Cost-Volume-Profit Analysis

CHAPTER 8 Cost-Volume-Profit Analysis

ANSWERS TO REVIEW QUESTIONS

8.1 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.

8-2 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.

8-3 a. In the contribution-margin approach, the break-even point in units is calculated using the following formula:

fixed expenses Break-even point  unitcontributi on margin

b. In the equation approach, the following profit equation is used:

 unit sales volume unit variable sales volume fixed          0 sales price in units   expense in units  expens es 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.

8-4 The safety margin is the amount by which budgeted sales revenue exceeds break-even 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.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-1 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.

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.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-2 Solutions Manual (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.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-3 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 multiproduct 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.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-4 Solutions Manual 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 Company B

Sales revenue: 350 units at $10...... $3,500 100 units at $20...... $2,000 Variable expenses: 350 units at $6...... 2,100 100 units at $6...... 600 Contribution margin...... $1,400 $1,400 Fixed expenses...... 1,000 1,000 Profit...... $ 400 $ 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.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-5 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.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-6 Solutions Manual SOLUTIONS TO EXERCISES EXERCISE 8-23 (25 MINUTES)

Total Break- Sales Variable Contributi Fixed Net even Revenu Expenses on Margin Expense Incom Sales e s e Revenue 1 $160,00 $40,000 $120,000 $30,000 $90,00 $40,000 0a 0 2 65,000 15,000 15,000b -0- 80,000 80,000 3 40,000 80,000 30,000 45,000c 120,000 50,000 4 22,000 88,000 50,000 62,500d 110,000 38,000

Explanatory notes for selected items: aBreak-even sales revenue...... $40,000 Fixed expenses...... 30,000 Variable expenses...... $10,000

Therefore, variable expenses are 25 percent of sales revenue.

When variable expenses amount to $40,000, sales revenue is $160,000. b$80,000 is the break-even sales revenue, so fixed expenses must be equal to the contribution margin of $15,000 and profit must be zero. c$45,000 = $30,000 ¸ (2/3), where 2/3 is the contribution-margin ratio. d$62,500 = $50,000/.80, where .80 is the contribution-margin ratio.

EXERCISE 8-24 (20 MINUTES)

fixed expenses 1. Break-even point (in units) = unitcontributi on margin

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-7 $40,000 = = 8,000 pizzas $10 $5

unitcontributi on margin 2. Contribution-margin ratio = unitsales price $10 $5 = = .5 $10 EXERCISE 8-24 (CONTINUED)

fixed expenses 3. Break-even point (in sales dollars) = contribution-margin ratio

$40,000 = = $80,000 .5

4. Let X denote the sales volume of pizzas required to earn a target net profit of $65,000.

$10X – $5X – $40,000 = $65,000

$5X = $105,000

X = 21,000 pizzas

fixed costs 1. Break-even point (in units) = unitcontributi on margin

4,000,000p = = 4,000 components 3,000p  2,000p

p denotes Argentina’s peso, worth 1.004 U.S. dollars on the day this exercise was written.

(4,000,000p) (1.10) 2. New break-even point (in units) = 3,000p  2,000p

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-8 Solutions Manual 4,400,000 p = = 4,400 components 1,000p

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

EXERCISE 8-25 (CONTINUED)

4,000,000p 4. New break-even point (in units) = 2,500p  2,000p

= 8,000 components

5. Analysis of price change decision: Price 3,000p 2,500p Sales revenue: (5,000  3,000p) 15,000,000 p 15,500,000 (6,200  2,500p) p

Variable costs: (5,000  2,000p)...... 10,000,000 12,400,000 (6,200  2,000p)...... p p Contribution margin 3,100,000 Fixed expenses 5,000,000 p p 4,000,000 Net income (loss)...... 4,000,000 p p (900,000 p ) 1,000,000 p

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-9 The price cut should not be made, since projected net income will decline.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-10 Solutions Manual EXERCISE 8-26 (25 MINUTES)

1. Cost-volume-profit graph:

Dollars per year Total revenue $300,00 0

Break-even point: Total expenses $250,00 20,000 tickets 0 Profit area Variable $200,00  expense 0 (at 30,000 tickets) $150,00 0 Loss area $100,00 Annual 0 fixed expenses

$50,000

Tickets sold per 5,000 10,000 15,000 20,000 25,000 30,000 year

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-11 EXERCISE 8-26 (CONTINUED)

2. Stadium capacity...... 10,000 Attendance rate......  50% Attendance per game...... 5,000

Break-even point(tickets) 20,000   4 Attendance per game 5,000 The team must play 4 games to break even.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-12 Solutions Manual EXERCISE 8-27 (25 MINUTES)

1. Profit-volume graph:

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-13 Dollars per year

$150,000

$100,000

$50,000 Break-even point: Profit 20,000 tickets area 0  Tickets sold 5,000 10,000 15,000 20,000 25,000 per year

Loss area $(50,000 )

$(100,000 ) Annual fixed expenses $(150,000 ) $(180,000 )

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-14 Solutions Manual EXERCISE 8-27 (CONTINUED)

2. Safety margin:

Budgeted sales revenue (12 games  10,000 seats  .30 full  $10)...... $360,000 Break-even sales revenue (20,000 tickets  $10)...... 200,000 Safety margin...... $160,000

3. Let P denote the break-even ticket price, assuming a 12-game season and 50 percent attendance:

(12)(10,000)(.50)P – (12)(10,000)(.50) = 0 ($1) – $180,000 60,000P = $240,000 P = $4 per ticket

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-15 EXERCISE 8-28 (25 MINUTES)

1. (a) Traditional income statement:

EUROPA PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20XX Sales ...... $2,000,000 Less: Cost of goods sold...... 1,500,000 Gross margin...... $ 500,000 Less: Operating expenses: Selling expenses...... $150,000 Administrative expenses...... 150,000 300,000 Net income...... $ 200,000

(b) Contribution income statement:

