Solutions to Ch 2

7/31/2019 Solutions to Ch 2

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Copyright 2007 Pearson Education Canada 16

CHAPTER 2

Q2-1 This is a good characterization of cost behaviour. Classifying cost drivers willidentify activities that affect costs, and the relationship between a cost driver and costsspecifies how the cost driver influences costs.

Q2-2 Examples of variable costs are the costs of merchandise, materials, parts,supplies, commissions, and many types of labour. Examples of fixed costs are realestate taxes, real estate insurance, many executive salaries, and space rentals.

Q2-3 Yes. Fixed costs, by definition, do not vary in total as volume changes.However, if fixed costs are allocated or spread over volume on a per-unit-of-volumebasis, they decline per unit as volume increases.

Q2-4 Yes. Fixed costs per unit change as the volume of activity changes. Therefore,for fixed cost per unit to be meaningful, you must identify an appropriate volume level. Incontrast, total fixed costs are independent of volume level.

Q2-5 No. Cost behaviour is much more complex than a simple division into fixed orvariable. For example, some costs are not linear, and some have more than one costdriver. Division of costs into fixed and variable categories is a useful simplification, but itis not a complete description of cost behaviour in most situations.

Q2-6 No. The relevant range pertains to both variable and fixed costs. Outside arelevant range, some variable costs, such as fuel consumed, may behave differently perunit of activity volume.

Q2-7 Two simplifying assumptions are linearity of costs and only one measure ofvolume.

Q2-8 The same cost may be regarded as variable in one decision situation and fixedin a second decision situation. For example, fuel costs are fixed with respect to theaddition of one more passenger on a bus because the added passenger has almost noeffect on total fuel costs. In contrast, total fuel costs are variable in relation to thedecision of whether to add one more kilometre to a city bus route.

Q2-9 No. Contribution margin is the excess of sales over all variable costs, not fixedcosts. It may be expressed as a total, as a ratio, as a percentage, or per unit.

Q2-10 A "break-even analysis" does not include a provision for minimum acceptable

profit required before deciding in favour of the project being analyzed. The break-evenpoint is often only incidental in studies of cost-volume relationships.


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Q2-11 No. break-even points can vary greatly within an industry. For example, RollsRoyce has a much lower break-even volume than does Chrysler (or Ford, Toyota, andother high-volume auto producers).

Q2-12 No. The CVP technique you choose is a matter of personal preference orconvenience. The equation technique is the most general, but it may not be the easiest

to apply. All three techniques yield the same results.

Q2-13 Three ways of lowering a break-even point, holding other factors constant, are:decrease total fixed costs; increase selling prices; and decrease unit variable costs.

Q2-14 No. In addition to being quicker, incremental analysis is simpler. This isimportant because it keeps the analysis from being cluttered by irrelevant andpotentially confusing data.

Q2-15 Operating leverage is a firm's ratio of fixed and variable costs. A highlyleveraged company has relatively high fixed costs and low variable costs. Such a firm is

risky because small changes in volume lead to large changes in income.

Q2-16 No. In retailing, the contribution margin is likely to be smaller than the grossmargin. For instance, sales commissions are deducted in computing the contributionmargin but not the gross margin.

Q2-17 No. CVP relationships pertain to both profit-seeking and nonprofit organizations.In particular, managers of not-for-profit organizations must deal with tradeoffs betweenvariable and fixed costs. To many government department managers, lump-sum budgetappropriations are regarded as the available revenues.

Q2-18 Contribution margin could be lower because of a decline in the proportion of theproduct bearing the higher unit contribution margin (change in product mix).

Q2-19Target income before

income taxes =Target after-tax net income

1 - tax rate

Q2-20

Change innet income = (

Change in volumein units ) x (

Contribution marginper unit ) x (1 - tax rate)


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P2-1 (5 min.)

No. The individual does not have a solid understanding of cost classification. Definitionsof variable and fixed cost behaviour are based on total cost behaviour, not unit costbehaviour.

P2-2 (5-10 min.)

1. Contribution margin = $900,000 - $ 500,000 = $ 400,000Net income = $400,000 - $ 350,000 = $ 50,000

2. Variable expenses = $800,000 - $ 350,000 = $ 450,000Fixed expenses = $350,000 - $ 80,000 = $ 270,000

3. Sales = $600,000 + $ 340,000 = $ 940,000Net income = $340,000 - $ 250,000 = $ 90,000

P2-3 (10-20 min.)

Leta = selling price per unitb = variable cost per unitc = total units soldd = contribution margine = fixed costsf = net income

1. d = c(a - b)$720,000 = 120,000($30 - b)

b = $24f = d - e= $720,000 - $640,000 = $80,000

2. d = c(a - b)= 100,000($10 - $6) = $400,000

f = d - e= $400,000 - $320,000 = $80,000

3. c = d (a - b)= $100,000 $5 = 20,000 units

e = d - f

= $100,000 - $15,000 = $85,000

4. d = c(a - b)= 70,000($30 - $20)= $700,000

e = d - f= $700,000 - $12,000 = $688,000


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5. d = c(a - b)$160,000 = 80,000(a - $9)

a = $11f = d - e

= $160,000 - $120,000 = $40,000

P2-4 (10 min.)

