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CHAPTER 8Cost-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:

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

fixed expenses

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.

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.

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

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.

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

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.


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...............................................100 units at $20...............................................

Variable expenses:350 units at $6.................................................100 units at $6.................................................

Contribution margin.............................................Fixed expenses.....................................................Profit.......................................................................

$3,500

2,100 $1,400 1,000$ 400

$2,000

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.


SOLUTIONS TO EXERCISESEXERCISE 8-23 (25 MINUTES)

Sales Revenue

Variable Expenses

Total Contribution

MarginFixed

ExpensesNet

Income

Break-even Sales

Revenue1 $160,000a $40,000 $120,000 $30,000 $90,000 $40,0002 80,000 65,000 15,000 15,000b -0- 80,0003 120,000 40,000 80,000 30,000 50,000 45,000c

4 110,000 22,000 88,000 50,000 38,000 62,500d

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)

1. Break-even point (in units) =

= = 8,000 pizzas

2. Contribution-margin ratio =

= = .5


EXERCISE 8-24 (CONTINUED)

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

= = $80,000

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


1. Break-even point (in units) =

= = 4,000 components

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

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

= = 4,400 components

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



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

= 8,000 components

5. Analysis of price change decision:Price

3,000p 2,500pSales revenue: (5,000 3,000p)................................

(6,200 2,500p)................................Variable costs: (5,000 2,000p)................................

(6,200 2,000p)................................Contribution margin.....................................................Fixed expenses .............................................................Net income (loss)..........................................................

15,000,000p

10,000,000p 5,000,000p 4,000,000 p 1,000,000 p

15,500,000p

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

(900,000 p )

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



1. Cost-volume-profit graph:


Break-even point:20,000 tickets

Total revenue

Total expenses

Variable expense

(at 30,000 tickets)

Annual fixed

expenses

Tickets sold per

year5,000 10,000 15,000 20,000 25,000 30,000

Dollars per year

$300,000

$250,000

$200,000

$150,000

$100,000

$50,000

Profitarea

Loss area


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

The team must play 4 games to break even.



1. Profit-volume graph:


Dollars per year

$150,000

$100,000

$50,000

0

$(50,000)

$(100,000)

$(150,000)

$(180,000)

Annual fixed expenses

Tickets sold per year

Break-even point:20,000 tickets Profit

area

Loss area

5,000 10,000 15,000 20,000 25,000


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)($1) – $180,000 = 060,000P = $240,000

P = $4 per ticket



1. (a) Traditional income statement:EUROPA PUBLICATIONS, INC.

INCOME STATEMENTFOR THE YEAR ENDED DECEMBER 31, 20XX

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

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

Net income..................................................................... $ 200,000

(b) Contribution income statement:EUROPA PUBLICATIONS, INC.

INCOME STATEMENTFOR THE YEAR ENDED DECEMBER 31, 20SXX

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

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

Contribution margin..................................................... $ 870,000Less: Fixed expenses:

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

Net income..................................................................... $ 200,000

2.



3.

= 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.

Bicycle TypeSales Price

Unit Variable Cost

Unit Contribution Margin

High-quality $500 $300 ($275 + $25) $200Medium-quality 300 150 ($135 + $15) 150

2. Sales mix:

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

3. Weighted-average unit contribution margin = ($200 25%) + ($150 75%)

= $162.50

4.

Bicycle TypeBreak-Even

Sales Volume Sales PriceSales

RevenueHigh-quality bicycles 100 (400

.25)$500 $ 50,000

Medium-quality bicycles 300 (400 .75)

300 90,000

Total $140,000


EXERCISE 8-29 (CONTINUED)5. Target net income:

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)


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

2.Decrease in

RevenueContribution Margin

PercentageDecrease inNet Income

$75,000* 40%† = $30,000

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



3.

4.


Requirement (1) Requirement (2)Revenue........................................................ $600,000 $ 500,000Less: 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 )


1.

2.



