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1. Break-Even Point (In Units) = Unit Contribution Margin $40,000 = = 8,000 Pizzas $10  $5 Unit Contribution Margin 2

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1. Break-Even Point (In Units) = Unit Contribution Margin $40,000 = = 8,000 Pizzas $10  $5 Unit Contribution Margin 2 EXERCISE 7-24 (20 MINUTES) fixed expenses 1. Break-even point (in units) = unit contribution margin $40,000 = = 8,000 pizzas $10 $5 unit contribution margin 2. Contribution-margin ratio = unit sales price $10 $5 = = .5 $10 fixed expenses 3. Break-even point (in sales dollars) = contribution-margin ratio $40,000 = = $80,000 .5 4. Let X denote the sales volume of pizzas required to earn a target net profit of $65,000. $10X – $5X – $40,000 = $65,000 $5X = $105,000 X = 21,000 pizzas EXERCISE 7-25 (25 MINUTES) fixed costs 1. Break-even point (in units) = unit contribution margin 4,000,000p = = 4,000 components 3,000p 2,000p p denotes Argentina’s peso (4,000,000p) (1.10) 2. New break-even point (in units) = 3,000p 2,000p 4,400,000 p = = 4,400 components 1,000p 7-1 3. Sales revenue (5,000 3,000p) ................................................. 15,000,000p Variable costs (5,000 2,000p) ........................................................ 10,000,000p Contribution margin .......................................................................... 5,000,000p Fixed costs ......................................................................................... 4,000,000p Net income ......................................................................................... 1,000,000p 4,000,000p 4. NEW BREAK-EVEN POINT (IN UNITS) = 2,500p 2,000p = 8,000 components 5. Analysis of price change decision: Price 3,000p 2,500p Sales revenue: (5,000 3,000p) ....................... 15,000,000p (6,200 2,500p) ....................... 15,500,000p Variable costs: (5,000 2,000p) ....................... 10,000,000p (6,200 2,000p) ....................... 12,400,000p Contribution margin ........................................... 5,000,000p 3,100,000p Fixed expenses .................................................. 4,000,000p 4,000,000p Net income (loss) ................................................ 1,000,000p (900,000p) The price cut should not be made, since projected net income will decline. 7-2 EXERCISE 7-28 (25 MINUTES) 1. (a) Traditional income statement: EUROPA PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20XX Sales .......................................................................... $2,000,000 Less: Cost of goods sold ......................................... 1,500,000 Gross margin ................................................................ $ 500,000 Less: Operating expenses: Selling expenses ............................................ $150,000 Administrative expenses ............................... 150,000 300,000 Net income .................................................................... $ 200,000 (b) Contribution income statement: EUROPA PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20XX Sales .......................................................................... $2,000,000 Less: Variable expenses: Variable manufacturing .................................. $1,000,000 Variable selling ............................................... 100,000 Variable administrative .................................. 30,000 1,130,000 Contribution margin ..................................................... $ 870,000 Less: Fixed expenses: Fixed manufacturing ...................................... $ 500,000 Fixed selling .................................................... 50,000 Fixed administrative ....................................... 120,000 670,000 Net income .................................................................... $ 200,000 contribution margin 2. Operating leverage factor (at $2,000,000 sales level) net income $870,000 4.35 $200,000 7-3 EXERCISE 7-28 (CONTINUED) percentage increase operating 3. Percentage increase in net income in sales revenue leverage factor = 10% 4.35 = 43.5% 4. Most operating managers prefer the contribution income statement for answering this type of question. The contribution format highlights the contribution margin and separates fixed and variable expenses. EXERCISE 7-29 (30 MINUTES) 1. Sales Unit Unit Bicycle Type Price Variable Cost Contribution Margin High-quality $500 $300 ($275 + $25) $200 Medium-quality 300 150 ($135 + $15) 150 2. Sales mix: High-quality bicycles .......................................................................................... 25% Medium-quality bicycles .................................................................................... 