EUROPA PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20SXX Sales ...... $2,000,000 Less: Variable expenses: Variable manufacturing...... $1,000,000 Variable selling...... 100,000 Variable administrative...... 30,000 1,130,000 Contribution margin...... $ 870,000 Less: Fixed expenses: Fixed manufacturing...... $ 500,000 Fixed selling...... 50,000 Fixed administrative...... 120,000 670,000 Net income...... $ 200,000

contribution margin 2. Operating leverage factor (at$2,000,000 sales level)  netincome $870,000   4.35 $200,000

percentage increase  operating 3. Percentage increase in netincome        in sales revenue leverage factor = 10%  4.35 = 43.5%

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

1. Sales Unit Unit Bicycle Type Price Variable Cost Contribution Margin High-quality $500 $300 ($275 + $200 $25) Medium- 300 150 ($135 + $15) 150 quality

2. Sales mix:

High-quality bicycles...... 25% Medium-quality bicycles...... 75%

3. Weighted-average unit = ($200  25%) + ($150  75%) contribution margin = $162.50 fixed expenses 4. Break-even point(in units)  weighted-average unitcontributi on margin $65,000   400 bicycles $162.50

Break- Sales Bicycle Type Even Sales Sales Price Revenue

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-17 Volume High-quality bicycles 100 (400 $500 $  .25) 50,000 Medium-quality bicycles 300 (400 300  .75) 90,000 Total $140,00 0

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-18 Solutions Manual EXERCISE 8-29 (CONTINUED) 5. Target net income: $65,000  $48,750 Sales volume required to earn targetnet income of $48,750  $162.50  700 bicycles This means that the shop will need to sell the following volume of each type of bicycle to earn the target net income: High-quality...... 175 (700  .25) Medium-quality...... 525 (700  .75)

EXERCISE 8-30 (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.

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

Amount Percent Revenue...... $500,000 100 Variable expenses...... 300,000 60 Contribution margin...... $200,000 40 Fixed expenses...... 150,000 30 Net income...... $ 50,000 10

2. Decrease Contribution Decrease in in Margin Net Income Revenue Percentage $75,000*  40%† = $30,000

*$75,000 = $500,000  15% †40% = $200,000/$500,000

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-19 EXERCISE 8-31 (CONTINUED)

contribution margin 3. Operating leverage factor (atrevenue of $500,000)  netincome $200,000   4 $50,000

percentage increase operating leverage 4. Percentage change in netincome            in revenue   factor  20% 4

 80%

Requirement Requiremen (1) t (2) Revenue...... $600,000 $500,000 Less: Variable expenses...... 360,000 600,000 Contribution margin...... $240,000 $ (100,000) Less: Fixed expenses...... 210,000 125,000 Net Income (loss)...... $ 30,000 $ (225,000)

fixed expenses 1. Break-even volume of service revenue  contribution margin ratio $120,000   $600,000 .20

targetafter -tax netincome 2. Targetbefore -tax income  1  tax rate $48,000   $80,000 1  .40

targetafter -tax netincome fixed expenses  3. Service revenue required (1  t)  to earn target after-tax contribution margin ratio income of $48,000 $48,000 $120,000   1  .40  $1,000,000 .20

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.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-21 SOLUTIONS TO PROBLEMS PROBLEM 8-34 (30 MINUTES)

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

$16X – ($10 + $2)X – = 0 $600,000 $4X = $600,000 $600,000 X = $4 = 150,000 units

2. New projected sales = 200,000  110% volume = 220,000 units Net income = (220,000)($16 – $12) – $600,000

= (220,000)($4) – $600,000

= $880,000 – $600,000 = $280,000

3. Target net income = $200,000 (from original problem data)

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

Volume of sales dollars required:

fixed expenses  targetnet profit Volume of sales dollars  required contribution-margin ratio $600,000  $200,000 $800,000   $16  $13  $2 .0625 $16  $12,800,000

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-22 Solutions Manual PROBLEM 8-34 (CONTINUED)

4. Let P denote the selling price that will yield the same contribution-margin ratio: $16  $10  $2 P  $13  $2  $16 P P  $15 .25  P .25P  P  $15 $15  .75P

P  $15/.75 P  $20

Check: New contribution-margin ratio is:

$20 $15  .25 $20 PROBLEM 8-35 (30 MINUTES)

1. Break-even point in sales dollars, using the contribution-margin ratio: fixed expenses Break-even point contribution-margin ratio $180,000  $72,000 $252,000   $20  $8  $4 .4 $20  $630,000

2. Target net income, using contribution-margin approach: fixed expenses  targetnet income Sales units required to earn income of $180,000  unitcontributi on margin $252,000  $180,000$432,000   $20  $8  $4 $8  54,000 units

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-23 PROBLEM 8-35 (CONTINUED)

3. New unit variable = $8  110% manufacturing cost = $8.80 Break-even point in sales dollars: $252,000 $252,000 Break-even point  $20.00  $8.80  $4.00 .36 $20  $700,000

4. Let P denote the selling price that will yield the same contribution-margin ratio: $20.00  $8.00  $4.00 P  $8.80  $4.00  $20.00 P P  $12.80 .4  P .4P  P  $12.80 $12.80  .6P P  $12.80/.6 P  $21.33 (rounded) Check: New contribution-margin ratio is: $21.33 $8.80 $4.00  .4 (rounded) $21.33

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-24 Solutions Manual PROBLEM 8-36 (30 MINUTES)

1. Unit contribution margin: Sales $64. price………………………………… 00 Less variable costs: Sales commissions ($64 x $ 5%)…… 3.20 System variable 16.0 19. costs……………… 0 20 Unit contribution $44. margin……………….. 80

Break-even point = fixed costs ÷ unit contribution margin = $985,600 ÷ $44.80 = 22,000 units

