SOLUTIONS TO BRIEF EERCISES BRIEF EERCISE 6-1 1. $80 = ($250 $170) 32% ($80 $250) 2. (c) $300 = ($500 $200) (d) 40% ($200 $500) 3. (e) $1,000 = ($300 30%) (f) $700 ($1,000 $300) BRIEF EERCISE 6-2 PESAVENTO MANUFACTURING INC. Income Statement For the Quarter Ended March 31, 2011 Sales... $1,800,000 Variable expenses Cost of goods sold... $760,000 Selling expenses... 95,000 Administrative expenses... 79,000 Total variable expenses... 934,000 Contribution margin... 866,000 Fixed expenses Cost of goods sold... 540,000 Selling expenses... 60,000 Administrative expenses... 66,000 Total fixed expenses... 666,000 Net income... $ 200,000 BRIEF EERCISE 6-3 Contribution margin ratio = [($250,000 $170,000) $250,000] = 32% Required sales in dollars = $120,000 32% = $375,000
BRIEF EERCISE 6-4 $400Q = $260Q + $210,000 + $0 $140Q = $210,000 Q = 1,500 units Contribution margin per unit $140, or ($400 $260) = $210,000 $140 = 1,500 units BRIEF EERCISE 6-5 =.70 + $210,000 + $60,000.30 = $270,000 = $900,000 BRIEF EERCISE 6-6 Margin of safety = $1,200,000 $900,000 = $300,000 Margin of safety ratio = $300,000 $1,200,000 = 25% BRIEF EERCISE 6-7 Model A12 B22 C124 Sales Mix Percentage 60% 25% 15% Unit Contribution Margin $10 ($50 $40) $30 ($100 $70) $100 ($400 $300) Weighted-Average Unit Contribution Margin $ 6.00 7.50 15.00 $28.50
BRIEF EERCISE 6-8 Total break-even = ($199,500 $28.50*) = 7,000 units *Computed in BE 6-7 Sales Units Units of A12 =.60 7,000 = 4,200 Units of B22 =.25 7,000 = 1,750 Units of C124 =.15 7,000 = 1,050 7,000 BRIEF EERCISE 6-9 Weighted-average contribution = (.30.10) + (.50.20) + (.20.45) =.22 margin ratio Total break-even point = ($440,000.22) = $2,000,000 in dollars Birthday $2,000,000.30 = $ 600,000 Standard tapered $2,000,000.50 = 1,000,000 Large scented $2,000,000.20 = 400,000 $ 2,000,000 BRIEF EERCISE 6-10 Sales Mix Bedroom Division $500,000 $1,250,000 =.40 Dining Room Division $750,000 $1,250,000 =.60 Weight-average contribution = $550,000 =.44 margin ratio $1,250,000 OR Contribution Margin Ratio Bedroom Division($250,000 $500,000) =.50 Dining Room Division($300,000 $750,000) =.40 Weighted-average contribution margin ratio = (.50.40) + (.40.60) =.44
BRIEF EERCISE 6-11 Contribution margin per unit Machine hours required Contribution margin per unit of limited resource [ ] Product A $10.0 2 $ 5 Product B $12 3 $ 4 BRIEF EERCISE 6-12 Degree of operating leverage (old) = $ 160,000 $40,000 = 4 Degree of operating leverage (new) = $ 240,000 $40,000 = 6 If John s sales change, the resulting change in net income will be 1.5 times (6 4) higher with the new machine than under the old system. BRIEF EERCISE 6-13 Break-even point in dollars: Turgro Co. Meriden Co. $50,000 ($90,000 $150,000) $95,000 ($135,000 $150,000) = $83,333 = $105,556 Meriden Company s cost structure relies much more heavily on fixed costs than that of Turgro Co. As result, Meriden has a higher contribution margin ratio of.90 ($135,000 $150,000) versus.60 for Turgro Co. ($90,000 $150,000). Meriden also has much higher fixed costs to cover. Its breakeven point is therefore higher than that of Turgro Co. BRIEF EERCISE 6-14 Degree of operating leverage = Contribution margin Net income Dousmann Corp. 1.4 = Contribution margin $50,000 Contribution margin = $50,000 1.4 = $70,000 PCB Co. 5.6 = Contribution margin $50,000 Contribution margin = $50,000 5.6 = $280,000
BRIEF EERCISE 6-15 Contribution margin per unit Machine hours required Contribution margin per unit of limited resource [ ] Product 1 Product 2 $ 42.14 $300 $ 36.10 $360 Product 2 has a higher contribution margin per limited resource, even though it has a lower contribution margin per unit. Given that machine hours are limited to 2,000 per month, Dye Corporation should produce Product 2. *BRIEF EERCISE 6-16 Variable Costing Direct materials $14,490 Direct labor 25,530 Variable manufacturing overhead 32,420 Total product costs $72,440 *BRIEF EERCISE 6-17 Absorption Costing Direct materials $14,490 Direct labor 25,530 Variable manufacturing overhead 32,420 Fixed manufacturing overhead 10,000 Total product costs $82,440 *BRIEF EERCISE 6-18 Absorption Costing... Direct materials... $20 Direct labor... 12 Variable manufacturing overhead... 15 Fixed manufacturing overhead ($120,000 12,000)... 10 Total manufacturing cost per unit... $57
*BRIEF EERCISE 6-18 (Continued) Variable Costing Direct materials... $20 Direct labor... 12 Variable manufacturing overhead... 15 Total manufacturing cost per unit... $47 *BRIEF EERCISE 6-19 MEMO To: From: Re: Chief financial officer Student Absorption and variable costing Under absorption costing, fixed manufacturing overhead is a product cost, while under variable costing, fixed manufacturing overhead is a period cost (expensed as incurred). Since units produced (50,000) exceeded units sold (47,000) last month, income under absorption costing will be higher than under variable costing. Some fixed overhead (3,000 units $3 = $9,000) will be assigned to ending inventory and therefore not expensed under absorption costing, whereas all fixed overhead is expensed under variable costing. Therefore, absorption costing net income will be higher than variable costing net income by $9,000.
