78718230-Hilton-Chapter-08-Solutions.pdf

CHAPTER 8 Cost-Volume-Profit Analysis ANSWERS TO REVIEW QUESTIONS 8-1

a. In the contribution-margin approach, the break-even point in units is calculated using the following formula: Break-even point =

fixed expenses unit contribution margin

b. In the equation approach, the following profit equation is used: sales volume ⎞ ⎛ unit variable sales volume ⎞ ⎛ unit fixed ⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ − × × = 0 in units ⎠ ⎝ expense in units ⎠ expenses ⎝ sales price

This equation is solved for the sales volume in units. c. In the graphical approach, sales revenue and total expenses are graphed. The break-even point occurs at the intersection of the total revenue and total expense lines. 8-2

The term unit contribution margin refers to the contribution that each unit of sales makes toward covering fixed expenses and earning a profit. The unit contribution margin is defined as the sales price minus the unit variable expense.

8-3

In addition to the break-even point, a CVP graph shows the impact on total expenses, total revenue, and profit when sales volume changes. The graph shows the sales volume required to earn a particular target net profit. The firm's profit and loss areas are also indicated on a CVP graph.

8-4

The safety margin is the amount by which budgeted sales revenue exceeds breakeven sales revenue.

8-5

An increase in the fixed expenses of any enterprise will increase its break-even point. In a travel agency, more clients must be served before the fixed expenses are covered by the agency's service fees.

8-6

A decrease in the variable expense per pound of oysters results in an increase in the contribution margin per pound. This will reduce the company's break-even sales volume.

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8-7

The president is correct. A price increase results in a higher unit contribution margin. An increase in the unit contribution margin causes the break-even point to decline. The financial vice president's reasoning is flawed. Even though the break-even point will be lower, the price increase will not necessarily reduce the likelihood of a loss. Customers will probably be less likely to buy the product at a higher price. Thus, the firm may be less likely to meet the lower break-even point (at a high price) than the higher break-even point (at a low price).

8-8

When the sales price and unit variable cost increase by the same amount, the unit contribution margin remains unchanged. Therefore, the firm's break-even point remains the same.

8-9

The fixed annual donation will offset some of the museum's fixed expenses. The reduction in net fixed expenses will reduce the museum's break-even point.

8-10

A profit-volume graph shows the profit to be earned at each level of sales volume.

8-11

The most important assumptions of a cost-volume-profit analysis are as follows: (a) The behavior of total revenue is linear (straight line) over the relevant range. This behavior implies that the price of the product or service will not change as sales volume varies within the relevant range. (b) The behavior of total expenses is linear (straight line) over the relevant range. This behavior implies the following more specific assumptions: (1) Expenses can be categorized as fixed, variable, or semivariable. (2) Efficiency and productivity are constant. (c) In multiproduct organizations, the sales mix remains constant over the relevant range. (d) In manufacturing firms, the inventory levels at the beginning and end of the period are the same.

8-12

Operating managers frequently prefer the contribution income statement because it separates fixed and variable costs. This format makes cost-volume-profit relationships more readily discernible.

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8-13

The gross margin is defined as sales revenue minus all variable and fixed manufacturing expenses. The total contribution margin is defined as sales revenue minus all variable expenses, including manufacturing, selling, and administrative expenses.

8-14

East Company, which is highly automated, will have a cost structure dominated by fixed costs. West Company's cost structure will include a larger proportion of variable costs than East Company's cost structure. A firm's operating leverage factor, at a particular sales volume, is defined as its total contribution margin divided by its net income. Since East Company has proportionately higher fixed costs, it will have a proportionately higher total contribution margin. Therefore, East Company's operating leverage factor will be higher.

8-15

When sales volume increases, Company X will have a higher percentage increase in profit than Company Y. Company X's higher proportion of fixed costs gives the firm a higher operating leverage factor. The company's percentage increase in profit can be found by multiplying the percentage increase in sales volume by the firm's operating leverage factor.

8-16

The sales mix of a multiproduct organization is the relative proportion of sales of its products. The weighted-average unit contribution margin is the average of the unit contribution margins for a firm's several products, with each product's contribution margin weighted by the relative proportion of that product's sales.

8-17

The car rental agency's sales mix is the relative proportion of its rental business associated with each of the three types of automobiles: subcompact, compact, and full-size. In a multi-product CVP analysis, the sales mix is assumed to be constant over the relevant range of activity.

8-18

Cost-volume-profit analysis shows the effect on profit of changes in expenses, sales prices, and sales mix. A change in the hotel's room rate (price) will change the hotel's unit contribution margin. This contribution-margin change will alter the relationship between volume and profit.

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8-19

Budgeting begins with a sales forecast. Cost-volume-profit analysis can be used to determine the profit that will be achieved at the budgeted sales volume. A CVP analysis also shows how profit will change if the sales volume deviates from budgeted sales. Cost-volume-profit analysis can be used to show the effect on profit when variable or fixed expenses change. The effect on profit of changes in variable or fixed advertising expenses is one factor that management would consider in making a decision about advertising.

8-20

The low-price company must have a larger sales volume than the high-price company. By spreading its fixed expense across a larger sales volume, the low-price firm can afford to charge a lower price and still earn the same profit as the high-price company. Suppose, for example, that companies A and B have the following expenses, sales prices, sales volumes, and profits.

Company A Sales revenue: 350 units at $10............................................... 100 units at $20............................................... Variable expenses: 350 units at $6................................................. 100 units at $6................................................. Contribution margin ............................................. Fixed expenses..................................................... Profit ......................................................................

Company B

$3,500 $2,000 2,100 $1,400 1,000 $ 400

600 $1,400 1,000 $ 400

8-21

The statement makes three assertions, but only two of them are true. Thus the statement is false. A company with an advanced manufacturing environment typically will have a larger proportion of fixed costs in its cost structure. This will result in a higher break-even point and greater operating leverage. However, the firm's higher break-even point will result in a reduced safety margin.

8-22

Activity-based costing (ABC) results in a richer description of an organization's cost behavior and CVP relationships. Costs that are fixed with respect to sales volume may not be fixed with respect to other important cost drivers. An ABC system recognizes these nonvolume cost drivers, whereas a traditional costing system does not.

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SOLUTIONS TO EXERCISES EXERCISE 8-23 (20 MINUTES) 1.

2.

3.

4.

Break-even point (in units) =

fixed expenses unit contribution margin

=

$54,000 = 13,500 pizzas $10 − $6

=

unit contribution margin unit sales price

=

$10 − $6 = .4 $10

Contribution-margin ratio

Break-even point (in sales dollars)

=

fixed expenses contribution-margin ratio

=

$54,000 = $135,000 .4

Let X denote the sales volume of pizzas required to earn a target net profit of $60,000. $10X – $6X – $54,000 = $60,000 $4X = $114,000 X = 28,500 pizzas

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EXERCISE 8-24 (25 MINUTES)

1 2 3 4

Sales Revenue $360,000 55,000 320,000 c 160,000

Variable Expenses $120,000 11,000 80,000 130,000

Total Contribution Margin $240,000 44,000 240,000 30,000

Fixed Expenses $90,000 25,000 60,000 30,000d

Net Income $150,000 19,000 180,000 -0-

Break-Even Sales Revenue $135,000 a 31,250b 80,000 160,000

Explanatory notes for selected items: a$135,000 b$31,250

= $90,000 ÷ (2/3), where 2/3 is the contribution-margin ratio.

= $25,000/.80, where .80 is the contribution-margin ratio.

cBreak-even

sales revenue ................................................................................ Fixed expenses.................................................................................................. Variable expenses .............................................................................................

$80,000 60,000 $20,000

Therefore, variable expenses are 25 percent of sales revenue. When variable expenses amount to $80,000, sales revenue is $320,000. d$160,000

is the break-even sales revenue, so fixed expenses must be equal to the contribution margin of $30,000 and profit must be zero.

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EXERCISE 8-25 (25 MINUTES) 1.

