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3 CHAPTER COST-VOLUME-PROFIT ANALYSIS NOTATION USED IN CHAPTER 3 SOLUTIONS SP: VCU: CMU: FC: TOI: 3-16 Selling price Variable cost per unit Contribution margin per unit Fixed costs Target operating income (10 min.) CVP computations. Revenues $2,000 2,000 1,000 1,500 Variable Costs $ 500 1,500 700 900 Fixed Costs $300 300 300 300 Total Costs $ 800 1,800 1,000 1,200 Operating Income $1,200 200 0 300 Contribution Margin $1,500 500 300 600 Contribution Margin % 75.0% 25.0% 30.0% 40.0% a. b. c. d. 3-17 (1015 min.) CVP computations. 1a. Sales ($30 per unit 200,000 units) Variable costs ($25 per unit 200,000 units) Contribution margin Contribution margin (from above) Fixed costs Operating income Sales (from above) Variable costs ($16 per unit 200,000 units) Contribution margin Contribution margin Fixed costs Operating income $6,000,000 5,000,000 $1,000,000 $1,000,000 800,000 $ 200,000 $6,000,000 3,200,000 $2,800,000 $2,800,000 2,400,000 $ 400,000 1b. 2a. 2b. Operating income is expected to increase by $200,000 if Ms. Schoenens 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. Patels management will have to consider the impact of such an action on employee morale. In addition, the proposal increases the companys fixed costs dramatically. This will increase the companys operating leverage and risk. 3. 3-18 (3540 min.) CVP analysis, changing revenues and costs. 3-1 1a. SP VCU CMU FC Q = 8% $1,000 = $80 per ticket = $35 per ticket = $80 $35 = $45 per ticket = $22,000 a month = $22,000 FC = $45 per ticket CMU = 489 tickets (rounded up) 1b. Q = $22,000 + $10,000 FC + TOI = $45 per ticket CMU $32,000 $45 per ticket = = 712 tickets (rounded up) 2a. SP VCU CMU FC Q = $80 per ticket = $29 per ticket = $80 $29 = $51 per ticket = $22,000 a month = $22,000 FC = $51 per ticket CMU = 432 tickets (rounded up) 2b. Q = $22,000 + $10,000 FC + TOI = $51 per ticket CMU $32,000 $51 per ticket = 628 tickets (rounded up) = 3a. SP VCU CMU FC Q = $48 per ticket = $29 per ticket = $48 $29 = $19 per ticket = $22,000 a month $22,000 FC = $19 per ticket CMU = 1,158 tickets (rounded up) = 3-2 3b. Q = $22,000 + $10,000 FC + TOI = $19 per ticket CMU $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 (Requirement 2) 432 628 Fixed Commission of $48 1,158 1,685 Breakeven point Attain OI of $10,000 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 VCU CMU FC Q = $53 ($48 + $5) per ticket = $29 per ticket = $53 $29 = $24 per ticket = $22,000 a month = $22,000 FC = $24 per ticket CMU = 917 tickets (rounded up) 4b. Q = $22,000 + $10,000 FC + TOI = $24 per ticket CMU $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 $10,000. 3-3 3-19 (20 min.) CVP exercises. Variable Costs $8,000,000G 7,800,000 8,200,000 8,000,000 8,000,000 8,640,000f 7,360,000h 8,800,000j 7,600,000l Contribution Margin $2,000,000 2,200,000a 1,800,000b 2,000,000 2,000,000 2,160,000 1,840,000 2,200,000 2,400,000 Fixed Costs $1,800,000G 1,800,000 1,800,000 1,890,000c 1,710,000d 1,800,000 1,800,000 1,980,000k 1,890,000m Budgeted Operating Income $200,000 400,000 0 110,000 290,000 360,000 40,000 220,000 510,000 Revenues Orig. 1. 2. 3. 4. 5. 6. 7. 8. Gstands $10,000,000G 10,000,000 10,000,000 10,000,000 10,000,000 10,800,000e 9,200,000g 11,000,000i 10,000,000 for given. a$2,000,000 1.10; b$2,000,000 0.90; c$1,800,000 1.05; d$1,800,000 0.95; e$10,000,000 1.08; f$8,000,000 1.08; g$10,000,000 0.92; h$8,000,000 0.92; i$10,000,000 1.10; j$8,000,000 1.10; k$1,800,000 1.10; l$8,000,000 0.95; m$1,800,000 1.05 3-20 1a. 1b. (20 min.) CVP exercises. [Units sold (Selling price Variable costs)] Fixed costs = Operating income [5,000,000 ($0.50 $0.30)] $900,000 = $100,000 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 - $0.30 = = 0.40 $0.50 Fixed costs Contribution margin ratio = Breakeven revenues $900,000 0.40 = $2,250,000 5,000,000 ($0.50 $0.34) $900,000 [5,000,000 (1.1) ($0.50 $0.30)] [$900,000 (1.1)] [5,000,000 (1.4) ($0.40 $0.27)] [$900,000 (0.8)] $900,000 (1.1) ($0.50 $0.30) ($900,000 + $20,000) ($0.55 $0.30) 3-4 = $ (100,000) = $ 110,000 = $ 190,000 = = 4,950,000 units 3,680,000 units 2. 3. 4. 5. 6. 3-21 (10 min.) CVP analysis, income taxes. $140,000 $ 3,500 40 cars 40% $63,000 1. Monthly fixed costs = $60,000 + $70,000 + $10,000 = Contribution margin per unit = $26,000 $22,000 $500 = Monthly fixed costs $140,000 Breakeven units per month = = = Contribution margin per unit $3,500 per car 2. Tax rate Target net income Target operating income = Target net income $63, 000 $63, 000 = = = $105,000 1 - tax rate (1 0.40) 0.60 Quantity of output units Fixed costs + Target operating income = $140, 000 + $105, 000 = 70 cars required to be sold = Contribution margin per unit $3,500 3-5 3-22 1. (2025 min.) CVP analysis, income taxes. Variable cost percentage is $3.20 $8.00 = 40% Let R = Revenues needed to obtain target net income $105,000 R 0.40R $450,000 = 1 0 .3 0 0.60R = $450,000 + $150,000 R = $600,000 0.60 R = $1,000,000 or, $105,000 Target net income $450,000 + 1 0.30 = $1,000,000 1 Tax rate = Breakeven revenues = 0.60 Contribution margin percentage Proof: Revenues Variable costs (at 40%) Contribution margin Fixed costs Operating income Income taxes (at 30%) Net income $1,000,000 400,000 600,000 450,000 150,000 45,000 $ 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 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 Using the shortcut approach: Change in net income = (1 Tax rate) = (150,000 125,000) $4.80 (1 0.30) = $120,000 0.7 = $84,000 New net income = $84,000 + $105,000 = $189,000 b. 3. 