ch03sol

CHAPTER 3COST-VOLUME-PROFIT ANALYSIS

3-1 Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, and operating income as changes occur in the output level, selling price, variable costs per unit, and/or fixed costs of a product.

3-2 The assumptions underlying the CVP analysis outlined in Chapter 3 are:

1. Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units produced and sold.

2. Total costs can be separated into a fixed component that does not vary with the output level and a component that is variable with respect to the output level.

3. When represented graphically, the behavior of total revenues and total costs are linear (represented as a straight line) in relation to output units within a per unit relevant range and time period.

4. The selling price, variable cost per unit, and fixed costs are known and constant.5. The analysis either covers a single product or assumes that the sales mix, when multiple

products are sold, will remain constant as the level of total units sold changes.6. All revenues and costs can be added and compared without taking into account the time

value of money.

3-3 Operating income is total revenues from operations for the accounting period minus cost of goods sold and operating costs (excluding income taxes):

Operating income = Total revenues from operations –

Net income is operating income plus nonoperating revenues (such as interest revenue) minus nonoperating costs (such as interest cost) minus income taxes. Chapter 3 assumes nonoperating revenues and nonoperating costs are zero. Thus, Chapter 3 computes net income as:

Net income = Operating income – Income taxes

3-4 Contribution margin is the difference between total revenues and total variable costs. Contribution margin per unit is the difference between selling price and variable cost per unit. Contribution-margin percentage is the contribution margin per unit divided by selling price.

3-5 Three methods to calculate the breakeven point are the equation method, the contribution margin method, and the graph method. In the first two methods, the breakeven units are calculated by dividing total fixed costs by contribution margin per unit.

3-6 Breakeven analysis denotes the study of the breakeven point, which is often only an incidental part of the relationship between cost, volume, and profit. Cost-volume-profit relationship is a more comprehensive term than breakeven analysis.

3-1

3-7 CVP certainly is simple, with its assumption of output as the only revenue and cost driver, and linear revenue and cost relationships. Whether these assumptions make it simplistic depends on the decision context. In some cases, these assumptions may be sufficiently accurate for CVP to provide useful insights. The examples in Chapter 3 (the software package context in the text and the travel agency example in the Problem for Self-Study) illustrate how CVP can provide such insights. In more complex cases, the basic ideas of simple CVP analysis can be expanded.

3-8 An increase in the income tax rate does not affect the breakeven point. Operating income at the breakeven point is zero, and no income taxes are paid at this point.

3-9 Sensitivity analysis is a "what-if" technique that managers use to examine how a result will change if the original predicted data are not achieved or if an underlying assumption changes. The advent of the electronic spreadsheet has greatly increased the ability to explore the effect of alternative assumptions at minimal cost. CVP is one of the most widely used software applications in the management accounting area.

3-10 Examples include:Manufacturing––substituting a robotic machine for hourly wage workers.Marketing––changing a sales force compensation plan from a percent of sales dollars to

a fixed salary.Customer service––hiring a subcontractor to do customer repair visits on an annual

retainer basis rather than a per-visit basis.

3-11 Examples include:Manufacturing––subcontracting a component to a supplier on a per-unit basis to avoid

purchasing a machine with a high fixed depreciation cost.Marketing––changing a sales compensation plan from a fixed salary to percent of sales

dollars basis.Customer service––hiring a subcontractor to do customer service on a per-visit basis

rather than an annual retainer basis.

3-12 Operating leverage describes the effects that fixed costs have on changes in operating income as changes occur in units sold, and hence, in contribution margin. Knowing the degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes.

3-13 CVP analysis is always conducted for a specified time horizon. One extreme is a very short-time horizon. For example, some vacation cruises offer deep price discounts for people who offer to take any cruise on a day's notice. One day prior to a cruise, most costs are fixed. The other extreme is several years. Here, a much higher percentage of total costs typically is variable.

CVP itself is not made any less relevant when the time horizon lengthens. What happens is that many items classified as fixed in the short run may become variable costs with a longer time horizon.