Cost-volume-profit graph:

Dollars per year Total revenue

$600,000

Total expenses

Break-even point: 20,000 tickets

$500,000

Profit area Variable expense (at 30,000 tickets)

•

$400,000

$300,000 Loss area $200,000

Annual fixed expenses

$100,000

5,000

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10,000

15,000

20,000

25,000

Tickets sold per 30,000 year

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EXERCISE 8-25 (CONTINUED) 2.

Stadium capacity................................................. Attendance rate ................................................... Attendance per game..........................................

6,000 × 2/3 4,000

Break - even point (tickets) 20,000 = =5 4,000 Attendance per game

The team must play 5 games to break even.

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EXERCISE 8-26 (25 MINUTES) 1.

Profit-volume graph:

Dollars per year $300,000

$200,000

$100,000 Break-even point: 20,000 tickets 0

$(100,000)

5,000

10,000

15,000

Profit area

•

20,000

25,000

Tickets sold per year

Loss area

$(200,000) Annual fixed expenses $(300,000) $(360,000)

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EXERCISE 8-26 (CONTINUED) 2.

Safety margin: Budgeted sales revenue (10 games × 6,000 seats × .45 full × $20) ................................................ Break-even sales revenue (20,000 tickets × $20)................................................................................. Safety margin ...................................................................................................

3.

$540,000 400,000 $140,000

Let P denote the break-even ticket price, assuming a 10-game season and 40 percent attendance: (10)(6,000)(.40)P – (10)(6,000)(.40)($12) – $360,000 = 0 24,000P = $408,000 P = $17 per ticket

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EXERCISE 8-27 (25 MINUTES) 1.

Break-even point (in units)

=

fixed costs unit contribution margin

=

2,000,000p = 4,000 components 1,500p − 1,000p

p denotes Argentina’s peso, worth 1.003 U.S. dollars on the day this exercise was written. 2.

New break-even point (in units)

=

(2,000,000p ) (1.05) 1,500p − 1,000p

=

2,100,000 p = 4,200 components 500p

3.

Sales revenue (7,000 × 1,500p) ................................................. Variable costs (7,000 × 1,000p) ........................................................ Contribution margin.......................................................................... Fixed costs......................................................................................... Net income .........................................................................................

4.

New break-even point (in units) =

10,500,000p 7,000,000p 3,500,000p 2,000,000p 1,500,000p

2,000,000p 1,400p − 1,000p

= 5,000 components 5.

Analysis of price change decision: Price 1,500p Sales revenue: (7,000 × 1,500p) ....................... 10,500,000p (8,000 × 1,400p) ....................... Variable costs: (7,000 × 1,000p) ....................... 7,000,000p (8,000 × 1,000p) ....................... Contribution margin ........................................... 3,500,000p Fixed expenses .................................................. 2,000,000p Net income (loss)................................................ 1,500,000p

1,400p 11,200,000p 8,000,000p 3,200,000p 2,000,000p 1,200,000p

The price cut should not be made, since projected net income will decline by 300,000p.

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EXERCISE 8-28 (25 MINUTES) 1.

(a) Traditional income statement: PACIFIC RIM PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20XX

Sales .......................................................................... Less: Cost of goods sold ......................................... Gross margin ................................................................ Less: Operating expenses: Selling expenses ............................................ Administrative expenses ............................... Net income ....................................................................

$1,000,000 750,000 $ 250,000 $75,000 75,000

150,000 $ 100,000

(b) Contribution income statement: PACIFIC RIM PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20XX

Sales .......................................................................... Less: Variable expenses: Variable manufacturing.................................. Variable selling ............................................... Variable administrative .................................. Contribution margin..................................................... Less: Fixed expenses: Fixed manufacturing ...................................... Fixed selling.................................................... Fixed administrative....................................... Net income .................................................................... 2.

$1,000,000 $500,000 50,000 15,000 $ 250,000 25,000 60,000

565,000 $ 435,000

335,000 $ 100,000

contribution margin net income $435,000 = = 4.35 $100,000

Operating leverage factor (at $1,000,000 sales level) =

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EXERCISE 8-28 (CONTINUED) 3.

⎛ percentage increase ⎞ ⎛ operating ⎞ ⎟⎟ × ⎜⎜ ⎟⎟ Percentage increase in net income = ⎜⎜ ⎝ in sales revenue ⎠ ⎝ leverage factor ⎠

= 12% × 4.35 = 52.2% 4.

Most operating managers prefer the contribution income statement for answering this type of question. The contribution format highlights the contribution margin and separates fixed and variable expenses.

EXERCISE 8-29 (30 MINUTES) Answers will vary on this question, depending on the airline selected as well as the year of the inquiry. In a typical year, most airlines report a breakeven load factor of around 65 percent.

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EXERCISE 8-30 (30 MINUTES) 1. Bicycle Type High-quality Medium-quality 2.

Sales Price $1,000 600

Unit Variable Cost $600 ($550 + $50) 300 ($270 + $30)

Unit Contribution Margin $400 300

Sales mix: High-quality bicycles.......................................................................................... Medium-quality bicycles ....................................................................................

3.

Weighted-average unit contribution margin

30% 70%

= ($400 × 30%) + ($300 × 70%) = $330

4.

fixed expenses weighted - average unit contribution margin $148,500 = = 450 bicycles $330

Break - even point (in units) =

Bicycle Type High-quality bicycles Medium-quality bicycles Total 5.

Break-Even Sales Volume 135 (450 × .30) 315 (450 × .70)

Sales Price $1,000 600

Sales Revenue $135,000 189,000 $324,000

Target net income: $148,500 + $99,000 $330 = 750 bicycles

Sales volume required to earn target net income of $99,000 =

This means that the shop will need to sell the following volume of each type of bicycle to earn the target net income: High-quality............................................................................ Medium-quality ......................................................................

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225 (750 × .30) 525 (750 × .70)

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EXERCISE 8-31 (25 MINUTES) 1.

The following income statement, often called a common-size income statement, provides a convenient way to show the cost structure.

Revenue.......................................................... Variable expenses ......................................... Contribution margin ...................................... Fixed expenses.............................................. Net income .....................................................

Amount $1,500,000 900,000 $600,000 450,000 $ 150,000

Percent 100 60 40 30 10

2. Decrease in Revenue $300,000*

×

Contribution Margin Percentage 40%†

Decrease in Net Income $120,000

=

*$300,000 = $1,500,000 × 20% †40%

= $600,000/$1,500,000 contribution margin net income $600,000 = =4 $150,000

3.

Operating leverage factor (at revenue of $1,500,000) =

4.

Percentage change in net income = ⎜⎜

⎛ percentage increase ⎞ ⎛ operating leverage ⎞ ⎟⎟ ⎟⎟ × ⎜⎜ in revenue factor ⎝ ⎠ ⎝ ⎠

= 25% × 4 = 100%

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EXERCISE 8-32 (10 MINUTES) Revenue........................................................ Less: Variable expenses ........................... Contribution margin .................................... Less: Fixed expenses................................ Net Income (loss).........................................

Requirement (1) $1,875,000 1,125,000 $ 750,000 675,000 $ 75,000

Requirement (2) $1,500,000 1,800,000 $ (300,000) 350,000 $ (650,000)

EXERCISE 8-33 (20 MINUTES) fixed expenses contribution margin ratio $200,000 = = $800,000 .25

1.

Break - even volume of service revenue =

2.

Target before - tax income =

target after - tax net income 1 − tax rate $120,000 = = $200,000 1 − .40

target after - tax net income (1 − t ) = contribution margin ratio $120,000 $200,000 + 1 − .40 = $1,600,000 = .25 fixed expenses +

3.

Service revenue required to earn target after-tax income of $120,000

4.

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

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SOLUTIONS TO PROBLEMS PROBLEM 8-34 (30 MINUTES) 1.

Break-even point in sales dollars, using the contribution-margin ratio: fixed expenses contribution - margin ratio $540,000 + $216,000 $756,000 = = $30 − $12 − $6 .4 $30 = $1,890,000

Break - even point =

2.

Target net income, using contribution-margin approach: fixed expenses + target net income unit contribution margin $756,000 + $540,000 $1,296,000 = = $30 − $12 − $6 $12 = 108,000 units

Sales units required to earn income of $540,000 =

3.