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 $ 189,000 3-23 (30min.) CVPanalysis,sensitivityanalysis. 3-6 1. SP = $30.00 (1 0.30 margin to bookstore) = $30.00 0.70 = $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 O pe rat in g in co m e (0 00 s) 1,000 0 10 0,0 00 20 0,0 00 30 0,0 00 40 0,0 00 50 0,0 00 U n its so ld -1,000 252,708 units -2,000 -3,000 $3.5 million -4,000 3-7 2a. FC CMU $3,500,000 = $13.85 = = 252,708 copies sold (rounded up) 2b. Target OI = FC + OI CMU $3,500,000 + $2,000,000 $13.85 $5,500,000 = $13.85 = 397,112 copies sold (rounded up) = 3a. Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30 has the following effects: = $30.00 (1 0.20) = $30.00 0.80 = $24.00 VCU = $ 4.00 variable production and marketing cost + 3.60 variable author royalty cost (0.15 $24.00) $ 7.60 SP CMU = $24.00 $7.60 = $16.40 per copy = FC CMU $3,500,000 $16.40 = 213,415 copies sold (rounded up) = The breakeven point decreases from 252,708 copies in requirement 2 to 213,415 copies. 3b. Increasing the listed bookstore price to $40 while keeping the bookstore margin at 30% has the following effects: = $40.00 (1 0.30) = $40.00 0.70 = $28.00 VCU = $ 4.00 variable production and marketing cost + 4.20 variable author royalty cost (0.15 $28.00) $ 8.20 SP CMU= $28.00 $8.20 = $19.80 per copy 3-8 = $3,500,000 $19.80 = 176,768 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. 3-24 (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 $15 0.40 = SP 0.40 SP = SP $15 0.60 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 Breakeven revenues Margin of safety $2,000,000 1,500,000 $ 500,000 3-9 3-25 1a. (25 min.) Operating leverage. Let Q denote the quantity of carpets sold Breakeven point under Option 1 $500Q $350Q = $5,000 $150Q = $5,000 Q = $5,000 $150 = 34 carpets (rounded up) 1b. Breakeven point under Option 2 $500Q $350Q (0.10 $500Q) = 0 100Q = Q= 0 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 $50 = 100 carpets Revenues = $500 100 carpets = $50,000 For Q = 100 carpets, operating income under both Option 1 and Option 2 = $10,000 For Q > 100, say, 101 carpets, Option 1 gives operating income = ($150 101) $5,000 = $10,150 Option 2 gives operating income = $100 101 = $10,100 So Color Rugs will prefer Option 1. For Q < 100, say, 99 carpets, Option 1 gives operating income = ($150 99) $5,000 = $9,850 Option 2 gives operating income = $100 99 = $9,900 So Color Rugs will prefer Option 2. 3. Contribution margin Operating income $150 100 Under Option 1, degree of operating leverage = = 1.5 $10,000 $100 100 Under Option 2, degree of operating leverage = = 1.0 $10,000 Degree of operating leverage = 4. The calculations in requirement 3 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. 3-10 3.26 (15 min.) CVP analysis, international cost structure differences. Operating Income for Budgeted Sales of 800,000 Sweaters (7)=[800,000 (5)] (2) $3,900,000 7,500,000 (4,000,000) Variable Variable Sales price Annual Manufacturing Marketing & Contribution Country to retail Fixed Cost Distribution Cost Margin Breakeven Breakeven outlets Costs per Sweater per Sweater Per Unit Units Revenues (1) (2) (3) (4) (5)=(1)-(3)-(4) (6)=(2) (5) (6) (1) Singapore $32.00 $ 6,500,000 $ 8.00 $11.00 $13.00 500,000 $16,000,000 Thailand 32.00 4,500,000 5.50 11.50 15.00 300,000 9,600,000 United States 32.00 12,000,000 13.00 9.00 10.00 1,200,000 38,400,000 Thailand has the lowest breakeven point since it has both the lowest fixed costs ($4,500,000) and the Requirement 1 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 2 3-11 3-27 1. (30 min.) Sales mix, new and upgrade customers. New Customers $210 90 120 Upgrade Customers $120 40 80 SP VCU CMU The 60%/40% sales mix implies that, in each bundle, 3 units are sold to new customers and 2 units are sold to upgrade customers. Contribution margin of the bundle = 3 $120 + 2 $80 = $360 + $160 = $520 $14,000,000 Breakeven point in bundles = = 26,923 bundles $520 Breakeven point in units is: Sales to new customers: 26,923 bundles 3 units per bundle 80,769 units Sales to upgrade customers: 26,923 bundles 2 units per bundle 53,846 units Total number of units to breakeven (rounded) 134,615 units Alternatively, 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 S 1.5S BEP = $14,000,000 = 53,846 units sold to upgrade customers (rounded) = 80,770 units sold to new customers (rounded) = 134,616 units $23,423,220 9,423,140 14,000,080 14,000,000 $ 80 Check Revenues ($210 80,770) + ($120 53,846) Variable costs ($90 80,770) + ($40 53,846) Contribution margin Fixed costs Operating income (caused by rounding) 3-12 2. 