SOLUTIONS TO DO IT! REVIEW EERCISES DO IT! 6-1 NAYLOR MANUFACTURING INC. Income Statement For the Month Ended January 31, 2011 Sales (8,000 units)... $400,000 Variable expenses Cost of goods sold... $184,000 Selling expenses... 40,000 Administrative expenses... 16,000 Total variable expenses... 240,000 Contribution margin 160,000 Fixed expenses Cost of goods sold... $ 70,000 Selling expenses... 30,000 Administrative expenses... 40,000 Total fixed expenses... 140,000 Net income... $ 20,000 Contribution margin per unit: $50 ($400,000 8,000 units) $30 ($240,000 8,000 units) = $20 per unit. Contribution margin ratio: $160,000 $400,000 = 40% or $20 $50 = 40%. DO IT! 6-2 Break-even point in units is 6,667 units (rounded) ($150,000 $22.50). Break-even point in sales dollars is $333,333 ($150,000.45*). The margin of safety in dollars is $116,667 ($450,000 $333,333). *$22.50 $50. Break-even point in units is 8,571 units (rounded) ($150,000 $17.50*). Break-even point in sales dollars is $384,615 ($150,000.39**). The margin of safety in dollars is $141,885 ($526,500*** $384,615). *$50 (.10 $50) 27.50 = $17.50. **$17.50 $45 =.39 ***9,000 + (.30 9,000) = 11,700 units, 11,700 units $45 = $526,500
DO IT! 6-2 (Continued) The increase in the break-even point from $333,333 to $384,615 indicates that management should not implement the proposed change while the increase in the margin of safety from $116,650 to $141,885 indicates that management should implement the proposed change. Since the expected 30% increase in sales volume will result in a contribution margin of $204,750 (11,700 $17.50) which is only $2,500 more than the current amount, management should be cautious before reducing unit prices. DO IT! 6-3 The sales mix percentages as a function of units sold is: Basic Basic Plus Premium 840 1,400 = 60% 350 1400 = 25% 210 1400 = 15% (c) (d) The weighted-average unit contribution margin is: [.60 ($250 $195)] + [.25 ($400 $288)] + [.15 ($800 $416)] = $118.60. The break-even point in units is: $140,000 $118.60 = 1,180 units. The break-even units to produce for each product are: Basic: 1,180 units 60% = 708 units Basic Plus 1,180 units 25% = 295 units Premium: 1,180 units 15% = 177 units 1,180 units DO IT! 6-4 The Best binoculars have the highest contribution margin per unit. Thus, ignoring any manufacturing constraints, it would appear that the company should shift toward production of more Best units.
DO IT! 6-4 (Continued) The contribution margin per unit of limited resource is calculated as: Good Better Best Contribution margin per unit $30 $120 $450 Limited resource consumed per unit.5 = $60 1.5 = $80 6 = $75 (c) The Better binoculars have the highest contribution margin per unit of limited resource, even though they do not have the highest contribution margin per unit. Given the resource constraint, any additional capacity should be used to make Better binoculars.
SOLUTIONS TO EERCISES EERCISE 6-1 1. Contribution margin per room = $50 ($5 + $33) Contribution margin per room = $12 Contribution margin ratio = $12 $50 = 24% Fixed costs = $8,500 + $2,000 + $1,000 + $500 = $12,000 Break-even point in rooms = $12,000 $12 = 1,000 2. Break-even point in dollars = 1,000 rooms $50 per room = $50,000 per month OR Fixed costs Contribution margin ratio = $12,000.24 = $50,000 per month 1. Margin of safety in dollars: Planned activity = 50 rooms per day 30 days = 1,500 rooms per month Expected rental revenue = 1,500 rooms $50 = $75,000 Margin of safety in dollars = $75,000 $50,000 = $25,000 2. Margin of safety ratio: $25,000 $75,000 = 331 / 3 % EERCISE 6-2 Contribution margin in dollars: Sales = 3,500 $30 = $105,000 Variable costs = $105,000.8 = 84,000 Contribution margin $ 21,000 Contribution margin per unit: $30 $24 ($30 80%) = $6. Contribution margin ratio: $6 $30 = 20%.
EERCISE 6-2 (Continued) Break-even sales in dollars: Break-even sales in units: $ 16, 800 = $84,000. 20% $16,800 = 2,800. $6 (c) Margin of safety in dollars: $105,000 $84,000 = $21,000. Margin of safety ratio: $21,000 $105,000 = 20%. EERCISE 6-3 Current selling price = $300,000 5,000 units Current selling price = $60 1. Increase selling price to $66 ($60 110%). Net income = $330,000* $210,000 $70,000 = $50,000. *($66 5,000) 2. Reduce variable costs to 58% of sales. Net income = $300,000 $174,000** $70,000 = $56,000. **($300,000.58) 3. Reduce fixed costs to $50,000 ($70,000 $20,000). Net income = $300,000 $210,000 $50,000 = $40,000. Alternative 2, decreasing variable costs, will produce the highest net income.
