CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS

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1 CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS NOTATION USED IN CHAPTER 3 SOLUTIONS SP: Selling price VCU: Variable cost per unit CMU: Contribution margin per unit FC: Fixed costs TOI: Target operating income 3-1 Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, and operating income as changes occur in the units sold, selling price, variable cost per unit, or fixed costs of a product. 3-2 The assumptions underlying the CVP analysis outlined in Chapter 3 are 1. Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units sold. 2. Total costs can be separated into a fixed component that does not vary with the units sold and a component that is variable with respect to the units sold. 3. When represented graphically, the behavior of total revenues and total costs are linear (represented as a straight line) in relation to units sold within a relevant range and time period. 4. The selling price, variable cost per unit, and fixed costs are known and constant. 3-3 Operating income is total revenues from operations for the accounting period minus cost of goods sold and operating costs (excluding income taxes): Operating income Total revenues from operations Costs of goods sold and operating costs (excluding income taxes) Net income is operating income plus nonoperating revenues (such as interest revenue) minus nonoperating costs (such as interest cost) minus income taxes. Chapter 3 assumes nonoperating revenues and nonoperating costs are zero. Thus, Chapter 3 computes net income as: Net income Operating income Income taxes 3-4 Contribution margin is the difference between total revenues and total variable costs. Contribution margin per unit is the difference between selling price and variable cost per unit. Contribution-margin percentage is the contribution margin per unit divided by selling price. 3-5 Three methods to express CVP relationships are the equation method, the contribution margin method, and the graph method. The first two methods are most useful for analyzing operating income at a few specific levels of sales. The graph method is useful for visualizing the effect of sales on operating income over a wide range of quantities sold. 3-1

2 3-6 Breakeven analysis denotes the study of the breakeven point, which is often only an incidental part of the relationship between cost, volume, and profit. Cost-volume-profit relationship is a more comprehensive term than breakeven analysis. 3-7 CVP certainly is simple, with its assumption of output as the only revenue and cost driver, and linear revenue and cost relationships. Whether these assumptions make it simplistic depends on the decision context. In some cases, these assumptions may be sufficiently accurate for CVP to provide useful insights. The examples in Chapter 3 (the software package context in the text and the travel agency example in the Problem for Self-Study) illustrate how CVP can provide such insights. In more complex cases, the basic ideas of simple CVP analysis can be expanded. 3-8 An increase in the income tax rate does not affect the breakeven point. Operating income at the breakeven point is zero, and no income taxes are paid at this point. 3-9 Sensitivity analysis is a what-if technique that managers use to examine how a result will change if the original predicted data are not achieved or if an underlying assumption changes. The advent of the electronic spreadsheet has greatly increased the ability to explore the effect of alternative assumptions at minimal cost. CVP is one of the most widely used software applications in the management accounting area Examples include: Manufacturing substituting a robotic machine for hourly wage workers. Marketing changing a sales force compensation plan from a percent of sales dollars to a fixed salary. Customer service hiring a subcontractor to do customer repair visits on an annual retainer basis rather than a per-visit basis Examples include: Manufacturing subcontracting a component to a supplier on a per-unit basis to avoid purchasing a machine with a high fixed depreciation cost. Marketing changing a sales compensation plan from a fixed salary to percent of sales dollars basis. Customer service hiring a subcontractor to do customer service on a per-visit basis rather than an annual retainer basis Operating leverage describes the effects that fixed costs have on changes in operating income as changes occur in units sold, and hence, in contribution margin. Knowing the degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes CVP analysis is always conducted for a specified time horizon. One extreme is a very short-time horizon. For example, some vacation cruises offer deep price discounts for people who offer to take any cruise on a day s notice. One day prior to a cruise, most costs are fixed. The other extreme is several years. Here, a much higher percentage of total costs typically is variable. 3-2

3 CVP itself is not made any less relevant when the time horizon lengthens. What happens is that many items classified as fixed in the short run may become variable costs with a longer time horizon A company with multiple products can compute a breakeven point by assuming there is a constant sales mix of products at different levels of total revenue Yes, gross margin calculations emphasize the distinction between manufacturing and nonmanufacturing costs (gross margins are calculated after subtracting fixed manufacturing costs). Contribution margin calculations emphasize the distinction between fixed and variable costs. Hence, contribution margin is a more useful concept than gross margin in CVP analysis (10 min.) CVP computations. Variable Fixed Total Operating Contribution Contribution Revenues Costs Costs Costs Income Margin Margin % a. \$2,000 \$ 500 \$300 \$ 800 \$1,200 \$1, % b. 2,000 1, , % c. 1, , % d. 1, , % 3-17 (10 15 min.) CVP computations. 1a. Sales (\$60 per unit 400,000 units) \$24,000,000 Variable costs (\$50 per unit 400,000 units) 20,000,000 Contribution margin \$ 4,000,000 1b. Contribution margin (from above) \$ 4,000,000 Fixed costs 1,600,000 Operating income \$ 2,400,000 2a. Sales (from above) \$24,000,000 Variable costs (\$32 per unit 400,000 units) 12,800,000 Contribution margin \$11,200,000 2b. Contribution margin \$11,200,000 Fixed costs 4,800,000 Operating income \$ 6,400, Operating income is expected to increase by \$6,400,000 if Mr. Davidson proposal is accepted. The management would consider other factors before making the final decision. It is likely that product quality would improve as a result of using state of the art equipment. Due to increased automation, probably many workers will have to be laid off. Wilsar s management will have to consider the impact of such an action on employee morale. In addition, the proposal increases the company s fixed costs dramatically. This will increase the company s operating leverage and risk. 3-3

4 3-18 (35 40 min.) CVP analysis, changing revenues and costs. 1a. SP 8% \$1,000 \$80 per ticket VCU \$35 per ticket CMU \$80 \$35 \$45 per ticket FC \$22,000 a month Q FC \$22,000 CMU \$45 per ticket 489 tickets (rounded up) 1b. Q FC + TOI CMU \$22,000 + \$10,000 \$45 per ticket \$32,000 \$45 per ticket 712 tickets (rounded up) 2a. SP \$80 per ticket VCU \$29 per ticket CMU \$80 \$29 \$51 per ticket FC \$22,000 a month Q FC \$22,000 CMU \$51per ticket 432 tickets (rounded up) 2b. Q FC + TOI CMU \$22,000 + \$10,000 \$51per ticket \$32,000 \$51per ticket 628 tickets (rounded up) 3a. SP \$48 per ticket VCU \$29 per ticket CMU \$48 \$29 \$19 per ticket FC \$22,000 a month Q FC \$22,000 CMU \$19 per ticket 1,158 tickets (rounded up) 3-4