1. Let TR = total revenueTR - 0.20(TR) - $40,000,000 = 0

0.80(TR) = $40,000,000TR = $50,000,000

2. Daily revenue per patient = $50,000,000 40,000 = $1,250. This may appearhigh, but it includes the room charge plus additional charges for drugs, x-rays,and so forth.

P2-5 (15 min.)

1. 100% Full 50% Full

Room revenue @ $50 $3,650,000 a $1,825,000 bVariable costs @ $10 730,000 c 365,000 dContribution margin 2,920,000 1,460,000Fixed costs 1,600,000 1,600,000Net income (loss) $1,320,000 $ (140,000)

a 200 x 365 = 173,000 rooms per year

73,000 x $50 = $3,650,000b 50% of $3,650,000 = $1,825,000

c 200 x 365 = 73,000 rooms per year73,000 x $10 = $730,000

d 50% x $730,000 = $365,000

2. Let N = number of rooms$50N - $10N - $1,600,000 = 0

N = $1,600,000 $40 = 40,000 roomsPercentage occupancy = 40,000 73,000 = 54.8%


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P2-6 (15-20 min.)

1. Let N = number of rooms$65N - $15N - $350,000 = 0

N = $350,000 $50N = 7,000 per month or 233 per day

2. $65N - $15N - $350,000 = $120,000N = $470,000 $50N = 9,400

3. Let P = room rate per day; 30 = days in the month; 400 = total rooms in hotel

Other contribution margin = $70,000 + $40,000 + $32,400 + $30,000= $172,400

[0.80(400)x30xP] + $172,400 - [0.80(400)x30x$15]

- $350,000 = $120,0009,600P + $172,400 - $144,000 - $350,000 = $120,0009,600P = $421,600

P = $43.92

The latter answer indicates how hotels frequently may be inclined to reduceroom rates if they can generate contribution margins from other hotel activities,such as conventions.

P2-7 (15-20 min.)

1. Let R = litres of raspberries and 2R = litres of strawberriessales - variable expenses - fixed expenses = zero net income$1.00(2R) + $1.35(R) - $0.65(2R) - $0.85(R) - $14,400 = 0$2.00R + $1.35R - $1.30R - $0.85R -$14,400 = 0$1.20R - $14,400 = 0R = 12,000 litres of raspberries

2R = 24,000 litres of strawberries

2. Let S = litres of strawberries($1.00 - $0.65) x S - $14,400 = 0$0.35S - $14,400 = 0S = 41,143 litres of strawberries


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3. Let R = litres of raspberries($1.35 - $0.85) x R - $14,400 = 0$0.50R - $14,400 = 0R = 28,800 litres of raspberries

P2-8 (10 min.)

The following format is only one of many ways to present a solution. This situation isreally a demonstration of sensitivity analysis, whereby a basic solution is tested to seehow much it is affected by changes in critical factors. Much discussion can ensue,particularly about the final three changes.

The basic contribution margin per revenue kilometre is $1.50 - $1.30 = $0.20

(1) (2) (3) (4) (5)(1) x (2) (3) - (4)

Revenue Contribution Total

Kilometres Margin Per Contribution Fixed NetSold Revenue Kilometre Margin Expenses Income

1. 800,000 $0.20 $160,000 $120,000 $40,000

2. (a) 880,000 0.20 176,000 120,000 56,000(b) 800,000 0.35 280,000 120,000 160,000(c) 800,000 0.07 56,000 120,000 (64,000)(d) 800,000 0.20 160,000 132,000 28,000(e) 840,000 0.17 142,800 120,000 22,800(f) 720,000 0.275 198,000 120,000 78,000(g) 840,000 0.20 168,000 132,000 36,000

P2-9 (15-25 min.)

1. 176 x ($30 - $10) - $2,400 = $3,520 - $2,400 = $1,120

2. a. 198 x ($30 - $10) - $2,400 = $3,960 - $2,400 = $1,560or (22 x $20) + $1,120 = $440 + $1,120 = $1,560

b. 176 x ($30 - $11) - $2,400 = $3,344 - $2,400 = $944or $1,120 - ($1 x 176) = $944

c. $1,120 - $200 = $920176 x ($30 - $10) - ($2,400 + $200) = $920


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d. [(9.5 x 22) x ($30 - $10)] - ($2,400 + $300) = $4,180 - $2,700 = $1,480

e. [(7 x 22) x ($33 - $10)] - $2,400 = $3,542 - $2,400 = $1,142

P2-10 (15 min.)

Several variations of the following general approach are possible:

Sales - Variable expenses - Fixed expenses =

Target after-taxnet income1 - tax rate

S - 0.7S - $440,000 =

$42,000

(1 0.4)

0.3S = $440,000 + $70,000

S = $510,000 0.3 = $1,700,000

Check: Sales $1,700,000Variable expenses (70%) 1,190,000Contribution margin 510,000Fixed expenses 440,000Income before taxes $ 70,000Income taxes 28,000Net income $ 42,000

P2-11 (10-15 min.)