EERCISE 6-4 1. Contribution margin ratio is: $27,000 $45,000 = 60% $20,250 Break-even point in dollars = 60% = $33,750 $45,000 2. Round-trip fare = 300 fares = $150 Break-even point in fares = $33,750 $150 = 225 fares At the break-even point fixed costs and contribution margin are equal. Therefore, the contribution margin at the break-even point would be $20,250. (c) Fare revenue ($135* 400**) $54,000 Variable costs ($18,000 1.35) 24,300 Contribution margin 29,700 Fixed costs 20,250 Net income $ 9,450 Yes, the fare decrease should be implemented because net income increases to $9,450. *$150 (.10 $150) **300 + 100 EERCISE 6-5 MOZENA COMPANY CVP Income Statement For the Year Ended December 31, 2011 Sales (60,000 $25)... Variable costs (60,000 $12)... Contribution margin (60,000 $13)... Fixed costs... Net income... Total $1,500,000 720,000 780,000 400,000 $ 380,000 Per Unit $25 12 $13
EERCISE 6-5 (Continued) MOZENA COMPANY CVP Income Statement For the Year Ended December 31, 2011 Sales [(60,000 105%) $23.50*]... Variable costs (63,000 $9.00**)... Contribution margin (63,000 $14.50)... Fixed costs ($400,000 + $150,000)... Net income... *$25.00 ($3 50%) = $23.50. **$12.00 ($12 25%) = $9.00. Total $1,480,500 567,000 913,500 550,000 $ 363,500 Per Unit $23.50 9.00 $14.50 EERCISE 6-6 Lawnmowers Weed-trimmers Chainsaws Sales Mix Percentage 30% 50% 20% Contribution Margin Per Unit $30 $20 $40 Weighted-Average Contribution Margin $ 9 $10 $ 8 $27 Total break-even sales in units = $4,600,000 $27 = 170,370 units Lawnmowers Weed-trimmers Chainsaws Total units Sales Mix Percentage 30% 50% 20% Total Break-even Sales in Units 170,370 170,370 170,370 = = = Sales Units Needed Per Product 51,111 units 85,185 units 34,074 units 170,370 units
EERCISE 6-7 Oil changes Brake repair Sales Mix Percentage 65% 35% Contribution Margin Ratio 20% 60% Weighted-Average Contribution Margin Ratio.13.21.34 Total break-even sales in dollars = $16,000,000.34 = $47,058,824 Oil changes Brake repair Total sales Sales Mix Percentage 65% 35% Total Break-even Sales in Dollars $47,058,824 $47,058,824 = = Sales Dollars Needed Per Product $30,588,236 $16,470,588 $47,058,824 Sales to achieve target net income = ($80,000 + $60,000).34 = $411,765 Oil changes Brake repair Total sales Sales Mix Percentage 65% 35% Total Sales Needed $411,765 $411,765 = = Sales Dollars Needed Per Product Per Store $267,647 $144,118 $411,765 EERCISE 6-8 Mail pouches and small boxes Non-standard boxes Sales Mix Percentage 80% 20% Contribution Margin Ratio 10% 60% Weighted-Average Contribution Margin Ratio.08.12.20 Total break-even sales in dollars = $12,000,000.20 = $60,000,000
EERCISE 6-8 (Continued) Mail pouches and small boxes Non-standard boxes Total sales Sales Mix Percentage 80% 20% Total Breakeven Sales in Dollars $60,000,000 $60,000,000 = = Sales Dollars Needed Per Product $48,000,000 $12,000,000 $60,000,000 Mail pouches and small boxes Non-standard boxes Sales Mix Percentage 40% 60% Contribution Margin Ratio 10% 60% Weighted-Average Contribution Margin Ratio.04.36.40 Total break-even sales in dollars = $12,000,000.40 = $30,000,000 Mail pouches and small boxes Non-standardized boxes Total sales Sales Mix Percentage 40% 60% Total Breakeven Sales in Dollars $30,000,000 $30,000,000 = = Sales Dollars Per Product $12,000,000 $18,000,000 $30,000,000 EERCISE 6-9 Weighted-average unit contribution margin = ($40.40) + ($20.50) + ($50.10) = $31 Break-even point in units = $620,000 $31 = 20,000 Shoes (20,000.40) = 8,000 pairs of shoes Gloves (20,000.50) = 10,000 pairs of gloves Range finders (20,000.10) = 2,000 range finders
EERCISE 6-9 (Continued) (c) Shoes: 8,000 $40 = $320,000 Gloves: 10,000 $20 = 200,000 Range finders: 2,000 $50 = 100,000 Total contribution margin 620,000 Fixed costs 620,000 Net income $ 0 EERCISE 6-10 Sales mix percentage TV division: $600,000 ($600,000 + $400,000) =.60 DVD division: $400,000 ($600,000 + $400,000) =.40 Contribution margin ratio: TV division: $150,000 $600,000 =.25 DVD division: $160,000 $400,000 =.40 Weighted-average contribution $310,000 = =.31 OR margin ratio $1,000,000 Weighted-average contribution margin ratio = (.60.25) + (.40.40) =.31 (c) Break-even point in dollars = $124,000.31 = $400,000 (d) Sales dollars needed at break-even point for each division TV division: $400,000.60 = $240,000 DVD division: $400,000.40 = $160,000 EERCISE 6-11 Contribution margin per unit Machine hours required Contribution margin per unit of limited resource Product A B C $6 2 $3 $2.50 1 $2.50 $2 2 $1 Product A should be manufactured because it results in the highest contribution margin per machine hour.