New unit variable manufacturing cost = $12 × 110% = $13.20 Break-even point in sales dollars: $756,000 $756,000 = $30.00 − $13.20 − $6.00 .36 $30 = $2,100,000

Break - even point =

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PROBLEM 8-34 (CONTINUED) 4.

Let P denote the selling price that will yield the same contribution-margin ratio: P − $13.20 − $6.00 $30.00 − $12.00 − $6.00 = P $30.00 P − $19.20 .4 = P .4P = P − $19.20 $19.20 = .6P P = $19.20/.6 P = $32.00

Check: New contribution-margin ratio is: $32.00 − $13.20 − $6.00 = .4 $32.00

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PROBLEM 8-35 (30 MINUTES) fixed costs unit contribution margin $702,000 = = 135,000 units $25.00 − $19.80

1.

Break - even point (in units) =

2.

Break - even point (in sales dollars) =

3.

Number of sales units required to earn target net profit

4.

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

fixed cost contribution - margin ratio $702,000 = = $3,375,000 $25.00 − $19.80 $25.00 fixed costs + target net profit unit contribution margin $702,000 + $390,000 = = 210,000 units $25.00 − $19.80 =

= (140,000)($25) – $3,375,000 = $125,000 5.

Break-even point if direct-labor costs increase by 10 percent: New unit contribution margin

= $25.00 – $8.20 – ($4.00)(1.10) – $6.00 – $1.60 = $4.80 fixed costs new unit contribution margin $702,000 = = 146,250 units $4.80

Break-even point =

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PROBLEM 8-35 (CONTINUED) 6.

Contribution margin ratio =

unit contribution margin sales price

$25.00 − $19.80 $25.00 = .208

Old contribution-margin ratio =

Let P denote sales price required to maintain a contribution-margin ratio of .208. Then P is determined as follows: P − $8.20 − ($4.00)(1.10) − $6.00 − $1.60 = .208 P P − $20.20 = .208P .792P = $20.20 P = $25.51 (rounded)

Check:

McGraw-Hill/Irwin 8-20

New contributionmargin ratio

$25.51 − $8.20 − ($4.00)(1.10) − $6.00 − $1.60 $25.51 = .208 (rounded)

=

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PROBLEM 8-36 (30 MINUTES) 1.

Break-even point in units, using the equation approach: $24X – ($15 + $3)X – $1,800,000 = 0 $6X = $1,800,000 X =

$1,800,000 $6

= 300,000 units 2.

New projected sales volume = 400,000 × 110% = 440,000 units Net income = (440,000)($24 – $18) – $1,800,000 = (440,000)($6) – $1,800,000 = $2,640,000 – $1,800,000 = $840,000

3.

Target net income = $600,000 (from original problem data) New disk purchase price = $15 × 130% = $19.50 Volume of sales dollars required: fixed expenses + target net profit contribution - margin ratio $1,800,000 + $600,000 $2,400,000 = = $24 − $19.50 − $3 .0625 $24 = $38,400,000

Volume of sales dollars required =

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PROBLEM 8-36 (CONTINUED) 4.

Let P denote the selling price that will yield the same contribution-margin ratio: P − $19.50 − $3 $24 − $15 − $3 = P $24 P − $22.50 .25 = P .25P = P − $22.50 $22.50 = .75P P = $22.50/.75 P = $30

Check: New contribution-margin ratio is: $30 − $22.50 = .25 $30

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PROBLEM 8-37 (30 MINUTES) 1.

Unit contribution margin: Sales price………………………………… Less variable costs: Sales commissions ($32 x 5%)…… $ 1.60 System variable costs……………… 8.00 Unit contribution margin………………..

$32.00 9.60 $22.40

Break-even point = fixed costs ÷ unit contribution margin = $1,971,200 ÷ $22.40 = 88,000 units 2.

Model A is more profitable when sales and production average 184,000 units.

Sales revenue (184,000 units x $32.00)……... Less variable costs: Sales commissions ($5,888,000 x 5%)… System variable costs:…………………… 184,000 units x $8.00…………………. 184,000 units x $6.40…………………. Total variable costs……………………….. Contribution margin…………………………... Less: Annual fixed costs…………………….. Net income……………………………………… 3.

Model A

Model B

$5,888,000

$5,888,000

$ 294,400

$ 294,400

1,472,000 $1,766,400 $4,121,600 1,971,200 $2,150,400

1,177,600 $1,472,000 $4,416,000 2,227,200 $2,188,800

Annual fixed costs will increase by $180,000 ($900,000 ÷ 5 years) because of straight-line depreciation associated with the new equipment, to $2,407,200 ($2,227,200 + $180,000). The unit contribution margin is $24 ($4,416,000 ÷ 184,000 units). Thus: Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($2,407,200 + $1,912,800) ÷ $24 = 180,000 units

4.

Let X = volume level at which annual total costs are equal $8.00X + $1,971,200 = $6.40X + $2,227,200 $1.60X = $256,000 X = 160,000 units

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PROBLEM 8-38 (25 MINUTES) 1.

Closing of mall store: Loss of contribution margin at Mall Store ...................................................... $(108,000) Savings of fixed cost at Mall Store (75%) ....................................................... 90,000 Loss of contribution margin at Downtown Store (10%) ................................ (14,400) Total decrease in operating income................................................................ $ (32,400)

2.

Promotional campaign: Increase in contribution margin (10%)............................................................ Increase in monthly promotional expenses ($180,000/12)............................ Decrease in operating income .........................................................................

3.

$10,800 (15,000) $(4,200)

Elimination of items sold at their variable cost: We can restate the November 20x4 data for the Mall Store as follows:

Sales .................................................................................... Less: variable expenses .................................................... Contribution margin ...........................................................

Mall Store Items Sold at Their Variable Cost Other Items $180,000* $180,000* 180,000 72,000 $ -0$108,000

If the items sold at their variable cost are eliminated, we have: Decrease in contribution margin on other items (20%)............................... Decrease in fixed expenses (15%)................................................................. Decrease in operating income .......................................................................

$(21,600) 18,000 $ (3,600)

*$180,000 is one half of the Mall Store's dollar sales for November 20x4.

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PROBLEM 8-39 (40 MINUTES) 1.

Sales mix refers to the relative proportion of each product sold when a company sells more than one product.

2.

(a)

Yes. Plan A sales are expected to total 65,000 units (19,500 + 45,500), which compares favorably against current sales of 60,000 units.

(b)

Yes. Sales personnel earn a commission based on gross dollar sales. As the following figures show, Cold King sales will comprise a greater proportion of total sales under Plan A. This is not surprising in light of the fact that Cold King has a higher selling price than Mister Ice Cream ($43 vs. $37). Current Units Mister Ice Cream.......... Cold King...................... Total ........................

(c)

21,000 39,000 60,000

Sales Mix 35% 65% 100%

Plan A Units 19,500 45,500 65,000

Sales Mix 30% 70% 100%

Yes. Commissions will total $267,800 ($2,678,000 x 10%), which compares favorably against the current flat salaries of $200,000. Mister Ice Cream sales: 19,500 units x $37 ............ Cold King sales: 45,500 units x $43 ........................ Total ......................................................................

McGraw-Hill/Irwin Managerial Accounting, 6/e

$ 721,500 1,956,500 $2,678,000

© 2005 The McGraw-Hill Companies, Inc. 8-25

PROBLEM 8-39 (CONTINUED) (d)

No. The company would be less profitable under the new plan.

Sales revenue: Mister Ice Cream: 21,000 units x $37; 19,500 units x $37.............. Cold King: 39,000 units x $43; 45,500 units x $43.......................... Total revenue ............................................................................... Less variable cost: Mister Ice Cream: 21,000 units x $20.50; 19,500 units x $20.50.... Cold King: 39,000 units x $32.50; 45,500 units x $32.50................ Sales commissions (10% of sales revenue) ................................... Total variable cost ....................................................................... Contribution margin................................................................................ Less fixed cost (salaries)........................................................................ Net income ............................................................................................... 3.