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 ($210 120,000) + ($120 80,000) Variable costs ($90 120,000) + ($40 80,000) Contribution margin Fixed costs Operating income $34,800,000 14,000,000 20,800,000 14,000,000 $ 6,800,000 3a. At New 50%/Upgrade 50% mix, each bundle contains 1 unit sold to new customer and 1 unit sold to upgrade customer. Contribution margin of the bundle = 1 $120 + 1 $80 = $120 + $80 = $200 $14,000,000 Breakeven point in bundles = = 70,000 bundles $200 Breakeven point in units is: Sales to new customers: 70,000 bundles 1 unit per bundle 70,000 units Sales to upgrade customers: 70,000 bundles 1 unit per bundle 70,000 units Total number of units to breakeven 140,000 units Alternatively, 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 = $14,000,000 200S = $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. At New 90%/ Upgrade 10% mix, each bundle contains 9 units sold to new customers and 1 unit sold to upgrade customers. Contribution margin of the bundle = 9 $120 + 1 $80 = $1,080 + $80 = $1,160 $14,000,000 Breakeven point in bundles = = 12,069 bundles (rounded) $1,160 Breakeven point in units is: Sales to new customers: 12,069 bundles 9 units per bundle 108,621 units Sales to upgrade customers: 12,069 bundles 1 unit per bundle 12,069 units Total number of units to breakeven 120,690 units 3-13 Alternatively, 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 ($210 108,621) + ($120 12,069) Variable costs ($90 108,621) + ($40 12,069) Contribution margin Fixed costs Operating income (caused by rounding) $24,258,690 10,258,650 14,000,040 14,000,000 $ 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: New Customers 50% 60 90 Upgrade Customers 50% 40 10 Breakeven Point 140,000 134,616 120,690 Requirement 3(a) Requirement 1 Requirement 3(b) 3-28 1a. (20 min.) CVP analysis, multiple cost drivers. Operating income Cost of picture Quantity of Cost of Number of Fixed = Revenues frames picture frames shipment shipments costs = ($45 40,000) ($30 40,000) ($60 1,000) $240,000 = $1,800,000 $1,200,000 $60,000 $240,000 = $300,000 = ($45 40,000) ($30 40,000) ($60 800) $240,000 = $312,000 1b. 2. Operating income 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) $240,000 = 0 15Q = $300,000 Q = 20,000 picture frames 3 3-14 Thebreakevenpointisnotuniquebecausetherearetwocostdriversquantityofpicture framesandnumberofshipments.Variouscombinationsofthetwocostdriverscanyieldzero operatingincome. 3-15 3.29 (25 mins) CVP, Not for profit. Contributions Fixed costs Cash available to purchase land Divided by cost per acre to purchase land Acres of land SG can purchase Contributions ($19,000,000 $5,000,000) Fixed costs Cash available to purchase land Divided by cost per acre to purchase land ($3,000 $1,000) Acres of land SG can purchase $19,000,000 1,000,000 $18,000,000 3,000 6,000 acres $14,000,000 1,000,000 $13,000,000 2,000 6,500 acres 1. 2. On financial considerations alone, SG should take the subsidy because it can purchase 500 more acres (6,500 acres 6,000 acres). 3. Let the decrease in contributions be $ x . Cash available to purchase land = $19,000,000 $ x $1,000,000 Cost to purchase land = $3,000 $1,000 = $2,000 To purchase 6,000 acres, we solve the following equation for x . 19,000,000 x 1,000,000 = 6,000 2,000 18,000,000 x = 6,000 2,000 18,000,000 x = 12,000,000 x = $6,000,000 SG will be indifferent between taking the government subsidy or not if contributions decrease by $6,000,000. 3-16 3-30 1. (15 min.) Contribution margin, decision making. Revenues Deduct variable costs: Cost of goods sold Sales commissions Other operating costs Contribution margin $500,000 $200,000 50,000 40,000 $210,000 = 42% $500,000 290,000 $210,000 2. Contribution margin percentage = 3. Incremental revenue (20% $500,000) = $100,000 Incremental contribution margin (42% $100,000) Incremental fixed costs (advertising) Incremental operating income $42,000 10,000 $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) Cost of goods sold (40% of sales) Gross margin 360,000 Operating costs: Salaries and wages Sales commissions (10% of sales) Depreciation of equipment and fixtures Store rent Advertising Other operating costs: $40,000 Variable ( $600,000) $500,000 Fixed Operating income $150,000 60,000 12,000 48,000 10,000 48,000 10,000 338,000 $ 22,000 $600,000 240,000 3-17 3-31 1. (20 min.) Contribution margin, gross margin and margin of safety. Mirabella Cosmetics Operating Income Statement, June 2008 Units sold Revenues Variable costs Variable manufacturing costs Variable marketing costs Total variable costs Contribution margin Fixed costs Fixed manufacturing costs Fixed marketing & administration costs Total fixed costs Operating income 10,000 $100,000 $ 55,000 5,000 60,000 40,000 $ 20,000 10,000 30,000 $ 10,000 2. $40,000 = $4 per unit 10,000 units Fixed costs $30, 000 = = 7,500 units Breakeven quantity = Contribution margin per unit $4 per unit Revenues $100, 000 = = $10 per unit Selling price = Units sold 10,000 units Breakeven revenues = 7,500 units $10 per unit = $75,000 Contribution margin per unit = Alternatively, Contribution margin percentage = Contribution margin $40, 000 = = 40% Revenues $100, 000 Breakeven revenues = 3. Fixed costs $30, 000 = = $75, 000 Contribution margin percentage 0.40 Margin of safety (in units) = Units sold Breakeven quantity = 10,000 units 7,500 units = 2,500 units Units sold Revenues (Units sold Selling price = 8,000 $10) Contribution margin (Revenues CM percentage = $80,000 40%) Fixed costs Operating income Taxes (30% $2,000) Net income 8,000 $80,000 $32,000 30,000 2,000 600 $ 1,400 4. 