The answer is $1,320,000.


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P2-12 (15-20 min.)

Film Refreshments Total1. Revenue from admissions $2,250 $270 b $2,520

Variable costs 1,125 a 162 c 1,287Contribution margin $1,125 $108 $1,233Fixed costs:

Auditorium rental $330Labour 400 730

Operating income $ 503

a 0.50 x $2,250 = $1,125b 0.12 x $2,250 = $270c 0.60 x $270 = $162

Some labour might be exclusively devoted to refreshments. Labour might beallocated, but such a discussion is not the major point of this chapter.

Film Refreshments Total2. Revenue from admissions $1,350 $162 b $1,512

Variable costs 750 a 97 c 847Contribution margin $ 600 $ 65 $ 665Fixed costs:

Auditorium rental $330Labour 400 730

Operating income (loss) $ (65)

a Minimum is $750

b 0.12 x $1,350 = $162c 0.60 x $162 = $97


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3. The risk is shifted completely to the movie producer, whereas a great deal of therisk is borne ordinarily by the theatre owner. The owner is assured of a specifiedincome; the producer then reaps the rewards or losses. On the other hand, theowner forgoes the chance of a large income should the movie be very popular.

P2-13 (20-30 min.)

Many shortcuts are available, but this solution uses the equation technique.

1. Let N = meals soldSales - Variable expenses - Fixed expenses = Profit before taxes$18N - $9.60N - $21,000 = $8,400

N = $29,400 $8.40N = 3,500

2. $18N - $9.60N - $21,000 = $8,400 = 0N = $21,000 $8.40

N = 2,500

3. $22N - $11.50N - $29,400 = $8,400N = $37,800 $10.50N = 3,600

4. Profit = $22(3,150)a - $11.50(3,150) - $29,400Profit = $3,675

a 90% x 3,500 = 3,150

5. Profit = $22(3,450) - $11.50(3,450) - ($29,400 + $2,000)Profit = $36,225 - $31,400Profit = $4,825, an increase of $1,150.

A shortcut, incremental approach follows:

Increase in contribution margin, 300 x $10.50 = $3,150Increase in fixed costs 2,000Increase in profit $1,150

P2-14 (25-30 min.)

This problem raises more issues than are apparent at first glance. For instance, unlessAndre is very wealthy and generous, he probably would not regard the five barbers asfixed costs over the entire possible range of volume. In short, if business declinesprecipitously, barbers would be discharged or laid off. Note how the later requirementsdemonstrate the effects of various mixes of variable and fixed costs on risks.


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1. Selling Price - Unit Variable Costs = Contribution Margin$12 - 0 = $12

2. Fixed Expenses (annual)Barbers' salaries (5 x $9.90 x 40 x 50) $ 99,000Rent and other fixed expenses (12 x $1,750) 21,000

$120,000

B.E. Point =Total Fixed ExpensesContribution Margin =

$120,000

$12= 10,000 haircuts

3. Two valid approaches:(a) Revenue (20,000 x $12) $240,000

Fixed expenses 120,000Operating income $ 120,000

(b) Haircuts in excess of break-even point:20,000 - 10,000 = 10,000 haircuts

10,000 haircuts @ $12 = $120,000

4. Even though fixed costs decline, the break-even point rises:Contribution margin per haircut = $12 - $6 = $6Fixed costs = (5 x $4 x 40 x 50) + (12 x $1,750) = $61,000

Break-even point =$61,000

$6.00= 10,167 haircuts

5. Contribution margin = $12.00 - $7.00 = $5.00Fixed costs = $21,000 given

Break-even point =

$21,000

$5.00 = 4,200 haircuts

6. Revenue (20,000 x $12.00) $240,000Variable expenses (20,000 x $7.00) 140,000Contribution margin $100,000Fixed expenses 21,000Operating income $ 79,000

Thus, if volume is 20,000 haircuts, the new arrangement would increase thebarbers' compensation from $99,000 to $140,000 and decrease operatingincome from $120,000 to $79,000. Note the risk-sharing here of the sales

commission plan. Generally, the lower the fixed costs, the lower the risks, butthe lower the rewards. If the volume declines markedly, Andre would still havean operating income as long as the total volume exceeds 4,200 haircuts.However, if volume soars to 20,000, Andres operating income would be lessthan that of the hourly wage plan.


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7. Let X = rate of commission20,000($12) - $120,000 = 20,000($12) - 20,000($12)X - $21,000

$240,000 - $120,000 = $240,000 - $240,000X - $21,000$240,000X = $120,000 - $21,000$240,000X = $99,000

X =

$99,000

$240,000 = 41.25%,

or 41.25% x $12 = $4.95 per haircutProof:

Contribution margin: $12.00 - $4.95 = $7.05Operating income: (20,000 x $7.05) - $21,000 = $120,000

P2-15 (15-25 min.)

