CHAPTER 7Cost-Volume-Profit Analysis

SOLUTIONS TO EXERCISES

EXERCISE 7-24 (20 MINUTES)

1. Break-even point (in units) =

= = 10,000 pizzas

2. Contribution-margin ratio =

= = .4

3. Break-even point (in sales dollars) =

= = $100,000

4. Let X denote the sales volume of pizzas required to earn a target operating income of $80,000.

$10X – $6X – $40,000 = $80,000

$4X = $120,000

X = 30,000 pizzas

EXERCISE 7-25 (25 MINUTES)

1. Break-even point (in units) =

= = 4,000 components

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2. New break-even point (in units) =

= = 4,400 components

3. Sales revenue (5,000 $3,000) .................................................. $15,000,000Variable costs (5,000 $2,000)........................................................ 10,000,000Contribution margin........................................................................... 5,000,000Fixed costs......................................................................................... 4,000,000Operating income............................................................................... $ 1,000,000

4. New break-even point (in units) =

= 8,000 components

5. Analysis of price change decision:

Price$3,000 $2,500

Sales revenue: (5,000 $3,000).................................(6,200 $2,500).................................

Variable costs: (5,000 $2,000).................................(6,200 $2,000).................................

Contribution margin.....................................................Fixed expenses .............................................................Operating income (loss)...............................................

$15,000,000

10,000,000 5,000,000 4,000,000

$ 1,000,000

$15,500,000

12,400,000 3,100,000 4,000,000

($900,000 )

The price cut should not be made, since projected operating income will decline.

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EXERCISE 7-28 (25 MINUTES)

1. (a) Traditional income statement:

EUROPA PUBLICATIONS, INC.INCOME STATEMENT

FOR THE YEAR ENDED DECEMBER 31, 20XX

Sales .......................................................................... $2,200,000Less: Cost of goods sold.......................................... 1,500,000Gross margin................................................................ $ 700,000Less: Operating expenses:

Selling expenses............................................. $150,000Administrative expenses................................ 150,000 300,000

Operating income......................................................... $ 400,000

(b) Contribution income statement:

EUROPA PUBLICATIONS, INC.INCOME STATEMENT

FOR THE YEAR ENDED DECEMBER 31, 20XX

Sales .......................................................................... $2,200,000Less: Variable expenses:

Variable manufacturing.................................. $1,000,000Variable selling................................................ 100,000Variable administrative................................... 30,000 1,130,000

Contribution margin..................................................... $ 1,070,000Less: Fixed expenses:

Fixed manufacturing....................................... $ 500,000Fixed selling.................................................... 50,000Fixed administrative....................................... 120,000 670,000

Operating income......................................................... $ 400,000

2.

3.

= 10% 2.6

= 26%

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.

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EXERCISE 7-29 (30 MINUTES)

1.

Bicycle TypeSales Price

Unit Variable Cost

Unit Contribution Margin

High-quality $500 $300 ($275 + $25) $200Medium-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

4.

Bicycle TypeBreak-Even

Sales Volume Sales PriceSales

RevenueHigh-quality bicycles 100 (400

.25)$500 $ 50,000

Medium-quality bicycles 300 (400 .75)

300 90,000

Total $140,000

5. Target operating income:

This means that the shop will need to sell the following volume of each type of bicycle to earn the target operating income:

High-quality............................................................................ 175 (700 .25)Medium-quality....................................................................... 525 (700 .75)

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EXERCISE 7-33 (20 MINUTES)

1.

2.

3. Service revenue required to earn target after-tax income of $48,000

4. A change in the tax rate will have no effect on the firm's break-even point. At the break-even point, the firm has no profit and does not have to pay any income taxes.

SOLUTIONS TO PROBLEMS

PROBLEM 7-34 (30 MINUTES)

1.

Break-even point in units, using the equation approach:

$16X – ($10 + $2)X – $600,000 = 0

$4X = $600,000

X =

= 150,000 units

2.

New projected sales volume = 200,000 110%

= 220,000 units

Operating income = (220,000)($16 – $12) – $600,000

= (220,000)($4) – $600,000

= $880,000 – $600,000 = $280,000

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3.

Target operating income = $200,000 (from original problem data)

New disk purchase price = $10 130% = $13

Volume of sales dollars required:

Volume of sales dollars required

4.

Let P denote the selling price that will yield the same contribution-margin ratio:

Check: New contribution-margin ratio is:

5. In the electronic version of the solutions manual, press the CTRL key and click on the following link: BUILD A SPREADSHEET 07-34.XLS

PROBLEM 7-35 (30 MINUTES)

1. Break-even point in sales dollars, using the contribution-margin ratio:

2. Target operating income, using contribution-margin approach:

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3. New unit variable manufacturing cost = $8 110%

= $8.80

Break-even point in sales dollars:

4. Let P denote the selling price that will yield the same contribution-margin ratio:

Check: New contribution-margin ratio is:

PROBLEM 7-36 (30 MINUTES)

1. Unit contribution margin:Sales price………………………………… $64.00Less variable costs:

Sales commissions ($64 x 5%)…… $ 3.20System 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 ModelNo. 6754 No. 4399

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Sales revenue (46,000 units x $64.00)……... $2,944,000 $2,944,000Less variable costs:

Sales commissions ($2,944,000 x 5%)… $ 147,200 $ 147,200System variable costs:……………………

46,000 units x $16.00…………………. 736,000 46,000 units x $12.80…………………. 588,800

Total variable costs……………………….. $ 883,200 $ 736,000Contribution margin…………………………... $2,060,800 $2,208,000Less: Annual fixed costs…………………….. 985,600 1,113,600 Operating 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 = $128,000X = 40,000 units

PROBLEM 7-40 (30 MINUTES)

1.