(a)

Plan A

$ 777,000 1,677,000 $2,454,000

$ 721,500 1,956,500 $2,678,000

$ 430,500 1,267,500

$ 399,750 1,478,750 267,800 $2,146,300 $ 531,700 ----___ $ 531,700

$1,698,000 $ 756,000 200,000 $ 556,000

The total units sold under both plans are the same; however, the sales mix has shifted under Plan B in favor of the more profitable product as judged by the contribution margin. Cold King has a contribution margin of $10.50 ($43.00 - $32.50), and Mister Ice Cream has a contribution margin of $16.50 ($37.00 - $20.50). Plan A Units Mister Ice Cream.............. Cold King.......................... Total ............................

McGraw-Hill/Irwin 8-26

Current

19,500 45,500 65,000

Plan B

Sales Mix 30% 70% 100%

Units 39,000 26,000 65,000

Sales Mix 60% 40% 100%

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-39 (CONTINUED) (b)

Plan B is more attractive both to the sales force and to the company. Salespeople earn more money under this arrangement ($274,950 vs. $200,000), and the company is more profitable ($641,550 vs. $556,000).

Sales revenue: Mister Ice Cream: 21,000 units x $37; 39,000 units x $37 ............. Cold King: 39,000 units x $43; 26,000 units x $43 ......................... Total revenue............................................................................... Less variable cost: Mister Ice Cream: 21,000 units x $20.50; 39,000 units x $20.50 ... Cold King: 39,000 units x $32.50; 26,000 units x $32.50 ............... Total variable cost ...................................................................... Contribution margin ............................................................................... Less: Sales force compensation: Flat salaries ....................................................................................... Commissions ($916,500 x 30%)....................................................... Net income...............................................................................................

McGraw-Hill/Irwin Managerial Accounting, 6/e

Current

Plan B

$ 777,000 1,677,000 $2,454,000

$1,443,000 1,118,000 $2,561,000

$ 430,500 1,267,500 $1,698,000 $ 756,000

$ 799,500 845,000 $1,644,500 $ 916,500

200,000 $ 556,000

274,950 $ 641,550

© 2005 The McGraw-Hill Companies, Inc. 8-27

PROBLEM 8-40 (35 MINUTES) 1.

Current income: Sales revenue………………………... Less: Variable costs………………… $1,008,000 Fixed costs……………………. 2,736,000 Net income…………………………….

$4,032,000 3,744,000 $ 288,000

CompTronics has a contribution margin of $72 [($4,032,000 - $1,008,000) ÷ 42,000 sets] and desires to increase income to $576,000 ($288,000 x 2). In addition, the current selling price is $96 ($4,032,000 ÷ 42,000 sets). Thus: Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($2,736,000 + $576,000) ÷ $72 = 46,000 sets, or $4,416,000 (46,000 sets x $96) 2.

If operations are shifted to Mexico, the new unit contribution margin will be $74.40 ($96.00 - $21.60). Thus: Break-even point = fixed costs ÷ unit contribution margin = $2,380,800 ÷ $74.40 = 32,000 units

3.

(a) CompTronics desires to have a 32,000-unit break-even point with a $72 unit contribution margin. Fixed costs must therefore drop by $432,000 ($2,736,000 $2,304,000), as follows: Let X = fixed costs X ÷ $72 = 32,000 units X = $2,304,000 (b)

As the following calculations show, CompTronics will have to generate a contribution margin of $85.50 to produce a 32,000-unit break-even point. Based on an $96.00 selling price, this means that the company can incur variable costs of only $10.50 per unit. Given the current variable cost of $24.00 ($96.00 - $72.00), a decrease of $13.50 per unit ($24.00 - $10.50) is needed. Let X = unit contribution margin $2,736,000 ÷ X = 32,000 units X = $85.50

McGraw-Hill/Irwin 8-28

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-40 (CONTINUED 4.

(a)

Increase

(b)

No effect

(c)

Increase

(d)

No effect

PROBLEM 8-41 (45 MINUTES) 1.

Break-even sales volume for each model: Break-even volume = (a)

(b)

(c)

annual rental cost unit contribution margin

Standard model: Break - even volume =

$16,000 = 25,000 tubs $3.50 − $2.86

Break - even volume =

$22,000 = 27,500 tubs $3.50 − $2.70

Break - even volume =

$40,000 = 40,816 tubs (rounded) $3.50 − $2.52

Super model:

Giant model:

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-29

PROBLEM 8-41 (CONTINUED) 2. Profit-volume graph:

Dollars per year (in thousands)

Profit

$40

$20 Break-even point: 40,816 tubs 0

10

20

30

•

40

Profit area

50

Tubs sold per year (in thousands)

Loss

Loss area ($20)

($40)

McGraw-Hill/Irwin 8-30

Fixed rental cost: $40,000 per year

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-41 (CONTINUED) 3.

The sales price per tub is the same regardless of the type of machine selected. Therefore, the same profit (or loss) will be achieved with the Standard and Super models at the sales volume, X, where the total costs are the same. Model Standard ..................................................... Super...........................................................

Variable Cost per Tub $2.86 2.70

Total Fixed Cost $16,000 22,000

This reasoning leads to the following equation: 16,000 + 2.86X = 22,000 + 2.70X Rearranging terms yields the following:

(2.86 – 2.70)X = 22,000 – 16,000 .16X = 6,000 X = 6,000/.16 X = 37,500

Or, stated slightly differently: Volume at which both machines produce the same profit

fixed cost differential variable cost differential $6,000 = $.16 = 37,500 tubs =

Check: the total cost is the same with either model if 37,500 tubs are sold. Standard Variable cost: Standard, 37,500 × $2.86........................... Super, 37,500 × $2.70 ................................ Fixed cost: Standard, $16,000 ...................................... Super, $22,000............................................ Total cost..........................................................

Super

$107,250 $101,250 16,000 $123,250

22,000 $123,250

Since the sales price for popcorn does not depend on the popper model, the sales revenue will be the same under either alternative.

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-31

PROBLEM 8-42 (40 MINUTES) 1. CVP graph:

Total revenue Dollars per year (in millions) 20 18

Profit area

Break-even point: 80,000 units or $8,000,000 of sales

16 14

Total expenses

12 10 8 6 4

Loss area

Fixed expenses

2 50

McGraw-Hill/Irwin 8-32

100

150

200

Units sold per year (in thousands)

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-42 (CONTINUED) 2.

Break-even point: contribution margin $12,000,000 = = .75 sales $16,000,000 fixed expenses $6,000,000 Break - even point = = contribution - margin ratio .75 = $8,000,000

Contribution - margin ratio =

3.

Margin of safety = budgeted sales revenue – break-even sales revenue = $16,000,000 – $8,000,000 = $8,000,000 contribution margin (at budgeted sales) net income (at budgeted sales) $12,000,000 = =2 $6,000,000

4.

Operating leverage factor (at budgeted sales)

=

5.

Dollar sales required to earn target net profit

=

6.

fixed expenses + target net profit contribution - margin ratio $6,000,000 + $9,000,000 = = $20,000,000 .75

Cost structure: Sales revenue........................................................ Variable expenses ................................................ Contribution margin ............................................. Fixed expenses ..................................................... Net income ............................................................

McGraw-Hill/Irwin Managerial Accounting, 6/e

Amount $16,000,000 4,000,000 $12,000,000 6,000,000 $ 6,000,000

Percent 100.0 25.0 75.0 37.5 37.5

© 2005 The McGraw-Hill Companies, Inc. 8-33

PROBLEM 8-43 (35 MINUTES) 1.

Plan A break-even point = fixed costs ÷ unit contribution margin = $33,000 ÷ $33* = 1,000 units Plan B break-even point = fixed costs ÷ unit contribution margin = $99,000 ÷ $45** = 2,200 units * $120 - [($120 x 10%) + $75] ** $120 - $75

2.

Operating leverage refers to the use of fixed costs in an organization’s overall cost structure. An organization that has a relatively high proportion of fixed costs and low proportion of variable costs has a high degree of operating leverage.

McGraw-Hill/Irwin 8-34

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-43 (CONTINUED) 3.