75% 3. Weighted-average unit contribution margin = ($200 25%) + ($150 75%) = $162.50 fixed expenses 4. Break-even point (in units) weighted-average unit contribution margin $65,000 400 bicycles $162.50 Break-Even Sales Bicycle Type Sales Volume Sales Price Revenue High-quality bicycles 100 (400 .25) $500 $ 50,000 Medium-quality bicycles 300 (400 .75) 300 90,000 Total $140,000 7-4 EXERCISE 7-29 (CONTINUED) 5. Target net income: $65,000 $48,750 Sales volume required to earn target net income of $48,750 $162.50 700 bicycles This means that the shop will need to sell the following volume of each type of bicycle to earn the target net income: High-quality ............................................................................ 175 (700 .25) Medium-quality ...................................................................... 525 (700 .75) SOLUTIONS TO PROBLEMS PROBLEM 7-36 (30 MINUTES) 1. Unit contribution margin: Sales price………………………………… $64.00 Less variable costs: Sales commissions ($64 x 5%)…… $ 3.20 System variable costs……………… 16.00 19.20 Unit contribution margin……………….. $44.80 Break-even point = fixed costs ÷ unit contribution margin = $985,600 ÷ $44.80 = 22,000 units 2. Model no. 4399 is more profitable when sales and production average 46,000 units. Model Model No. 6754 No. 4399 Sales revenue (46,000 units x $64.00)……... $2,944,000 $2,944,000 Less variable costs: Sales commissions ($2,944,000 x 5%)… $ 147,200 $ 147,200 System variable costs:…………………… 46,000 units x $16.00…………………. 736,000 46,000 units x $12.80…………………. 588,800 7-5 Total variable costs……………………….. $ 883,200 $ 736,000 Contribution margin…………………………... $2,060,800 $2,208,000 Less: Annual fixed costs…………………….. 985,600 1,113,600 Net income……………………………………… $1,075,200 $1,094,400 3. Annual fixed costs will increase by $90,000 ($450,000 ÷ 5 years) because of straight- line depreciation associated with the new equipment, to $1,203,600 ($1,113,600 + $90,000). The unit contribution margin is $48 ($2,208,000 ÷ 46,000 units). Thus: Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($1,203,600 + $956,400) ÷ $48 = 45,000 units 4. Let X = volume level at which annual total costs are equal $16.00X + $985,600 = $12.80X + $1,113,600 $3.20X = $128,000 X = 40,000 units PROBLEM 7-37 (35 MINUTES) 1. Current income: Sales revenue………………………... $3,360,000 Less: Variable costs………………… $ 840,000 Fixed costs……………………. 2,280,000 3,120,000 Net income……………………………. $ 240,000 Advanced Electronics has a contribution margin of $60 [($3,360,000 - $840,000) ÷ 42,000 sets] and desires to increase income to $480,000 ($240,000 x 2). In addition, the current selling price is $80 ($3,360,000 ÷ 42,000 sets). Thus: Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($2,280,000 + $480,000) ÷ $60 = 46,000 sets, or $3,680,000 (46,000 sets x $80) 2. If operations are shifted to Mexico, the new unit contribution margin will be $62 ($80 - $18). Thus: Break-even point = fixed costs ÷ unit contribution margin = $1,984,000 ÷ $62 = 32,000 units 7-6 3. (a) Advanced Electronics desires to have a 32,000-unit break-even point with a $60 unit contribution margin. Fixed cost must therefore drop by $360,000 ($2,280,000 - $1,920,000), as follows: Let X = fixed costs X ÷ $60 = 32,000 units X = $1,920,000 (b) As the following calculations show, Advanced Electronics will have to generate a contribution margin of $71.25 to produce a 32,000-unit break-even point. Based on an $80.00 selling price, this means that the company can incur variable costs of only $8.75 per unit. Given the current variable cost of $20.00 ($80.00 - $60.00), a decrease of $11.25 per unit ($20.00 - $8.75) is needed. Let X = unit contribution margin $2,280,000 ÷ X = 32,000 units X = $71.25 4. (a) Increase (b) No effect (c) Increase (d) No effect PROBLEM 7-39 (35 MINUTES) 1. Plan A break-even point = fixed costs ÷ unit contribution margin = $22,000 ÷ $22* = 1,000 units Plan B break-even point = fixed costs ÷ unit contribution margin = $66,000 ÷ $30** = 2,200 units * $80 - [($80 x 10%) + $50] ** $80 - $50 7-7 1. Operating leverage refers to the use of fixed costs in an organization’s overall cost structure. An organization that has a relatively high proportion of fixed costs and low proportion of variable costs has a high degree of operating leverage. 2. Calculation of contribution margin and profit at 6,000 units of sales: Plan A Plan B Sales revenue: 6,000 units x $80………………. $480,000 $480,000 Less variable costs: Cost of purchasing product: 6,000 units x $50…………………….…… $300,000 $300,000 Sales commissions: $480,000 x 10%……... 48,000 ---- Total variable cost……………………….. $348,000 $300,000 Contribution margin……………………………… $132,000 $180,000 Fixed costs…………………………………………. 22,000 66,000 Net income…………………………………………. $110,000 $114,000 Operating leverage factor = contribution margin ÷ net income Plan A: $132,000 ÷ $110,000 = 1.2 Plan B: $180,000 ÷ $114,000 = 1.58 (rounded) Plan B has the higher operating leverage factor. 4 & 5. Calculation of profit at 5,000 units: Plan A Plan B Sales revenue: 5,000 units x $80………………. $400,000 $400,000
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