CHAPTER 3 COST-VOLUME-PROFIT ANALYSIS. 3-2 The assumptions underlying the CVP analysis outlined in Chapter 3 are

Transcription

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 output level, 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 produced and sold. 2. Total costs can be separated into a fixed component that does not vary with the output level and a component that is variable with respect to the output level. 3. When represented graphically, the behavior of total revenues and total costs are linear (represented as a straight line) in relation to output level within a relevant range and time period. 4. The selling price, variable cost per unit, and fixed costs are known and constant. 5. The analysis either covers a single product or assumes that the sales mix, when multiple products are sold, will remain constant as the level of total units sold changes. 6. All revenues and costs can be added and compared without taking into account the time value of money. 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. 3-1

2 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. 3-6 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. 3-2

3 3-13 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. 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, , % 3-3

4 3-17 (10 15 min.) CVP computations. 1a. Sales ($25 per unit 180,000 units) $4,500,000 Variable costs ($20 per unit 180,000 units) 3,600,000 Contribution margin $ 900,000 1b. Contribution margin (from above) $ 900,000 Fixed costs 800,000 Operating income $ 100,000 2a. Sales (from above) $4,500,000 Variable costs ($10 per unit 180,000 units) 1,800,000 Contribution margin $2,700,000 2b. Contribution margin $2,700,000 Fixed costs 2,500,000 Operating income $ 200, Operating income is expected to increase by $100,000 if Ms. Schoenen s 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. Patel 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. 3-4

5 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 CMU $22,000 $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 $51 per ticket 432 tickets (rounded up) 2b. Q FC TOI CMU $22,000 $10,000 $51 per ticket $32,000 $51 per 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) 3-5

6 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,

7 3-19 (20 min.) CVP exercises. Revenues Variable Costs Contribution Margin Fixed Costs Budgeted Operating Income Orig. $10,000,000 G $8,200,000 G $1,800,000 $1,700,000 G $100, ,000,000 8,020,000 1,980,000 a 1,700, , ,000,000 8,380,000 1,620,000 b 1,700,000 (80,000) 3. 10,000,000 8,200,000 1,800,000 1,785,000 c 15, ,000,000 8,200,000 1,800,000 1,615,000 d 185, ,800,000 e 8,856,000 f 1,944,000 1,700, , ,200,000 g 7,544,000 h 1,656,000 1,700,000 (44,000) 7. 11,000,000 i 9,020,000 j 1,980,000 1,870,000 k 110, ,000,000 7,790,000 l 2,210,000 1,785,000 m 425,000 G stands for given. a $1,800, ; b $1,800, ; c $1,700, ; d $1,700, ; e $10,000, ; f $8,200, ; g $10,000, ; h $8,200, ; i $10,000, ; j $8,200, ; k $1,700, ; l $8,200, ; m $1,700, (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 Contribution margin ratio Selling price $ $ $0.50 Fixed costs Contribution margin ratio Breakeven revenues $900, $2,250,000 costs 2. 5,000,000 ($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 3-7

8 3-21 (10 min.) CVP analysis, income taxes. 1. Monthly fixed costs $50,000 + $60,000 + $10,000 $120,000 Contribution margin per unit $25,000 $22,000 $500 $ 2,500 Monthly fixed costs Breakeven units per month Contribution margin per unit $120,000 $2,500 per car 48 cars 2. Tax rate 40% Target net income $54,000 Target net income $54,000 $54,000 Target operating income 1 - tax rate (1 0.40) 0.60 $90,000 Quantity of output units Fixed costs + Target operating income $12 0,000 $90,000 required to be sold 84 cars Contribution margin per unit $2, (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,

9 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 number of customers Unit 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,