2. Model no. 4399 is more profitable when sales and production average 46,000 units.

Model Model No. No. 6754 4399

Sales revenue (46,000 units x $2,944, $2,944, $64.00)……... 000 000 Less variable costs: Sales commissions $ $ ($2,944,000 x 5%)… 147,200 147,200 System variable costs: …………………… 46,000 units x 736,0 $16.00…………………. 00 46,000 units x 588,8 $12.80…………………. 00 Total variable $ $ costs……………………….. 883,200 736,000 Contribution $2,060, $2,208, margin…………………………... 800 000 Less: Annual fixed 985,6 1,113,6 costs…………………….. 00 00 Net $1,075, $1,094,

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-25 income…………………………………… 200 400 …

3. Annual fixed costs will increase by $90,000 ($450,000 ÷ 5 years) because of straight-line depreciation associated with the new equipment, to $1,203,600 ($1,113,600 + $90,000). The unit contribution margin is $48 ($2,208,000 ÷ 46,000 units). Thus:

Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($1,203,600 + $956,400) ÷ $48 = 45,000 units

4. Let X = volume level at which annual total costs are equal $16.00X + $985,600 = $12.80X + $1,113,600 $3.20X = $128,000 X = 40,000 units

1. Current income:

Sales $3,360, revenue………………………... 000 Less: Variable $ costs………………… 840,000 Fixed 2,280,0 3,120,0 costs……………………. 00 00 Net $ income…………………………… 240,000 .

Advanced Electronics has a contribution margin of $60 [($3,360,000 - $840,000) ÷ 42,000 sets] and desires to increase income to $480,000 ($240,000 x 2). In addition, the current selling price is $80 ($3,360,000 ÷ 42,000 sets). Thus:

Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($2,280,000 + $480,000) ÷ $60 = 46,000 sets, or $3,680,000 (46,000 sets x $80)

2. If operations are shifted to Mexico, the new unit contribution margin will be $62 ($80 - $18). Thus:

Break-even point = fixed costs ÷ unit contribution margin = $1,984,000 ÷ $62 = 32,000 units

3. (a) Advanced Electronics desires to have a 32,000-unit break- even point with a $60 unit contribution margin. Fixed cost must therefore drop by $360,000 ($2,280,000 - $1,920,000), as follows:

Let X = fixed costs X ÷ $60 = 32,000 units X = $1,920,000

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-27 (b) As the following calculations show, Advanced Electronics will have to generate a contribution margin of $71.25 to produce a 32,000-unit break-even point. Based on an $80.00 selling price, this means that the company can incur variable costs of only $8.75 per unit. Given the current variable cost of $20.00 ($80.00 - $60.00), a decrease of $11.25 per unit ($20.00 - $8.75) is needed.

Let X = unit contribution margin $2,280,000 ÷ X = 32,000 units X = $71.25

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-28 Solutions Manual PROBLEM 8-37 (CONTINUED

4. (a) Increase

(b) No effect

(c) Increase

(d) No effect

PROBLEM 8-38 (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 (45,500 + 19,500), 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, Deluxe sales will comprise a greater proportion of total sales under Plan A. This is not surprising in light of the fact that Deluxe has a higher selling price than Basic ($86 vs. $74).

Current Plan A

Sale Sale Unit s Unit s s Mix s Mix

Deluxe… 39,0 65 45,5 70 …... 00 % 00 % Basic…… 21,0 35 19,5 30 …. 00 % 00 % Total 60,0 100 65,0 100 00 % 00 %

(c) Yes. Commissions will total $535,600 ($5,356,000 x 10%), which compares favorably against the current flat salaries of $400,000.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-29 Deluxe sales: 45,500 $3,913, units x $86… 000 Basic sales: 19,500 units 1,443,0 x $74….. 00 Total………………………… $5,356, ……. 000

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

Current Plan A Sales revenue: Deluxe: 39,000 units x $86; 45,500 $3,354, $3,913, units x $86… 000 000 Basic: 21,000 units x $74; 19,500 1,554,0 1,443,0 units x $74….. 00 00 Total $4,908, $5,356, revenue……………………………………. 000 000 Less variable cost: Deluxe: 39,000 units x $65; 45,500 $2,535, $2,957, units x $65… 000 500 Basic: 21,000 units x $41; 19,500 861,0 799,5 units x $41….. 00 00 Sales commissions (10% of sales 535,6 revenue)……. 00 Total variable $3,396, $4,292, cost……………………………… 000 600 Contribution $1,512, $1,063, margin…………………………………….. 000 400 Less fixed cost (salaries) 400,0 ---- ………………………………. 00 Net $1,112, $1,063, income……………………………………………… 000 400 ...

3. (a) 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. Deluxe has a contribution margin of $21 ($86 - $65), and Basic has a contribution margin of $33 ($74 - $41).

Plan A Plan B

Sale Sale Unit s Unit s s Mix s Mix

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-31 Deluxe… 45,5 70 26,0 40 …... 00 % 00 % Basic…… 19,5 30 39,0 60 …. 00 % 00 % Total… 65,0 100 65,0 100 … 00 % 00 %

(b) Plan B is more attractive both to the sales force and to the company. Salespeople earn more money under this arrangement ($549,900 vs. $400,000) and the company is more profitable ($1,283,100 vs. $1,112,000).

Current Plan B Sales revenue: Deluxe: 39,000 units x $86; 26,000 $3,354, $2,236, units x $86… 000 000 Basic: 21,000 units x $74; 39,000 1,554,0 2,886,0 units x $74….. 00 00 Total $4,908, $5,122, revenue……………………………………. 000 000 Less variable cost: Deluxe: 39,000 units x $65; 26,000 $2,535, $1,690, units x $65… 000 000 Basic: 21,000 units x $41; 39,000 861,0 1,599,0 units x $41….. 00 00 Total variable $3,396, $3,289, cost……………………………… 000 000 Contribution $1,512, $1,833, margin…………………………………….. 000 000 Less: Sales force compensation: Flat 400,0 salaries…………………………………………... 00 Commissions ($1,833,000 x 30%) 549,9 ………………… 00 Net income $1,112, $1,283, ……………………………………………….. 000 100

1. Plan A break-even point = fixed costs ÷ unit contribution margin = $22,000 ÷ $22* = 1,000 units

Plan B break-even point = fixed costs ÷ unit contribution margin = $66,000 ÷ $30** = 2,200 units

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-33 * $80 - [($80 x 10%) + $50] ** $80 - $50

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.