5 3b. Q FC + TOI CMU \$22,000 + \$10,000 \$19 per ticket \$32,000 \$19 per ticket 1,685 tickets (rounded up) The reduced commission sizably increases the breakeven point and the number of tickets required to yield a target operating income of \$10,000: 8% Commission Fixed (Requirement 2) Commission of \$48 Breakeven point 432 1,158 Attain OI of \$10, ,685 4a. The \$5 delivery fee can be treated as either an extra source of revenue (as done below) or as a cost offset. Either approach increases CMU \$5: SP \$53 (\$48 + \$5) per ticket VCU \$29 per ticket CMU \$53 \$29 \$24 per ticket FC \$22,000 a month Q FC \$22,000 CMU \$24 per ticket 917 tickets (rounded up) 4b. Q FC + TOI CMU \$22,000 + \$10,000 \$24 per ticket \$32,000 \$24 per ticket 1,334 tickets (rounded up) The \$5 delivery fee results in a higher contribution margin which reduces both the breakeven point and the tickets sold to attain operating income of \$10,

6 3-19 (20 min.) CVP exercises. Revenues Variable Costs Contribution Margin Fixed Costs Budgeted Operating Income Orig. \$12,500,000 G \$10,000,000 G \$2,500,000 \$2,250,000 G \$250, ,500,000 9,625,000 2,875,000 a 2,250, , ,500,000 10,375,000 2,125,000 b 2,250, , ,500,000 10,000,000 2,500,000 2,430,000 c 70, ,500,000 10,000,000 2,500,000 2,070,000 d 180, ,750,000 e 11,000,000 f 2,750,000 2,250, , ,250,000 g 9,000,000 h 2,250,000 2,250, ,375,000 i 11,500,000 j 2,875,000 2,587,500 k 287, ,500,000 9,200,000 l 3,300,000 2,430,000 m 870,000 G stands for given. a \$2,500, ; b \$2,500, ; c \$2,250, ; d \$2,250, ; e \$12,500, ; f \$10,000, ; g \$12,500, ; h \$10,000, ; i \$12,500, ; j \$10,000, ; k \$2,250, ; l \$10,000, ; m \$2,250, (20 min.) CVP exercises. 1a. [Units sold (Selling price Variable costs)] Fixed costs Operating income [5,000,000 (\$0.50 \$0.30)] \$900,000 \$100,000 1b. Fixed costs Contribution margin per unit Breakeven units \$900,000 [(\$0.50 \$0.30)] 4,500,000 units Breakeven units Selling price Breakeven revenues 4,500,000 units \$0.50 per unit \$2,250,000 or, Selling price -Variable costs Contribution margin ratio Selling price \$ \$ \$0.50 Fixed costs Contribution margin ratio Breakeven revenues \$900, \$2,250, ,000,000 (\$0.50 \$0.34) \$900,000 \$ (100,000) 3. [5,000,000 (1.1) (\$0.50 \$0.30)] [\$900,000 (1.1)] \$ 110, [5,000,000 (1.4) (\$0.40 \$0.27)] [\$900,000 (0.8)] \$ 190, \$900,000 (1.1) (\$0.50 \$0.30) 4,950,000 units 6. (\$900,000 + \$20,000) (\$0.55 \$0.30) 3,680,000 units 3-6

7 3-21 (10 min.) CVP analysis, income taxes. 1. Monthly fixed costs \$65,000 + \$75,000 + \$12,000 \$152,000 Contribution margin per unit \$29,000 \$25,000 \$600 \$ 3,400 Monthly fixed costs Breakeven units per month Contribution margin per unit \$152,000 \$3,400 per car 45 cars 2. Tax rate 25% Target net income \$69,000 Target net income \$69,000 \$69,000 Target operating income 1 - tax rate (1 0.25) 0.75 \$92,000 Quantity of output units Fixed costs + Target operating income \$152,000 + \$92, cars required to be sold Contribution margin per unit \$3,

8 3-22 (20 25 min.) CVP analysis, income taxes. 1. Variable cost percentage is \$3.20 \$ % Let R Revenues needed to obtain target net income \$105,000 R 0.40R \$450, R \$450,000 + \$150,000 R \$600, R \$1,000,000 or, Target net income \$105,000 \$450, Tax rate Breakeven revenues \$1,000,000 Contribution margin percentage 0.60 Proof: Revenues \$1,000,000 Variable costs (at 40%) 400,000 Contribution margin 600,000 Fixed costs 450,000 Operating income 150,000 Income taxes (at 30%) 45,000 Net income \$ 105,000 2.a. Customers needed to earn net income of \$105,000: Total revenues Sales check per customer \$1,000,000 \$8 125,000 customers b. Customers needed to break even: Contribution margin per customer \$8.00 \$3.20 \$4.80 Breakeven number of customers Fixed costs Contribution margin per customer \$450,000 \$4.80 per customer 93,750 customers 3. Using the shortcut approach: Change in net income Change in Unit number of customers contribution margin (1 Tax rate) (150, ,000) \$4.80 (1 0.30) \$120, \$84,000 New net income \$84,000 + \$105,000 \$189,000 The alternative approach is: Revenues, 150,000 \$8.00 \$1,200,000 Variable costs at 40% 480,000 Contribution margin 720,000 Fixed costs 450,000 Operating income 270,000 Income tax at 30% 81,000 Net income \$ 189,

9 3-23 (30 min.) CVP analysis, sensitivity analysis. 1. SP \$25.00 ( margin to bookstore) \$ \$20.00 VCU \$ 5.00 variable production and marketing cost 2.00 variable author royalty cost (0.10 \$20.00) \$ 7.00 CMU \$20.00 \$7.00 \$13.00 per copy FC \$ 630,000 fixed production and marketing cost 4,000,000 up-front payment to Washington \$4,630,000 Solution Exhibit 3-23A shows the PV graph. SOLUTION EXHIBIT 3-23A 3-9

10 2a. Breakeven number of units FC CMU \$4,630,000 \$ ,154 copies sold (rounded up) 2b. Target OI FC + OI CMU \$4,630,000 + \$3,000,000 \$13.00 \$7,630,000 \$ ,923 copies sold (rounded up) 3a. Decreasing the normal bookstore margin to 10% of the listed bookstore price of \$25 has the following effects: SP \$25.00 (1 0.10) \$ \$22.50 VCU \$ 5.00 variable production and marketing cost variable author royalty cost (0.10 \$22.50) \$ 7.25 CMU \$22.50 \$7.25 \$15.25 per copy Breakeven number of units FC CMU \$4,630,000 \$ ,607 copies sold (rounded up) The breakeven point decreases from 356,154 copies in requirement 2 to 303,607 copies. 3b. Increasing the listed bookstore price to \$32.50 while keeping the bookstore margin at 20% has the following effects: SP \$32.50 (1 0.20) \$ \$26.00 VCU \$ 5.00 variable production and marketing cost variable author royalty cost (0.10 \$26.00) \$ 7.60 CMU \$26.00 \$7.60 \$18.40 per copy 3-10