Calculation of contribution margin and profit at 6,000 units of sales:

Sales revenue: 6,000 units x $120………………. Less variable costs: Cost of purchasing product: 6,000 units x $75…………………….…… Sales commissions: $720,000 x 10%……... Total variable cost……………………….. Contribution margin……………………………… Fixed costs…………………………………………. Net income………………………………………….

Plan A

Plan B

$720,000

$720,000

$450,000 72,000 $522,000 $198,000 33,000 $165,000

$450,000 ----__ $450,000 $270,000 99,000 $171,000

Plan A has a higher percentage of variable costs to sales (72.5%) compared to Plan B (62.5%). Plan B’s fixed costs are 13.75% of sales, compared to Plan A’s 4.58%. Operating leverage factor = contribution margin ÷ net income Plan A: $198,000 ÷ $165,000 = 1.2 Plan B: $270,000 ÷ $171,000 = 1.58 (rounded) Plan B has the higher degree of operating leverage. 4 & 5. Calculation of profit at 5,000 units: Sales revenue: 5,000 units x $120………………. Less variable costs: Cost of purchasing product: 5,000 units x $75………………………….. Sales commissions: $600,000 x 10%……... Total variable cost……………………….. Contribution margin……………………………… Fixed costs………………………………………… Net income………………………………………….

McGraw-Hill/Irwin Managerial Accounting, 6/e

Plan A

Plan B

$600,000

$600,000

$375,000 60,000 $435,000 $165,000 33,000 $132,000

$375,000 ---- __ $375,000 $225,000 99,000 $126,000

© 2005 The McGraw-Hill Companies, Inc. 8-35

PROBLEM 8-43 (CONTINUED) Plan A profitability decrease: $165,000 - $132,000 = $33,000; $33,000 ÷ $165,000 = 20% Plan B profitability decrease: $171,000 - $126,000 = $45,000; $45,000 ÷ $171,000 = 26.3% (rounded) PneumoTech would experience a larger percentage decrease in income if it adopts Plan B. This situation arises because Plan B has a higher degree of operating leverage. Stated differently, Plan B’s cost structure produces a greater percentage decline in profitability from the drop-off in sales revenue. Note: The percentage decreases in profitability can be computed by multiplying the percentage decrease in sales revenue by the operating leverage factor. Sales dropped from 6,000 units to 5,000 units, or 16.67%. Thus: Plan A: 16.67% x 1.2 = 20.0% Plan B: 16.67% x 1.58 = 26.3% (rounded) 6.

Heavily automated manufacturers have sizable investments in plant and equipment, along with a high percentage of fixed costs in their cost structures. As a result, there is a high degree of operating leverage. In a severe economic downturn, these firms typically suffer a significant decrease in profitability. Such firms would be a more risky investment when compared with firms that have a low degree of operating leverage. Of course, when times are good, increases in sales would tend to have a very favorable effect on earnings in a company with high operating leverage.

McGraw-Hill/Irwin 8-36

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-44 (45 MINUTES) 1.

Break-even point in units: Break-even point =

fixed costs unit contribution margin

Calculation of contribution margins:

Selling price ...................................... Variable costs: Direct material .............................. Direct labor ................................... Variable overhead ........................ Variable selling cost .................... Contribution margin per unit (a)

LaborIntensive Production System $45.00 $8.40 10.80 7.20 3.00

29.40 $15.60

ComputerAssisted Manufacturing System $45.00 $7.50 9.00 4.50 3.00

24.00 $21.00

Labor-intensive production system: $1,980,000 + $750,000 $15.60 $2,730,000 = $15.60 = 175,000 units

Break - even point in units =

(b)

Computer-assisted manufacturing system: $3,660,000 + $750,000 $21 $4,410,000 = $21 = 210,000 units

Break - even point in units =

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-37

PROBLEM 8-44 (CONTINUED) 2.

Zodiac’s management would be indifferent between the two manufacturing methods at the volume (X) where total costs are equal. $29.40X + $2,730,000 =

$24X + $4,410,000

$5.40X =

$1,680,000

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.

5.

Zodiac’s 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.

McGraw-Hill/Irwin 8-38

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-45 (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 Steven Clark and his colleagues, as the following calculations show. Fixed expenses: Advertising................................................................................ $ 980,000 Rent (6,000 × $56)..................................................................... 336,000 Property insurance................................................................... 54,000 Utilities ...................................................................................... 74,000 Malpractice insurance.............................................................. 360,000 Depreciation ($120,000/4) ........................................................ 30,000 Wages and fringe benefits: Regular wages ($50 + $40 + $30 + $20) × 16 hours × 360 days ......... $806,400 Overtime wages (200 × $30 × 1.5) + (200 × $20 × 1.5) .......................... 15,000 Total wages............................................................. $821,400 Fringe benefits at 40% ....................................................... 328,560 1,149,960 Total fixed expenses ...................................................................... $2,983,960

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-39

PROBLEM 8-45 (CONTINUED) Break-even point: 0 = revenue – variable cost – fixed cost 0 = $60X + ($4,000 × .2X × .3)* – $8X – $2,983,960 0 = $60X + $240X – $8X – $2,983,960 $292X = $2,983,960

X = 10,220 clients (rounded) *Revenue calculation: $60X represents the $60 consultation fee per client. ($4,000 × .2X × .30) represents the predicted average settlement of $4,000, 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 = 10,220 (rounded) Safety margin = [($60 × 18,000) + ($4,000 × 18,000 × .20 × .30)] – [($60 × 10,220) + ($4,000 × 10,220 × .20 × .30)] = [$60 + ($4,000 × .20 × .30)] × (18,000 – 10,220) = $300 × 7,780 = $2,334,000

McGraw-Hill/Irwin 8-40

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-46 (35 MINUTES) 1.

Unit contribution margin =

$1,250,000 − $750,000 25,000 units

= $20 per unit Break - even point (in units) = =

2.

3.

fixed costs unit contribution margin $300,000 = 15,000 units $20

Number of sales units required to earn target net profit

New break - even point (in units) = =

=

fixed costs + target net profit unit contribution margin

=

$300,000 + $280,000 = 29,000 units $20

new fixed costs new unit contribution margin $300,000 + ($36,000/6) * = 19,125 units $20 − $4 †

*Annual straight-line depreciation on new machine †$4.00

4.

= $9.00 – $5.00 increase in the unit cost of the new part

Number of sales units required to earn target net profit, given manufacturing changes

new fixed costs + target net profit new unit contribution margin $306,000 + $200,000 * = $16 = 31,625 units =

*Last year's profit: ($50)(25,000) – $1,050,000 = $200,000

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-41

PROBLEM 8-46 (CONTINUED) unit contribution margin sales price $20 Old contribution - margin ratio = = .40 $50 * Contribution - margin ratio =

5.

*Sales price, given in problem. Let P denote the price required to cover increased direct-material cost and maintain the same contribution margin ratio: P − $30 * − $4 † P P − $34 .60P P

= .40 = .40P = $34 = $56.67 (rounded)

*Old unit variable cost = $30 = $750,000 ÷ 25,000 units †Increase

in direct-material cost = $4

Check: $56.67 − $30 − $4 $56.67 = .40 (rounded)

New contribution - margin ratio =

McGraw-Hill/Irwin 8-42

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-47 (40 MINUTES) 1.

Memorandum

Date:

Today

To:

Vice President for Manufacturing, Saturn Game Company

From:

I.M. Student, Controller

Subject:

Activity-Based Costing

The $300,000 cost that has been characterized as fixed is fixed with respect to sales volume. This cost will not increase with increases in sales volume. However, as the activitybased costing analysis demonstrates, these costs are not fixed with respect to other important cost drivers. This is the difference between a traditional costing system and an ABC system. The latter recognizes that costs vary with respect to a variety of cost drivers, not just sales volume. 2.

New break-even point if automated manufacturing equipment is installed: Sales price....................................................................................................... Costs that are variable (with respect to sales volume): Unit variable cost (.8 × $750,000 ÷ 25,000)............................................ Unit contribution margin ............................................................................... Costs that are fixed (with respect to sales volume): Setup (300 setups at $100 per setup)............................................ Engineering (800 hours at $56 per hour) ...................................... Inspection (100 inspections at $90 per inspection)..................... General factory overhead............................................................... Total............................................................................................ Fixed selling and administrative costs ............................................... Total costs that are fixed (with respect to sales volume) ........... Break - even point (in units) = =

$52 24 $28 $ 30,000 44,800 9,000 332,200 $416,000 60,000 $476,000

fixed costs unit contribution margin $476,000 $28

= 17,000 units

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-43

PROBLEM 8-47 (CONTINUED) 3.