3-18 3-32 (30 min.) Uncertainty and expected costs. 1. Monthly Number of Orders 300,000 400,000 500,000 600,000 700,000 Monthly Number of Orders 300,000 400,000 500,000 600,000 700,000 Monthly Number of Orders 300,000 400,000 500,000 600,000 700,000 2. Current System Expected Cost: $13,000,000 0.1 = $ 1,300,000 17,000,000 0.25 = 4,250,000 21,000,000 0.40 = 8,400,000 25,000,000 0.15 = 3,750,000 29,000,000 0.10 = 2,900,000 $ 20,600,000 Partially Automated System Expected Cost: $14,000,000 0.1 = $ 1 ,400,000 17,000,000 0.25 = 4,250,000 20,000,000 0.40 = 8,000,000 23,000,000 0.15 = 3,450,000 26,000,000 0.1 = 2,600,000 $19,700,000 Fully Automated System Expected Cost: $16,000,000 0.1 = $ 1,600,000 18,000,000 0.25 = 4,500,000 20,000,000 0.40 = 8,000,000 22,000,000 0.15 = 3,300,000 24,000,000 0.10 = 2,400,000 $19,800,000 Cost of Current System $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 Cost of Partially Automated System $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 Cost of Fully Automated System $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) = $24,000,000 3-19 3. Dawmart should consider the impact of the different systems on its relationship with suppliers. The interface with Dawmarts 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 Dawmarts 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. 3-33 1. (1520 min.) CVP analysis, service firm. Revenue per package Variable cost per package Contribution margin per package $4,000 3,600 $ 400 Breakeven (units) = Fixed costs Contribution margin per package $480,000 = = 1,200 tour packages $400 per package 2. Contribution margin ratio = Contribution margin per package $400 = = 10% Selling price $4,000 Revenue to achieve target income = (Fixed costs + target OI) Contribution margin ratio $480,000 + $100,000 = = $5,800,000, or 0.10 $480,000 + $100,000 Number of tour packages to earn $100,000 operating income: = = 1,450 tour packages $400 Revenues to earn $100,000 OI = 1,450 tour packages $4,000 = $5,800,000. 3. Fixed costs = $480,000 + $24,000 = $504,000 Breakeven (units) = Fixed costs Contribution margin per unit Fixed costs Breakeven (units) $504,000 = = $420 per tour package 1,200 tour packages Contribution margin per unit = 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 3-20 3.34 (30 min.) 1. CVP, target income, service firm. $600 200 $400 Revenue per child Variable costs per child Contribution margin per child Breakeven quantity = Fixed costs Contribution margin per child $5,600 = 14 children $400 = 2. Target quantity = Fixed costs + Target operating income Contribution margin per child $5,600 + $10,400 = 40 children $400 $1,000 1,000 $2,000 40 $ 50 = 3. Increase in rent ($3,000 $2,000) Field trips Total increase in fixed costs Divide by the number of children enrolled Increase in fee per child Therefore, the fee per child will increase from $600 to $650. Alternatively, New contribution margin per child = $5,600 + $2,000 + $10,400 = $450 40 New fee per child = Variable costs per child + New contribution margin per child = $200 + $450 = $650 3-21 3.35 (2025 min.) 1. CVP analysis. $16.00 12.00 $ 4.00 Selling price Variable costs per unit: Purchase price $10.00 Shipping and handling 2.00 Contribution margin per unit (CMU) Breakeven point in units = Fixed costs $600,000 = = 150,000 units Contr. margin per unit $4.00 Margin of safety (units) = 200,000 150,000 = 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. Galaxys operating income in 2008 would be $200,000 + $80,000 = $280,000. 3. Selling price Variable costs: Purchase price $10 130% Shipping and handling Contribution margin per unit Target sales in units = $16.00 $13.00 2.00 15.00 $ 1.00 $600,000 + $200,000 FC + TOI = = 800,000 units $1 CMU Target sales in dollars = $16 800,000 = $12,800,000 3-22 3-36 1. (3040 min.) CVP analysis, income taxes. Revenues Variable costs Fixed costs = Let X = Net income for 2008 Target net income 1 Tax rate X 1 0.40 X 20,000($25.00) 20,000($13.75) $135,000 = $500,000 $275,000 $135,000 = 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 = $54,000 2. Let Q = Number of units to break even $25.00Q $13.75Q $135,000 = 0 Q = $135,000 $11.25 = 12,000 units 3. Let X = Net income for 2009 22,000($25.00) 22,000($13.75) ($135,000 + $11,250) $550,000 $302,500 $146,250 $101,250 = = = X 1 0.40 X 0.60 X 0.60 X = $60,750 4. Let Q = Number of units to break even with new fixed costs of $146,250 $25.00Q $13.75Q $146,250 Q = $146,250 $11.25 Breakeven revenues = 13,000 $25.00 =0 = 13,000 units = $325,000 5. Let S = Required sales units to equal 2008 net income $25.00S $13.75S $146,250 = $54,000 0.60 $11.25S = $236,250 S = 21,000 units Revenues = 21,000 units $25 = $525,000 6. Let A = Amount spent for advertising in 2009 $550,000 $302,500 ($135,000 + A) = $60,000 0.60 $550,000 $302,500 $135,000 A = $100,000 $550,000 $537,500 = A A = $12,500 3-23 3-37 (25 min.) CVP, sensitivity analysis. Contribution margin per corkscrew = $4 3 = $1 Fixed costs = $6,000 Units sold = Total sales Selling price = $40,000 $4 per corkscrew = 10,000 corkscrews Sales increase 10% Sales revenues 10,000 1.10 $4.00 Variable costs 10,000 1.10 $3.00 Contribution margin Fixed costs Operating income 1. 