EERCISE 6-11 (Continued) (c) 1. Product A B C Machine hours (1,500 3) Contribution margin per unit of limited resource Total contribution margin [ ] 500 $ 3 $1,500 500 $ 2.50 $1,250 The total contribution margin = ($1,500 + $1,250 + $500) = $3,250. 500 $1 $500 2. Product A Machine hours Contribution margin per unit of limited resource Total contribution margin [ ] 1,500 $3 $4,500 EERCISE 6-12 Product D: $25 $10 = 2.5 hours per unit Product E: $75 $10 = 7.5 hours per unit Product F: $30 $10 = 3.0 hours per unit Product D E F Selling price $200 $300 $250 Variable costs 130 165 178 Contribution margin 70 135 72 Direct labor hours per unit 2.5 7.5 3.0 Contribution margin per direct labor hour $ 28 $ 18 $ 24 (c) Product D should be produced because it generates the highest contribution margin per direct labor hour. Product D Total direct labor hours available 2,000 Contribution margin per direct labor hour $28 Total contribution margin $56,000
EERCISE 6-13 Product Basic Deluxe Selling price per unit -Variable costs per unit $40 18 $52 24 Contribution margin per unit $22 $28 Machine hours required.5.7 Contribution margin per machine hour $44 $40 The Basic product should be manufactured because it results in the higher contribution margin per machine hour. (c) 1. Basic Deluxe Total Machine hours allocated 500 500 1,000 Contribution margin per machine hour $44 $40 Contribution margin $22,000 $20,000 $42,000 2. Basic Deluxe Total Machine hours allocated 1,000 0 1,000 Contribution margin per machine hour $44 $40 Contribution margin $44,000 0 $44,000 EERCISE 6-14 Grissom Moran Contribution Margin $320,000 $520,000 Net Income = $150,000 = $150,000 = Degree of Operating Leverage 2.133 3.467 Interpretation: Moran has a higher degree of operating leverage. Its earnings would increase (decrease) by a greater amount than Grissom if each experienced an equal increase (decrease) in sales.
EERCISE 6-14 (Continued) Sales Variable costs Contribution margin Fixed costs Net income Grissom Company $660,000** 308,000** 352,000** 170,000** $182,000** Moran Company $660,000*** 88,000*** 572,000*** 370,000*** $202,000*** *$600,000 1.1 **$280,000 1.1 ***$ 80,000 1.1 (c) Each company experienced a $60,000 increase in sales. However, because of Moran s higher operating leverage, it experienced a $52,000 ($202,000 $150,000) increase in net income while Grissom experienced only a $32,000 ($182,000 $150,000) increase. This is what we would have expected, since Moran s degree of operating leverage exceeds that of Grissom. EERCISE 6-15 Manual system Computerized system Contribution Margin Net Income = $300,000 $240,000 = $900,000 $240,000 = Degree of Operating Leverage 1.25 3.75 The computerized system would produce profits that are 3.0 times (3.75 1.25) as much as the manual system. With a $100,000 increase in sales, net income would increase $20,000 ($260,000 $240,000) under the manual system and $60,000 ($300,000 $240,000) under the computerized system.
EERCISE 6-15 (Continued) Sales Variable costs Contribution margin Fixed costs Net income Manual System $1,600,000 1,280,000* 320,000 60,000 $ 260,000 Computerized System $1,600,000 640,000** 960,000 660,000 $ 300,000 *($1,200,000 $1,500,000) $1,600,000 **($600,000 $1,500,000) $1,600,000 (c) Manual system Computerized system (Actual Sales Break-even Sales) Actual Sales = Margin of Safety Ratio ($1,500,000 $300,000*) $1,500,000 =.80 ($1,500,000 $1,100,000**) $1,500,000 =.27 *$60,000 ($300,000 $1,500,000) **$660,000 ($900,000 $1,500,000) The manual system could weather the greater decline in sales before reaching the break-even point. Under the manual system sales could drop 80% before suffering a loss, while sales under the computerized system could only decline by 27% before suffering a loss. EERCISE 6-16 Old Fashion Mech-Apple Contribution Margin $ 80,000 $240,000 Net Income = $60,000 $60,000 = = Degree of Operating Leverage 1.33 4.00 Mech-Apple, which relies more heavily on fixed costs, has the higher degree of operating leverage, 4.0 versus 1.33. That means for every dollar of increase (decrease) in sales, Mech-Apple will generate 3 (4 1.33) times more (less) in contribution margin and net income.