11 Breakeven number of units \$4,630,000 \$ ,630 copies sold (rounded up) The breakeven point decreases from 356,154 copies in requirement 2 to 251,630 copies. 3c. The answers to requirements 3a and 3b decrease the breakeven point relative to that in requirement 2 because in each case fixed costs remain the same at \$4,630,000 while the contribution margin per unit increases (10 min.) CVP analysis, margin of safety. Fixed costs 1. Breakeven point revenues Contribution margin percentage \$600,000 Contribution margin percentage 0.40 or 40% \$1,500,000 Selling price Variable cost per unit 2. Contribution margin percentage Selling price SP \$ SP 0.40 SP SP \$ SP \$15 SP \$25 3. Breakeven sales in units Revenues Selling price \$1,500,000 \$25 60,000 units Margin of safety in units sales in units Breakeven sales in units 80,000 60,000 20,000 units Revenues, 80,000 units \$25 \$2,000,000 Breakeven revenues 1,500,000 Margin of safety \$ 500,

12 3-25 (25 min.) Operating leverage. 1a. Let Q denote the quantity of cars sold Breakeven point under Option 1 \$3,500Q \$2,800Q \$5,250 \$700Q \$5,250 Q \$5,250 \$700 8 cars (rounded up) 1b. Breakeven point under Option 2 \$3,500Q \$2,800Q (0.15 \$3,500Q) 0 175Q 0 Q 0 2. Operating income under Option 1 \$700Q \$5,250 Operating income under Option 2 \$175Q Find Q such that \$700Q \$5,250 \$175Q \$525Q \$5,250 Q \$5,250 \$ cars Revenues \$3, cars \$35,000 For Q 10 cars, operating income under both Option 1 and Option 2 \$1,750 For Q > 10, say, 11 cars, Option 1 gives operating income (\$700 11) \$5,250 \$2,450 Option 2 gives operating income \$ \$1,925 So Harry s will prefer Option 1. For Q < 10, say, 9 cars, Option 1 gives operating income (\$700 9) \$5,250 \$1,050 Option 2 gives operating income \$175 9 \$1,575 So Harry s will prefer Option 2. Contribution margin 3. Degree of operating leverage Operating income \$ Under Option 1, degree of operating leverage \$1,750 \$ Under Option 2, degree of operating leverage \$1, The calculations in requirement 3 indicate that when sales are 10 units, a percentage change in sales and contribution margin will result in 4 times that percentage change in operating income for Option 1, but the same percentage change in operating income for Option 2. The degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes. 3-12

13 3-26 (15 min.) CVP analysis, international cost structure differences. Variable Variable Operating Income for Sales price Annual Manufacturing Marketing & Contribution Budgeted Sales of Country to retail Fixed Cost Distribution Cost Margin Breakeven Breakeven 800,000 outlets Costs per Sweater per Sweater Per Unit Units Revenues Sweaters (1) (2) (3) (4) (5)(1)-(3)-(4) (6)(2) (5) (6) (1) (7)[800,000 (5)] (2) Singapore \$32.00 \$ 6,500,000 \$ 8.00 \$11.00 \$ ,000 \$16,000,000 \$3,900,000 Thailand ,500, ,000 9,600,000 7,500,000 United States ,000, ,200,000 38,400,000 (4,000,000) Requirement 1 Requirement 2 Thailand has the lowest breakeven point since it has both the lowest fixed costs (\$4,500,000) and the lowest variable cost per unit (\$17.00). Hence, for a given selling price, Thailand will always have a higher operating income (or a lower operating loss) than Singapore or the U.S. The U.S. breakeven point is 1,200,000 units. Hence, with sales of only 800,000 units, it has an operating loss of \$4,000,

14 3-27 (30 min.) Sales mix, new and upgrade customers. 1. SP VCU CMU New Customers \$ Upgrade Customers \$ The 70%/30% sales mix implies that, in each bundle, 7 units are sold to new customers and 3 units are sold to upgrade customers. Contribution margin of the bundle 7 \$ \$60 \$700 + \$180 \$880 Breakeven point in bundles \$15,000,000 17,045 bundles \$88 Breakeven point in units is: Sales to new customers: 17,045 bundles 7 units per bundle 119,315 units Sales to upgrade customers: 17,045 bundles 3 units per bundle 51,135 units Total number of units to breakeven (rounded) 170,450 units Alternatively, Let S Number of units sold to upgrade customers 2.33S Number of units sold to new customers Revenues Variable costs Fixed costs Operating income [\$230 (2.33S) + \$140S] [\$130 (2.33S) + \$80S] \$15,000,000 OI \$675.9S \$382.9S \$15,000,000 OI Breakeven point is 170,479 units when OI 0 because \$293S \$15,000,000 S 51,195 units sold to upgrade customers (rounded) 2.33S 119,284 units sold to new customers (rounded) BEP 170,479 units Check Revenues (\$ ,284) + (\$140 51,195) \$34,602,620 Variable costs (\$ ,284) + (\$80 51,195) 19,602,520 Contribution margin 15,000,100 Fixed costs 15,000,000 Operating income (caused by rounding) \$ When 400,000 units are sold, mix is: Units sold to new customers (70% 400,000) 280,000 Units sold to upgrade customers (30% 400,000) 120,

15 Revenues (\$ ,000) + (\$ ,000) \$81,200,000 Variable costs (\$ ,000) + (\$80 120,000) 46,000,000 Contribution margin 35,200,000 Fixed costs 15,000,000 Operating income \$20,200,000 3a. At New 60%/Upgrade 40% mix, each bundle contains 3 units sold to new customer and 2 units sold to upgrade customer. Contribution margin of the bundle 3 \$ \$60 \$300 + \$120 \$420 Breakeven point in bundles \$15,000,000 35,714 bundles \$42 Breakeven point in units is: Sales to new customers: 35,714 bundles 3 units per bundle 107,142 units Sales to upgrade customers: 35,714 bundles 2 units per bundle 71,428 units Total number of units to breakeven 178,570 units Alternatively, Let S Number of units sold to upgrade customers Then 1.5S Number of units sold to new customers [\$230 (1.5S) + \$140S] [\$130 (1.5S) + \$80S] \$15,000,000 OI 485S 275S \$15,000, S \$15,000,000 S 71,429 units sold to upgrade customers 1.5S 107,144 units sold to new customers BEP 178,573 units Check Revenues (\$ ,144) + (\$140 71,429) \$34,643,180 Variable costs (\$ ,144) + (\$80 71,429) 19,643,040 Contribution margin 15,000,140 Fixed costs 15,000,000 Operating income (caused by rounding) \$ 140 3b. At New 80%/ Upgrade 20% mix, each bundle contains 4 units sold to new customers and 1 unit sold to upgrade customers. Contribution margin of the bundle 4 \$ \$60 \$400 + \$60 \$460 Breakeven point in bundles \$15,000,000 32,609 bundles (rounded) \$460 Breakeven point in units is: Sales to new customers: 32,609 bundles 4 units per bundle 130,436 units Sales to upgrade customers: 32,609 bundles 1 unit per bundle 32,609 units Total number of units to breakeven 163,405 units 3-15