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

Plan A Plan B

Sales revenue: 6,000 units x $480,0 $480,0 $80………………. 00 00 Less variable costs: Cost of purchasing product: 6,000 units x $300,0 $300,0 $50…………………….…… 00 00 Sales commissions: $480,000 x 48,0 ---- 10%……... 00 Total variable $348,0 $300,0 cost……………………….. 00 00 Contribution $132,0 $180,0 margin……………………………… 00 00 Fixed 22,0 66,0 costs…………………………………………. 00 00 Net $110,0 $114,0 income……………………………………… 00 00 ….

Operating leverage factor = contribution margin ÷ net income Plan A: $132,000 ÷ $110,000 = 1.2 Plan B: $180,000 ÷ $114,000 = 1.58 (rounded)

Plan B has the higher degree of operating leverage.

4 & 5. Calculation of profit at 5,000 units: Plan A Plan B

Sales revenue: 5,000 units x $400,0 $400,0 $80………………. 00 00 Less variable costs: Cost of purchasing product: 5,000 units x $250,0 $250,0 $50………………………….. 00 00 Sales commissions: $400,000 x 40,0 ----

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-35 10%……... 00 Total variable $290,0 $250,0 cost……………………….. 00 00 Contribution $110,0 $150,0 margin……………………………… 00 00 Fixed 22,0 66,0 costs………………………………………… 00 00 Net $ $ income……………………………………… 88,000 84,000 ….

Plan A profitability decrease: $110,000 - $88,000 = $22,000; $22,000 ÷ $110,000 = 20%

Plan B profitability decrease: $114,000 - $84,000 = $30,000; $30,000 ÷ $114,000 = 26.3% (rounded)

Consolidated 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  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-37 PROBLEM 8-40 (30 MINUTES) fixed costs 1. Break-even point(in units)  unitcontributi on margin $468,000   90,000 units $25.00  $19.80

fixed cost 2. Break-even point(in sales dollars)  contribution-margin ratio $468,000   $2,250,000 $25.00  $19.80 $25.00

fixed costs  targetnet profit 3. Number of sales units  required to earn target unitcontributi on margin net profit $468,000  $260,000   140,000 units $25.00  $19.80

4. Margin of = budgeted sales revenue – break-even sales safety revenue = (120,000)($25) – $2,250,000 = $750,000

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

New unit contribution = $25.00 – $10.50 – ($5.00)(1.08) – $3.00 margin – $1.30 = $4.80 fixed costs Break-even point  new unitcontributi on margin $468,000   97,500 units $4.80

unitcontributi on margin 6. Contribution margin  ratio sales price $25.00 $19.80 Old contribution-  margin ratio $25.00  .208

Let P denote sales price required to maintain a contribution- margin ratio of .208. Then P is determined as follows: P  $10.50 ($5.00)(1.08) $3.00 $1.30  .208 P P  $20.20  .208P .792P  $20.20 P  $25.51 (rounded) Chec New $25.51 $10.50 ($5.00)(1.08) $3.00 $1.30  k: contribution- $25.51 margin ratio  .208 (rounded)

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-39 PROBLEM 8-41 (40 MINUTES)

1. CVP graph:

Total revenue Dollars per year (in millions)

9 Profit Break-even point: area 8 80,000 units or $4,000,000 of sales 7 Total 6 expenses 5 4 3 Loss 2 area Fixed 1 expenses Units sold per 50 100 150 200 year (in thousands)

2. Break-even point: contribution margin $6,000,000 Contribution-margin ratio    .75 sales $8,000,000 fixed expenses $3,000,000 Break-even point  contribution-margin ratio .75  $4,000,000

3. Margin of = budgeted sales revenue – break-even sales safety revenue = $8,000,000 – $4,000,000 = $4,000,000

contribution margin (atbudgeted sales) 4. Operating leverage  factor (at budgeted netincome (atbudgeted sales) sales) $6,000,000   2 $3,000,000

fixed expenses  targetnet profit 5. Dollar sales  required to earn contribution-margin ratio target net profit $3,000,000  $4,500,000   $10,000,000 .75

6. Cost structure:

Amount Percent Sales revenue...... $8,000,000 100.0 Variable expenses...... 2,000,000 25 .0 Contribution margin...... $6,000,000 75.0 Fixed expenses...... 3,000,000 37 .5 Net income...... $3,000,000 37 .5

sales  variable costs 1. (a Unitcontributi on margin  ) units sold $1,000,000  $700,000   $3 per unit 100,000

fixed costs Break-even point(in units)  unitcontributi on margin $210,000   70,000 units $3

contribution margin (b Contribution-margin ratio  ) sales revenue $1,000,000  $700,000   .3 $1,000,000

fixed costs Break-even point(in sales dollars)  contribution-margin ratio $210,000   $700,000 .3

targetafter -tax netincome fixed costs  2. Number of units of sales (1  t)  required to earn target unitcontributi on margin after-tax net income $90,000 $210,000  (1  .4) $360,000   $3 $3  120,000 units

3. If fixed costs increase by $31,500: $210,000  $31,500 Break-even point(in units)   80,500 units $3

Dollars per year

$750,000

$500,000

Profit $250,000 Break-even area point: 70,000 units Units sold 0  per year Loss25,000 50,000 75,000 100,000 area

$(250,000 )

$(500,000 )

$(750,000 )

targetafter -tax netincome fixed costs  5. Number of units of (1  t) sales required to  unitcontributi on margin earn target after- tax net income $90,000 $210,000  (1  .5) $390,000   $3 $3