EERCISE 6-16 (Continued) 10% decrease: Old Fashion Mech-Apple % Change in Sales (10%) (10%) Degree of Operating Leverage = 1.33 4.00 = = % Change in Net Income (13.3%) (40.0%) 5% increase: Old Fashion Mech-Apple 5% 5% 1.33 4.00 = = 6.65% 20.0% (c) There are several possible answers that could be given. For example, if the candied apple business is fairly stable, Mech-Apple might be the choice, because it will generate the higher contribution margin and net income. If, however, sales swing widely from year to year, Old Fashion might be chosen because it will provide the more stable contribution margin and net income. Finally, if the investment banker is a risk taker, she might choose Mech-Apple in spite of year to year sales swings. EERCISE 6-17 Unit Cost Direct materials $ 7.50 Direct labor 2.45 Variable manufacturing overhead 5.75 Manufacturing cost per unit $15.70
EERCISE 6-17 (Continued) MATT S COMPANY Income Statement For the Year Ended December 31, 2011 Variable Costing Sales (80,000 lures $25) $2,000,000 Variable cost of goods sold (80,000 lures $15.70) $1,256,000 Variable selling and administrative expenses (80,000 lures $3.90) 312,000 1,568,000 Contribution margin 432,000 Fixed manufacturing overhead 234,650 Fixed selling and administrative expenses 240,100 474,750 Net Income (loss) $ (42,750) (c) (d) Unit Cost Direct materials $ 7.50 Direct labor 2.45 Variable manufacturing overhead 5.75 Fixed manufacturing overhead ($234,650 95,000) 2.47 Manufacturing cost per unit $18.17 MATT S COMPANY Income Statement For the Year Ended December 31, 2011 Absorption Costing Sales (80,000 lures $25) $2,000,000 Cost of goods sold (80,000 lures $18.17) 1,453,600 Gross profit 546,400 Variable selling and administrative expenses (80,000 lures $3.90) $312,000 Fixed selling and administrative expenses 240,100 552,100 Net Income $ (5,700)
*EERCISE 6-18 Direct materials used $ 90,000 Direct labor incurred 30,000 Variable manufacturing overhead 24,000 Variable manufacturing costs $144,000 Variable manufacturing cost per unit = $144,000 10,000 = $14.40 per unit Finished goods inventory cost = (10,000 9,000 units) $14.40 = $14,400 Absorption costing would show a higher net income because a portion of the fixed costs are deferred to future periods. The following computation indicates that finished goods inventory will be $5,000 higher under absorption costing which will cause its net income to be $5,000 higher. Direct materials used $ 90,000 Direct labor incurred 30,000 Variable manufacturing overhead 24,000 Fixed manufacturing overhead 50,000 Total manufacturing costs $194,000 Total manufacturing costs per unit = $194,000 10,000 = $19.40 per unit Finished goods inventory cost = (10,000 9,000 units) $19.40 = $19,400 Inventory (absorption costing) $19,400 Inventory (variable costing) 14,400 $ 5,000 *EERCISE 6-19 Months in a year Utility Expense Kilowatt Hourly hours Charge = Variable Utilities 12 500 $0.45 = $2,700 Months in a year Monthly Fee = Fixed Utilities 12 $2,000 = $24,000
*EERCISE 6-19 (Continued) Variable Costing Labor: Crate builders $37,000 Material: Wood 54,000 Variable Overhead: Utilities 2,700 Nails 340 Total manufacturing costs $94,040 Absorption Costing Labor: Crate builders $37,000 Material: Wood 54,000 Variable overhead: Utilities 2,700 Nails 340 Fixed overhead: Utilities 24,000 Rent 21,400 Total manufacturing costs $139,440 (c) The entire difference in costs between the two methods is due to the fact that fixed overhead is included as part of manufacturing costs only under the absorption costing method. This difference amounts to $45,400 ($24,000 + $21,400).
SOLUTIONS TO PROBLEMS PROBLEM 6-1A Sales were $1,600,000 and variable expenses were $900,000, which means contribution margin was $700,000 and CM ratio was.4375. Fixed expenses were $840,000. Therefore, the break-even point in dollars is: $840,000.4375 = $1,920,000 1. The effect of this alternative is to increase the selling price per unit to $25 ($20 125%). Total sales become $2,000,000 (80,000 $25). Thus, contribution margin ratio changes to 55% [($2,000,000 $900,000) $2,000,000]. The new break-even point is: $840,000.55 = $1,527,273 (rounded) 2. The effects of this alternative are: (1) fixed costs decrease by $160,000, (2) variable costs increase by $80,000 ($1,600,000 5%), (3) total fixed costs become $680,000 ($840,000 $160,000), and the contribution margin ratio becomes.3875 [($1,600,000 $900,000 $80,000) $1,600,000]. The new break-even point is: $680,000.3875 = $1,754,839 (rounded) 3. The effects of this alternative are: (1) variable and fixed cost of goods sold become $600,000 each, (2) total variable costs become $720,000 ($600,000 + $75,000 + $45,000), (3) total fixed costs are $1,020,000 ($600,000 + $345,000 + $75,000) and the contribution margin ratio becomes.55 [($1,600,000 $720,000) $1,600,000]. The new break-even point is: $1,020,000.55 = $1,854,545 (rounded) Alternative 1 is the recommended course of action using break-even analysis because it has the lowest break-even point.