2.

3. Number of sales units required to earn target operating income

4. Margin of safety = budgeted sales revenue – break-even sales revenue

= (120,000)($25) – $2,250,000 = $750,000

5. Break-even point if direct-labor costs increase by 8 percent:

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New unit contribution margin = $25.00 – $6.00 – ($5.00)(1.08) – $4.50 – $3.00 – $1.30

= $4.80

Break-even point

6. Contribution margin ratio

Old contribution-margin ratio

Let P denote sales price required to maintain a contribution-margin ratio of .208. Then P is determined as follows:

Check: New contribution-margin ratio

PROBLEM 7-43 (40 MINUTES)

1. In order to break even, during the first year of operations, 10,220 clients must visit the law office being considered by Martin Wong and his colleagues, as the following calculations show.

Fixed expenses:Advertising................................................................................ $ 350,000Rent (600 $480)..................................................................... 288,000Property insurance................................................................... 27,000Utilities ...................................................................................... 37,000Malpractice insurance.............................................................. 160,000Depreciation ($120,000/4)......................................................... 30,000Wages and fringe benefits:

Regular wages($25 + $20 + $15 + $10) 16 hours 360 days........ $403,200

Overtime wages(200 $15 1.5) + (200 $10 1.5)....................... 7,500

Total wages............................................................. $410,700

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Fringe benefits at 40%........................................................ 164,280 574,980Total fixed expenses....................................................................... $1,466,980

Break-even point:

0 = revenue – variable cost – fixed cost

0 = $30X + ($2,000 .2X .3)* – $4X – $1,466,980

0 = $30X + $120X – $4X – $1,466,980

$146X = $1,466,980

X = 10,048 clients (rounded)

*Revenue calculation:

$30X represents the $30 consultation fee per client. ($2,000 .2X .30) represents the predicted average settlement of $2,000, multiplied by the 20% of the clients whose judgments are expected to be favorable, multiplied by the 30% of the judgment that goes to the firm.

2. Safety margin:

Safety margin = budgeted sales revenue break-even sales revenue

Budgeted (expected) number of clients = 50 360 = 18,000

Break-even number of clients = 10,048 (rounded)

Safety margin = [($30 18,000) + ($2,000 18,000 .20 .30)]

– [($30 10,048) + ($2,000 10,048 .20 .30)]

= [$30 + ($2,000 .20 .30)] (18,000 – 10,048)

= $150 7,852

= $1,192,800PROBLEM 7-44 (45 MINUTES)

1. Break-even point in units:

Calculation of contribution margins:

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Computer-Assisted Manufacturing System

Labor-Intensive Production System

Selling price....................................... $30.00 $30.00Variable costs:

Direct material............................... $5.00 $5.60Direct labor.................................... 6.00 7.20Variable overhead......................... 3.00 4.80Variable selling cost..................... 2.00 16.00 2.00 19.60

Contribution margin per unit $14.00 $10.40

(a) Computer-assisted manufacturing system:

(b) Labor-intensive production system:

2. Celestial Products, Inc. would be indifferent between the two manufacturing methods at the volume (X) where total costs are equal.

$16X + $2,940,000 = $19.60X + $1,820,000

$3.60X = $1,120,000

X = 311,111 units (rounded)

3. Operating leverage is the extent to which a firm's operations employ fixed operating costs. The greater the proportion of fixed costs used to produce a product, the greater the degree of operating leverage. Thus, the computer-assisted manufacturing method utilizes a greater degree of operating leverage.

The greater the degree of operating leverage, the greater the change in operating income (loss) relative to a small fluctuation in sales volume. Thus, there is a higher degree of variability in operating income if operating leverage is high.

4. Management should employ the computer-assisted manufacturing method if annual sales are expected to exceed 311,111 units and the labor-intensive manufacturing method if annual sales are not expected to exceed 311,111 units.

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5. Celestial Products’ management should consider many other business factors other than operating leverage before selecting a manufacturing method. Among these are:

Variability or uncertainty with respect to demand quantity and selling price.

The ability to produce and market the new product quickly.

The ability to discontinue production and marketing of the new product while incurring the least amount of loss.

PROBLEM 7-52 (45 MINUTES)

1. SUMMARY OF EXPENSES

Expenses per Year (in thousands)

Variable FixedManufacturing..................................................................... $ 7,200 $2,340Selling and administrative................................................. 2,400 1,920Interest................................................................................. 540

Costs from budgeted income statement..................... $ 9,600 $4,800If the company employs its own sales force:

Additional sales force costs.......................................... 2,400Reduced commissions [(.15 – .10) $16,000]............ (800 )

Costs with own sales force............................................... $ 8,800 $7,200If the company sells through agents:

Deduct cost of sales force............................................. (2,400)Increased commissions [(.225 – .10) $16,000]........ 2,000

(a)

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(b)

2.

3. The volume in sales dollars (X) that would result in equal net income is the volume of sales dollars where total expenses are equal.

Total expenses with agents paid increased commission

= total expenses with own sales force

Therefore, at a sales volume of $19,200,000, the company will earn equal before-tax income under either alternative. Since before-tax income is the same, so is after-tax net income.

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