 130,000 units

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

Fixed expenses: Advertising...... $ 490,000 Rent (6,000  $28)...... 168,000 Property insurance...... 27,000 Utilities...... 37,000 Malpractice insurance...... 180,000 Depreciation ($60,000/4)...... 15,000 Wages 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 Fringe benefits at 40%...... 164,280 574,980 Total fixed expenses...... $1,491,980

Break-even point: 0 = revenue – variable cost – fixed cost

0 = $30X + ($2,000  .2X  .3)* – $4X – $1,491,980

0 = $30X + $120X – $4X – $1,491,980

$146X = $1,491,980 X = 10,220 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 = 10,220 (rounded)

Safety margin = [($30  18,000) + ($2,000  18,000  .20  .30)] – [($30  10,220) + ($2,000  10,220  .20  .30)]

= [$30 + ($2,000  .20  .30)]  (18,000 – 10,220)

= $150  7,780 = $1,167,000

1. Break-even point in units: fixed costs Break-even point unitcontributi on margin

Calculation of contribution margins:

Computer- Labor- Assisted Intensive Manufacturing Production System System Selling price...... $30.00 $30.0 0 Variable costs: Direct material...... $5.00 $5.60 Direct labor...... 6.00 7.20 Variable overhead...... 3.00 4.80 Variable selling cost...... 2.00 16.00 2.00 19.60 Contribution margin per $14.00 unit $10.4 0

(a Computer-assisted manufacturing system: )

$2,440,000  $500,000 Break-even pointin units  $14 $2,940,000  $14  210,000 units

(b Labor-intensive production system: )

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-46 Solutions Manual $1,320,000  $500,000 Break-even pointin units  $10.40 $1,820,000  $10.40  175,000 units

2. Celestial Products, Inc. would be indifferent between the two manufacturing methods at the volume (X) where total costs are equal. $16X + = $19.60X + $1,820,000 $2,940,000 $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.

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.

1. Break-even sales volume for each model: annual rental cost Break-even volume  unitcontributi on margin

(a Economy model: ) $8,000 Break-even volume   25,000 tubs $1.75  $1.43

(b Regular model: ) $11,000 Break-even volume   27,500 tubs $1.75  $1.35

(c Super model: ) $20,000 Break-even volume   40,816 tubs (rounded) $1.75  $1.26

Dollars per year (in thousands)

$20 t i f $10 o r

P Break-even point: Profit 40,816 tubs area Units sold 0  per year 10 20 30 40 50 (in Loss thousands) area s

s ($10) o L

Fixed rental cost: $20,000 per ($20) year

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 Economy and Regular models at the sales volume, X, where the total costs are the same. Variable Total Model Cost per Fixed Cost Tub Economy...... $1.43 $ 8,000 Regular...... 1.35 11,000

This reasoning leads to the following equation: 8,000 + 1.43X = 11,000 + 1.35X

Rearranging terms yields the following: (1.43 – 1.35)X = 11,000 – 8,000 .08X = 3,000 X = 3,000/.08 X = 37,500 Or, stated slightly differently:

Volume at which both fixed costdifferenti al  machines produce the variable costdifferenti al same profit $3,000  $.08  37,500 tubs

Check: the total cost is the same with either model if 37,500 tubs are sold.

Economy Regular Variable cost: Economy, 37,500  $1.43...... $53,625 Regular, 37,500  $1.35...... $50,625 Fixed cost: Economy, $8,000...... 8,000 Regular, $11,000...... 11,000 McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-51 Total cost...... $61,625 $61,625

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

$625,000  $375,000 1. Unitcontributi on margin  25,000 units  $10 per unit

fixed costs Break-even point(in units)  unitcontributi on margin $150,000   15,000 units $10

2. Number of sales units fixed costs  targetnet profit  required to earn target unitcontributi on margin net profit $150,000  $140,000   29,000 units $10

new fixed costs 3. New break-even point(in units)  new unitcontributi on margin $150,000  ($18,000/6)*   19,125 units $10  $2†

*Annual straight-line depreciation on new machine †$2.00 = $4.50 – $2.50 increase in the unit cost of the new part

4. Number of sales units new fixed costs  targetnet profit to earn target net  profit, given new unitcontributi on margin manufacturing changes $153,000  $100,000*  $8

 31,625 units *Last year's profit: ($25)(25,000) – $525,000 = $100,000

unitcontributi on margin 5. Contribution-margin ratio  sales price $10 Old contribution-margin ratio   .40 $25*

*Sales price = $25 = $625,000  25,000 units.

Let P denote the price required to cover increased direct- material cost and maintain the same contribution margin ratio:

P  $15*  $2†  .40 P P  $17  .40P .60P  $17 P  $28.33 (rounded)

*Old unit variable cost = $15 = $375,000  25,000 units †Increase in direct-material cost = $2

Check:

$28.33  $15  $2 New contribution-margin ratio  $28.33  .40 (rounded)

1. Memorandum

Date: Today

To: Vice President for Manufacturing, Jupiter Game Company

From: I.M. Student, Controller

Subject: Activity-Based Costing

The $150,000 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 activity-based 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...... $26 Costs that are variable (with respect to sales volume): Unit variable cost (.8  $375,000  25,000)...... 12 Unit contribution margin...... $14

Costs that are fixed (with respect to sales volume): Setup (300 setups at $50 per setup)...... $ 15,000 Engineering (800 hours at $28 per hour)...... 22,400 Inspection (100 inspections at $45 per inspection) 4,500 General factory overhead...... 166,100 Total...... $208,000 Fixed selling and administrative costs...... 30,000 Total costs that are fixed (with respect to sales volume) $238,000

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-55 fixed costs Break-even point(in units)  unitcontributi on margin $238,000  $14  17,000 units

3. Sales (in units) required to show a profit of $140,000:

Number of sales units fixed cost targetnet profit  required to earn target unitcontributi on margin net profit $238,000  $140,000  $14  27,000 units

4. 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 ) $140,000 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 ($14 instead of $10) earns a profit at a faster rate. This results in the firm needing to sell fewer units to reach a given target profit level.