3-2

3-14 A company with multiple products can compute a breakeven point by assuming there is a constant mix of products at different levels of total revenue.

3-15 Yes, gross margin calculations emphasize the distinction between manufacturing and nonmanufacturing costs (gross margins are calculated after subtracting fixed manufacturing costs). Contribution margin calculations emphasize the distinction between fixed and variable costs. Hence, contribution margin is a more useful concept than gross margin in CVP analysis.

3-16 (10 min.) CVP computations.

Variable Fixed Total Operating Contribution ContributionRevenues Costs Costs Costs Income Margin Margin %

a. $2,000 $ 500 $300 $ 800 $1,200 $1,500 75.0%b. 2,000 1,500 300 1,800 200 500 25.0%c. 1,000 700 300 1,000 0 300 30.0%d. 1,500 900 300 1,200 300 600 40.0%

3-17 (10-15 min.) CVP computations.

1a. Sales ($25 per unit × 180,000 units) $4,500,000Variable costs ($20 per unit × 180,000 units) 3,600,000Contribution margin $ 900,000

1b. Contribution margin (from above) $ 900,000Fixed costs 800,000Operating income $ 100,000

2a. Sales (from above) $4,500,000Variable costs ($10 per unit × 180,000 units) 1,800,000Contribution margin $2,700,000

2b. Contribution margin $2,700,000Fixed costs 2,500,000Operating income $ 200,000

3. Operating income is expected to increase by $100,000 if Ms. Schoenen’s proposal is accepted.

The management would consider other factors before making the final decision. It is likely that product quality would improve as a result of using state of the art equipment. Due to increased automation, probably many workers will have to be laid off. Patel’s management will have to consider the impact of such an action on employee morale. In addition, the proposal increases the company’s fixed costs dramatically. This will increase the company’s operating leverage and risk.

3-3

3-18 (35-40 min.) CVP analysis, changing revenues and costs.

1a. SP = 8% × $1,000 = $80 per ticketVCU = $35 per ticketCMU = $80 – $35 = $45 per ticket per ticketFC = $22,000 a month

Q = =

= 489 tickets (rounded up)

1b. Q = =

=

= 712 tickets (rounded up)

2a. SP = $80 per ticketVCU = $29 per ticketCMU = $80 – $29 = $51 per ticketFC = $22,000 a month

Q = =

= 432 tickets (rounded up)

2b. Q = =

=

= 628 tickets (rounded up)

3a. SP = $48 per ticketVCU = $29 per ticketCMU = $48 – $29 = $19 per ticketFC = $22,000 a month

Q = =

3-18 (Cont’d.)

= 1,158 tickets (rounded up)

3-4

3b. Q = =

=

= 1,685 tickets (rounded up)

The reduced commission sizably increases the breakeven point and the number of tickets required to yield a target operating income of $10,000:

8%Commission Fixed

(Requirement 2) Commission of $48Breakeven point 432 1,158Attain OI of $10,000 628 1,685

4a. The $5 delivery fee can be treated as either an extra source of revenue (as done below) or as a cost offset. Either approach increases UCM by $5:

SP = $53 ($48 + $5) per ticketVCU = $29 per ticketCMU = $53 – $29 = $24 per ticketFC = $22,000 a month

Q = =

= 917 tickets (rounded up)

4b. Q = =

=

= 1,334 tickets (rounded up)

The $5 delivery fee results in a higher contribution margin which reduces both the breakeven point and the tickets sold to attain operating income of $10,000.

3-19 (15 min.) Gross margin and contribution margin, making decisions.

Salaries and wages of $150,000 could be variable costs and fixed costs. The answer assumes they are all fixed costs.

3-5

1. Revenues $500,000Deduct variable costs:

Cost of goods sold $200,000Sales commissions 50,000Other operating costs 40,000 290,000

Contribution margin $210,000

2. Contribution margin percentage = = 42%

3. Incremental revenue (20% × $500,000) = $100,000Incremental contribution margin

(42% × $100,000) $42,000Incremental fixed costs (advertising) 10,000Incremental operating income $32,000

If Mr. Schmidt spends $10,000 more on advertising, the operating income will increase by $32,000 converting an operating loss of $10,000 to an operating income of $22,000.