10 3-23 (30 min.) CVP analysis, sensitivity analysis. 1. SP $30.00 ( margin to bookstore) $ $21.00 VCU $ 4.00 variable production and marketing cost 3.15 variable author royalty cost (0.15 $21.00) $ 7.15 CMU $21.00 $7.15 $13.85 per copy FC $ 500,000 fixed production and marketing cost 3,000,000 up-front payment to Washington $3,500,000 Solution Exhibit 3-23A shows the PV graph. SOLUTION EXHIBIT 3-23A PV Graph for Media Publishers $4,000 FC $3,500,000 CMU $13.85 per book sold 3,000 2,000 Operating income (000 s) 1,000 0 Units so ld 100, , , , , 000-1, ,708 units -2,000-3,000 $3.5 million -4,

11 2a. Breakeven number of units FC CMU $3,500,000 $ b. Target OI 252,708 copies sold (rounded up) FC OI CMU $3,500,000 $2,000,000 $13.85 $5,500,000 $ ,112 copies sold (rounded up) 3a. Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30 has the following effects: SP $30.00 (1 0.20) $ $24.00 VCU $ 4.00 variable production and marketing cost variable author royalty cost (0.15 $24.00) $ 7.60 CMU $24.00 $7.60 $16.40 per copy Breakeven number of units FC CMU $3,500,000 $ ,415 copies sold (rounded up) The breakeven point decreases from 252,708 copies in requirement 2 to 213,415 copies. 3-11

12 3b. Increasing the listed bookstore price to $40 while keeping the bookstore margin at 30% has the following effects: SP $40.00 (1 0.30) $ $28.00 VCU $ 4.00 variable production and marketing cost variable author royalty cost (0.15 $28.00) $ 8.20 CMU $28.00 $8.20 $19.80 per copy Breakeven number of units $3,500,000 $ ,768 copies sold (rounded up) The breakeven point decreases from 252,708 copies in requirement 2 to 176,768 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 $3,500,000 while the contribution margin per unit increases (10 min.) CVP analysis, margin of safety. Fixed costs 1. Breakeven point revenues Contributi on margin percentage $400,000 Contribution margin percentage 0.40 or 40% $1,000,000 Selling price Variable cost per unit 2. Contribution margin percentage Selling price SP $ SP 0.40 SP SP $ SP $12 SP $20 3. Revenues, 80,000 units $20 $1,600,000 Breakeven revenues 1,000,000 Margin of safety $ 600,

13 3-25 (25 min.) Operating leverage. 1a. Let Q denote the quantity of carpets sold Breakeven point under Option 1 $500Q $350Q $5,000 $150Q $5,000 Q $5,000 $ carpets (rounded up) 1b. Breakeven point under Option 2 $500Q $350Q (0.10 $500Q) 0 100Q 0 Q 0 2. Operating income under Option 1 $150Q $5,000 Operating income under Option 2 $100Q Find Q such that $150Q $5,000 $100Q $50Q $5,000 Q $5,000 $ carpets For Q 100 carpets, operating income under both Option 1 and Option 2 $10,000 3a. For Q > 100, say, 101 carpets, Option 1 gives operating income ($ ) $5,000 $10,150 Option 2 gives operating income $ $10,100 So Color Rugs will prefer Option 1. 3b. For Q < 100, say, 99 carpets, Option 1 gives operating income ($150 99) $5,000 $9,850 Option 2 gives operating income $ $9,900 So Color Rugs will prefer Option 2. Contributi on margin 4. Degree of operating leverage Operating income $ Under Option 1, degree of operating leverage 1.5 $10,000 $ Under Option 2, degree of operating leverage 1.0 $10, The calculations in requirement 4 indicate that when sales are 100 units, a percentage change in sales and contribution margin will result in 1.5 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. 3-13

14 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) 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 $4,000,000. Requirement 1 Requirement

