S 90 15 s 40 s 14000000 oi 435 s 175 s 14000000 oi

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S ] [$90 (1.5 S ) + $40 S ] $14,000,000 = OI $435 S $175 S $14,000,000 = OI Breakeven point is 134,616 units when OI = 0 because $260 S = $14,000,000 S = 53,846 units sold to upgrade customers (rounded) 1.5 S = 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) $ 80 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) $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 $ 6,800,000
3-16 3a. Let S = Number of units sold to upgrade customers then S = Number of units sold to new customers [$210 S + $120 S ] [$90 S + $40 S ] $14,000,000 = OI 330 S 130 S = $14,000,000 200 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 9 S = Number of units sold to new customers [$210 (9 S ) + $120 S ] [$90 (9 S ) + $40 S ] $14,000,000 = OI 2,010 S 850 S = $14,000,000 1,160S = $14,000,000 S = 12,069 units sold to upgrade customers (rounded up) 9 S = 108,621 units sold to new customers (rounded up) 120,690 units Check Revenues ($210 108,621) + ($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: New Customers Upgrade Customers Breakeven Point Requirement 3(a) Requirement 1 Requirement 3(b) 50% 60 90 50% 40 10 140,000 134,616 120,690
3-17 3-28 (20 min.) CVP analysis, multiple cost drivers. 1a. income Operating = Revenues shipments of Number shipment of Cost frames picture of Quantity frames picture of Cost costs Fixed = ($45 40,000) ($30 40,000) ($60 1,000) $240,000 = $1,800,000 $1,200,000 $60,000 $240,000 = $300,000 1b. income Operating = ($45 40,000) ($30 40,000) ($60 800) $240,000 = $312,000 2. 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 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.
3-18 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 ÷ $22,000 = 200 scholarships 2. Total budget for next year = $5,000,000 × (1.00 0.22) = $3,900,000 Then $22,000 Q = $3,900,000 $600,000 = $3,300,000 Q = $3,300,000 ÷ $22,000 = 150 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 $3,300,000 ÷ 200 $16,500 Variable operating cost per scholarship 2,000 Amount per scholarship $14,500
3-19 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 40,000 290,000 Contribution margin $210,000 2. Contribution margin percentage = $500,000 $210,000 = 42% 3. Incremental revenue (20% × $500,000) = $100,000 Incremental contribution margin (42% × $100,000) $42,000 Incremental fixed costs (advertising) 10,000

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