Proof (Optional):

Revenues (120% × $500,000) $600,000Cost of goods sold (40% of sales) 240,000Gross margin 360,000

Operating costs:Salaries and wages $150,000Sales commissions (10% of sales) 60,000Depreciation of equipment and fixtures 12,000Store rent 48,000Advertising 10,000Other operating costs:

Variable ( × $600,000) 48,000

Fixed 10,000 338,000Operating income $ 22,000

3-6

3-20 (20 min.) CVP exercises.

RevenuesVariableCosts

ContributionMargin

FixedCosts

BudgetedOperatingIncome

Orig. $10,000,000G $8,200,000G $1,800,000 $1,700,000G $100,0001. 10,000,000 8,020,000 1,980,000a 1,700,000 280,0002. 10,000,000 8,380,000 1,620,000b 1,700,000 (80,000)3. 10,000,000 8,200,000 1,800,000 1,785,000c 15,0004. 10,000,000 8,200,000 1,800,000 1,615,000d 185,0005. 10,800,000e 8,856,000f 1,944,000 1,700,000 244,0006. 9,200,000g 7,544,000h 1,656,000 1,700,000 (44,000)7. 11,000,000i 9,020,000j 1,980,000 1,870,000k 110,0008. 10,000,000 7,790,000l 2,210,000 1,785,000m 425,000Gstands for given.

a$1,800,000 × 1.10; b$1,800,000 × 0.90; c$1,700,000 × 1.05; d$1,700,000 × 0.95; e$10,000,000 × 1.08; f$8,200,000 × 1.08; g$10,000,000 × 0.92; h$8,200,000 × 0.92; i$10,000,000 × 0.10; j$8,200,000 × 1.10; k$1,700,000 × 1.10; l$8,200,000 × 0.95; m$1,700,000 × 1.05

3-21 (20 min.) CVP exercises.1a. [Unit’s sold (Selling price – Variable costs)] – Fixed costs = Operating income

[5,000,000 ($0.50 – $0.30)] – $900,000 = $100,000

1b. Fixed costs ÷ Contribution margin per unit = Breakeven units$900,000 ÷ [($0.50 – $0.30)] = 4,500,000 units

Breakeven units × Selling price = Breakeven revenues4,500,000 units × $0.50 per unit = $2,250,000

or,Fixed costs ÷ Contribution margin ratio = Breakeven revenues $900,000 ÷ 0.40 = $2,250,000

Contribution margin ratio =

= = 0.40

2. 5,000,000 ($0.50 – $0.34) – $900,000 = $ (100,000)

3. [5,000,000 (1.1) ($0.50 – $0.30)] – [$900,000 (1.1)] = $ 110,000

4. [5,000,000 (1.4) ($0.40 – $0.27)] – [$900,000 (0.8)] = $ 190,000

5. $900,000( 1.1) ÷ ($0.50 – $0.30) = 4,950,000 units

6. ($900,000 + $20,000) ÷ ($0.55 – $0.30) = 3,680,000 units

3-7

3-22 (10–15 min.) CVP analysis, income taxes.1. Operating income = Net income ÷ (1 – tax rate)

= $84,000 ÷ (1 – 0.40) = $140,0002. Contribution margin – Fixed costs = Operating income

Contribution margin – $300,000 = $140,000 Contribution margin = $440,000

3. Revenues – Variable costs = Contribution marginRevenues – 0.80 Revenues = Contribution margin

0.20 Revenues = $440,000 Revenues = $2,200,000

4. Breakeven revenues = Fixed costs Contribution margin percentageBreakeven revenues = $300,000 ÷ 0.20 = $1,500,000

3-23 (20–25 min.) CVP analysis, income taxes.