15 3-27 (30 min.) Sales mix, new and upgrade customers. 1. SP VCU CMU New Customers $ Upgrade Customers $ Let S Number of units sold to upgrade customers 1.5S Number of units sold to new customers Revenues Variable costs Fixed costs Operating income [$210 (1.5S) + $120S] [$90 (1.5S) + $40S] $14,000,000 OI $435S $175S $14,000,000 OI Breakeven point is 134,616 units when OI 0 because $260S $14,000,000 S 53,846 units sold to upgrade customers (rounded) 1.5S 80,770 units sold to new customers (rounded) BEP 134,616 units Check Revenues ($210 80,770) + ($120 53,846) $23,423,220 Variable costs ($90 80,770) + ($40 53,846) 9,423,140 Contribution margin 14,000,080 Fixed costs 14,000,000 Operating income (caused by rounding) $ When 200,000 units are sold, mix is: Units sold to new customers (60% 200,000) 120,000 Units sold to upgrade customers (40% 200,000) 80,000 Revenues ($ ,000) + ($120 80,000) $34,800,000 Variable costs ($90 120,000) + ($40 80,000) 14,000,000 Contribution margin 20,800,000 Fixed costs 14,000,000 Operating income $ 6,800,

16 3a. Let S Number of units sold to upgrade customers then S Number of units sold to new customers [$210S + $120S] [$90S + $40S] $14,000,000 OI 330S 130S $14,000, S $14,000,000 S 70,000 units sold to upgrade customers S 70,000 units sold to new customers BEP 140,000 units Check Revenues ($210 70,000) + ($120 70,000) $23,100,000 Variable costs ($90 70,000) + ($40 70,000) 9,100,000 Contribution margin 14,000,000 Fixed costs 14,000,000 Operating income $ 0 3b. Let S Number of units sold to upgrade customers then 9S Number of units sold to new customers [$210 (9S) + $120S] [$90 (9S) + $40S] $14,000,000 OI 2,010S 850S $14,000,000 1,160S $14,000,000 S 12,069 units sold to upgrade customers (rounded up) 9S 108,621 units sold to new customers (rounded up) 120,690 units Check Revenues ($ ,621) + ($120 12,069) $24,258,690 Variable costs ($90 108,621) + ($40 12,069) 10,258,650 Contribution margin 14,000,040 Fixed costs 14,000,000 Operating income (caused by rounding) $ 40 3c. As Zapo 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 50% Upgrade Customers 50% Breakeven Point 140, , ,

17 3-28 (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 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. 3-17

18 3-29 (25 30 min.) Athletic scholarships, CVP analysis. 1. Variable costs per scholarship offer: Scholarship amount $20,000 Operating costs 2,000 Total variable costs $22,000 Let the number of scholarships be denoted by Q $22,000 Q $5,000,000 $600,000 $22,000 Q $4,400,000 Q $4,400,000 $22, scholarships 2. Total budget for next year $5,000,000 ( ) $3,900,000 Then $22,000 Q $3,900,000 $600,000 $3,300,000 Q $3,300,000 $22, scholarships 3. Total budget for next year from above $3,900,000 Fixed costs 600,000 Variable costs for scholarships $3,300,000 If the total number of scholarships is to remain at 200: Variable cost per scholarship $3,300, $16,500 Variable operating cost per scholarship 2,000 Amount per scholarship $14,

19 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, Contribution margin percentage $210,000 $500,000 42% 3. 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,

20 3-31 (20 min.) Contribution margin, gross margin and margin of safety. 1. Mirabella Cosmetics Operating Income Statement, June 2005 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,

21 3-32 (15 20 min.) Uncertainty, CVP analysis (chapter appendix). 1. Pay-per-view Audience (number of homes subscribing to the event) Probability Expected Audience Expected Payment to Foreman (1) (2) (3) (1) (2) (4) (3) (25% $16) 100, ,000 $ 20, , ,000 80, , , , , , , , , ,000 1,000, , ,000 Total 380,000 1,520,000 Fixed payment 2,000,000 Total expected payment to Foreman $3,520, Selling price $ 16 Variable cost per subscribing home ($4 to Foreman + $2 to cable company) 6 Contribution margin per subscribing home $ 10 Fixed costs (Foreman, $2,000,000 + other costs, $1,000,000) $3,000,000 FC $3,000,000 Breakeven number of subscribing homes CMU $10 300,000 homes 3. Brady s expected audience size of 380,000 homes is more than 25% bigger than the breakeven audience size of 300,000 homes. So, if she is confident of the assumed probability distribution, she has a good margin of safety, and should proceed with her plans for the fight. She will only lose money if the pay-per-view audience is 100,000 or 200,000, which together have a 0.15 probability of occurring. 3-21