1. Average revenue per person $4.00 + 3($1.50) = $8.50Total revenue, 200 @ $8.50 = $1,700Rent 800

Total available for prizesand operating income $ 900

The church could award $900 and break even.

2. Number of persons 100 200 300Total revenue @ $8.50 $ 850 $1,700 $2,550Fixed costs

Rent $800Prizes 900 1,700 1,700 1,700

Operating income (loss) $(850) $ 0 $ 850

Note how "leverage" works. Leverage means having relatively high fixed costs.In this case, there are no variable costs. Therefore, the revenue is the same asthe contribution margin. As volume departs from the break-even point, operatingincome is affected at a significant rate of $8.50 per person.


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3. Number of persons 100 200 300Revenue $ 850 $1,700 $2,550Variable costs (2 x # of persons) 200 400 600Contribution margin $ 650 $1,300 $1,950Fixed costs:

Rent $400

Prizes 900 1,300 1,300 1,300Operating income $ (650) $ 0 $ 650

Note how the risk is lower because of less leverage. Fixed costs are less, andsome of the risk has been shifted to the hotel. Note too that lower risk bringslower rewards and lower punishments. The income and losses are $650 insteadof the $850 shown in part (2).

P2-16 (15 min.)

1. Let X = amount of additional fixed costs for advertising

(1,100,000 x 13) + 300,000 - 0.30(1,100,000 x 13) (8,000,000 + X)14,300,000 + 300,000 - 4,290,000 - 8,000,000 X = 0X = 14,600,000 - 12,290,000X = 2,310,000

2. Let Y = number of seats sold13Y + 300,000 - 0.30(13)Y - 9,000,000 = 500,000

9.10Y = 9,200,000Y = 1,010,989 seats

P2-17 (15-25 min.)

1. Let N = number of hamburgers per month$1.10N = $0.70N + $1,560$0.40N = $1,560

N = 3,900 per month, or 3,900 30 = 130 per day

2. Multiply the answers in (1) by $1.10

3,900 x $1.10 = $4,290 per month130 x $1.10 = $143 per day


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3. Hamburgers per month = (3,600 2) = 1,800Revenue per month = 1,800 x $1.10 = $1,980Variable expenses, 1,800 x $0.70 1,260Contribution margin $ 720Fixed expenses 1,560Operating income (loss) $ (840)

4. Contribution margin on extra beers:

Per day, 60 x $0.60 = $36Per month, 30 x 36 = $1,080

Income would increase by $1,080, which more than offsets the $630 loss on thehamburger operation, making the net increase in operating income$1,080 - $840 = $240.

5. Operating loss on hamburgers $(840)

Desired contribution margin on extra beers 840Overall effect on operating income $ 0

Desired number of extra beers to provide overall effect on operating income ofzero:

Per month = $840 0.60 = 1,400 beersPer day = 1,400 30 = 46.7 beers

Or, desired contribution margin per day is $840 30 = $28Daily number of beers = $28 $0.60 = 46.7

Therefore, if Andy believed that the extra beers sold amounted to 47 dailyinstead of 60, the hamburger operation would have provided an overall effect onoperating income of zero.


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P2-18 (40 min.)

1. Let N = the number of people to be admitted for the season

Revenue:Rights for concession $50,000

Admissions $1.00NPercentage of bets 10% of $27N = $2.70N

Total revenue = $50,000 + $3.70N

Expense:Fixed costs:

Wages of cashiers and ticket takers $ 160,000Commissioner's salary 20,000Maintenance 20,000Utilities 30,000

Other expense 90,000Purses 810,000Total fixed costs $1,130,000

Variable costs:Parking is $6.00 per car or $2.00 per person(3 persons attended per car, so $6.00 3 = $2.00)

Number of attendees arriving by car = N/2 or 0.5NTotal variable costs: $2.00 x 0.5N = $1.00N

Total expense = $1,130,000 + $1.00N

(a) Break-even Point:$50,000 + $3.70N - $1,130,000 - $1.00N = 0

$2.70N = $1,080,000N = 400,000 people

(b) $1,130,000

(c) Desired Operating Profit $270,000:$50,000 + $3.70N - $1,130,000 - $1.00N = $270,000

$2.70N = $1,350,000N = 500,000 people


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2. Previous level of attendance 600,000 people20% increase in attendance 720,000 peopleTotal bets: 720,000 x $27 $19,440,000

Revenue:Concession $ 50,000Admission None

Percentage of bets (10% x $19,440,000) 1,944,000Total revenue $1,994,000

Expense:Fixed $1,130,000Variable ($1.00 x 720,000) 720,000 $1,850,000

Operating profit $ 144,000

3. The purses are doubled:Previous fixed expense $1,130,000Additional purse money 810,000

New fixed expense $1,940,000

Variable expense $1.00 per personRevenue $50,000 + $3.70N

$50,000 + $3.70N - $1,940,000 - $1.00N = 0$2.70N = $1,890,000

N = 700,000 people

P2-19 (20-25 min.)