Sales (in units) required to show a profit of $280,000: Number of sales units required to earn target net profit

4.

fixed cost + target net profit unit contribution margin $476,000 + $280,000 = $28 = 27,000 units =

If management adopts the new manufacturing technology: (a)

Its break-even point will be higher (17,000 units instead of 15,000 units).

(b)

The number of sales units required to show a profit of $280,000 will be lower (27,000 units instead of 29,000 units).

(c)

These results are typical of situations where firms adopt advanced manufacturing equipment and practices. The break-even point increases because of the increased fixed costs due to the large investment in equipment. However, at higher levels of sales after fixed costs have been covered, the larger unit contribution margin ($28 instead of $20) earns a profit at a faster rate. This results in the firm needing to sell fewer units to reach a given target profit level.

McGraw-Hill/Irwin 8-44

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-47 (CONTINUED) 5.

The controller should include the break-even analysis in the report. The Board of Directors needs a complete picture of the financial implications of the proposed equipment acquisition. The break-even point is a relevant piece of information. The controller should accompany the break-even analysis with an explanation as to why the break-even point will increase. It would also be appropriate for the controller to point out in the report that the advanced manufacturing equipment would require fewer sales units at higher volumes in order to achieve a given target profit, as in requirement (3) of this problem. To withhold the break-even analysis from the controller's report would be a violation of the following ethical standards: (a)

Competence: Prepare complete and clear reports and recommendations after appropriate analysis of relevant and reliable information.

(b)

Integrity: Communicate unfavorable as well as favorable information and professional judgments or opinions.

(c)

Objectivity: Communicate information fairly and objectively. Disclose fully all relevant information that could reasonably be expected to influence an intended user's understanding of the reports, comments, and recommendations presented.

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-45

PROBLEM 8-48 (45 MINUTES) 1.

Unit contribution margin =

$810,000 = $450 per ton 1,800

Break - even volume in tons =

fixed costs unit contribution margin

=

2.

$495,000 = 1,100 tons $450

Projected net income for sales of 2,100 tons: Projected contribution margin (2,100 × $450)........................................ Projected fixed costs ................................................................................ Projected net income................................................................................

3.

$945,000 495,000 $450,000

Projected net income including foreign order: Variable cost per ton = $990,000/1,800 = $550 per ton Sales price per ton for regular orders = $1,800,000/1,800 = $1,000 per ton

Sales in tons...................................................................... Contribution margin per ton: Foreign order ($900 – $550) ....................................... Regular sales ($1,000 – $550).................................... Total contribution margin ................................................

Foreign Order 1,500 ×

$350

$525,000

Contribution margin on foreign order........................................................ Contribution margin on Regular sales....................................................... Total contribution margin............................................................................ Fixed costs.................................................................................................... Net income ....................................................................................................

McGraw-Hill/Irwin 8-46

Regular Sales 1,500 × $450 $675,000 $ 525,000 675,000 $1,200,000 495,000 $ 705,000

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-48 (CONTINUED) 4.

New sales territory: To maintain its current net income, Central Pennsylvania Limestone Company just needs to break even on sales in the new territory. Break - even point in tons = =

5.

fixed costs in new territory unit contribution margin on sales in new territory $123,000 = 307.5 tons $450 − $50

Automated production process: Break - even point in tons = =

$495,000 + $117,000 $450 + $50 $612,000 = 1,224 tons $500

Break - even point in sales dollars = 1,224 tons × $1,000 per ton = $1,224,000

6.

Changes in selling price and unit variable cost: New unit contribution margin = ($1,000)(90%) − ($550 + $80) = $270 $270 ($1,000)(90%) = .30

New contribution margin ratio =

fixed costs + target net profit contribution margin ratio $495,000 + $189,000 = .30 = $2,280,000

Dollar sales required to earn target net profit =

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-47

PROBLEM 8-49 (45 MINUTES) 1. TOLEDO TOOL COMPANY BUDGETED INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20X4

Unit selling price ............................ Variable manufacturing cost......... Variable selling cost....................... Total variable cost.......................... Contribution margin per unit ........ Unit sales ........................................ Total contribution margin .........

Hedge Clippers $84 $39 15 $54 $30 × 50,000 $1,500,000

Line Trimmers $108 $ 36 12 $ 48 $ 60 × 50,000 $3,000,000

Leaf Blowers $144 $ 75 18 $ 93 $ 51 × 100,000 $5,100,000

Fixed manufacturing overhead..... Fixed selling and administrative costs.................. Total fixed costs ........................ Income before taxes....................... Income taxes (40%)........................ Budgeted net income.....................

Total

$9,600,000 $6,000,000 1,800,000 $7,800,000 $1,800,000 720,000 $1,080,000

2. (a) Unit Contribution Hedge Clippers .......................................... $30 Line Trimmers............................................ 60 51 Leaf Blowers .............................................. Weighted-average unit contribution margin.............................

(b) Sales Proportion .25 .25 .50

(a) × (b) $ 7.50 15.00 25.50 $48.00

total fixed costs weighted - average unit contribution margin $7,800,000 = = 162,500 units $48

Total unit sales to break even =

McGraw-Hill/Irwin 8-48

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-49 (CONTINUED) Sales proportions:

Hedge Clippers .............................................. Line Trimmers................................................ Leaf Blowers .................................................. Total................................................................

Sales Proportion .25 .25 .50

Total Unit Product Line Sales Sales 162,500 40,625 162,500 40,625 162,500 81,250 162,500

3. (a) (b) Unit Sales Contribution Proportion Hedge Clippers ................................................. $30 .20 Line Trimmers*.................................................. 57 .20 † 36 .60 Leaf Blowers .................................................... Weighted-average unit contribution margin..

(a) × (b) $ 6.00 11.40 21.60 $39.00

*Variable selling cost increases. Thus, the unit contribution decreases to $57 [$108 – ($36 + $12 + $3)]. †The

variable manufacturing cost increases 20 percent. Thus, the unit contribution decreases to $36 [$144 – (1.2 × $75) – $18]. total fixed costs weighted - average unit contribution margin $7,800,000 = = 200,000 units $39

Total unit sales to break even =

Sales proportions: Sales Proportions Hedge Clippers................................................ .20 Line Trimmers ................................................. .20 .60 Leaf Blowers.................................................... Total..................................................................

McGraw-Hill/Irwin Managerial Accounting, 6/e

Total Unit Sales 200,000 200,000 200,000

Product Line Sales 40,000 40,000 120,000 200,000

© 2005 The McGraw-Hill Companies, Inc. 8-49

PROBLEM 8-50 (35 MINUTES) 1.

(a)

Unit contribution margin = =

sales − variable costs units sold $2,000,000 − $1,400,000 = $6 per unit 100,000

Break - even point (in units) =

fixed costs unit contribution margin

=

$420,000 = 70,000 units $6

Contribution - margin ratio =

(b)

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

2.

Number of units of sales required to earn target after-tax net income

contribution margin sales revenue $2,000,000 − $1,400,000 = .3 $2,000,000 fixed costs contribution - margin ratio $420,000 = $1,400,000 .3 target after - tax net income (1 − t ) unit contribution margin

fixed costs + =

$180,000 $720,000 (1 − .4) = $6 $6

$420,000 + =

= 120,000 units

3.

If fixed costs increase by $63,000: Break - even point (in units) =

McGraw-Hill/Irwin 8-50

$420,000 + $63,000 = 80,500 units $6

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-50 (CONTINUED) 4. Profit-volume graph:

Dollars per year $1,500,000

$1,000,000

$500,000

0

Break-even point: 70,000 units

Loss 25,000 area

50,000

• 75,000

Profit area

100,000

Units sold per year

$(500,000)

$(1,000,000)

$(1,500,000)

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-51

PROBLEM 8-50 (CONTINUED) 5.