22 3-33 (15 20 min.) CVP analysis, service firm. 1. Revenue per package $4,000 Variable cost per package 3,600 Contribution margin per package $ 400 Breakeven (units) Fixed costs Contribution margin per package $480,000 $400 per package 1,200 tour packages 2. Contribution margin ratio Contributi on margin per package Selling price $400 $4,000 10% Revenue to achieve target income (Fixed costs + target OI) Contribution margin ratio $480,000 $100,000 $5,800,000, or 0.10 Number of tour packages to earn $100,000 operating income: $480,000 $100,000 1,450 tour packages $400 Revenues to earn $100,000 OI 1,450 tour packages $4,000 $5,800, Fixed costs $480,000 + $24,000 $504,000 Breakeven (units) Fixed costs Contributi on margin per unit Contribution margin per unit Fixed costs Breakeven (units) $504,000 1,200 tour packages $420 per tour package Desired variable cost per tour package $4,000 $420 $3,580 Because the current variable cost per unit is $3,600, the unit variable cost will need to be reduced by $20 to achieve the breakeven point calculated in requirement 1. Alternate Method: If fixed cost increases by $24,000, then total variable costs must be reduced by $24,000 to keep the breakeven point of 1,200 tour packages. Therefore, the variable cost per unit reduction $24,000 1,200 $20 per tour package. 3-22

23 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 Contributi on margin per child $5,600 $ children 2. Target quantity Fixed costs Target operating income Contributi on 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 $

24 3-35 (20 25 min.) CVP analysis. 1. Selling price $16.00 Variable costs per unit: Purchase price $10.00 Shipping and handling Contribution margin per unit (CMU) $ 4.00 Fixed costs $600,000 Breakeven point in units 150,000 units Contr. margin per unit $4.00 Margin of safety (units) 200, ,000 50,000 units 2. Since Galaxy is operating above the breakeven point, any incremental contribution margin will increase operating income dollar for dollar. Increase in units sales 10% 200,000 20,000 Incremental contribution margin $4 20,000 $80,000 Therefore, the increase in operating income will be equal to $80,000. Galaxy s operating income in 2005 would be $200,000 + $80,000 $280, Selling price $16.00 Variable costs: Purchase price $10 130% $13.00 Shipping and handling Contribution margin per unit $ 1.00 Target sales in units FC TOI CMU $600,000 $200,000 $1 800,000 units Target sales in dollars $16 800,000 $12,800,

25 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 ,000($25.00) 20,000($13.75) $135,000 $500,000 $275,000 $135,000 X X 0.60 $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 2005 net income $25.00S $13.75S $146,250 $54, $11.25S $236,250 S 21,000 units Revenues 21,000 units $25 $525, Let A Amount spent for advertising in 2006 $550,000 $302,500 ($135,000 + A) $60, $550,000 $302,500 $135,000 A $100,000 $550,000 $537,500 A A $12,

26 3-37 (20 min.) CVP analysis, decision making. 1. Tocchet s current operating income is as follows: Revenues, $105 40,000 $4,200,000 Variable costs, $55 40,000 2,200,000 Contribution margin 2,000,000 Fixed costs 1,400,000 Operating income $ 600,000 Let the fixed marketing and distribution costs be F. We calculate F when operating income is $600,000 and the selling price is $99. ($99 50,000) ($55 50,000) F $600,000 $4,950,000 $2,750,000 F $600,000 F $4,950,000 $2,750,000 $600,000 F $1,600,000 Hence, the maximum increase in fixed marketing and distribution costs that will allow Tocchet to reduce the selling price and maintain $600,000 in operating income is $200,000 ($1,600,000 $1,400,000). 2. Let the selling price be P. We calculate P for which, after increasing fixed manufacturing costs by $100,000 to $900,000 and variable manufacturing cost per unit by $2 to $47, operating income is $600,000. $40,000 P ($47 40,000) ($10 40,000) $900,000 $600,000 $600,000 $40,000 P $1,880,000 $400,000 $900,000 $600,000 $600,000 $40,000 P $600,000 + $1,880,000 + $400,000 + $900,000 + $600,000 $40,000 P $4,380,000 P $4,380,000 40,000 $ Tocchet will consider adding the new features provided the selling price is at least $ per unit. 3-26