PROBLEM 6-2A (1) Sales Variable costs Direct materials Direct labor Manufacturing overhead ($360,000.70) Selling expenses ($240,000.40) Administrative expenses ($280,000.20) Total variable costs Contribution margin Current Year $1,600,000 511,000 285,000 252,000 96,000 56,000 1,200,000 $ 400,000 Sales Current Year $1,600,000 1.1 Projected Year $1,760,000 Variable costs Direct materials Direct labor Manufacturing overhead Selling expenses Administrative expenses Total variable costs Contribution margin 511,000 285,000 252,000 96,000 56,000 1,200,000 $ 400,000 1.1 1.1 1.1 1.1 1.1 1.1 1.1 562,100 313,500 277,200 105,600 61,600 1,320,000 $ 440,000 (2) Fixed Costs Current Year Projected year Manufacturing overhead ($360,000.30) Selling expenses ($240,000.60) Administrative expenses ($280,000.80) Total fixed costs $108,000 144,000 224,000 $476,000 $108,000 144,000 224,000 $476,000
PROBLEM 6-2A (Continued) Unit selling price = $1,600,000 100,000 = $16 Unit variable cost = $1,200,000 100,000 = $12 Unit contribution margin = $16 $12 = $4 Contribution margin ratio = $4 $16 =.25 Break-even point in units = Fixed costs Unit contribution margin 119,000 units = $476,000 $4.00 Break-even point in dollars = Fixed costs Contribution margin ratio $1,904,000 = $476,000.25 (c) Sales dollars required for = (Fixed costs + Target net income) Contribution margin ratio target net income $3,144,000 = ($476,000 + $310,000).25 (d) Margin of safety = (Expected sales Break-even sales) Expected sales ratio 39.4% = ($3,144,000 $1,904,000) $3,144,000 (e) (1) Sales Variable costs Direct materials Direct labor ($285,000 $104,000) Manufacturing overhead ($360,000.30) Selling expenses ($240,000.90) Administrative expenses ($280,000.20) Total variable costs Contribution margin Current Year $1,600,000 511,000 181,000 108,000 216,000 56,000 1,072,000 $ 528,000
PROBLEM 6-2A (Continued) Fixed cost Manufacturing overhead ($360,000.70) Selling expenses ($240,000.10) Administrative expenses ($280,000.80) Total fixed costs $252,000 24,000 224,000 $500,000 (2) Contribution margin ratio = $528,000 $1,600,000 =.33 (3) Break-even point in dollars = $500,000.33 = $1,515,152 (rounded) The break-even point in dollars declined from $1,904,000 to $1,515,152. This means that overall the company s risk has declined because it doesn t have to generate as much in sales. The two changes actually had opposing effects on the break-even point. By changing to a more commission-based approach to compensating its sales staff the company reduced its fixed costs, and therefore reduced its break-even point. In contrast, the purchase of the new equipment increased the company s fixed costs (by increasing its equipment depreciation) which would increase the break-even point.
PROBLEM 6-3A Product Economy Standard Deluxe Selling price $30 $50 $100 Less: Variable costs 12 18 42 Contribution margin per unit $18 $32 $ 58 Ignoring the machine time constraint, the Deluxe product should be produced because it has the highest contribution margin per unit. (c) Product Economy Standard Deluxe Contribution margin per unit $18 $32 $ 58 Machine hours required.5.8 1.6 Contribution margin per limited resource / $36 $40 $36.25 If additional machine hours become available, the additional time should be used to produce the Standard product since it has the highest contribution margin per machine hour.
PROBLEM 6-4A Appetizers Main entrees Desserts Beverages Sales Mix Percentage 10% 60% 10% 20% Contribution Margin Ratio = 60% = 30% = 50% = 80% = Weighted-Average Contribution Margin Ratio.06.18.05.16.45 Total sales required to achieve target net income = ( $1,200,000 + $150,000 ).45 = $3,000,000 Appetizers Main entrees Desserts Beverages Sales Mix Percentage 10% 60% 10% 20% Total Sales Needed = $3,000,000 = $3,000,000 = $3,000,000 = $3,000,000 = Sales from Each Product $ 300,000 $1,800,000 $ 300,000 $ 600,000 $3,000,000 Appetizers Main entrees Desserts Beverages Sales Mix Percentage 20% 30% 10% 40% Contribution Margin Ratio = 60% = 10% = 50% = 80% = Weighted-Average Contribution Margin Ratio.12.03.05.32.52 Total sales required to achieve target net income = ( $1,800,000* + $150,000).52 = $ 3,750,000 *$1,200,000 1.5
PROBLEM 6-4A (Continued) Thus, sales would have to increase by $750,000 ($3,750,000 $3,000,000) to achieve the target net income. This increase in sales is driven by the increase in fixed costs. The sales of each product line would be: Appetizers Main entrees Desserts Beverages (c) Appetizers Main entrees Desserts Beverages Sales Mix Percentage 20% 30% 10% 40% Sales Mix Percentage 10% 60% 10% 20% Total Sales Needed = $3,750,000 = $3,750,000 = $3,750,000 = $3,750,000 = Contribution Margin Ratio = 60% = 10% = 50% = 80% = Sales from Each Product $ 750,000 $1,125,000 $ 375,000 $1,500,000 $3,750,000 Weighted-Average Contribution Margin Ratio.06.06.05.16.33 The weighted-average contribution margin ratio computed in part was 45%. With the contribution margin ratio on entrees falling to 10%, that average will now be 33% as shown previously. Applying this to the new fixed costs of $1,800,000 and target net income of $150,000 we get: Total sales required to achieve target net income = ($1,800,000 + $150,000).33 = $ 5,909,091 Appetizers Main entrees Desserts Beverages Sales Mix Percentage 10% 60% 10% 20% Total Sales Needed = $5,909,091 = $5,909,091 = $5,909,091 = $5,909,091 = Sales from Each Product $ 590,909 $3,545,455 $ 590,909 $1,181,818 $5,909,091 Relative to parts and, the total required sales for (c) would increase. It appears that the least risky approach would be for Will to switch to the new sales mix, but not to incur the additional fixed costs of expanding operations. If the switch in sales mix appears to be successful, then it may be appropriate for him to incur the additional fixed costs necessary for expansion of operations.