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.

1. Closing of downtown store:

Loss of contribution margin at Downtown Store...... $(36,000) Savings of fixed cost at Downtown Store (75%)...... 30,000 Loss of contribution margin at Mall Store (10%)...... (4,800) Total decrease in operating income...... $(10,800)

2. Promotional campaign:

Increase in contribution margin (10%)...... $ 3,600 Increase in monthly promotional expenses ($60,000/12) (5,000) Decrease in operating income...... $(1,400)

3. Elimination of items sold at their variable cost:

We can restate the November 20x1 data for the Downtown Store as follows:

Downtown Store Items Sold at Their Variable Other Cost Items Sales...... $60,000* $60,000* Less: variable expenses...... 60,000 24,000 Contribution margin...... $ -0- $ 36,000

If the items sold at their variable cost are eliminated, we have: Decrease in contribution margin on other items (20%). $ (7,200) Decrease in fixed expenses (15%)...... 6,000 Decrease in operating income...... $ (1,200)

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-59 *$60,000 is one half of the Downtown Store's dollar sales for November 20x1.

1. CINCINNATI TOOL COMPANY BUDGETED INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20X2 Hedge Weeders Clippers Leaf Total Blowers Unit selling price...... $28 $36 $48 Variable manufacturing $13 $12 $25 cost...... Variable selling cost...... 5 4 6 Total variable cost...... $18 $16 $31 Contribution margin per $10 $20 $17 unit...... Unit sales......  50,000   50,000 100,000 Total contribution margin...... $500,00 $1,000,0 $1,700,00 $3,200,0 0 00 0 00

Fixed manufacturing overhead...... $2,000,0 00 Fixed selling and administrative costs... 600,000 Total fixed costs...... $2,600,0 00 Income before taxes...... $600,000 Income taxes (40%)...... 240,000 Budgeted net income..... $ 360,000

2. (a) (b)

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-61 Unit Sales Contributio Proportion (a)  (b) n Weeders...... $10 .25 $ 2.50 Hedge Clippers...... 20 .25 5.00 Leaf Blowers...... 17 .50 8.50 Weighted-average unit contribution margin...... $16.00 total fixed costs Total unitsales to breakeven  weighted-average unitcontributi on margin $2,600,000   162,500 units $16

Sales proportions:

Sales Total Product Proporti Unit Line on Sales Sales Weeders...... 25 162,50 40,625 0 Hedge Clippers...... 25 162,50 40,625 0 Leaf Blowers...... 50 162,50 81,250 0 Total...... 162,500

3. (a) (b) Unit Sales Contribut Proporti (a)  ion on (b) Weeders...... $10 .20 $ 2.00 Hedge Clippers*...... 19 .20 3.80 Leaf Blowers†...... 12 .60 7.20 Weighted-average unit $13.00 contribution margin......

*Variable selling cost increases. Thus, the unit contribution decreases to $19 [$36 – ($12 + $4 + $1)]. †The variable manufacturing cost increases 20 percent. Thus, the unit contribution decreases to $12 [$48 – (1.2  $25) – $6]. total fixed costs Total unitsales to breakeven  weighted-average unitcontributi on margin $2,600,000   200,000 units $13 Sales proportions:

Sales Total Product Proporti Unit Line

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-63 ons Sales Sales Weeders...... 20 200,000 40,000 Hedge Clippers...... 20 200,000 40,000 Leaf Blowers...... 60 200,000 120,000 Total...... 200,000

1. $405,000 Unitcontributi on margin   $225 per ton 1,800

fixed costs Break-even volume in tons  unitcontributi on margin

$247,500   1,100 tons $225

2. Projected net income for sales of 2,100 tons:

Projected contribution margin (2,100  $225)...... $472,500 Projected fixed costs...... 247,500 Projected net income...... $225,000

3. Projected net income including foreign order: Variable cost per ton = $495,000/1,800 = $275 per ton

Sales price per ton for regular orders = $900,000/1,800 = $500 per ton

Foreign Regular Order Sales Sales in tons...... 1,500 1,500 Contribution margin per ton: Foreign order ($450 – $275)......  $175 Regular sales ($500 – $275)......  $225 Total contribution margin...... $337,500 $262,500

Contribution margin on foreign order...... $262,500 Contribution margin on regular sales...... 337,500 Total contribution margin...... $600,000 Fixed costs...... 247,500 Net income...... $352,500

4. New sales territory:

To maintain its current net income, Ohio Limestone Company just needs to break even on sales in the new territory.

fixed costs in new territory Break-even pointin tons  unitcontributi on margin on sales in new territory $61,500   307.5 tons $225  $25

5. Automated production process: $247,500  $58,500 Break-even pointin tons  $225  $25 $306,000   1,224 tons $250

Break-even pointin sales dollars  1,224 tons  $500 per ton  $612,000

6. Changes in selling price and unit variable cost: New unitcontributi on margin  ($500)(90%)  ($275  $40)  $135

$135 New contribution margin ratio  ($500)(90%)  .30

fixed costs  targetnet profit Dollar sales required to earn targetnet profit  contribution margin ratio $247,500  $94,500  .30  $1,140,000

$80.00  $52.80 1. Contribution margin ratio   .34 $80.00

targetafter -tax netincome fixed expenses  2. Number of units of sales (1  t)  required to earn target unitcontributi on margin after-tax income $22,080 $316,800  (1  .40) $353,600 X   $80.00  $52.80 $27.20 X  13,000 units

3. Break-even point (in $369,600   10,500 units units) for the $88.00 $52.80 mountaineering model

Let Y denote the variable cost of the touring model such that the break-even point for the touring model is 10,500 units.

Then we have: $316,800 10,500  $80.00Y (10,500)($80.00Y)  $316,800 $840,00010,500Y  $316,800 10,500Y  $523,200 Y  $49.83 (rounded)

Thus, the variable cost per unit would have to decrease by $2.97 ($52.80 – $49.83).