27 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,

28 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,

29 3-39 (30 min.) CVP analysis, shoe stores (continuation of 3-38). Salaries + Commission Plan Higher Fixed Salaries Only No. of units sold CM per Unit CM 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,

30 1. See table above. 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 forboth 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-fixedsalaries-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, 2005 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,

31 3-40 (20 min.) Alternative cost structures, sensitivity analysis. Requirement 1 Requirement 2 Fixed fee $2,000 Fixed fee $800 Percent of Revenues 0% Percent of Revenues 15% Selling price $ 200 $ 230 $ 275 $ 300 $ 200 $ 230 $ 275 $ 300 Demand Cost per package $ 120 $ 120 $ 120 $ 120 $ 120 $ 120 $ 120 $ 120 Revenues Demand SP $8,400 $6,900 $5,500 $4,500 $8,400 $6,900 $5,500 $4,500 Package costs $120 Demand 5,040 3,600 2,400 1,800 5,040 3,600 2,400 1,800 Booth variable costs Revenues Percent of revenues ,260 1, Contribution margin 3,300 3,300 3,100 2,700 2,100 2,265 2,275 2,025 Booth fixed fee 2,000 2,000 2,000 2, Operating income $1,360 $1,300 $1,100 $ 700 $1,300 $1,465 $1,475 $1, See section of table labeled Requirement 1 above. If Mary pays a fixed fee of $2,000 to rent the booth, she should sell the Do-All packages at $200 each in order to maximize operating income. Contribution margin can also be calculated as contribution margin per unit demand. For example, when selling price is $230, contribution margin per unit is $110 ($230 $120) and contribution margin is $3,300 ($110 per unit 30 units) 2. See section of table labeled Requirement 2 above. If Mary pays a fixed fee of $800 plus 15% of revenues to rent the booth, she should sell the Do-All packages at $275 each in order to maximize operating income. Contribution margin can also be calculated as contribution margin per unit demand. For example, when selling price is $230, contribution margin per unit is $75.50 ($230 $120 15% $230) and contribution margin is $2,265 ($75.50 per unit 30 units) 3-31

32 3-41 (30 min.) Alternative fixed-cost/variable-cost structures Manual Automated Annual fixed costs (FC) $20,000 $30,000 Selling price $ 20 $ 20 Variable cost per unit 10 8 Contribution margin per unit (CMU) $ 10 $ 12 Annual breakeven units FC CMU 2,000 2,500 Manual Units 2,000 3,000 4,000 5,000 6,000 7,000 CMU $ 10 $ 10 $ 10 $ 10 $ 10 $ 10 Contribution margin $20,000 $30,000 $40,000 $50,000 $60,000 $70,000 Fixed costs 20,000 20,000 20,000 20,000 20,000 20,000 Operating income $ 0 $10,000 $20,000 $30,000 $40,000 $50,000 Automated Units 2,000 3,000 4,000 5,000 6,000 7,000 CMU $ 12 $ 12 $ 12 $ 12 $ 12 $ 12 Contribution margin $20,000 $36,000 $48,000 $60,000 $72,000 $84,000 Fixed costs 30,000 30,000 30,000 30,000 30,000 30,000 Operating income $ (6,000) $ 6,000 $18,000 $30,000 $42,000 $54,