PROBLEM 6-5A To determine the break-even point in dollars we must first calculate the contribution margin ratio for each company. Old Company New Company Contribution Margin Sales = $220,000 $400,000 = $320,000 $400,000 = Contribution Margin Ratio.55.80 Old Company New Company Fixed Costs $170,000 $270,000 Contribution Margin Ratio =.55 =.80 = Break-even Point in Dollars $309,091 $337,500 Old Company New Company (Actual Sales Break-even Sales) Actual Sales = ($400,000 $309,091) $400,000 = ($400,000 $337,500) $400,000 = Margin of Safety Ratio.23.16 Old Company New Company Contribution Margin $220,000 $320,000 Net Income = $50,000 = $50,000 = Degree of Operating Leverage 4.4 6.4 Because New Company relies more heavily on fixed costs, it has a higher degree of operating leverage. This means that its net income will be more sensitive to changes in sales. For a given change in sales, the change in net income will be 1.45 (6.4 4.4) times higher for New Company than for Old Company. (c) Old Company New Company Sales $480,000* $480,000 Variable costs 216,000** 96,000*** Contribution margin 264,000 384,000 Fixed costs 170,000 270,000 Net income $ 94,000 $114,000 *$400,000 1.2 **$180,000 1.2 ***$ 80,000 1.2
PROBLEM 6-5A (Continued) (d) (e) Old Company New Company Sales $320,000* $320,000 Variable costs 144,000** 64,000*** Contribution margin 176,000 256,000 Fixed costs 170,000 270,000 Net income $ 6,000 ($ 14,000) *$400,000.80 **$180,000.80 ***$ 80,000.80 In part the degree of operating leverage of New Company was higher than that of Old Company, telling us that the net income of New Company was more sensitive to changes in sales than that of Old Company. In part (c) we see that a 20% increase in sales increased the net income of New Company by $64,000 ($114,000 $50,000), while the net income of Old Company increased by only $44,000 ($94,000 $50,000). However, in part (d) we see that a 20% decrease in sales resulted in a $64,000 ($50,000 + $14,000) decline in net income for New Company, while Old Company s net income only declined by $44,000 ($50,000 $6,000). The increased risk caused by higher operating leverage is also seen in part. New Company has a higher break-even point, and a lower margin of safety ratio than Old Company. Thus, while operating leverage can be very beneficial for a company that expects its sales to increase, it can also significantly increase a company s risk.
PROBLEM 6-6A Reformat the income statement to CVP format. All amount are in $000s. Sales... $78,000 Variable costs ($35,100 + $14,040)... 49,140 Contribution margin... 28,860 Less: Fixed costs ($8,610 + $10,260)... 18,870 Operating income... $ 9,990 Contribution margin ratio = $28,860 $78,000 = 37% Break-even point = $18,870 37% = $51,000 If a hired workforce replaces sales agents, commissions will be reduced to 8% of sales, or $6,240; but fixed costs will increase by $7,800. Sales... $78,000 Variable costs ($35,100 + $6,240)... 41,340 Contribution margin... 36,660 Less: Fixed costs ($18,870* + $7,800)... 26,670 Operating income... $ 9,990 *($8,610 + $10,260) Contribution margin ratio = $36,660 $78,000 = 47% Break-even point = $26,670 47% = $56,745 (rounded) (c) Operating leverage = contribution margin operating income (1) Current situation: from part $28,860 $9,990 = 2.89 (2) Proposed situation: from part $36,660 $9,990 = 3.67
PROBLEM 6-6A (Continued) The calculations indicate that at a sales level of $78 million, a percentage change in sales and contribution margin will result in 2.89 times that percentage change in operating income if Olin continues to use sales agents. If they choose to employ their own, the change in operating income will be 3.67 times the percentage change in sales. The higher contribution margin per dollar of sales and higher fixed costs from Olin employing their own agents gives them more operating leverage. This will result in greater benefits (increases in operating income) if revenues increase, but greater risks (decreases in operating income) if revenues decline. (d) The sales level at which operating incomes will be identical is called the point of indifference. This would be when the cost of the network of agents (18% of sales) is exactly equal to the cost of paying employees 10% commission along with additional fixed costs of $7.8 million. None of the other costs is relevant, because they will not change between alternatives. Let the sales volume = S 18% S = (10% S) + $7,800,000.18S =.10S + $7,800,000.08S = $7,800,000 S = $97,500,000
*PROBLEM 6-7A MAROTTA COMPANY Income Statement For the Year Ended December 31, 2010 Variable Costing Sales (3,000 tons $2,000)... Variable cost of goods sold Inventory, January 1... Variable cost of goods manufactured [4,000 tons ($2,000.15)]... Variable cost of goods available for sale... Inventory, December 31 [1,000 tons ($2,000.15)]... Variable cost of goods sold... Variable selling expenses [3,000 tons ($2,000.10)]... Contribution margin... Fixed manufacturing overhead... Fixed administrative expenses... Net income... $ 0 1,200,000 1,200,000 300,000 900,000 600,000 $2,400,000 600,000 $6,000,000 1,500,000 4,500,000 3,000,000 $1,500,000