1. Variable cost percentage is $3.20 $8.00 = 40%

Let R = Revenues needed to obtain target net income

R – 0.40R – $450,000 =

0.60R = $450,000 + $150,000R = $600,000 0.60R = $1,000,000

or,

Contribution margin percentage

Proof: Revenues $1,000,000Variable costs (at 40%) 400,000Contribution margin 600,000Fixed costs 450,000Operating income 150,000Income taxes (at 30%) 45,000Net income $ 105,000

2. a. Customers needed to earn net income of $105,000:Total revenues Sales check per customer $1,000,000 $8 = 125,000 customers

b. Customers needed to break even:

Contribution margin per customer = $8.00 – $3.20 = $4.80Breakeven number of customers = Fixed costs Contribution margin per customer

= $450,000 $4.80 per customer = 93,750 customers

3-23 (Cont’d.)

3-8

$450,000 +

0.60Breakeven revenues = = = $1,000,000

3. Using the shortcut approach:

Change in net income = (1 – Tax rate)

= (150,000 – 125,000) $4.80 (1 – 0.30)= $120,000 0.7 = $84,000

New net income = $84,000 + $105,000 = $189,000

The alternative approach is:Revenues, 150,000 $8.00 $1,200,000Variable costs at 40% 480,000Contribution margin 720,000Fixed costs 450,000Operating income 270,000Income tax at 30% 81,000Net income $ 189,000

3-24 (30 min.) CVP analysis, sensitivity analysis.

1. SP = $30.00 (1 – 0.30 margin to bookstore) = $30.00 0.70 = $21.00

VCU = $ 4.00 variable production and marketing cost 3.15 variable author royalty cost (0.15 $30.00 0.70) $ 7.15

CMU = $21.00 – $7.15 = $13.85 per copy

FC = $ 500,000 fixed production and marketing cost 3,000,000 up-front payment to Washington $3,500,000

Exhibit 3-24A shows the PV graph.

3-9

3-24 (Cont’d.)

EXHIBIT 3-24APV Graph for Media Publishers

2a.

=

=

= 252,708 copies sold (rounded up)

2b. Target OI =

3-10

100,000 200,000 300,000 400,000 500,000

0

Units sold

Ope

ratin

g in

com

e (0

00’s

)

(0; $3.5 million)

252,708; $0

FC = $3,500,000UCM = $13.85 per book sold

$4,000

3,000

2,000

1,000

-1,000

-2,000

-3,000

-4,000

3-24 (Cont’d.)

=

=

= 397,112 copies sold (rounded up)3a. Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30 has the following effects:

SP = $30.00 (1 – 0.20) = $30.00 0.80 = $24.00VCU =$ 4.00 variable production and marketing cost

+ 3 .60 variable author royalty cost (0.15 $30.00 0.80)$ 7 .60

CMU = $24.00 – $7.60 = $16.40 per copy

=

=

= 213,415 copies sold (rounded)The breakeven point decreases from 252,708 copies in requirement 2 to 213,415 copies.3b. Increasing the listed bookstore price to $40 while keeping the bookstore margin at 30% has the following effects:

SP = $40.00 (1 – 0.30) = $40.00 0.70 = $28.00VCU = $ 4.00 variable production and marketing cost

+ 4 .20 variable author royalty cost (0.15 $40.00 0.70)$ 8 .20

CMU= $28.00 – $8.20 = $19.80 per copy

=

= 176,768 copies sold (rounded)The breakeven point decreases from 252,708 copies in requirement 2 to 176,768 copies.

3c. The answer to requirements 3a and 3b decreases the breakeven point relative to requirement 2 because in each case fixed costs remain the same at $3,500,000 while contribution margin per unit increases.

3-11

3-25 (10 min.) CVP analysis, margin of safety.

1. Breakeven point revenues =

Contribution margin percentage = = 0.40

2. Contribution margin percentage =

0.40 =

0.40 SP = SP – $12 0.60 SP = $12 SP = $20

3. Revenues, 80,000 units $20 $1,600,000Breakeven revenues 1,000,000Margin of safety $ 600,000

3-26 (25 min.) Operating leverage.