33 Cut-n-Sew Operating Income: Manual vs. Automated Plant $55,000 $45,000 Operating Income $35,000 $25,000 $15,000 $5,000 Manual Automated $(5,000) 2,000 3,000 4,000 5,000 6,000 7,000 $(15,000) Units As seen from the above tables and graph, the two types of plants will result in the same operating income of $30,000 at a sales volume of 5,000 jackets. This can also be computed analytically: Let Q be the volume at which the operating incomes of both plants are equal. Equating operating income (CMU Units) Fixed Costs for both plants, $10Q $20,000 $12Q $30,000 $2Q $10,000 Q 5,000 units 3. If Cut-n-Sew anticipates sales of 4,000 jackets per year, it will earn an operating income of $20,000 from the manual plant, versus an operating income of $18,000 from the automated plant. So, it will choose the manual plant. However, note that the 4,000 jacket volume is only 1,000 short of the volume at which the automated plant becomes more profitable. If Cut-n-Sew anticipates a 25% or greater growth in sales volume in the near term, it should consider investing in the automated plant which will be more profitable at higher volumes. Also, competitive issues may suggest that Cut-n-Sew invest in the automated plant to benefit from other new technologies that may be available in the future. 3-33

34 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 $

35 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 Marston s income statement to emphasize contribution margin, and then use it to compute the required CVP parameters. Marston Corporation Income Statement For the Year Ended December 31, 2005 Using Sales Agents Using Own Sales Force Revenues $26,000,000 $26,000,000 Variable Costs Cost of goods sold variable $11,700,000 $11,700,000 Marketing commissions 4,680,000 16,380,000 2,600,000 14,300,000 Contribution margin $9,620,000 $11,700,000 Fixed Costs Cost of goods sold fixed 2,870,000 2,870,000 Marketing fixed 3,420,000 6,290,000 5,500,000 8,370,000 Operating income $3,330,000 $ 3,330,000 Contribution margin percentage ($9,620,000 26,000,000; $11,700,000 $26,000,000) 37% 45% Breakeven revenues ($6,290, ; $8,370, ) $17,000,000 $18,600,000 Degree of operating leverage ($9,620,000 $3,330,000; $11,700,000 $3,330,000) The calculations indicate that at sales of $26,000,000, a percentage change in sales and contribution margin will result in 2.89 times that percentage change in operating income if Marston continues to use sales agents and 3.51 times that percentage change in operating income if Marston employs its own sales staff. The higher contribution margin per dollar of sales and higher fixed costs gives Marston more operating leverage, that is, greater benefits (increases in operating income) if revenues increase but greater risks (decreases in operating income) if revenues decrease. Marston 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, Marston s 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. 3-35

36 3. Variable costs of marketing 15% of Revenues Fixed marketing costs $5,500,000 Operating income Revenues Variable manuf. costs Fixed manuf. costs Variable marketing costs Fixed marketing costs Denote the revenues required to earn $3,330,000 of operating income by R, then R 0.45R $2,870, R $5,500,000 $3,330,000 R 0.45R 0.15R $3,330,000 + $2,870,000 + $5,500, R $11,700,000 R $11,700, $29,250, (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. 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 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,

37 Let Q 4Q 5Q Number of units of A to break even Number of units of B to break even 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 (30 min.) Multiproduct breakeven, decision making. 1. Breakeven point in 2005 (units) Fixed costs Contributi on margin per unit $495,000 $50 $20 16,500 units Breakeven point in 2005 (in revenues) 16,500 units $50 $825,000 in sales revenues 2. Breakeven point in 2006 (in units) Evenkeel expects to sell 3 units of Plumar for every 2 units of Ridex in 2006, so consider a bundle consisting of 3 units of Plumar and 2 units of Ridex. Unit contribution Margin from Plumar $50 $20 $30 Unit contribution Margin from Ridex $25 $15 $10 The contribution margin for the bundle is $30 3 units of Plumar + $10 2 units of Ridex $110 So bundles to be sold to break even Breakeven point in 2006 (in units) Plumar, 4, ,500 units Ridex, 4, ,000 units Breakeven point in revenues: Plumar 13,500 units $50 per unit $675,000 Ridex 9,000 units $25 per unit 225,000 Total $900,000 $495,000 4,500 bundles $