Number of units of sales required to earn target after-tax net income

target after - tax net income (1 − t ) unit contribution margin

fixed costs + =

$420,000 + =

$180,000 (1 − .5)

$6

=

$780,000 $6

= 130,000 units

McGraw-Hill/Irwin 8-52

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-51 (35 MINUTES) 1.

2.

Contribution margin ratio =

$120.00 − $79.20 = .34 $120.00 target after - tax net income (1 − t) unit contribution margin

fixed expenses +

Number of units of sales required to earn target after-tax income

=

$33,120 (1 − .40) $530,400 X= = $120.00 − $79.20 $40.80 $475,200 +

X = 13,000 units

3.

Break-even point (in units) for the touring model

=

$554,400 = 10,500 units $132.00 − $79.20

Let Y denote the variable cost of the mountaineering model such that the break-even point for the mountaineering model is 10,500 units. Then we have: $475,200 $120.00 − Y (10,500) × ($120.00 − Y ) = $475,200 10,500 =

$1,260,000 − 10,500Y = $475,200 10,500Y = $784,800

Y = $74.74 (rounded)

Thus, the variable cost per unit would have to decrease by $4.46 ($79.20 – $74.74).

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-53

PROBLEM 8-51 (CONTINUED) $475,200 × 110% $120.00 − ($79.20)(90%) $522,720 = $48.72 = 10,729 units (rounded)

4.

5.

New break - even point =

Weighted-average unit contribution margin Break-even point

= (50% × $52.80) + (50% × $40.80) = $46.80 fixed costs = weighted - average unit contribution margin $514,800 = = 11,000 units (or 5,500 of each type) $46.80

PROBLEM 8-52 (45 MINUTES) 1.

SUMMARY OF EXPENSES

Manufacturing .................................................................... Selling and administrative................................................. Interest ................................................................................ Costs from budgeted income statement..................... If the company employs its own sales force: Additional sales force costs ......................................... Reduced commissions [(.15 – .10) × $24,000] ............ Costs with own sales force............................................... If the company sells through agents: Deduct cost of sales force ............................................ Increased commissions [(.225 – .10) × $24,000]......... Costs with agents paid increased commissions............

McGraw-Hill/Irwin 8-54

Expenses per Year (in thousands) Variable Fixed $ 10,800 $3,510 3,600 2,880 810 $ 14,400 $7,200 3,600 (1,200) $ 13,200

$10,800 (3,600)

3,000 $ 16,200

$7,200

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-52 (CONTINUED) total fixed expenses contribution margin ratio total variable expenses Contribution-margin ratio = 1 − sales revenue

Break-even sales dollars =

(a)

$14,400,000 $24,000,000 = 1 − .60 = .40

Contribution margin ratio = 1 −

$7,200,000 .40 = $18,000,000

Break - even sales dollars =

(b)

2.

$13,200,000 $24,000,000 = 1 − .55 = .45 $10,800,000 Break - even sales dollars = .45 = $24,000,000 Contribution margin ratio = 1 −

Required sales dollars =

total fixed costs + target income before income taxes contribution margin ratio $16,200 $24,000 = 1 − .675 = .325

Contribution margin ratio = 1 −

$7,200,000 + $2,400,000 .325 $9,600,000 = .325 = $29,538,462 (rounded)

Required sales dollars to break even =

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-55

PROBLEM 8-52 (CONTINUED) 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

$16,200,000 $13,200,000 X + $7,200,000 = X + $10,800,000 $24,000,000 $24,000,000 .675 X + $7,200,000 = .55 X + $10,800,000 .125 X = $3,600,000 X = $28,800,000

Therefore, at a sales volume of $28,800,000, the company will earn equal before-tax income under either alternative. Since before-tax income is the same, so is after-tax net income.

McGraw-Hill/Irwin 8-56

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 8-53 (45 MINUTES) 1.

a. In order to break even, Columbus Canopy Company must sell 500 units. This amount represents the point where revenue equals total costs. Revenue = variable costs + fixed costs $800X = $400X + $200,000 $400X = $200,000 X = 500 units

b. In order to achieve its after-tax profit objective, Columbus Canopy Company must sell 2,500 units. This amount represents the point where revenue equals total costs plus the before-tax profit objective.

Revenue = variable costs + fixed costs + before - tax profit $800X = $400X + $200,000 + [$480,000 ÷ (1 − .4)] $800X = $400X + $200,000 + $800,000 $400X = $1,000,000 X = 2,500 units 2.

To achieve its annual after-tax profit objective, management should select the first alternative, where the sales price is reduced by $80 and 2,700 units are sold during the remainder of the year. This alternative results in the highest profit and is the only alternative that equals or exceeds the company’s profit objective. Calculations for the three alternatives follow.

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-57

PROBLEM 8-53 (CONTINUED) Alternative (1): Re venue = ($800)(350) + ($720)( 2,700) = $2,224,000 Variable cost = $400 × 3,050 = $1,220,000 Before - tax profit = $2,224,000 − $1,220,000 − $200,000 = $804,000 After - tax profit = $804,000 × (1 − .4) = $482,400

Alternative (2): Re venue = ($800)(350) + ($740)( 2,200) = $1,908,000 Variable cost = ($400)(350) × ($350)( 2,200) = $910,000 Before - tax profit = $1,908,000 − $910,000 − $200,000 = $798,000 After - tax profit = $798,000 × (1 − .4) = $478,800

Alternative (3): Re venue = ($800)(350) + ($760)( 2,000) = $1,800,000 Variable cost = $400 × 2,350 = $940,000 Before - tax profit = $1,800,000 − $940,000 − $180,000 = $680,000 After - tax profit = $680,000 × (1 − .4) = $408,000

McGraw-Hill/Irwin 8-58

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

SOLUTIONS TO CASES CASE 8-54 (50 MINUTES) 1.

The break-even point is 16,900 patient-days calculated as follows: SUSQUEHANNA MEDICAL CENTER COMPUTATION OF BREAK-EVEN POINT IN PATIENT-DAYS: PEDIATRICS FOR THE YEAR ENDED JUNE 30, 20X6

Total fixed costs: Medical center charges........................................................................................... Supervising nurses ($30,000 × 4) ........................................................................ Nurses ($24,000 × 10) ...................................................................... Aids ($10,800 × 20) ...................................................................... Total fixed costs ..............................................................................................

$3,480,000 120,000 240,000 216,000 $4,056,000

Contribution margin per patient-day: Revenue per patient-day.........................................................................................

$360

Variable cost per patient-day: ($7,200,000 ÷ $360 = 20,000 patient-days) ($2,400,000 ÷ 20,000 patient-days).................................................................... Contribution margin per patient-day .....................................................................

120 $240

Break-even point in patient-days

McGraw-Hill/Irwin Managerial Accounting, 6/e

total fixed costs $4,056,000 = contribution margin per patient - day $240 = 16,900 patient days

=

© 2005 The McGraw-Hill Companies, Inc. 8-59

CASE 8-54 (CONTINUED) 2. Net earnings would decrease by $728,000, calculated as follows: SUSQUEHANNA MEDICAL CENTER COMPUTATION OF LOSS FROM RENTAL OF ADDITIONAL 20 BEDS: PEDIATRICS FOR THE YEAR ENDED JUNE 30, 20X6

Increase in revenue (20 additional beds × 90 days × $360 charge per day) ....................................

$ 648,000

Increase in expenses: Variable charges by medical center (20 additional beds × 90 days × $120 per day) ............................................

$ 216,000

Fixed charges by medical center ($3,480,000 ÷ 60 beds = $58,000 per bed) ($58,000 × 20 beds).........................................................................................

1,160,000

Salaries (20,000 patient-days before additional 20 beds + 20 additional beds × 90 days = 21,800, which does not exceed 22,000 patient-days; therefore, no additional personnel are required) ......................................... Total increase in expenses...................................................................................... Net change in earnings from rental of additional 20 beds ...................................

-0$1,376,000 $ (728,000)

McGraw-Hill/Irwin 8-60

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

CASE 8-55 (50 MINUTES) 1.