16 Alternatively, Let S Number of units sold to upgrade customers then 4S Number of units sold to new customers [\$230 (4S) + \$140S] [\$130 (4S) + \$80S] \$15,000,000 OI 1,060S 600S \$15,000, S \$15,000,000 S 32,609 units sold to upgrade customers (rounded up) 4S 130,436 units sold to new customers (rounded up) 163,045 units Check Revenues (\$ ,436) + (\$140 32,609) \$34,565,540 Variable costs (\$ ,436) + (\$80 32,609) 19,565,400 Contribution margin 15,000,140 Fixed costs 15,000,000 Operating income (caused by rounding) \$ 140 3c. As MediaPro increases its percentage of new customers, which have a higher contribution margin per unit than upgrade customers, the number of units required to break even decreases: Requirement 3(a) Requirement 1 Requirement 3(b) New Customers 60% Upgrade Customers 40% Breakeven Point 178, , , (20 min.) CVP analysis, multiple cost drivers. 1a. 1b. Operating income Operating income Revenues Cost of picture Quantity of Cost of Number of frames picture frames shipment shipments (\$45 40,000) (\$30 40,000) (\$60 1,000) \$240,000 \$1,800,000 \$1,200,000 \$60,000 \$240,000 \$300,000 Fixed costs (\$45 40,000) (\$30 40,000) (\$60 800) \$240,000 \$312, Denote the number of picture frames sold by Q, then \$45Q \$30Q (500 \$60) \$240,000 0 \$15Q \$30,000 + \$240,000 \$270,000 Q \$270,000 \$15 18,000 picture frames 3. Suppose Susan had 1,000 shipments. \$45Q \$30Q (1,000 \$60) \$240, Q \$300,000 Q 20,000 picture frames 3-16

17 The breakeven point is not unique because there are two cost drivers quantity of picture frames and number of shipments. Various combinations of the two cost drivers can yield zero operating income (25 mins) CVP, Not for profit. 1. Contributions \$20,000,000 Fixed costs 2,000,000 Cash available to purchase land \$18,000,000 Divided by cost per acre to purchase land 4,000 Acres of land PG can purchase 4,500 acres 2. Contributions (\$20,000,000 \$6,000,000) \$14,000,000 Fixed costs 2,000,000 Cash available to purchase land \$12,000,000 Divided by cost per acre to purchase land (\$4,000 \$2,000) 2,000 Acres of land PG can purchase 6,000 acres On financial considerations alone, SG should take the subsidy because it can purchase 1,500 more acres (6,000 acres 4,500 acres). 3. Let the decrease in contributions be\$x. Cash available to purchase land \$20,000,000 \$x \$2,000,000 Cost to purchase land \$4,000 \$2,000 \$2,000 To purchase 4,500 acres, we solve the following equation for x. PG will be indifferent between taking the government subsidy or not if contributions decrease by \$9,000,

18 3-30 (15 min.) Contribution margin, decision making. 1. Revenues \$500,000 Deduct variable costs: Cost of goods sold \$200,000 Sales commissions 50,000 Other operating costs 40, ,000 Contribution margin \$210,000 \$210, Contribution margin percentage 42% \$500, Incremental revenue (20% \$500,000) \$100,000 Incremental contribution margin (42% \$100,000) \$42,000 Incremental fixed costs (advertising) 10,000 Incremental operating income \$32,000 If Mr. Schmidt spends \$10,000 more on advertising, the operating income will increase by \$32,000, converting an operating loss of \$10,000 to an operating income of \$22,000. Proof (Optional): Revenues (120% \$500,000) \$600,000 Cost of goods sold (40% of sales) 240,000 Gross margin 360,000 Operating costs: Salaries and wages \$150,000 Sales commissions (10% of sales) 60,000 Depreciation of equipment and fixtures 12,000 Store rent 48,000 Advertising 10,000 Other operating costs: \$40,000 Variable ( \$600,000) \$500,000 48,000 Fixed 10, ,000 Operating income \$ 22,

19 3-31 (20 min.) Contribution margin, gross margin and margin of safety. 1. Mirabella Cosmetics Operating Income Statement, June 2008 Units sold 10,000 Revenues \$100,000 Variable costs Variable manufacturing costs \$ 55,000 Variable marketing costs 5,000 Total variable costs 60,000 Contribution margin 40,000 Fixed costs Fixed manufacturing costs \$ 20,000 Fixed marketing & administration costs 10,000 Total fixed costs 30,000 Operating income \$ 10,000 \$40, Contribution margin per unit \$4 per unit 10,000 units Fixed costs \$30,000 Breakeven quantity 7,500 units Contribution margin per unit \$4 per unit Selling price Revenues \$100,000 \$10 per unit Units sold 10,000 units Breakeven revenues 7,500 units \$10 per unit \$75,000 Alternatively, Contribution margin percentage Contribution margin \$40,000 40% Revenues \$100, 000 Breakeven revenues Fixed costs \$30,000 \$75, 000 Contribution margin percentage Margin of safety (in units) Units sold Breakeven quantity 10,000 units 7,500 units 2,500 units 4. Units sold 8,000 Revenues (Units sold Selling price 8,000 \$10) \$80,000 Contribution margin (Revenues CM percentage \$80,000 40%) \$32,000 Fixed costs 30,000 Operating income 2,000 Taxes (30% \$2,000) 600 Net income \$ 1,

20 3-32 (30 min.) Uncertainty and expected costs. 1. Monthly Number of Orders Cost of Current System 300,000 \$1,000,000 + \$40(300,000) \$13,000, ,000 \$1,000,000 + \$40(400,000) \$17,000, ,000 \$1,000,000 + \$40(500,000) \$21,000, ,000 \$1,000,000 + \$40(600,000) \$25,000, ,000 \$1,000,000 + \$40(700,000) \$29,000,000 Monthly Number of Orders Cost of Partially Automated System 300,000 \$5,000,000 + \$30(300,000) \$14,000, ,000 \$5,000,000 + \$30(400,000) \$17,000, ,000 \$5,000,000 + \$30(500,000) \$20,000, ,000 \$5,000,000 + \$30(600,000) \$23,000, ,000 \$5,000,000 + \$30(700,000) \$26,000,000 Monthly Number of Orders Cost of Fully Automated System 300,000 \$10,000,000 + \$20(300,000) \$16,000, ,000 \$10,000,000 + \$20(400,000) \$18,000, ,000 \$10,000,000 + \$20(500,000) \$20,000, ,000 \$10,000,000 + \$20(600,000) \$22,000, ,000 \$10,000,000 + \$20(700,000) \$24,000, Current System Expected Cost: \$13,000, \$ 1,300,000 17,000, ,250,000 21,000, ,400,000 25,000, ,750,000 29,000, ,900,000 \$ 20,600,000 Partially Automated System Expected Cost: \$14,000, \$ 1,400,000 17,000, ,250,000 20,000, ,000,000 23,000, ,450,000 26,000, ,600,000 \$19,700,000 Fully Automated System Expected Cost: \$16,000, \$ 1,600,000 18,000, ,500,000 20,000, ,000,000 22,000, ,300,000 24,000, ,400,000 \$19,800,