38 3. Contribution margin percentage in 2005 Contribution margin per unit in 2005 Selling price in 2005 $30 $50 60% Contribution margin percentage in 2006 Contribution margin of bundle in 2006 Selling price of bundle in 2006 $110 (3 $50) (2 $25) $110 55% $200 The breakeven point in 2006 increases because fixed costs are the same in both years but the contribution margin generated by each dollar of sales revenue at the given product mix decreases in 2006 relative to Despite the breakeven sales revenue being higher, Evenkeel should accept Glaston s offer. The breakeven points are irrelevant because Evenkeel is already above the breakeven sales volume in By accepting Glaston s offer, Evenkeel has the ability to sell all the 30,000 units of Plumar in 2006 and make more sales of Ridex to Glaston without incurring any more fixed costs. Operating income in 2006 with and without Ridex are expected to be as follows: without Ridex with Ridex Sales $1,500,000 1 $2,000,000 2 Variable costs 600, ,000 4 Contribution margin 900,000 1,100,000 Fixed costs 495, ,000 Operating income $ 405,000 $ 605,000 1 $50 30,000 units 2 ($50 30,000 units) + ($25 20,000 units) 3 $20 30,000 units 4 ($20 30,000 units) + ($15 20,000 units) 3-38

39 3-46 (20 25 min.) Sales mix, two products. 1. Let Q Number of units of Deluxe carrier to break even 3Q Number of units of Standard carrier to break even Revenues Variable costs Fixed costs Zero operating income $20(3Q) + $30Q $14(3Q) $18Q $1,200,000 0 $60Q + $30Q $42Q $18Q $1,200,000 $30Q $1,200,000 Q 40,000 units of Deluxe 3Q 120,000 units of Standard The breakeven point is 120,000 Standard units plus 40,000 Deluxe units, a total of 160,000 units. 2a. Unit contribution margins are: Standard: $20 $14 $6; Deluxe: $30 $18 $12 If only Standard carriers were sold, the breakeven point would be: $1,200,000 $6 200,000 units. 2b. If only Deluxe carriers were sold, the breakeven point would be: $1,200,000 $12 100,000 units 3. Operating income Contribution margin of Standard + Contribution margin of Deluxe Fixed costs 180,000($6) + 20,000($12) $1,200,000 $1,080,000 + $240,000 $1,200,000 $120,000 Let Q Number of units of Deluxe product to break even 9Q Number of units of Standard product to break even $20(9Q) + $30Q $14(9Q) $18Q $1,200,000 0 $180Q + $30Q $126Q $18Q $1,200,000 $66Q $1,200,000 Q 18,182 units of Deluxe (rounded up) 9Q 163,638 units of Standard The breakeven point is 163,638 Standard + 18,182 Deluxe, a total of 181,820 units. The major lesson of this problem is that changes in the sales mix change breakeven points and operating incomes. In this example, the budgeted and actual total sales in number of units were identical, but the proportion of the product having the higher contribution margin declined. Operating income suffered, falling from $300,000 to $120,000. Moreover, the breakeven point rose from 160,000 to 181,820 units. 3-39

40 3-47 (20 min.) Gross margin and contribution margin. 1a. Cost of goods sold $1,600,000 Fixed manufacturing costs 500,000 Variable manufacturing costs $1,100,000 Variable manufacturing costs per unit $1,100, ,000 $5.50 per unit 1b. Total marketing and distribution costs $1,150,000 Variable marketing and distribution (200,000 $4) 800,000 Fixed marketing and distribution costs $ 350, Selling price $2,600, ,000 units $13 per unit Contributi on margin Variable Variable marketing manufacturing per unit costs per unit and distribution costs per unit $13 $5.50 $4.00 $3.50 Selling price Operating income Contributi on margin per unit Sales quantity Fixed manufactur costs ($ ,000) $500,000 $350,000 $45,000 ing Fixed marketing and distributi on costs Foreman has confused gross margin with contribution margin. He has interpreted gross margin as if it were all variable, and interpreted marketing and distribution costs as all fixed. In fact, both the manufacturing costs (subtracted from sales to calculate gross margin) and the marketing and distribution costs, contain fixed and variable components. 3. Breakeven point in units Fixed manufactur ing, marketing and distributi Contributi on margin per unit $850, ,858 units (rounded up) $3.50 Breakeven point in revenues 242,858 $13 $3,157,154. on costs 3-40