “free” shipping.

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Cost-volume-Profit Analysis 4. (LO3 and LO4) a. Margin of safety

=

Current sales - Breakeven sales ( ) Current sales $7,500 = (0.4  $150,000) – Fixed costs Fixed costs = $52,500. $0 = (0.4  Breakeven revenue) – $52,500 Breakeven revenue = $131,250.

Cottage Bakery’s Margin of safety = 12.5%.

(

$150,000 - $131,250 $150,000

)

=

In dollars, the margin of safety equals $150,000 – $131,250 = $18,750.

b. Operating leverage = Fixed costs/Total costs. Contribution margin = 0.4  150,000 = $60,000. Because contribution margin = revenues – variable costs, variable costs can be calculated as $90,000. Given that fixed costs are $52,500, the total costs are $142,500. Consequently, Operating leverage = fixed costs / total costs = $52,500/$142,500 = 0.368 (rounded) c. If 30% of the fixed costs represent non-cash expenses, the cash fixed expenses equal: 0.70  $52,500 = $36,750. We are now in a position to write the cash profit as: Cash profit = (Contribution margin ratio  Revenue) – Cash fixed costs. To calculate the breakeven point, we set cash profit = $0. $0 = (0.40  Cash breakeven revenue) – $36,750. Cash breakeven revenue = $91,875.

5. (LO5) a. Weighted contribution margin is:[3 × ($100-$35) + 1 × ($150 -$60)] / 4 = $71.25. 0 = $71.25 × total memberships - $42,750, Total memberships = $42,750/$71.25 per average membership= 600. Hercules has (3/4) × 600 = 450 individual and (1/4) × 600 = 150 family memberships. b. Contribution margin for individual and family memberships at 0.65 (= [($100-$35)/$100] and 0.60 (= [($150-$60)/$150] respectively. Weighted contribution margin ratio is: [(2/3) × 0.65 + (1/3) × 0.60] = 0.6333 = 63.33%.

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Balakrishnan Managerial Accounting 0 = 0.63333 × total revenue - $42,750 Total memberships = $42,750/0.63333 = $67,500.

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