1. Let N = number of unitsSales = Fixed expenses + Variable expenses + Net income

$1.00N = $3,000 + $0.80 N + 0$0.20N = $3,000

N = 15,000 unitsor,

Let S = sales in dollarsS = $3,000 + 0.80 S + 0

0.20 S = $3,000S = $15,000

Alternatively, the 15,000 units may be multiplied by the $1.00 to obtain $15,000.


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In formula form:

In units

Fixed costs + Net incomeContribution margin per unit =

($3,000 0)

$0.20

+= 15,000 units

In dollars

Fixed costs + Net incomeContribution margin percent =

($3,000 0)

$0.20

+= $15,000

2. The quick way: (18,000 - 15,000) x $0.20 = $600

Compare income statements:

Break-evenPoint Increment Total

Volume in units 15,000 3,000 18,000

Sales $15,000 $3,000 $18,000

Deduct expenses:

Variable 12,000 2,400 14,400

Fixed 3,000 3,000

Total expenses $15,000 $2,400 $17,400

Effect on net income $ 0 $ 600 $ 600

3. Total fixed expenses would be $3,000 + $576 = $3,576

($3,576)

$0.20= 17,880 units;

($3,576)

0.20= $17,880 sales

or 17,880 x $1.00 = $17,880 sales

4. New contribution margin is $0.19 ($0.20 - $0.01) per unit; $3,000 $0.19 =15,789 units

15,789 units x $1.00 = $15,789 in sales

5. The quick way: (18,000 - 15,000) x $0.18 = $540. On a graph, the slope of thetotal cost line would have a kink upward, beginning at the break-even point.


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P2-20 (30-40 min.)

1. Fixed costs:Amortization ($13,500 - $6,000) 3 = $2,500Insurance 700Total fixed costs $3,200

Variable costs:Gas, $0.60 6 kilometres $0.10Oil, $30.00 3,000 kilometres 0.01Maintenance, $240 6,000 kilometres 0.04Variable cost per kilometre $0.15

Let N = Number of kilometres to break evenRevenue - Variable costs - Fixed costs = 0$0.23N - $3,200 - $0.15N = 0N = $3,200 $0.08 = 40,000 kilometres

2. An "equitable" rate might be based on the actual number of business-related

kilometres expected. The days not on the road are:Days

Weekends, 52 x 2 104Vacation 10Holidays 6Home office 15Not on the road 135On the road, 365 - 135 = 230Kilometres, 230 x 120 = 27,600

Let X = Reimbursement per kilometre to break even27,600X = $3,200 - 27,600($0.15)27,600X - $3,200 - $4,140 = 0

X = $7,340 27,600 = $0.266

Therefore, a rate of $0.27 seems more equitable than $0.23.

P2-21 (15-20 min.)

Note in requirements 2 and 3 how the percentage declines exceed the 15% budgetreduction.

1. Let N = number of personsRevenue - Variable expenses - Fixed expenses = 0$900,000 - $5,000N - $290,000 = 0

5,000N = $900,000 - $290,000N = $610,000 $5,000N = 122


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2. Revenue is now 0.85($900,000) = $765,000$765,000 - $5,000y - $290,000 = 0

$5,000y = $765,000 - $290,000y = $475,000 $5,000y = 95

Percentage drop: (122 - 95) 122 = 22.1%

3. Let y = supplement per person$765,000 - 122y - $290,000 = 0

122y = $765,000 - $290,000y = $475,000 122y = $3,893

Percentage drop: ($5,000 - $3,893) $5,000 = 22.1%

Regarding requirements 2 and 3, note that the cut in service can be measured by aformula:

% cut in service =% budget change% variable cost

The variable cost ratio is $610,000 $900,000 = 67.8%

% cut in service =15%67.8% = 22.1%

P2-22 (10-15 min.) Amounts are in millions.

Net sales (1.10 x $24,002) $26,402Variable costs:

Cost of goods sold (1.10 x $20,442) 22,486Contribution margin 3,916Fixed costs

Selling, administrative, and general expenses $2,265

Interest expense 277Total fixed costs 2,542Operating income $1,374

The percentage increase in operating income would be ($1,374 $1,018) - 1 = 0.35 or35%, compared with a 10% increase in sales. The contribution margin would increaseby 10% or 0.10 x ($24,002 - $20,442) = $356 million. Because fixed costs would notchange (assuming the new volume is within the relevant range), operating incomewould also increase by $356 million, from $1,018 million to $1,374 million. If all costshad been variable, costs would have increased by an additional 0.10 x $2,542 =$254 million, making operating income $1,374 - $254 = $1,120 million, a 10% increaseover the 1997 operating income of $1,018 million. Because of the existence of fixed

costs, the percentage increase in operating income will exceed the percentage increasein sales.


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P2-23 (15-20 min.) Answers are in millions.