Break-even point for 20x4, based on current budget: $15,000,000 − $9,000,000 − $3,000,000 = .20 $15,000,000 fixed expenses Break - even point = contribution - margin ratio $150,000 = = $750,000 .20

Contribution - margin ratio =

2.

Break-even point given employment of sales personnel: New fixed expenses: Previous fixed expenses ......................................................................... Sales personnel salaries (3 x $45,000)................................................... Sales managers’ salaries (2 × $120,000)................................................ Total ...........................................................................................................

$ $

150,000 135,000 240,000 525,000

New contribution-margin ratio: Sales .......................................................................................................... Cost of goods sold................................................................................... Gross margin ............................................................................................ Commissions (at 5%) ............................................................................... Contribution margin................................................................................. Contribution - margin ratio =

$15,000,000 9,000,000 $ 6,000,000 750,000 $ 5,250,000

$5,250,000 = .35 $15,000,000

fixed expenses contribution - margin ratio $525,000 = = $1,500,000 .35

Estimated break - even point =

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-61

CASE 8-55 (CONTINUED) 3.

Assuming a 25% sales commission: New contribution-margin ratio: Sales .......................................................................................................... Cost of goods sold................................................................................... Gross margin ............................................................................................ Commissions (at 25%) ............................................................................. Contribution margin................................................................................. Contribution - margin ratio =

Sales volume in dollars required to earn after-tax net income

$15,000,000 9,000,000 $ 6,000,000 3,750,000 $ 2,250,000

$2,250,000 = .15 $15,000,000 target after - tax net income (1 − t ) contribution - margin ratio

fixed expenses + =

$1,995,000 $3,000,000 (1 − .3) = = .15 .15 = $20,000,000 $150,000 +

Check: Sales ..................................................................... Cost of goods sold (60% of sales)..................... Gross margin ....................................................... Selling and administrative expenses: Commissions................................................. All other expenses (fixed) ............................ Income before taxes............................................ Income tax expense (30%).................................. Net income ...........................................................

McGraw-Hill/Irwin 8-62

$ 20,000,000 12,000,000 $ 8,000,000 $ 5,000,000 150,000

5,150,000 $ 2,850,000 855,000 $ 1,995,000

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

CASE 8-55 (CONTINUED) 4.

Sales dollar volume at which Lake Champlain Sporting Goods Company is indifferent: Let X denote the desired volume of sales. Since the tax rate is the same regardless of which approach management chooses, we can find X so that the company’s before-tax income is the same under the two alternatives. (In the following equations, the contribution-margin ratios of .35 and .15, respectively, were computed in the preceding two requirements.) .35X – $525,000 = .15X – $150,000 .20X = $375,000 X = $375,000/.20 X = $1,875,000

Thus, the company will have the same before-tax income under the two alternatives if the sales volume is $1,875,000. Check:

Sales .............................................................................. Cost of goods sold (60% of sales).............................. Gross margin ................................................................ Selling and administrative expenses: Commissions............................................................ All other expenses (fixed)........................................ Income before taxes..................................................... Income tax expense (30%)........................................... Net income ....................................................................

Alternatives Employ Sales Pay 25% Personnel Commission $1,875,000 $1,875,000 1,125,000 1,125,000 $ 750,000 $ 750,000 93,750* 525,000 $ 131,250 39,375 $ 91,875

468,750† 150,000 $ 131,250 39,375 $ 91,875

*$1,875,000 × 5% = $93,750 †$1,875,000 × 25% = $468,750

McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-63

CURRENT ISSUES IN MANAGERIAL ACCOUNTING ISSUE 8-56 “PLANES, TRAINS AND POLITICIANS,” BUSINESS WEEK, OCTOBER 7, 2002, P. 49, ALLAN SLOAN. The break-even point is the volume of operating activity at which revenue and expenses are equal. Amtrak was originally established to provide a public service, namely lowcost transportation. It traditionally had a price structure that depended on tax-base funding to fund fixed infrastructure expenses. It is only in recent years that the government has acted to transition Amtrak to a self-sufficient operation. The airlines, by contrast, were from the outset privately owned, for-profit businesses. However, since the earliest days the airlines have struggled to be profitable; they are now asking for a massive subsidy to offset losses, which have accumulated because of overexpansion, huge debt, high labor costs, and the effects of September 11, 2001, along with other security issues. Now, both these industries should be encouraged to cut costs in order to break even. It is not an impossible mission; Southwest and JetBlue have both successfully achieved this goal. ISSUE 8-57 “TO REDRESS INDUSTRY BLUES, DELTA TURNS TO SONG,” THE WALL STREET JOURNAL, JAN 29, 2003, P. A3, NICOLE HARRIS; “COSTLY RACE IN THE SKY: SAME ROUTE, SAME PLANE, YET UNITED'S FLIGHT COSTS MORE TO OPERATE THAN JETBLUE'S,” THE WALL STREET JOURNAL, SEPTEMBER 9, 2002, P. B1, SUSAN CAREY. Labor costs are a significant proportion of any airline’s cost structure. Major airlines, such as United Airlines, have developed very high labor costs because (1) most of their staff belong to labor unions, which have strong wage and benefits negotiation power; and (2) wages tend to be tied to seniority rather than productivity. By comparison, the low cost competitors such as Jet Blue pay their air and ground crews lower wages and benefits. As a result, labor costs account for 47% of revenue at United, but just 25% at Jet Blue, allowing the latter to operated profitably. Another significant source of costs for airlines is ground crews. The larger airlines have pioneered a “hub-and-spoke” model, which allows them to increase passenger loads by funneling all flights through major hubs. By contrast, the low-cost airlines have tended to offer “point-to-point” services, which may offer lower passenger volumes, but also require smaller ground crews. The point-to-point model provides an added cost advantage to the low-cost airlines, allowing them to offer lower prices to customers. McGraw-Hill/Irwin 8-64

© 2005 The McGraw-Hill Companies, Inc. Solutions Manual

ISSUE 8-58 “IT’S TIME TO CASH IN SOME CHIPS, BIG BLUE”, BUSINESS WEEK, JUNE 3, 2002, P. 43, SPENCER E. ANTE. The cost structure is the relative proportion of fixed to variable costs. Because semiconductor manufacturing requires capital-intensive, high-technology, equipment, it is characterized by very high fixed costs. In organizations like these, profit is very sensitive to changes in volume. For this reason, analysts are concerned that IBM should be making significant efforts to reduce fixed costs (by shutting down manufacturing lines) rather than making minor adjustments to labor levels. ISSUE 8-59 "RELIANCE GROUP MAY SEE SHIELD FROM CREDITORS," THE WALL STREET JOURNAL, AUGUST 15, 2000, DEVON SPURGON, GREGORY ZUCKERMAN, AND FRANCINE L. POPE. Managers apply operating leverage to convert small changes in sales into large changes in a firm’s profitability. Fixed costs are the lever that managers use to take a small increase in sales and obtain a much larger increase in net income. Having a cost structure with relatively high fixed costs provides rewards and risks to a firm. With a high degree of operating leverage, each additional sale decreases the average cost per unit. Each dollar of revenue becomes pure profit once the fixed costs are covered. This is beneficial if sales are increasing; however, the reverse is true if sales are decreasing. With decreasing sales, the fixed costs do not decrease, and profit declines significantly more than revenue. In the article, high operating leverage was not working to benefit Reliance Group Holdings, Inc. Consequently, its stock rating was downgraded.

ISSUE 8-60 “LEVI WILL CUT 20% OF WORK FORCE, SHUT SIX PLANTS IN RESTRUCTURING,” THE WALL STREET JOURNAL, APRIL 9, 2002, TERI AGINS. The cost structure is the relative proportion of fixed to variable costs. Outsourcing can lead to lower fixed costs, if it enables a company to divest of fixed assets (such as plant and equipment) or eliminate salaried personnel (such as department supervisors). As fixed costs are reduced, the company moves toward a cost structure with a larger proportion of variable costs. McGraw-Hill/Irwin Managerial Accounting, 6/e

© 2005 The McGraw-Hill Companies, Inc. 8-65