21 3. Dawmart should consider the impact of the different systems on its relationship with suppliers. The interface with Dawmart s system may require that suppliers also update their systems. This could cause some suppliers to raise the cost of their merchandise. It could force other suppliers to drop out of Dawmart s supply chain because the cost of the system change would be prohibitive. Dawmart may also want to consider other factors such as the reliability of different systems and the effect on employee morale if employees have to be laid off as it automates its systems (15 20 min.) CVP analysis, service firm. 1. Revenue per package \$4,500 Variable cost per package 3,600 Contribution margin per package \$ 900 Breakeven (units) Fixed costs Contribution margin per package \$540, tour packages \$900 per package 2. Contribution margin ratio Contribution margin per package Selling price \$900 \$4,500 20% Revenue to achieve target income (Fixed costs + target OI) Contribution margin ratio \$540,000 + \$90,000 \$3,150,000, or 0.20 \$540,000 + \$90,000 Number of tour packages to earn \$90,000 operating income: 700 tour packages \$900 Revenues to earn \$90,000 OI 700 tour packages \$4,500 \$3,150, Fixed costs \$540,000 + \$30,000 \$570,000 Breakeven (units) Fixed costs Contribution margin per unit Fixed costs Contribution margin per unit Breakeven (units) \$570,000 \$950 per tour package 600 tour packages Desired variable cost per tour package \$4,500 \$950 \$3,550 Because the current variable cost per unit is \$3,600, the unit variable cost will need to be reduced by \$50 to achieve the breakeven point calculated in requirement 1. Alternate Method: If fixed cost increases by \$30,000, then total variable costs must be reduced by \$30,000 to keep the breakeven point of 600 tour packages. 3-21

22 Therefore, the variable cost per unit reduction \$30, \$50 per tour package 3-34 (30 min.) CVP, target income, service firm. 1. Revenue per child \$600 Variable costs per child 200 Contribution margin per child \$400 Breakeven quantity Fixed costs Contribution margin per child \$5, children \$ Target quantity Fixed costs + Target operating income Contribution margin per child \$5,600 + \$10,400 \$ children 3. Increase in rent (\$3,000 \$2,000) \$1,000 Field trips 1,000 Total increase in fixed costs \$2,000 Divide by the number of children enrolled 40 Increase in fee per child \$ 50 Therefore, the fee per child will increase from \$600 to \$650. Alternatively, New contribution margin per child \$5,600 + \$2,000 + \$10, \$450 New fee per child Variable costs per child + New contribution margin per child \$200 + \$450 \$

23 3-35 (20 25 min.) CVP analysis. 1. Selling price \$34.00 Variable costs per unit: Purchase price \$20.00 Shipping and handling Contribution margin per unit (CMU) \$ 9.00 Fixed costs Breakeven point in units \$50,000 Contr. margin per unit \$9.00 Margin of safety (units) 10,000 5,556 4,444 units 5,556 units 2. Since Winston is operating above the breakeven point, any incremental contribution margin will increase operating income dollar for dollar. Increase in units sales 15% 10,000 1,500 Incremental contribution margin \$9 1,500 \$13,500 Therefore, the increase in operating income will be equal to \$13,500. Winston s operating income in 2008 would be \$40,000 + \$13,500 \$53, Selling price \$34.00 Variable costs: Purchase price \$20 125% \$25.00 Shipping and handling Contribution margin per unit \$ 4.00 Target sales in units FC + TOI CMU \$50,000 + \$40,000 \$4 22,500 units Target sales in dollars \$34 22,500 \$7,650,

24 3-36 (30 40 min.) CVP analysis, income taxes. 1. Revenues Variable costs Fixed costs Target net income 1 Tax rate Let X Net income for 2008 X 20,000(\$25.00) 20,000(\$13.75) \$135, X \$500,000 \$275,000 \$135, \$300,000 \$165,000 \$81,000 X X \$54,000 Alternatively, Operating income Revenues Variable costs Fixed costs \$500,000 \$275,000 \$135,000 \$90,000 Income taxes 0.40 \$90,000 \$36,000 Net income Operating income Income taxes \$90,000 \$36,000 \$54, Let Q Number of units to break even \$25.00Q \$13.75Q \$135,000 0 Q \$135,000 \$ ,000 units 3. Let X Net income for ,000(\$25.00) 22,000(\$13.75) (\$135,000 + \$11,250) X \$550,000 \$302,500 \$146,250 X 0.60 \$101,250 X 0.60 X \$60, Let Q Number of units to break even with new fixed costs of \$146,250 \$25.00Q \$13.75Q \$146,250 0 Q \$146,250 \$ ,000 units Breakeven revenues 13,000 \$25.00 \$325, Let S Required sales units to equal 2008 net income \$25.00S \$13.75S \$146,250 \$54, \$11.25S \$236,250 S 21,000 units Revenues 21,000 units \$25 \$525,

25 6. Let A Amount spent for advertising in 2009 \$550,000 \$302,500 (\$135,000 + A) \$60, \$550,000 \$302,500 \$135,000 A \$100,000 \$550,000 \$537,500 A A \$12, (25 min.) CVP, sensitivity analysis. Contribution margin per corkscrew \$ \$50 Fixed costs \$50,000 Units sold Total sales Selling price \$375,000 \$250 per unit 1,500 units 1. Sales increase 12% Sales revenues 1, \$250 \$420,000 Variable costs 1, \$ ,000 Contribution margin 84,000 Fixed costs 50,000 Operating income \$ 34, Increase fixed costs \$2,000; Increase sales 40% Sales revenues 1, \$250 \$525,000 Variable costs 1, \$ ,000 Contribution margin 105,000 Fixed costs (\$50,000 + \$2,000) 52,000 Operating income \$ 53, Increase selling price to \$300; Sales decrease 25% Sales revenues 1, \$300 \$337,500 Variable costs 1, \$ ,000 Contribution margin 112,500 Fixed costs 50,000 Operating income \$ 62, Increase selling price to \$375; Variable costs increase \$70 per corkscrew Sales revenues 1,500 \$375 \$562,500 Variable costs 1,500 \$ ,000 Contribution margin 157,500 Fixed costs 50,000 Operating income \$107,500 Alternative 4 yields the highest operating income. If APP is confident that unit sales will not decrease despite increasing the selling price, it should choose alternative