1. Sales $15,968Variable costs:

Variable costs of goods sold ($8,326 - $1,800) $6,526

Variable other operating expenses ($6,086 - $4,000) 2,086 8,612Contribution margin $ 7,356Contribution margin percentage = $7,356 $15,968 = 46.07%

The contribution margin is sales less all variable costs, while gross margin issales less cost of goods sold. The variable costs will include part of the costs ofgoods sold and also part of the other operating costs. Note that contributionmargin can be either larger than or smaller than the gross margin. If most of thecost of goods sold and a good portion of the other operating costs are variable,then variable costs may exceed the cost of goods sold, and the contributionmargin will be smaller than the gross margin, as is the case for Photography,Inc. However, if a large portion of both the cost of goods sold and the other

expenses are fixed, cost of goods sold may exceed the variable cost, resulting inthe contribution margin exceeding the gross margin.

2. Predicted sales increase = $15,968 x 0.10 = $1,596.8Additional contribution margin = $1,596.8 x 0.4607 = $735.6Fixed costs do not changePredicted 2007 operating income = $1,556 + $735.6 = $2,291.6Percentage increase in operating income = $735.6 $1,556 = 47.28%

Original

10%Increasein sales

andvariablecosts

2006 2007

Sales $15,968 $17,564.8

Variable Costs:

Variable cost of goods sold 6,526 7,178.6Variable other operatingexpenses 2,086 2,294.6

Total Variable costs 8,612 9,473.2

Contribution Margin 7,356 8,091.6

Fixed Costs:

Fixed cost of goods sold 1,800 1,800Fixed other operating expenses 4,000 4,000

Total fixed costs 5,800 5,800

Operating Income $1,556 $2,291.63. Assumptions include:

Expenses can be classified into variable and fixed categories thatcompletely describe their behaviour within the relevant range.


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Costs and revenues are linear within the relevant range. 2007 volume is within the relevant range. Efficiency and productivity are unchanged. Sales mix is unchanged. Changes in inventory levels are insignificant.

P2-24 (20-30 min.)

Variable costs per box are:Economy ($0.14 + $0.09 + $0.22) = $0.45Regular ($0.14 + $0.09 + $0.14) = $0.37Super ($0.14 + $0.09 + $0.05) = $0.28

1. Let N = volume level in boxes that would earn same profit$8,000 + $0.45N = $11,200 + $0.37N

$0.08N = $3,200

N = 40,000 boxes

2. As volume increases, the more expensive models would generate more profits.Compare the regular and super models:

Let N = volume level in boxes that would earn same profit$20,200 + $0.28N = $11,200 + 0.37N

$0.09N = $9,000N = 100,000 boxes

Therefore, the decision rule is as shown below.

Anticipated AnnualSales Between Use Model

0 - 40,000 Economy40,000 - 100,000 Regular100,000 and above Super

The decision rule places volume well within the capacity of each model.

3. No, management cannot use theatre capacity or average boxes sold becausethe number of seats per theatre does not indicate the number of patronsattending nor the popcorn buying habits in different geographic locations. Each

theatre may have a different "boxes sold per seat" average with significantvariations. The decision rule does not take into account variations in demandthat could affect model choice.


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P2-25 (20-25 min.)

1. Net income = 250,000($3) + 125,000($4) - $1,320,000= $750,000 + $500,000 - $1,320,000= $(70,000)

2. Let V = number of units of veal to break even (V)2V = number of units of chicken to break even (C)

Total contribution margin - fixed expenses = zero net income

$4V + $3(2V) - $1,320,000 = 0$10V = $1,320,000

V = 132,0002V = 264,000 = C

The break-even point is 132,000 units of veal plus 264,000 units of chicken, a

grand total of 396,000 units.

3. If veal, break-even would be $1,320,000 $4 = 330,000 units.If chicken, break-even would be $1,320,000 $3 = 440,000 units.

Note that as the mixes change from 1 veal to 2 chicken, to 0 chicken to 1 veal,and to 1 chicken to 0 veal, the break-even point changes from 396,000 to330,000 to 440,000.

4. Net income (loss) = 297,000($3) + 99,000($4) - $1,320,000= $891,000 + $396,000 - $1,320,000= ($33,000)

Let V = number of units of veal to break even (V)3V = number of units of chicken to break even (C)

Total contribution margin - fixed expenses = zero net income$4V + $3(3V) - $1,320,000 = 0

$13V = $1,320,000V = 101,538

3V = 304,614 = C

The major lesson of this problem is that changes in sales mix change break-

even points and net incomes. The break-even point is 101,538 units of veal plus304,614 units of chicken, a total of 406,152 units. Thus, the unfavourablechange in mix results in a net loss of $33,000 at the old total break-even level of396,000 units. In short, the break-even level is higher because the sales mix isless profitable when chicken represents a higher proportion of sales. In thisexample, the budgeted and actual total sales in number of units were identical,but the proportion of product having the higher contribution margin declined.


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P2-26 (15-25 min.)

1. Let N = number of rooms

$105N - $25N - $10,000,000 =$720,000

1 0.40

$80N - $10,000,000 = $1,200,000$80N = $11,200,000

N = 140,000 rooms

$80N - $10,000,000 =$360,000

1 0.40

$80N = $10,600,000N = 132,500 rooms

2. $105N - $25N - $10,000,000 = 0$80N = $10,000,000

N = 125,000 rooms

Number of rooms at 100% capacity = 600 x 365 = 219,000Percentage occupancy to break even = 125,000 219,000 = 57%

3. Using the shortcut approach described in the chapter appendix:

Change innet income = (

Change in volumein units ) x (Contribution marginin units ) x (1 - tax rate)

= 15,000 x $80 x (1 - 0.40)= 15,000 x $48= $720,000, a large increase because of a high contribution

margin per dollar of revenue.