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

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


SOLUTIONS TO PROBLEMSPROBLEM 8-34 (30 MINUTES)

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

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

X =

= 150,000 units

2. New projected sales volume = 200,000 110%= 220,000 units

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:

Volume of sales dollars required


PROBLEM 8-34 (CONTINUED)

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

Check: New contribution-margin ratio is:

PROBLEM 8-35 (30 MINUTES)

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

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



3. New unit variable manufacturing cost = $8 110%= $8.80

Break-even point in sales dollars:

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

Check: New contribution-margin ratio is:



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

Sales commissions ($64 x 5%)…… $ 3.20System variable costs……………… 16.00 19.20

Unit contribution margin……………….. $44.80

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

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

Model ModelNo. 6754 No. 4399

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

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

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

Total variable costs……………………….. $ 883,200 $ 736,000Contribution margin…………………………... $2,060,800 $2,208,000Less: Annual fixed costs…………………….. 985,600 1,113,600 Net income……………………………………… $1,075,200 $1,094,400

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

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

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



1. Current income:

Sales revenue………………………... $3,360,000Less: Variable costs………………… $ 840,000

Fixed costs……………………. 2,280,000 3,120,000 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 costsX ÷ $60 = 32,000 unitsX = $1,920,000

(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 unitsX = $71.25


PROBLEM 8-37 (CONTINUED

4. (a) Increase

(b) No effect

(c) Increase

(d) No effect


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), whichcompares 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

UnitsSales Mix Units

Sales Mix

Deluxe……... 39,000 65% 45,500 70%Basic………. 21,000 35% 19,500 30%

Total 60,000 100% 65,000 100%

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

Deluxe sales: 45,500 units x $86… $3,913,000Basic sales: 19,500 units x $74….. 1,443,000

Total………………………………. $5,356,000



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

Current Plan ASales revenue:

Deluxe: 39,000 units x $86; 45,500 units x $86… $3,354,000 $3,913,000Basic: 21,000 units x $74; 19,500 units x $74….. 1,554,000 1,443,000

Total revenue……………………………………. $4,908,000 $5,356,000Less variable cost:

Deluxe: 39,000 units x $65; 45,500 units x $65… $2,535,000 $2,957,500Basic: 21,000 units x $41; 19,500 units x $41….. 861,000 799,500Sales commissions (10% of sales revenue)……. 535,600

Total variable cost……………………………… $3,396,000 $4,292,600Contribution margin…………………………………….. $1,512,000 $1,063,400Less fixed cost (salaries)………………………………. 400,000 ---- Net income………………………………………………... $1,112,000 $1,063,400

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

UnitsSales Mix Units

Sales Mix

Deluxe……... 45,500 70% 26,000 40%Basic………. 19,500 30% 39,000 60%

Total…… 65,000 100% 65,000 100%



(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 BSales revenue:

Deluxe: 39,000 units x $86; 26,000 units x $86… $3,354,000 $2,236,000Basic: 21,000 units x $74; 39,000 units x $74….. 1,554,000 2,886,000

Total revenue……………………………………. $4,908,000 $5,122,000Less variable cost:

Deluxe: 39,000 units x $65; 26,000 units x $65… $2,535,000 $1,690,000Basic: 21,000 units x $41; 39,000 units x $41….. 861,000 1,599,000

Total variable cost……………………………… $3,396,000 $3,289,000Contribution margin…………………………………….. $1,512,000 $1,833,000Less: Sales force compensation:

Flat salaries…………………………………………... 400,000 Commissions ($1,833,000 x 30%)………………… 549,900

Net income ……………………………………………….. $1,112,000 $1,283,100


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

* $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 $80………………. $480,000 $480,000Less variable costs:

Cost of purchasing product: 6,000 units x $50…………………….…… $300,000 $300,000Sales commissions: $480,000 x 10%……... 48,000 ----

Total variable cost……………………….. $348,000 $300,000Contribution margin……………………………… $132,000 $180,000Fixed costs…………………………………………. 22,000 66,000 Net income…………………………………………. $110,000 $114,000

Operating leverage factor = contribution margin ÷ net incomePlan A: $132,000 ÷ $110,000 = 1.2Plan 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 $80………………. $400,000 $400,000Less variable costs:

Cost of purchasing product: 5,000 units x $50………………………….. $250,000 $250,000Sales commissions: $400,000 x 10%……... 40,000 ----

Total variable cost……………………….. $290,000 $250,000Contribution margin……………………………… $110,000 $150,000Fixed costs………………………………………… 22,000 66,000 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.