2. $44,000 33,000 11,000 6,000 $ 5,000 Increase fixed costs $2,000; Increase sales 50% Sales revenues 10,000 1.50 $4.00 $60,000 1.50 $3.00 Variable costs 10,000 45,000 Contribution margin 15,000 Fixed costs ($6,000 + $2,000) 8,000 Operating income $ 7,000 Increase selling price to $5.00; Sales decrease 20% Sales revenues 10,000 0.80 $5.00 $40,000 Variable costs 10,000 0.80 $3.00 24,000 Contribution margin 16,000 Fixed costs 6,000 Operating income $10,000 3. Increase selling price to $6.00; Variable costs increase $1 per corkscrew Sales revenues 10,000 $6.00 $60,000 Variable costs 10,000 $4.00 40,000 Contribution margin 20,000 Fixed costs 6,000 Operating income $14,000 4. Alternative yields 4 the highest operating income. If TOP is confident that unit sales will not decrease despite increasing the selling price, it should choose alternative 4. 3-24 3-38 (2030 min.) CVP analysis, shoe stores. $ 9.00 40,000 1. CMU (SP VCU = $30 $21) a. Breakeven units (FC CMU = $360,000 $9 per unit) b. Breakeven revenues (Breakeven units SP = 40,000 units $30 per unit) 2. Pairs sold Revenues, 35,000 $30 Total cost of shoes, 35,000 $19.50 Total sales commissions, 35,000 $1.50 Total variable costs Contribution margin Fixed costs Operating income (loss) 3. Unit variable data (per pair of shoes) Selling price Cost of shoes Sales commissions Variable cost per unit Annual fixed costs Rent Salaries, $200,000 + $81,000 Advertising Other fixed costs Total fixed costs CMU, $30 $19.50 a. Breakeven units, $441,000 $10.50 per unit b. Breakeven revenues, 42,000 units $30 per unit 4. Unit variable data (per pair of shoes) Selling price Cost of shoes Sales commissions Variable cost per unit Total fixed costs CMU, $30 $21.30 a. Break even units = $360,000 $8.70 per unit b. Break even revenues = 41,380 units $30 per unit 5. Pairs sold Revenues (50,000 pairs $30 per pair) Total cost of shoes (50,000 pairs $19.50 per pair) Sales commissions on first 40,000 pairs (40,000 pairs $1.50 per pair) Sales commissions on additional 10,000 pairs 3-25 $1,200,000 35,000 $1,050,000 682,500 52,500 735,000 315,000 360,000 $ (45,000) $ $ $ 30.00 19.50 0 19.50 60,000 281,000 80,000 20,000 $ 441,000 $ 10.50 42,000 $1,260,000 $ 30.00 19.50 1.80 $ 21.30 $ 360,000 $ 8.70 41,380 (rounded up) $1,241,400 50,000 $1,500,000 $ 975,000 60,000 [10,000 pairs ($1.50 + $0.30 per pair)] Total variable costs Contribution margin Fixed costs Operating income Alternative approach: 18,000 $1,053,000 $ 447,000 360,000 $ 87,000 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 = $87,000. 3-26 3.39 (30 min.) CVP analysis, shoe stores (continuation of 3-38). Salaries + Commission Plan Higher Fixed Salaries Only CM per Unit (6) $10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 10.50 Operating CM Fixed Costs Income (7)=(1) (6) (8) (9)=(7)(8) $420,000 $441,000 $ (21,000) 441,000 441,000 0 462,000 441,000 21,000 483,000 441,000 42,000 504,000 441,000 63,000 525,000 441,000 84,000 546,000 441,000 105,000 567,000 441,000 126,000 588,000 441,000 147,000 609,000 441,000 168,000 630,000 441,000 189,000 651,000 441,000 210,000 672,000 441,000 231,000 693,000 441,000 252,000 Difference in favor of higher-fixedsalary-only (10)=(9)(5) $(21,000) (18,000) (15,000) (12,000) (9,000) (6,000) (3,000) 0 3,000 6,000 9,000 12,000 15,000 18,000 No. of units CM sold per Unit (1) (2) 40,000 $9.00 42,000 9.00 44,000 9.00 46,000 9.00 48,000 9.00 50,000 9.00 52,000 9.00 54,000 9.00 56,000 9.00 58,000 9.00 60,000 9.00 62,000 9.00 64,000 9.00 66,000 9.00 CM (3)=(1) (2) $360,000 378,000 396,000 414,000 432,000 450,000 468,000 486,000 504,000 522,000 540,000 558,000 576,000 594,000 Fixed Costs (4) $360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 360,000 Operating Income (5)=(3)(4) 0 18,000 36,000 54,000 72,000 90,000 108,000 126,000 144,000 162,000 180,000 198,000 216,000 234,000 3-27 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 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-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 $10.50TQ TQ TQ For the salary-plus-commission plan, $30.00TQ $21.00TQ $360,000 $9.00TQ TQ TQ = $168,000 = $609,000 = $609,000 $10.50 = 58,000 units = $168,000 = $528,000 = $528,000 $9.00 = 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) Cost of shoes, 50,000 pairs $19.50 Commissions = Revenues 5% = $1,476,000 0.05 Contribution margin Fixed costs Operating income $1,476,000 975,000 73,800 427,200 360,000 $ 67,200 3-28 3.40 1. (40 min.) Alternative cost structures, uncertainty, and sensitivity analysis. 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. 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 $10 = 500 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: Operating Income (Loss) (5)=(2)(3)(4) $ (1,000) $ 3,000 $ 7,000 $11,000 $15,000 Bouquets Fixed Sold Revenue Costs (1) (2) (3) 200 200 $50=$10,000 $5,000 400 400 $50=$20,000 $5,000 600 600 $50=$30,000 $5,000 800 800 $50=$40,000 $5,000 1,000 1,000 $50=$50,000 $5,000 Expected value of rent agreement Variable Costs (4) 200 $30=$ 6,000 400 $30=$12,000 600 $30=$18,000 800 $30=$24,000 1,000 $30=$30,000 Probability (6) 0.20 0.20 0.20 0.20 0.20 Expected Operating Income (7)=(5) (6) $ ( 200) 600 1,400 2,200 3,000 $7,000 3-29 Royalty agreement: Bouquets Variable Sold Revenue Costs (1) (2) (3) $50=$10,000 $40=$ 8,000 200 200 200 400 400 $50=$20,000 400 $40=$16,000 600 600 $50=$30,000 600 $40=$24,000 800 800 $50=$40,000 800 $40=$32,000 1,000 1,000 $50=$50,000 1,000 $40=$40,000 Expected value of royalty agreement Operating Income (4)=(2)(3) $2,000 $4,000 $6,000 $8,000 $10,000 Probability (5) 0.20 0.20 0.20 0.20 0.20 Expected Operating Income (6)=(4) (5) $ 400 800 1,200 1,600 2,000 $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. 