Note that a 10% increase in rooms sold increased net income by$720,000 $1,200,000 or 60%.

Rooms sold 150,000 165,000Contribution margin @ $80 $12,000,000 $13,200,000Fixed expenses 10,000,000 10,000,000Income before taxes 2,000,000 3,200,000Income taxes @ 40% 800,000 1,280,000

Net income $ 1,200,000 $ 1,920,000

Increase in net income $720,000Percentage increase 60%


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P2-27 (25-35 min.)

1.$12,000,000

$800= 15,000 patient-days

2. Variable costs = $3,150,00015,000

= $210 per patient-day

Contribution margin = $800 - $210 = $590 per patient-day

To recoup the specified fixed expenses:$5,900,000 $590 = 10,000 patient-days

3. The fixed cost levels differ as the relevant range changes:

Non-Nursing Nursing Total

Patient-Days Fixed Expenses Fixed Expenses Fixed Expenses10,000-12,000 $5,900,000 $1,350,000(a) $7,250,00012,001-16,000 5,900,000 1,575,000(b) 7,475,000

(a) $45,000 x 30 = $1,350,000(b) $45,000 x 35 = $1,575,000

To break even on a lower level of fixed costs:$7,250,000 $590 = 12,288 patient-days

This answer exceeds the lower-level maximum; therefore, this answer isinfeasible. The department must operate at a $7,475,000 level of fixed costs to

break even: $7,475,000 $590 = 12,669 patient-days.

4. The nursing costs would have been variable instead of fixed. The contributionmargin per patient-day would have been $800 - $210 - $200 = $390. The break-even point would be higher: $5,900,000 390 = 15,128 patient-days.

Some instructors might want to point out that hospitals have been under severepressures to reduce costs. More than ever, nursing costs are controlled asvariable rather than fixed costs. For example, more part-time help is used, andnurses may be used for full shifts but only as volume requires.


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P2-28 (25-30 min.)

This case is based on real data that has been simplified so that the numbers are easierto handle.

1. Daily break-even volume is 85 dinners and 170 lunches:

First, compute contribution margins on lunches and dinners:Variable cost percentage = ($1,246,500 + $222,380) $2,098,400

= 70%

Contribution margin percentage = 1 - variable cost percentage= 1 - 70% = 30%

Lunch contribution margin = 0.30 x $20 = $6Dinner contribution margin = 0.30 x $40 = $12

Annual fixed cost is $170,700 + $451,500 = $622,200

Let X = number of dinners and 2X = number of lunches

12(X) + 6(2X) - $622,200 = 024(X) = 622,200X = 25,925 dinners annually to break even2X = 51,850 lunches annually to break even

On a daily basis:Dinners to break even = 25,925 305 = 85 dinners daily

Lunches to break even = 85 x 2 = 170 lunches daily or 51,850 305 = 170lunches daily.

To determine the actual volume, let Y be a combination of 1 dinner and 2lunches. The price of Y is $40 + (2 x $20) = $80, and total volume in units of Y is$2,098,400 $80 = 26,230 and daily volume is 26,230 305 = 86. Therefore,86 dinners and 2 x 86 = 172 lunches were served on an average day. This is 1dinner and 2 lunches above the break-even volume.

2. The extra annual contribution margin from the 3 dinners and 6 lunches is:

3 x $40 x 0.30 x 305 = $10,980

+ 6 x $20 x 0.30 x 305 = 10,980Total $21,960


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The added contribution margin is greater than the $15,000 advertisingexpenditure. Therefore, the advertising expenditure would be warranted. Itwould increase operating income by $21,960 - $15,000 = $6,960.

3. Let Y again be a combination of 1 dinner and 2 lunches, priced at $80. Variablecosts are 0.70 x $80 = $56, of which $56 x 0.25 = $14 is food cost. Cutting food

costs by 20% reduces variable costs by 0.20 x $14 = $2.80, making thevariable cost of Y $56 - $2.80 = $53.20 and the contribution margin $80 -$53.20 = $26.80. (This could also be determined by adding the $2.80 saving infood cost directly to the old contribution margin of $24.) The required annualvolume in Y needed to keep operating income at $7,320 is:

$26.80 (Y) - $622,200 = $7,320$26.80 (Y) = $629,520Y = 23,490Therefore, daily volume = 23,490 305 = 77 (rounded)

If volume drops no more than 86 - 77 = 9 dinners and 172 - 154 = 18 lunches,using the less costly food is more profitable. However, there are manysubjective factors to be considered. Volume may not fall in the short run, butthe decline in quality may eventually affect repeat business and cause a long-run decline. Much may depend on the skill of the chef. If the quality difference isnot readily noticeable, so that volume falls less than, say, 10%, saving moneyon the purchases of food may be desirable.