1.

2.

3. Number of sales units required to earn target net profit

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

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

New unit contribution margin = $25.00 – $10.50 – ($5.00)(1.08) – $3.00 – $1.30 = $4.80

Break-even point



6. Contribution margin ratio

Old contribution-margin ratio

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

Check: New contribution-margin ratio



1. CVP graph:


Total expenses

Break-even point:80,000 units or

$4,000,000 of sales

Total revenue

Fixed expenses

Units sold per year (in thousands)50 100 150 200

Dollars per year(in millions)

10

9

8

7

6

5

4

3

2

1

Profit area

Loss area


2. Break-even point:

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

4. Operating leverage factor (at budgeted sales)

5. Dollar sales required to earn target net profit

6. Cost structure:

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



1. (a)

(b)

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

3. If fixed costs increase by $31,500:





Dollars per year

$750,000

$500,000

$250,000

0

$(250,000)

$(500,000)

$(750,000)

Loss area

25,000 50,000 75,000 100,000Units sold per year

Break-even point:70,000 units

Profitarea


5. Number of units of sales required to earn target

after-tax net income


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................................................................................ $ 490,000Rent (6,000 $28).................................................................... 168,000Property insurance................................................................... 27,000Utilities ...................................................................................... 37,000Malpractice insurance.............................................................. 180,000Depreciation ($60,000/4)........................................................... 15,000Wages and fringe benefits:

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

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

Total wages............................................................. $410,700Fringe 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 = $1,491,980X = 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:

Calculation of contribution margins:

Computer-Assisted Manufacturing System

Labor-Intensive Production System

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

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

Contribution margin per unit $14.00 $10.40

(a) Computer-assisted manufacturing system:

(b) Labor-intensive production system:



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

$3.60X = $1,120,000X = 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:

(a) Economy model:

(b) Regular model:

(c) Super model:





Dollars per year (in thousands)

$20

$10

0

($10)

($20)

10 20 30 40 50Units sold per year

(in thousands)

Break-even point:40,816 tubs

Fixed rental cost: $20,000 per year

Prof

itLo

ss

Loss area

Profit area


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.

ModelVariable Cost

per TubTotal

Fixed CostEconomy..................................................... $1.43 $ 8,000Regular........................................................ 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 = 37,500Or, stated slightly differently:

Volume at which both machines produce the same profit

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

Economy RegularVariable cost:

Economy, 37,500 $1.43.......................... $53,625Regular, 37,500 $1.35............................. $50,625

Fixed cost:Economy, $8,000........................................ 8,000Regular, $11,000......................................... 11,000

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.



1.

2. Number of sales units required to earn target net profit

3.

*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 requiredto earn target net profit, given

manufacturing changes

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



5.

*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:

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

Check:



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...................................................................................................... $26Costs that are variable (with respect to sales volume):

Unit variable cost (.8 $375,000 ¸ 25,000).......................................... 12Unit contribution margin............................................................................... $14

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

Total............................................................................................ $208,000Fixed selling and administrative costs............................................... 30,000

Total costs that are fixed (with respect to sales volume)........... $238,000



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

Number of sales units required to earn target net profit

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%)............................................ 30,000Loss of contribution margin at Mall Store (10%)........................................... (4,800)Total decrease in operating income................................................................ $(10,800)

2. Promotional campaign:

Increase in contribution margin (10%)............................................................ $ 3,600Increase 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 StoreItems Sold at

Their Variable Cost Other 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 )

*$60,000 is one half of the Downtown Store's dollar sales for November 20x1.



1.CINCINNATI TOOL COMPANY

BUDGETED INCOME STATEMENTFOR THE YEAR ENDED DECEMBER 31, 20X2

WeedersHedge

Clippers Leaf Blowers TotalUnit selling price............................... $28 $36 $48 Variable manufacturing cost............ $13 $12 $25Variable selling cost.......................... 5 4 6Total variable cost............................. $18 $16 $31Contribution margin per unit............ $10 $20 $17Unit sales........................................... 50,000 50,000 100,000

Total contribution margin............ $500,000 $1,000,000 $1,700,000 $3,200,000

Fixed manufacturing overhead........ $2,000,000Fixed selling and

administrative costs..................... 600,000 Total fixed costs........................... $2,600,000