3-41 (20-30 min.) CVP, alternative cost structures. 1. Variable cost per glass of lemonade = $0.15 + ($0.10 2) = $0.20 Contribution margin per glass = Selling price Variable cost per glass = $0.50 $0.20 = $0.30 Breakeven point = Fixed costs Contribution margin per glass = $6.00 $0.30 = 20 glasses (per day) Target number of glasses = Fixed costs + Target operating income Contribution margin per glass $6 + $3 = = 30 glasses $0.30 3. Contribution margin per glass = Selling price Variable cost per glass = $0.50 $0.15 = $0.35 Fixed costs = $6 + $1.70 = $7.70 Fixed costs $7.70 Breakeven point = = = 22 glasses Contribution margin per glass $0.35 2. 4. Let x be the number of glasses for which Sarah is indifferent between hiring Jessica or hiring David. Sarah will be indifferent when the profits under the two alternatives are equal. $0.30 x $6 = $0.35 x $7.70 1.70 = 0.05 x x = $1.70 $0.05 = 34 glasses For sales between 0 and 34 glasses, Sarah prefers Jessica to squeeze the lemons because in this range, $0.30 x $6 > $0.35 x $7.70. For sales greater than 34 glasses, Sarah prefers David to squeeze the lemons because in this range, $0.35 x $7.70 > $0.30 x $6. 3-30 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 $200 = 500 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 companys net income objective. Calculations for the three alternatives are shown below. Alternative 1 Revenues Variable costs Operating income Net income Alternative 2 Revenues Variable costs Operating income Net income c$400 $30; d$200 $10. = = = = a$400 $40; b350 units + 2,700 units. ($400 350) + ($360a 2,700) = $1,112,000 $200 3,050b = $610,000 $1,112,000 $610,000 $100,000 = $402,000 $402,000 (1 0.40) = $241,200 = = = = ($400 350) + ($370c 2,200) = $954,000 ($200 350) + ($190d 2,200) = $488,000 $954,000 $488,000 $100,000 = $366,000 $366,000 (1 0.40) = $219,600 3-31 Alternative 3 Revenues Variable costs Operating income Net income = = = = ($400 350) + ($380e 2,000) = $900,000 $200 2,350f = $470,000 $900,000 $470,000 $90,000g = $340,000 $340,000 (1 0.40) = $204,000 e$400 (0.05 $400) = $400 $20; f350 units + 2,000 units; g$100,000 $10,000 3-43 (30 min.) Choosing between compensation plans, operating leverage. 1. We can recast Marstons 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, 2008 Using Sales Agents $26,000,00 0 $11,700,00 0 4,680,000 2,870,000 3,420,000 16,380,00 0 $9,620,000 6,290,000 $3,330,000 Using Own Sales Force $26,000,000 $11,700,00 0 2,600,000 2,870,000 5,500,000 14,300,000 $11,700,000 8,370,000 $ 3,330,000 Revenues Variable Costs Cost of goods soldvariable Marketing commissions Contribution margin Fixed Costs Cost of goods soldfixed Marketingfixed Operating income Contribution margin percentage ($9,620,000 26,000,000; $11,700,000 $26,000,000) Breakeven revenues ($6,290,000 0.37; $8,370,000 0.45) Degree of operating leverage ($9,620,000 $3,330,000; $11,700,000 $3,330,000) 2. 37% $17,000,00 0 2. 89 45% $18,600,000 3. 51 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 3-32 to increase sales. On the other hand, Marstons own sales force may be more knowledgeable and skilled in selling the companys products. That is, the sales volume itself will be affected by who sells and by the nature of the compensation plan. 3. Variable costs of marketing Fixed marketing costs = 15% of Revenues = $5,500,000 Variable Fixed Variable Fixed Operating income = Revenues manuf. costs manuf. costs marketing marketing costs costs Denote the revenues required to earn $3,330,000 of operating income by R, then R 0.45R $2,870,000 0.15R $5,500,000 = $3,330,000 R 0.45R 0.15R = $3,330,000 + $2,870,000 + $5,500,000 0.40R = $11,700,000 R = $11,700,000 0.40 = $29,250,000 3-44 (1525 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 $255,000 Breakeven point in bundles = = 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 $17Q Q 5Q 4Q Total =0 = $255,000 = 15,000 ($255,000 $17) units of A = 75,000 units of B = 60,000 units of C = 150,000 units 3-33 2. Contribution margin: A: 20,000 $3 B: 100,000 $2 C: 80,000 $1 Contribution margin Fixed costs Operating income Contribution margin A: 20,000 $3 B: 80,000 $2 C: 100,000 $1 Contribution margin Fixed costs Operating income $ 60,000 200,000 80,000 $340,000 255,000 $ 85,000 $ 60,000 160,000 100,000 $320,000 255,000 $ 65,000 3. 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 $255,000 Breakeven point in bundles = = 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 $16Q Q 4Q 5Q Total =0 = $255,000 = 15,938 ($255,000 $16) units of A (rounded up) = 63,752 units of B = 79,690 units of C = 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. 3-34 3-45 (40 min.) Multi-product CVP and decision making. 