P2-29 (10-15 min.)

1. Total variable cost = $10 x 75,000 = $750,000Total fixed cost = $1,000,000 - $12,000 - $750,000 = $238,000

2. (a) Operating income = $1,700,000 - $10 x 92,000 - $238,000= $1,700,000 - $1,158,000= $542,000

(b) Operating income = $1,870,000 - $10 x 101,200 - $238,000= $1,870,000 - $1,250,000= $620,000

(c) Operating income = $1,530,000 - $10 x 82,800 - $238,000= $1,530,000 - $1,066,000

= $464,000


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3. There are two reasons for the increased operating income: increased sales priceand increased volume. In 1993 the sales price was $1,000,000 75,000 or$13.33, creating a unit contribution margin of $13.33 - $10.00 or $3.33. In 1994the sales price is predicted to be $1,700,000 92,000 or $18.48, creating a unitcontribution margin of $8.48. Even with no increase in sales volume, the extracontribution margin would increase operating income by ($8.48 - $3.33) x 75,000

= $386,250. Further, each of the 17,000 additional units to be sold in 1994 wouldhave a unit contribution margin of $8.48, creating additional operating income of$8.48 x 17,000 = $144,160. The total extra operating income in 1994 would be$386,250 + $144,160 = $530,410, which is within a rounding error of the$530,000 by which predicted 1994 operating income exceeds 1993 operatingincome.

P2-30 (15-20 min.)

1. Old: (Contribution margin x 600,000) - $585,000 = Budgeted profit[($3.10 - $2.10) x 600,000] - $585,000 = $15,000

New: (Contribution margin x 600,000) - $1,140,000 = Budgeted profit[($3.10 - 1.10) x 600,000] - $1,140,000 = $60,000

2. Old: $585,000 $1.00 = 585,000 unitsNew: $1,140,000 $2.00 = 570,000 units

3. A fall in volume will be more devastating under the new system because the highfixed costs will not be affected by the fall in volume:

Old: ($1.00 x 500,000) - $585,000 = $85,000 (a $85,000 loss)New: ($2.00 x 500,000) - $1,140,000 = $140,000 (a $140,000 loss)

The 100,000 unit fall in volume caused a $15,000 - (-$85,000) = $100,000decrease in profits under the old environment and a $60,000 - (-$140,000) =$200,000 decrease under the new environment.

4. Increases in volume create larger increases in profit in the new environment:

Old: ($1.00 x 700,000) - $585,000 = $115,000New: ($2.00 x 700,000) - $1,140,000 = $260,000

The 100,000 unit increase in volume caused a $115,000 - $15,000 = $100,000

increase in profit under the old environment and a $260,000 - $60,000 =$200,000 increase under the new environment.


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5. Changes in volume affect profits in the new environment (a high fixed cost, lowvariable cost environment) more than they affect profits in the old environment.Therefore, profits in the old environment are more stable and less risky. Thehigher risk new environment promises greater rewards when conditions arefavourable, but also leads to greater losses when conditions are unfavourable, amore risky situation.

P2-31 (20-30 min.)

1. 2006 revenue = 61,000 million x 0.681 x $0.1310 = $5,442 million2005 revenue = 61,000 million x 0.656 x $0.1251 = $5,006 million

2. a) $3,000 million ($0.1251 - $0.05) = 39,947 million revenue passenger miles39,947 61,000 = 65.5% load factor

b) $3,000 million ($0.1310 - $0.05) = 37,037 million revenue passenger miles37,037 61,000 = 60.7% load factor

3. $3,400 million ($0.13 - $0.05) = 42,500 million revenue passenger miles42,500 61,000 = 69.7% load factor

P2-32 (25 min.)

1. Break even = $950 million ($70 million - $45 million)= $950 million $25 million = 38 airplanes

Sales = $70 million x 38 = $2.660 billion

2. There are two efficient ways to compute the profit:

a) (42 - 38) x $25 million = $100 millionb) 42 x $25 million - $950 million = $100 million

3. Operating profit = 42 x ($70 million - $43 million) - $1,034 million= 42 x $27 million - $1,034 million = $100 million

Break even = $1,034 million ($70 million - $43 million)= $1,034 million $27 million = 38.3 airplanes

Although the change in cost structure does not change the operating profit at theprojected level of sales, the break-even point increases from 38 to 38.3

airplanes. The additional fixed costs add to the risk of not breaking even.However, it also adds to the potential rewards if sales exceed the projected levelof 42 airplanes.


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4. Break even = $950 million [$70 million - (1.1 x $45 million)]= $950 million $20.5 million= 46.3 airplanes

Notice the substantial increase in the break-even point with a 10% increase invariable costs. Boeing might want an escalation clause in its contracts so that the

price charged for airplanes increases with cost increases. They might want toenter into long-term contracts with suppliers to limit the possibilities for costincreases. Finally, they might want to undertake changes in their productionprocess to limit cost increases.

Solutions to Ch 2

Documents

Transcript of Solutions to Ch 2