Income before taxes.......................... $600,000Income taxes (40%)........................... 240,000Budgeted net income........................ $ 360,000

2.(a) Unit

Contribution

(b) Sales

Proportion (a) (b)Weeders........................................................ $10 .25 $ 2.50Hedge Clippers............................................. 20 .25 5.00Leaf Blowers................................................. 17 .50 8.50Weighted-average unit

contribution margin............................... $16.00



Sales proportions:

Sales Proportion

Total Unit Sales

Product Line Sales

Weeders......................................................... .25 162,500 40,625 Hedge Clippers.............................................. .25 162,500 40,625 Leaf Blowers.................................................. .50 162,500 81,250 Total................................................................ 162,500

3.(a) Unit

Contribution

(b) Sales

Proportion (a) (b)Weeders.................................................................... $10 .20 $ 2.00Hedge Clippers*....................................................... 19 .20 3.80Leaf Blowers†........................................................... 12 .60 7.20Weighted-average unit contribution margin......... $13.00

*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].

Sales proportions:

Sales Proportions

Total Unit Sales

Product Line Sales

Weeders............................................................... .20 200,000 40,000Hedge Clippers.................................................... .20 200,000 40,000Leaf Blowers........................................................ .60 200,000 120,000 Total...................................................................... 200,000



1.

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

Projected contribution margin (2,100 $225)....................................... $472,500Projected fixed costs................................................................................ 247,500Projected 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 Order

Regular Sales

Sales in tons...................................................................... 1,500 1,500Contribution margin per ton:

Foreign order ($450 – $275)....................................... $175Regular sales ($500 – $275)....................................... $225

Total contribution margin................................................ $262,500 $337,500

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

5. Automated production process:

6. Changes in selling price and unit variable cost:



1.

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

3. Break-even point (in units) for the 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:

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



4.

5. Weighted-average unitcontribution margin

Break-even point


1. SUMMARY OF EXPENSES

Expenses per Year (in thousands)

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

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

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

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

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

Costs with agents paid increased commissions............ $ 10,800 $4,800



(a)

(b)

2.



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

Total expenses with agents paid increased commission = total expenses with own sales force

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


SOLUTIONS TO CASESCASE 8-53 (50 MINUTES)

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

COMPUTATION OF BREAK-EVEN POINTIN PATIENT-DAYS: PEDIATRICS

FOR THE YEAR ENDED JUNE 30, 20X2

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


CASE 8-53 (CONTINUED)

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

COMPUTATION OF LOSS FROM RENTALOF ADDITIONAL 20 BEDS: PEDIATRICSFOR 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 )


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.

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.

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):

Alternative (2):

Alternative (3):


CASE 8-55 (50 MINUTES)

1. Break-even point for 20x2, based on current budget:

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

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

New contribution-margin ratio:

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



3. Assuming a 25% sales commission:

New contribution-margin ratio:

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

Sales volume in dollars required to earn after-tax

net income

Check (all figures rounded to the nearest dollar):

Sales..................................................................... $ 13,333,333Cost of goods sold (60% of sales)..................... 8,000,000 Gross margin....................................................... $ 5,333,333Selling and administrative expenses:

Commissions................................................. $ 3,333,333All other expenses (fixed)............................. 100,000 3,433,333

Income before taxes............................................ $ 1,900,000Income tax expense (30%).................................. 570,000 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 = $250,000X = $250,000/.20X = $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:

AlternativesEmploy Sales

PersonnelPay 25%

CommissionSales.............................................................................. $1,250,000 $1,250,000Cost of goods sold (60% of sales).............................. 750,000 750,000 Gross margin................................................................ $ 500,000 $ 500,000Selling and administrative expenses:

Commissions............................................................ 62,500* 312,500†

All other expenses (fixed)....................................... 350,000 100,000 Income before taxes..................................................... $ 87,500 $ 87,500Income tax expense (30%)........................................... 26,250 26,250 Net income.................................................................... $ 61,250 $ 61,250

*$1,250,000 5% = $62,500 †$1,250,000 25% = $312,500


CURRENT ISSUES IN MANAGERIAL ACCOUNTINGISSUE 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.


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 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.


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.


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