1. Faucet filter: Selling price Variable cost per unit Contribution margin per unit Pitcher-cum-filter: Selling price Variable cost per unit Contribution margin per unit $80 20 $60 $90 25 $65 Each bundle contains 2 faucet models and 3 pitcher models. So contribution margin of a bundle = 2 $60 + 3 $65 = $315 Breakeven Fixed costs $945,000 point in = = = 3,000 bundles Contribution margin per bundle $315 bundles Breakeven point in units of faucet models and pitcher models is: Faucet models: 3,000 bundles 2 units per bundle = 6,000 units Pitcher models: 3,000 bundles 3 units per bundle = 9,000 units Total number of units to breakeven 15,000 units Breakeven point in dollars for faucet models and pitcher models is: Faucet models: 6,000 units $80 per unit = $ 480,000 Pitcher models: 9,000 units $90 per unit = 810,000 Breakeven revenues $ 1,290,000 Alternatively, weighted average contribution margin per unit = Breakeven point = Faucet filter: $945,000 = 15,000 units $63 (2 $60) + (3 $65) = $63 5 2 15,000 units = 6,000 units 5 3 Pitcher-cum-filter: 15,000 units = 9,000 units 5 Breakeven point in dollars Faucet filter: 6,000 units $80 per unit = $480,000 Pitcher-cum-filter: 9,000 units $90 per unit = $810,000 2. Faucet filter: Selling price Variable cost per unit Contribution margin per unit $80 15 $65 3-35 Pitcher-cum-filter: Selling price Variable cost per unit Contribution margin per unit $90 16 $74 Each bundle contains 2 faucet models and 3 pitcher models. So contribution margin of a bundle = 2 $65 + 3 $74 = $352 Breakeven Fixed costs $945,000 + $181, 400 point in = = = 3, 200 bundles Contribution margin per bundle $352 bundles Breakeven point in units of faucet models and pitcher models is: Faucet models: 3,200 bundles 2 units per bundle = 6,400 units Pitcher models: 3,200 bundles 3 units per bundle = 9,600 units Total number of units to breakeven 16,000 units Breakeven point in dollars for faucet models and pitcher models is: Faucet models: 6,400 bundles $80 per unit = $ 512,000 Pitcher models: 9,600 bundles $90 per unit = 864,000 Breakeven revenues $1,376,000 Alternatively, weighted average contribution margin per unit = Breakeven point = Faucet filter: $945,000+181,400 = 16, 000 units $70.40 (2 $65) + (3 $74) = $70.40 5 2 16,000 units = 6,400 units 5 3 Pitcher-cum-filter: 16, 000 units = 9, 600 units 5 Breakeven point in dollars: Faucet filter: 6,400 units $80 per unit = $512,000 Pitcher-cum-filter: 9,600 units $90 per unit = $864,000 3. Let x be the number of bundles for Pure Water Products to be indifferent between the old and new production equipment. Operating income using old equipment = $315 x $945,000 Operating income using new equipment = $352 x $945,000 $181,400 At point of indifference: $315 x $945,000 = $352 x $1,126,400 $352 x $315 x = $1,126,400 $945,000 $37 x = $181,400 x = $181,400 $37 = 4,902.7 bundles = 4,903 bundles (rounded) 3-36 Faucet models = 4,903 bundles 2 units per bundle = 9,806 units Pitcher models = 4,903 bundles 3 units per bundle = 14,709 units Total number of units 24,515 units Let x be the number of bundles, When total sales are less than 24,515 units (4,903 bundles), $315x $945,000 > $352x $1,126,400, so Pure Water Products is better off with the old equipment. When total sales are greater than 24,515 units (4,903 bundles), $352x $1,126,400 > $315x $945,000, so Pure Water Products is better off buying the new equipment. At total sales of 30,000 units (6,000 bundles), Pure Water Products should buy the new production equipment. Check $352 6,000 $1,126,400 = $985,600 is greater than $315 6,000 $945,000 = $945,000. 3-46 (2025 min.) Sales mix, two products. 1. Sales of standard and deluxe carriers are in the ratio of 150,000 : 50,000. So for every 1 unit of deluxe, 3 (150,000 50,000) units of standard are sold. Contribution margin of the bundle = 3 $6 + 1 $12 = $18 + $12 = $30 $1, 200,000 Breakeven point in bundles = = 40,000 bundles $30 Breakeven point in units is: Standard carrier: 40,000 bundles 3 units per bundle 120,000 units Deluxe carrier: 40,000 bundles 1 unit per bundle 40,000 units Total number of units to breakeven 160,000 units Alternatively, 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 = $60Q + $30Q $42Q $18Q = $30Q = Q= 3Q = units. 0 $1,200,000 $1,200,000 40,000 units of Deluxe 120,000 units of Standard The breakeven point is 120,000 Standard units plus 40,000 Deluxe units, a total of 160,000 3-37 2a. 2b. 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. 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 Sales of standard and deluxe carriers are in the ratio of 180,000 : 20,000. So for every 1 unit of deluxe, 9 (180,000 20,000) units of standard are sold. Contribution margin of the bundle = 9 $6 + 1 $12 = $54 + $12 = $66 $1, 200,000 Breakeven point in bundles = = 18,182 bundles (rounded up) $66 Breakeven point in units is: Standard carrier: 18,182 bundles 9 units per bundle 163,638 units Deluxe carrier: 18,182 bundles 1 unit per bundle 18,182 units Total number of units to breakeven 181,820 units Alternatively, 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 $180Q + $30Q $126Q $18Q $66Q Q 9Q = = = = = 0 $1,200,000 $1,200,000 18,182 units of Deluxe (rounded up) 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. 