26 3-38 (20 30 min.) CVP analysis, shoe stores. 1. CMU (SP VCU \$30 \$21) \$ 9.00 a. Breakeven units (FC CMU \$360,000 \$9 per unit) 40,000 b. Breakeven revenues (Breakeven units SP 40,000 units \$30 per unit) \$1,200, Pairs sold 35,000 Revenues, 35,000 \$30 \$1,050,000 Total cost of shoes, 35,000 \$ ,500 Total sales commissions, 35,000 \$ ,500 Total variable costs 735,000 Contribution margin 315,000 Fixed costs 360,000 Operating income (loss) \$ (45,000) 3. Unit variable data (per pair of shoes) Selling price \$ Cost of shoes Sales commissions 0 Variable cost per unit \$ Annual fixed costs Rent \$ 60,000 Salaries, \$200,000 + \$81, ,000 Advertising 80,000 Other fixed costs 20,000 Total fixed costs \$ 441,000 CMU, \$30 \$19.50 \$ a. Breakeven units, \$441,000 \$10.50 per unit 42,000 b. Breakeven revenues, 42,000 units \$30 per unit \$1,260, Unit variable data (per pair of shoes) Selling price \$ Cost of shoes Sales commissions 1.80 Variable cost per unit \$ Total fixed costs \$ 360,000 CMU, \$30 \$21.30 \$ 8.70 a. Break even units \$360,000 \$8.70 per unit 41,380 (rounded up) b. Break even revenues 41,380 units \$30 per unit \$1,241,

27 5. Pairs sold 50,000 Revenues (50,000 pairs \$30 per pair) \$1,500,000 Total cost of shoes (50,000 pairs \$19.50 per pair) \$ 975,000 Sales commissions on first 40,000 pairs (40,000 pairs \$1.50 per pair) 60,000 Sales commissions on additional 10,000 pairs [10,000 pairs (\$ \$0.30 per pair)] 18,000 Total variable costs \$1,053,000 Contribution margin \$ 447,000 Fixed costs 360,000 Operating income \$ 87,000 Alternative approach: Breakeven point in units 40,000 pairs Store manager receives commission of \$0.30 on 10,000 (50,000 40,000) pairs. Contribution margin per pair beyond breakeven point of 10,000 pairs \$8.70 (\$30 \$21 \$0.30) per pair. Operating income 10,000 pairs \$8.70 contribution margin per pair \$87,

28 3-39 (30 min.) CVP analysis, shoe stores (continuation of 3-38). No. of units sold CM per Unit CM Salaries + Commission Plan Higher Fixed Salaries Only Fixed Costs Operating Income CM per Unit CM Fixed Costs Operating Income Difference in favor of higher-fixedsalary-only (1) (2) (3)(1) (2) (4) (5)(3) (4) (6) (7)(1) (6) (8) (9)(7) (8) (10)(9) (5) 40,000 \$9.00 \$360,000 \$360,000 0 \$10.50 \$420,000 \$441,000 \$ (21,000) \$(21,000) 42, , ,000 18, , ,000 0 (18,000) 44, , ,000 36, , ,000 21,000 (15,000) 46, , ,000 54, , ,000 42,000 (12,000) 48, , ,000 72, , ,000 63,000 (9,000) 50, , ,000 90, , ,000 84,000 (6,000) 52, , , , , , ,000 (3,000) 54, , , , , , , , , , , , , ,000 3,000 58, , , , , , ,000 6,000 60, , , , , , ,000 9,000 62, , , , , , ,000 12,000 64, , , , , , ,000 15,000 66, , , , , , ,000 18,

29 1. See preceding table. The new store will have the same operating income under either compensation plan when the volume of sales is 54,000 pairs of shoes. This can also be calculated as the unit sales level at which both compensation plans result in the same total costs: Let Q unit sales level at which total costs are same for both plans \$19.50Q + \$360,000 + \$ \$81,000 \$21Q + \$360,000 \$1.50 Q \$81,000 Q 54,000 pairs 2. When sales volume is above 54,000 pairs, the higher-fixed-salaries plan results in lower costs and higher operating incomes than the salary-plus-commission plan. So, for an expected volume of 55,000 pairs, the owner would be inclined to choose the higher-fixed-salaries-only plan. But it is likely that sales volume itself is determined by the nature of the compensation plan. The salary-plus-commission plan provides a greater motivation to the salespeople, and it may well be that for the same amount of money paid to salespeople, the salary-plus-commission plan generates a higher volume of sales than the fixed-salary plan. 3. Let TQ Target number of units For the salary-only plan, \$30.00TQ \$19.50TQ \$441,000 \$168,000 \$10.50TQ \$609,000 TQ \$609,000 \$10.50 TQ 58,000 units For the salary-plus-commission plan, \$30.00TQ \$21.00TQ \$360,000 \$168,000 \$9.00TQ \$528,000 TQ \$528,000 \$9.00 TQ 58,667 units (rounded up) The decision regarding the salary plan depends heavily on predictions of demand. For instance, the salary plan offers the same operating income at 58,000 units as the commission plan offers at 58,667 units. 4. WalkRite Shoe Company Operating Income Statement, 2008 Revenues (48,000 pairs \$30) + (2,000 pairs \$18) \$1,476,000 Cost of shoes, 50,000 pairs \$ ,000 Commissions Revenues 5% \$1,476, ,800 Contribution margin 427,200 Fixed costs 360,000 Operating income \$ 67,