*PROBLEM 6-7A (Continued) MAROTTA COMPANY Income Statement For the Year Ended December 31, 2011 Variable Costing Sales (4,000 tons $2,000)... Variable cost of goods sold Inventory, January 1... Variable cost of goods manufactured [3,000 tons ($2,000.15)]... Variable cost of goods available for sale... Inventory, December 31... Variable cost of goods sold... Variable selling expenses [4,000 tons ($2,000.10)]... Contribution margin... Fixed manufacturing overhead... Fixed administrative expenses... Net income... $ 300,000 900,000 1,200,000 0 1,200,000 800,000 $2,400,000 600,000 $8,000,000 2,000,000 6,000,000 3,000,000 $3,000,000 MAROTTA COMPANY Income Statement For the Year Ended December 31, 2010 Absorption Costing Sales (3,000 tons $2,000)... Cost of goods sold Inventory, January 1... Cost of goods manufactured... Cost of goods available for sale... Inventory, December 31... Cost of goods sold... Gross profit... Variable selling expenses [3,000 tons ($2,000.10)]... Fixed administrative expenses... Net income... $ 0 3,600,000 3,600,000 900,000 (1) 4,000 [($2,000.15) + ($2,400,000 4,000)] (2) 1,000 [($2,000.15) + ($2,400,000 4,000)] 600,000 600,000 (1) (2) $6,000,000 2,700,000 3,300,000 1,200,000 $2,100,000
*PROBLEM 6-7A (Continued) MAROTTA COMPANY Income Statement For the Year Ended December 31, 2011 Absorption Costing Sales (4,000 tons $2,000)... Cost of goods sold Inventory, January 1... Cost of goods manufactured... Cost of goods available for sale... Inventory, December 31... Cost of goods sold... Gross profit... Variable selling expenses [4,000 tons ($2,000.10)]... Fixed administrative expenses... Net income... $ 900,000 3,300,000 4,200,000 0 (1) 3,000 [($2,000.15) + ($2,400,000 3,000)] 800,000 600,000 (1) $8,000,000 4,200,000 3,800,000 1,400,000 $2,400,000 (c) The variable costing and the absorption costing net income can be reconciled as follows: Variable costing net income Fixed manufacturing overhead expensed with variable costing Less: Fixed manufacturing overhead expensed with absorption costing Difference Absorption costing net income $2,400,000 (1,800,000) (1) 2010 2011 $1,500,000 600,000 $2,100,000 $2,400,000 (3,000,000) (2) $3,000,000 (600,000) $2,400,000 3, 000 units sold (1) In 2010, with absorption costing $1,800,000 $2, 400, 000 of the 4, 000 units produced fixed manufacturing overhead is expensed as part of cost of goods sold, and $600,000 $2, 400, 000 1, 000 units in inventory is included in the ending inventory. 4, 000 units produced (2) In 2011, with absorption costing $3,000,000 of fixed manufacturing overhead is expensed as part of cost of goods sold. This includes the fixed manufacturing overhead for 2011 of $2,400,000 plus $600,000 of fixed manufacturing overhead from 2010 that was included in the beginning inventory for 2011.
*PROBLEM 6-7A (Continued) (d) Income parallels sales under variable costing as seen in the increase in net income in 2011 when 1,000 additional units were sold. In contrast, under absorption costing, income parallels production as seen in the higher net income in 2010 when production exceeded sales by 1,000 tons.
*PROBLEM 6-8A BASIC ELECTRIC MOTORS DIVISION Income Statement For the Year Ended December 31, 2011 Absorption Costing 50,000 80,000 Produced Produced Sales (50,000 units $30) $1,500,000 $1,500,000 Cost of goods sold (50,000 units $20) 1,000,000 (50,000 $17) 850,000 Gross profit 500,000 650,000 Variable selling and administrative expenses (50,000 units x $2) 100,000 100,000 Fixed selling and administrative expenses 40,000 40,000 Net income $ 360,000 $ 510,000 BASIC ELECTRIC MOTORS DIVISION Income Statement For the Year Ended December 31, 2011 Variable Costing 50,000 80,000 Produced Produced Sales (50,000 units $30) $1,500,000 $1,500,000 Variable cost of goods sold (50,000 units $12) 600,000 600,000 Variable selling and administrative expenses (50,000 units $2) 100,000 100,000 Contribution margin 800,000 800,000 Fixed manufacturing overhead 400,000 400,000 Fixed selling and administrative expenses 40,000 40,000 Net income $ 360,000 $ 360,000
*PROBLEM 6-8A (Continued) (c) If the company produces 80,000 units, but only sells 50,000 units, then 30,000 units will remain in ending inventory. Under absorption costing these 30,000 units will each include $5 of fixed manufacturing overhead a total of $150,000. However, under variable costing, fixed manufacturing overhead is expensed when incurred. This accounts for the $150,000 difference ($510,000 $360,000) in net income. This is summarized as: Net income under absorption costing $510,000 Less: Fixed manufacturing overhead included in ending inventory (30,000 units $5) 150,000 Net income under variable costing $360,000 (d) Variable costing has a number of advantages over absorption costing for decision making and evaluation purposes. (1) The use of variable costing is consistent with cost-volume-profit and incremental analysis. (2) Net income computed under variable costing is unaffected by changes in production levels. Note that in our example, under variable costing the company s net income is $360,000 no matter what the level of production is. (3) Net income computed under variable costing is closely tied to changes in sales levels (not production levels), and therefore provides a more realistic assessment of the company s success or failure during a period. (4) The presentation of fixed and variable cost components on the face of the variable costing income statement makes it easier to identify these costs and understand their effect on the business. Under absorption costing the allocation of fixed costs to inventory makes it difficult to evaluate the impact of fixed costs on the company s results.