3-38 3-47 1. (20 min.) Gross margin and contribution margin. Ticket sales ($20 500 attendees) Variable cost of dinner ($10a 500 attendees) Variable invitations and paperwork ($1b 500) Contribution margin Fixed cost of dinner Fixed cost of invitations and paperwork Operating profit (loss) a b $10,000 $5,000 500 6,000 2,500 5,500 4,500 8,500 $ (4,000) $5,000/500 attendees = $10/attendee $500/500 attendees = $1/attendee $20,000 $10,000 1,000 6,000 2,500 11,000 9,000 8,500 $ 500 2. Ticket sales ($20 1,000 attendees) Variable cost of dinner ($10 1,000 attendees) Variable invitations and paperwork ($1 1,000) Contribution margin Fixed cost of dinner Fixed cost of invitations and paperwork Operating profit (loss) (30 min.) Ethics, CVP analysis. 3-48 1. Contribution margin percentage = = = Breakeven revenues = = Revenues Variable costs Revenues $5,000,000 $3,000,000 $5,000,000 $2,000,000 = 40% $5,000,000 Fixed costs Contribution margin percentage $2,160,000 = $5,400,000 0.40 2. If variable costs are 52% of revenues, contribution margin percentage equals 48% (100% 52%) Breakeven revenues = = Fixed costs Contribution margin percentage $2,160,000 = $4,500,000 0.48 $5,000,000 2,600,000 2,160,000 $ 240,000 3. Revenues Variable costs (0.52 $5,000,000) Fixed costs Operating income 3-39 4. Incorrect reporting of environmental costs with the goal of continuing operations is unethical. In assessing the situation, the specific Standards of Ethical Conduct for Management Accountants (described in Exhibit 1-7) that the management accountant should consider are listed below. Competence Clear reports using relevant and reliable information should be prepared. Preparing reports on the basis of incorrect environmental costs to make the companys performance look better than it is violates competence standards. It is unethical for Bush not to report environmental costs to make the plants performance look good. Integrity The management accountant has a responsibility to avoid actual or apparent conflicts of interest and advise all appropriate parties of any potential conflict. Bush may be tempted to report lower environmental costs to please Lemond and Woodall and save the jobs of his colleagues. This action, however, violates the responsibility for integrity. The Standards of Ethical Conduct require the management accountant to communicate favorable as well as unfavorable information. Credibility The management accountants Standards of Ethical Conduct require that information should be fairly and objectively communicated and that all relevant information should be disclosed. From a management accountants standpoint, underreporting environmental costs to make performance look good would violate the standard of objectivity. Bush should indicate to Lemond that estimates of environmental costs and liabilities should be included in the analysis. If Lemond still insists on modifying the numbers and reporting lower environmental costs, Bush should raise the matter with one of Lemonds superiors. If after taking all these steps, there is continued pressure to understate environmental costs, Bush should consider resigning from the company and not engage in unethical behavior. 3-49 (35 min.) Deciding where to produce. Peoria Selling price Variable cost per unit Manufacturing Marketing and distribution Contribution margin per unit (CMU) Fixed costs per unit Manufacturing Marketing and distribution Operating income per unit CMU of normal production (as shown above) CMU of overtime production ($64 $3; $48 $8) $150.00 $72.00 14.00 30.00 19.00 86.00 64.00 49.00 $ 15.00 $64 61 $88.00 14.00 15.00 14.50 Moline $150.00 102.00 48.00 29.50 $ 18.50 $48 40 3-40 1. Annual fixed costs = Fixed cost per unit Daily production rate Normal annual capacity ($49 400 units 240 days; $29.50 320 units 240 days) Breakeven volume = FC CMU of normal production ($4,704,000 $64; $2,265,600 48) 2. Units produced and sold Normal annual volume (units) (400 240; 320 240) Units over normal volume (needing overtime) CM from normal production units (normal annual volume CMU normal production) (96,000 $64; 76,800 48) CM from overtime production units (0; 19,200 $40) Total contribution margin Total fixed costs Operating income Total operating income $4,704,000 73,50 0 units 96,000 96,000 0 $6,144,000 0 6,144,000 4,704,000 $1,440,000 $3,628,800 $2,265,600 47,200 96,000 76,800 19,200 $3,686,400 768,000 4,454,400 2,265,600 $2,188,800 Units 3. The optimal production plan is to produce 120,000 units at the Peoria plant and 72,000 units at the Moline plant. The full capacity of the Peoria plant, 120,000 units (400 units 300 days), should be used because the contribution from these units is higher at all levels of production than is the contribution from units produced at the Moline plant. Contribution margin per plant: Peoria, 96,000 $64 Peoria 24,000 ($64 $3) Moline, 72,000 $48 Total contribution margin Deduct total fixed costs Operating income $ 6,144,000 1,464,000 3,456,000 11,064,000 6,969,600 $ 4,094,400 The contribution margin is higher when 120,000 units are produced at the Peoria plant and 72,000 units at the Moline plant. As a result, operating income will also be higher in this case since total fixed costs for the division remain unchanged regardless of the quantity produced at each plant. 3-41 ... View Full Document

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