4. $316,800  110% New break-even point $80.00  ($52.80)(90%) $348,480  $32.48  10,729 units (rounded)

5. Weighted-average unit  (50%  $35.20)  (50%  $27.20) contribution  $31.20 margin fixed costs  weighted-average unitcontributi on margin $343,200 Break-even point   11,000 units (or 5,500 of each type) $31.20

1. SUMMARY OF EXPENSES

Expenses per Year (in thousands) Variable Fixed Manufacturing...... $7,200 $2,340 Selling and administrative...... 2,400 1,920 Interest...... 540 Costs from budgeted income statement $9,600 $4,800 If the company employs its own sales force: Additional sales force costs...... 2,400 Reduced commissions [(.15 – .10)  (800) $16,000]...... Costs with own sales force...... $8,800 $7,200 If the company sells through agents: Deduct cost of sales force...... (2,400) Increased commissions [(.225 – .10)  2,000 $16,000]...... Costs with agents paid increased $ 10,800 $4,800 commissions......

total fixed expenses Break-even sales dollars  contribution margin ratio total variable expenses Contribution-margin ratio  1  sales revenue $9,600,000 (a Contribution margin ratio  1  ) $16,000,000  1  .60  .40 $4,800,000 Break-even sales dollars  .40  $12,000,000

$8,800,000 (b Contribution margin ratio  1  ) $16,000,000  1  .55  .45 $7,200,000 Break-even sales dollars  .45  $16,000,000

total fixed costs  targetincome before income taxes 2. Required sales dollars  contribution margin ratio

$10,800 Contribution margin ratio  1  $16,000  1  .675  .325

$4,800,000  $1,600,000 Required sales dollars to breakeven  .325 $6,400,000  .325  $19,692,308

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 = total expenses with own sales agents paid increased force commission $10,800,000 $8,800,000 X  $4,800,000 X  $7,200,000 $16,000,000 $16,000,000 .675X  $4,800,000  .55X  $7,200,000 .125X  $2,400,000 X  $19,200,000

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.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-70 Solutions Manual SOLUTIONS TO CASES CASE 8-53 (50 MINUTES)

1. The break-even point is 16,900 patient-days calculated as follows:

COMPUTATION OF BREAK-EVEN POINT IN PATIENT-DAYS: PEDIATRICS FOR THE YEAR ENDED JUNE 30, 20X2

Total fixed costs: Medical center charges...... $2,900,000 Supervising nurses...... ($25,000  4) 100,000 Nurses ($20,000  10)...... 200,000 Aids ($9,000  20)...... 180,000 Total fixed costs...... $3,380,000 Contribution margin per patient-day: Revenue per patient-day...... $300 Variable cost per patient-day: ($6,000,000 ÷ $300 = 20,000 patient-days) ($2,000,000 ÷ 20,000 patient-days)...... 100 Contribution margin per patient-day...... $200

Break-even total fixed costs $3,380,000   point in contribution margin per patient-day $200 patient-days  16,900 patientdays

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-71 CASE 8-53 (CONTINUED)

2. Net earnings would decrease by $606,660, calculated as follows:

COMPUTATION OF LOSS FROM RENTAL OF ADDITIONAL 20 BEDS: PEDIATRICS FOR THE YEAR ENDED JUNE 30, 20X2

Increase in revenue (20 additional beds  90 days  $300 charge per day)..... $ 540,000

Increase in expenses: Variable charges by medical center (20 additional beds  90 days  $100 per day)...... $180,000

Fixed charges by medical center ($2,900,000  60 beds = $48,333 per bed, rounded) ($48,333  20 beds)...... 966,660

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)...... -0- Total increase in expenses...... $1,146,660 Net change in earnings from rental of additional 20 beds... $ (606,660)

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-72 Solutions Manual CASE 8-54 (45 MINUTES)

1. a. In order to break even, Oakley must sell 500 units. This amount represents the point where revenue equals total costs.

Revenue variable costs  fixed costs $400X $200X $100,000 $200X $100,000 X  500 units

b. In order to achieve its after-tax profit objective, Oakley 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 $400X $200X $100,000 [$240,000 (1 .4)] $400X $200X $100,000 $400,000 $200X $500,000 X 2,500 units

2. To achieve its annual after-tax profit objective, Oakley should select the first alternative, where the sales price is reduced by $40 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.

Alternative (1):

Revenue ($400)(350) ($360)(2,700)  $1,112,000 Variable cost $200 3,050  $610,000 Before-tax profit $1,112,000 $610,000 $100,000  $402,000 After-tax profit $402,000 (1 .4)  $241,200

Alternative (2):

Revenue ($400)(350) ($370)(2,200)  $954,000 Variable cost ($200)(350) ($175)(2,200)  $455,000 Before-tax profit $954,000 $455,000 $100,000  $399,000 After-tax profit $399,000 (1 .4)  $239,400

Alternative (3):

Revenue ($400)(350) ($380)(2,000)  $900,000 Variable cost $200 2,350  $470,000 Before-tax profit $900,000 $470,000 $90,000  $340,000 After-tax profit $340,000 (1 .4)  $204,000

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-74 Solutions Manual CASE 8-55 (50 MINUTES)

1. Break-even point for 20x2, based on current budget: $10,000,000  $6,000,000  $2,000,000 Contribution-margin ratio   .20 $10,000,000 fixed expenses Break-even point contribution-margin ratio $100,000   $500,000 .20

2. Break-even point given employment of sales personnel: New fixed expenses:

Previous fixed expenses...... $100,000 Sales personnel salaries...... 90,000 Sales manager's salary...... 160,000 Total...... $ 350,000

New contribution-margin ratio:

Sales...... $10,000,000 Cost of goods sold...... 6,000,000 Gross margin...... $ ...... 4,000,000 Commissions (at 5%)...... 500,000 Contribution margin...... $ ...... 3,500,000 $3,500,000 Contribution-margin ratio   .35 $10,000,000

fixed expenses Estimated break-even point contribution-margin ratio $350,000   $1,000,000 .35