30 3-40 (40 min.) Alternative cost structures, uncertainty, and sensitivity analysis. 1. Contribution margin assuming fixed rental arrangement \$50 \$30 \$20 per bouquet Fixed costs \$5,000 Breakeven point \$5,000 \$20 per bouquet 250 bouquets Contribution margin assuming \$10 per arrangement rental agreement \$50 \$30 \$10 \$10 per bouquet Fixed costs \$0 Breakeven point \$0 \$10 per bouquet 0 (i.e. EB makes a profit no matter how few bouquets it sells) 2. Let x denote the number of bouquets EB must sell for it to be indifferent between the fixed rent and royalty agreement. Bouquets Sold (1) To calculate x we solve the following equation. \$50 x \$30 x \$5,000 \$50 x \$40 x \$20 x \$5,000 \$10 x \$10 x \$5,000 x \$5,000 \$ bouquets For sales between 0 to 500 bouquets, EB prefers the royalty agreement because in this range, \$10 x > \$20 x \$5,000. For sales greater than 500 bouquets, EB prefers the fixed rent agreement because in this range, \$20 x \$5,000 > \$10 x. 3. If we assume the \$5 savings in variable costs applies to both options, we solve the following equation for x. \$50 x \$25 x \$5,000 \$50 x \$35 x \$25 x \$5,000 \$15 x \$10 x \$5,000 x \$5,000 \$10 per bouquet 500 bouquets The answer is the same as in Requirement 2, that is, for sales between 0 to 500 bouquets, EB prefers the royalty agreement because in this range, \$15 x > \$25 x \$5,000. For sales greater than 500 bouquets, EB prefers the fixed rent agreement because in this range, \$25 x \$5,000 > \$15 x. 4. Fixed rent agreement: Fixed Costs (3) Variable Costs (4) Operating Income (Loss) (5)(2) (3) (4) Expected Operating Income (7)(5) (6) Revenue Probability (2) (6) \$50\$10,000 \$5, \$30\$ 6,000 \$ (1,000) 0.20 \$ ( 200) \$50\$20,000 \$5, \$30\$12,000 \$ 3, \$50\$30,000 \$5, \$30\$18,000 \$ 7, , \$50\$40,000 \$5, \$30\$24,000 \$11, ,200 1,000 1,000 \$50\$50,000 \$5,000 1,000 \$30\$30,000 \$15, ,000 Expected value of rent agreement \$7,

31 Royalty agreement: Bouquets Sold (1) Variable Costs (3) Operating Income (4)(2) (3) Expected Operating Income (6)(4) (5) Revenue Probability (2) (5) \$50\$10, \$40\$ 8,000 \$2, \$ \$50\$20, \$40\$16,000 \$4, \$50\$30, \$40\$24,000 \$6, , \$50\$40, \$40\$32,000 \$8, ,600 1,000 1,000 \$50\$50,000 1,000 \$40\$40,000 \$10, ,000 Expected value of royalty agreement \$6,000 EB should choose the fixed rent agreement because the expected value is higher than the royalty agreement. EB will lose money under the fixed rent agreement if EB sells only 200 bouquets but this loss is more than made up for by high operating incomes when sales are high (20-30 min.) CVP, alternative cost structures. 1. Variable cost per doughnut \$ \$0.10 \$0.30 Contribution margin per doughnut Selling price Variable cost per doughnut \$0.80 \$0.30 \$0.50 Breakeven point Fixed costs Contribution margin per doughnut \$70 \$ doughnuts (per day) Fixed costs + Target operating income 2. Target number of doughnuts Contribution margin per doughnut \$70 + \$ doughnuts \$ Contribution margin per doughnut Selling price Variable cost per doughnut \$0.80 \$0.20 \$0.60 Fixed costs \$70 + \$20 \$90 Fixed costs \$90 Breakeven point 150 doughnuts Contribution margin per doughnut \$ Let x be the number of doughnuts for which Dom is indifferent between hiring Jason or hiring Alan. Dom will be indifferent when the profits under the two alternatives are equal. \$0.50 x \$70 \$0.60 x \$ x x \$20 \$ doughnuts For sales between 0 and 200 doughnuts, Dom prefers Jason to repackage the doughnuts because in this range, \$0.50 x \$70 > \$0.60 x \$50. For sales greater than 200 doughnuts, Dom prefers Alan to repackage the doughnuts because in this range, \$0.60 x \$90 > \$0.50 x \$

32 3-42 (30 min.) CVP analysis, income taxes, sensitivity. 1a. To break even, Almo Company must sell 500 units. This amount represents the point where revenues equal total costs. Let Q denote the quantity of canopies sold. Revenue Variable costs + Fixed costs \$400Q \$200Q + \$100,000 \$200Q \$100,000 Q 500 units Breakeven can also be calculated using contribution margin per unit. Contribution margin per unit Selling price Variable cost per unit \$400 \$200 \$200 Breakeven Fixed Costs Contribution margin per unit \$100,000 \$ units 1b. To achieve its net income objective, Almo Company must sell 2,500 units. This amount represents the point where revenues equal total costs plus the corresponding operating income objective to achieve net income of \$240,000. Revenue Variable costs + Fixed costs + [Net income (1 Tax rate)] \$400Q \$200Q + \$100,000 + [\$240,000 (1 0.4)] \$400 Q \$200Q + \$100,000 + \$400,000 Q 2,500 units 2. To achieve its net income objective, Almo Company should select the first alternative where the sales price is reduced by \$40, and 2,700 units are sold during the remainder of the year. This alternative results in the highest net income and is the only alternative that equals or exceeds the company s net income objective. Calculations for the three alternatives are shown below. Alternative 1 Revenues (\$ ) + (\$360 a 2,700) \$1,112,000 Variable costs \$200 3,050 b \$610,000 Operating income \$1,112,000 \$610,000 \$100,000 \$402,000 Net income \$402,000 (1 0.40) \$241,200 a \$400 \$40; b 350 units + 2,700 units. Alternative 2 Revenues (\$ ) + (\$370 c 2,200) \$954,000 Variable costs (\$ ) + (\$190 d 2,200) \$488,000 Operating income \$954,000 \$488,000 \$100,000 \$366,000 Net income \$366,000 (1 0.40) \$219,600 c \$400 \$30; d \$200 \$

33 Alternative 3 Revenues (\$ ) + (\$380 e 2,000) \$900,000 Variable costs \$200 2,350 f \$470,000 Operating income \$900,000 \$470,000 \$90,000 g \$340,000 Net income \$340,000 (1 0.40) \$204,000 e \$400 (0.05 \$400) \$400 \$20; f 350 units + 2,000 units; g \$100,000 \$10, (30 min.) Choosing between compensation plans, operating leverage. 1. We can recast Secure Seniors income statement to emphasize contribution margin, and then use it to compute the required CVP parameters. Secure Seniors Corporation Income Statement For the Year Ended December 31, 2008 Using Sales Agents Using Own Sales Force Revenues \$35,000,000 \$35,000,000 Variable Costs Cost of goods sold variable \$16,500,000 \$16,500,000 Marketing commissions 7,000,000 23,500,000 2,800,000 19,300,000 Contribution margin \$11,500,000 \$15,700,000 Fixed Costs Cost of goods sold fixed 3,000,000 3,000,000 Marketing fixed 2,500,000 5,500,000 6,700,000 9,700,000 Operating income \$6,000,000 \$ 6,000,000 Contribution margin percentage (\$11,500,000 35,000,000; \$15,700,000 \$35,000,000) 33% 45% Breakeven revenues (\$5,500, ; \$9,700, ) \$16,666,667 \$21,555,556 Degree of operating leverage (\$11,500,000 \$6,000,000; \$15,700,000 \$6,000,000) The calculations indicate that at sales of \$35,000,000, a percentage change in sales and contribution margin will result in 1.92 times that percentage change in operating income if Secure Seniors continues to use sales agents and 2.62 times that percentage change in operating income if Secure Seniors employs its own sales staff. The higher contribution margin per dollar of sales and higher fixed costs gives Secure Seniors more operating leverage, that is, greater benefits (increases in operating income) if revenues increase but greater risks (decreases in operating income) if revenues decrease. Secure Seniors also needs to consider the skill levels and incentives under the two alternatives. Sales agents have more incentive compensation and hence may be more motivated to increase sales. On the other hand, Secure Seniors own sales force may be more knowledgeable and skilled in selling the company s products. That is, the sales volume itself will be affected by who sells and by the nature of the compensation plan. 3-33

34 3. Variable costs of marketing 12% of Revenues Fixed marketing costs \$6,700,000 Operating income Revenues Variable manuf. costs Fixed manuf. costs Variable marketing costs Fixed marketing costs Denote the revenues required to earn \$6,000,000 of operating income by R, then R 0.45R \$3,000, R \$6,700,000 \$6,000,000 R 0.45R 0.12R \$6,000,000 + \$3,000,000 + \$6,700, R \$15,700,000 R \$15,700, \$36,511, (15 25 min.) Sales mix, three products. 1. Sales of A, B, and C are in ratio 20,000 : 100,000 : 80,000. So for every 1 unit of A, 5 (100,000 20,000) units of B are sold, and 4 (80,000 20,000) units of C are sold. Contribution margin of the bundle 1 \$3 + 5 \$2 + 4 \$1 \$3 + \$10 + \$4 \$17 Breakeven point in bundles \$255,000 15,000 bundles \$17 Breakeven point in units is: Product A: 15,000 bundles 1 unit per bundle 15,000 units Product B: 15,000 bundles 5 units per bundle 75,000 units Product C: 15,000 bundles 4 units per bundle 60,000 units Total number of units to breakeven 150,000 units Alternatively, Let Q Number of units of A to break even 5Q Number of units of B to break even 4Q Number of units of C to break even Contribution margin Fixed costs Zero operating income \$3Q + \$2(5Q) + \$1(4Q) \$255,000 0 \$17Q \$255,000 Q 15,000 (\$255,000 \$17) units of A 5Q 75,000 units of B 4Q 60,000 units of C Total 150,000 units 3-34

35 2. Contribution margin: A: 20,000 \$3 \$ 60,000 B: 100,000 \$2 200,000 C: 80,000 \$1 80,000 Contribution margin \$340,000 Fixed costs 255,000 Operating income \$ 85, Contribution margin A: 20,000 \$3 \$ 60,000 B: 80,000 \$2 160,000 C: 100,000 \$1 100,000 Contribution margin \$320,000 Fixed costs 255,000 Operating income \$ 65,000 Sales of A, B, and C are in ratio 20,000 : 80,000 : 100,000. So for every 1 unit of A, 4 (80,000 20,000) units of B and 5 (100,000 20,000) units of C are sold. Contribution margin of the bundle 1 \$3 + 4 \$2 + 5 \$1 \$3 + \$8 + \$5 \$16 Breakeven point in bundles \$255,000 15,938 bundles (rounded up) \$16 Breakeven point in units is: Product A: 15,938 bundles 1 unit per bundle 15,938 units Product B: 15,938 bundles 4 units per bundle 63,752 units Product C: 15,938 bundles 5 units per bundle 79,690 units Total number of units to breakeven 159,380 units Alternatively, Let Q Number of units of A to break even 4Q Number of units of B to break even 5Q Number of units of C to break even Contribution margin Fixed costs Breakeven point \$3Q + \$2(4Q) + \$1(5Q) \$255,000 0 \$16Q \$255,000 Q 15,938 (\$255,000 \$16) units of A (rounded up) 4Q 63,752 units of B 5Q 79,690 units of C Total 159,380 units Breakeven point increases because the new mix contains less of the higher contribution margin per unit, product B, and more of the lower contribution margin per unit, product C. 3-35

36 3-45 (40 min.) Multi-product CVP and decision making. 1. Gas oven: Selling price \$1,850 Variable cost per unit 1,100 Contribution margin per unit \$ 750 Electric oven: Selling price \$1,650 Variable cost per unit 650 Contribution margin per unit \$1,000 Each bundle contains 1 gas model and 3 electric models. So contribution margin of a bundle 1 \$ \$1,000 \$3,750 Breakeven Fixed costs \$15,000,000 point in 4, 000 bundles bundles Contribution margin per bundle \$3,750 Breakeven point in units of gas models and electric models is: Gas models: 4,000 bundles 1 unit per bundle 4,000 units Electric models: 4,000 bundles 3 units per bundle 12,000 units Total number of units to breakeven 16,000 units Breakeven point in dollars for gas models and electric models is: Gas models: 4,000 units \$1,850 per unit \$ 7,400,000 Electric models: 12,000 units \$1,650 per unit 19,800,000 Breakeven revenues \$ 27,200,000 Alternatively, weighted average contribution margin per unit (1 \$750) + (3 \$1,000) \$ \$15,000,000 Breakeven point 16,000 units \$ Gas: 16,000 units 4,000 units 4 3 Electric: 16, 000 units 12,000 units 4 Breakeven point in dollars Gas: 4,000 units \$1,850 per unit \$7,400,000 Electric: 12,000 units \$1,650 per unit \$19,800,

37 2. Gas oven: Selling price \$1,850 Variable cost per unit 900 Contribution margin per unit \$ 950 Electric oven: Selling price \$1,650 Variable cost per unit 400 Contribution margin per unit \$1,250 Each bundle contains 1 gas model and 3 electric models. So contribution margin of a bundle 1 \$ \$1,250 \$4,700 Breakeven Fixed costs \$15,000,000 + \$3,500,000 point in Contribution margin per bundle \$4,700 bundles 3,936 bundles Breakeven point in units of gas models and electric models is: Gas models: 3,936 bundles 1 unit per bundle 3,936 units Electric models: 3,936 bundles 3 units per bundle 11,808 units Total number of units to breakeven 15,744 units Breakeven point in dollars for gas models and electric models is: Gas models: 3,936 bundles \$1,850 per unit \$ 7,281,600 Electric models: 11,808 bundles \$1,650 per unit 19,483,200 Breakeven revenues \$26,764,800 Alternatively, (1 \$950) + (3 \$1,250) weighted average contribution margin per unit \$1,175 4 \$15,000,000+3,500,000 Breakeven point 15,745 units \$1,175 1 Gas oven: 15,745 units 3,936 units 4 3 Electric oven: 15,745 units 11,809 units 4 Breakeven point in dollars: Gas oven: 3,936 units \$1,850 per unit \$7,281,600 Electric oven: 11,809 units \$1,650 per unit \$19,484, Let x be the number of bundles for Ovens Only Incorporated to be indifferent between the old and new production equipment. Operating income using old equipment \$3,750 x \$15,000,

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