3. Assuming a 25% sales commission:

New contribution-margin ratio:

Sales...... $10,000,000 Cost of goods sold...... 6,000,000 Gross margin...... $ ...... 4,000,000 Commissions (at 25%)...... 2,500,000 Contribution margin...... $ ...... 1,500,000

$1,500,000 Contribution-margin ratio   .15 $10,000,000 targetafter -tax netincome fixed expenses  Sales volume in (1  t)  dollars required to contribution-margin ratio earn after-tax net $1,330,000 income $100,000  (1  .3) $2,000,000   .15 .15  $13,333,333 (rounded)

Check (all figures rounded to the nearest dollar):

Sales...... $ 13,333,333 Cost of goods sold (60% of sales)... 8,000,000 Gross margin...... $ 5,333,333 Selling and administrative expenses: Commissions...... $ 3,333,333 All other expenses (fixed)...... 100,000 3,433,333 Income before taxes...... $ 1,900,000 Income tax expense (30%)...... 570,000

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-76 Solutions Manual Net income...... $ 1,330,000

4. Sales dollar volume at which Niagra Falls 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 – $350,000 = .15X – $100,000 .20X = $250,000 X = $250,000/.20 X = $1,250,000

Thus, the company will have the same before-tax income under the two alternatives if the sales volume is $1,250,000.

Check:

Alternatives Employ Sales Pay 25% Personne Commissi l on Sales...... $1,250,0 00 $1,250,00 0 Cost of goods sold (60% of sales)...... 750,000 750,000 Gross margin...... $500,000 $500,000 Selling and administrative expenses: Commissions...... 62,500* 312,500† All other expenses (fixed)...... 350,000 100,000 Income before taxes...... $87,500 $87,500 Income tax expense (30%)...... 26,250 26,250 Net income...... $ 61,250 $ 61,250

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-78 Solutions Manual *$1,250,000  5% = $62,500 †$1,250,000  25% = $312,500

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-79 CURRENT ISSUES IN MANAGERIAL ACCOUNTING ISSUE 8-56

"RELIANCE GROUP MAY SEE SHIELD FROM CREDITORS," THE WALL STREET JOURNAL, AUGUST 15, 2000, DEVON SPURGON, GREGORY ZUCKERMAN, AND FRANCINE L. POPE.

1. 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.

2. In the article, high operating leverage was not working to benefit Reliance Group Holdings, Inc. Consequently, its stock rating was downgraded.

ISSUE 8-57

"E-COMMERCE -- DEBATE -- TALKING TO THE PLAYERS: WILL THE INTERNET TAKE OVER COMMERCE? WE ASKED THREE PEOPLE WHO ASK THEMSELVES THAT QUESTION ALL THE TIME," THE WALL STREET JOURNAL, JULY 12, 1999, THOMAS E. WEBER.

According to Ken Seiff, Amazon is capturing such a huge amount of market share that it will eventually be able to build the most cost efficient distribution system, not only in the e-commerce field, but also in the traditional retail world. Once Amazon has developed this system and cemented its place as the online retailer of choice, price wars will not be as costly for Amazon as for its competitors.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-80 Solutions Manual ISSUE 8-58

"HAPPY SHOPPER," MANAGEMENT ACCOUNTING, JULY/AUGUST 2000, TONY BRABAZON.

The cost of losing a customer will vary across the customer life cycle. The loss can be estimated using discounted customer contribution margin, where the discounted customer contribution margin is calculated as the gross profit per customer less customer- related costs such as administration, distribution and financing.

ISSUE 8-59

"POSTAL SERVICE COULD FACE LOSS," THE ASSOCIATED PRESS, AUGUST 31, 2000, RANDOLPH E. SCHMID.

1. It is important for the U.S. Postal Service to forecast the volume and cost variables discussed in the article so its management can determine the revenue required to cover costs and determine cost of postage.

2. Unexpected costs will increase the break-even point in cost- volume-profit analysis. A decline in the volume of first-class mail will decrease the weighted-average contribution margin and increase the break-even point. An increase in advertising mail will increase revenue and decrease the breakeven point.

ISSUE 8-60

"START YOUR OWN FIRM," JOURNAL OF ACCOUNTANCY, MAY 2000, ROBERT B. SCOTT, JR.

1. The contribution margin is defined as sales revenue less all variable costs.

2. For a CPA firm, as described in the article, the contribution margin would be calculated as a client’s total fees less all direct-service costs, such as staff time. According to the article, a client who generates total fees that are one and one half times the cost to service the engagement, especially a large

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-81 client, may be worth keeping and developing. If the CPA is unable to recover at least one and one half times the direct- service cost, the CPA should consider ending the relationship.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. 8-82 Solutions Manual ISSUE 8-61

"CHAIN REACTION," CMA MANAGEMENT, MARCH 1999, ANDREA SIGURDSON.

1. Cost-volume-profit analysis is a study of the relationships between sales volume, expenses, revenue, and profit.

2. CVP analysis can be applied to determine the effectiveness of an investment, for example, in seasonal price discounting or price specials. In price-sensitive categories, managers can use detailed studies of consumer price elasticity to better understand the ongoing relationship between pricing, volume and category profits. The principles of activity-based management applied to product categories can help management understand the actual costs of distribution and warehousing at the individual item level. A true picture of category and subcategory profitability can then be determined. Real estate and occupancy costs are also charged back to product categories within the store to develop a comprehensive picture of total profit or loss for each category. Using this information, retailers can assign strategic roles to each product category. High profile ones, although not always strong profit contributors, can help build overall customer traffic. Assigning clear category roles aids in the decision making process when allocating investment resources or scarce retail space among competing product categories.

McGraw-Hill/Irwin  2002 The McGraw-Hill Companies, Inc. Managerial Accounting, 5/e 8-83