1a. Let Q denote the quantity of carpets sold

Breakeven point under Option 1$500Q $350Q = $5,000

$150Q = $5,000Q = $5,000 $150 = 34 carpets (rounded)

1b. Breakeven point under Option 2$500Q $350Q (0.10 $500Q) = 0

100Q = 0Q = 0

2. Operating income under Option 1 = $150Q $5,000Operating income under Option 2 = $100Q

Find Q such that $150Q $5,000 = $100Q $50Q = $5,000

Q = $5,000 $50 = 100 carpets

For Q = 100 carpets, operating income under both Option 1 and Option 2 = $10,000

3a. For Q > 100, say, 101 carpets,Option 1 gives operating income = $150 101 $5,000 = $10,150Option 2 gives operating income = $100 101 = $10,100So Color Rugs will prefer Option 1.

3-26 (Cont’d.)

3-12

3b. For Q < 100, say, 99 carpets,Option 1 gives operating income = $150 99 $5,000 = $9,850Option 2 gives operating income = $100 99 = $9,900So Color Rugs will prefer Option 2.

4. Degree of operating leverage =

Under Option 1, degree of operating leverage = = 1.5

Under Option 2, degree of operating leverage = = 1.0

5. The calculations in requirement 4 indicate that when sales are 100 units, a percentage change in sales and contribution margin will result in 1.5 times that percentage change in operating income for Option 1, but the same percentage change in operating income for Option 2. The degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuations in sales on operating incomes.

3-27 (10 min.) CVP analysis, international cost structure differences.

1.

Annual Fixed Costs(1)

Selling Price(2)

Variable Manuf. Costs per Sweater(3)

Variable Mark./Distr. Costs per Sweater(4)

Unit Contrib. Margin(5)=(2) – (3) – (4)

Breakeven Point in Units(6) = (1) (5)

Singapore $ 6,500,000 $32 $ 8.00 $11.00 $13 500,000Thailand 4,500,000 32 5.50 11.50 15 300,000U.S. 12,000,000 32 13.00 9.00 10 1,200,000

3-13

(a)Breakeven point in units sold

(b)Breakeven point in revenuesCol. (a) $32

Singapore 500,000 $16,000,000Thailand 300,000 9,600,000U.S. 1,200,000 38,400,000

3-27 (Cont’d.)

2. Revenues$32 800,000

VariableCosts

FixedCosts

OperatingIncome

Singapore $25,600,000 $15,200,0001 $6,500,000 $3,900,000Thailand 25,600,000 13,600,0002 4,500,000 7,500,000U.S. 25,600,000 17,600,0003 12,000,000 (4,000,000)

1($8 + $11) 800,000 2($5.50 + $11.50) 800,000 3($13 + $9) 800,000

Thailand has the lowest breakeven point––it has both the lowest fixed costs ($4,500,000) and the lowest variable cost per unit ($17.00). Hence, for a given selling price, Thailand will always have a higher operating income (or a lower operating loss) than Singapore or the U.S.

The U.S. breakeven point is 1,200,000 units. Hence, with sales of 800,000 units, it has an operating loss of $4,000,000.

3-28 (30 min.) Sales mix, new and upgrade customers.

1. New Customers Upgrade Customers SPVCUCMU

$21090

120

$1204080

Let S = Number of units sold to upgrade customers1.5S = Number of units sold to new customers

Revenues – Variable costs – Fixed costs = Operating income[$210 (1.5S) + $120S] – [$90 (1.5S) + $40S] – $14,000,000 = OI$435S – $175S – $14,000,000 = OIBreakeven point is 134,616 units when OI = 0

$260S = $14,000,000S = 53,846 units sold to upgrade customers

1.5S = 80,770 units sold to new customers134,616 units

CheckRevenues ($210 80,770; $120 53,846) $23,423,220Variable costs ($90 80,770; $40 53,846) 9,423,140Contribution margin 14,000,080Fixed costs 14,000,000Operating income (subject to rounding) $ 0

3-14

3-28 (Cont’d.)

2. When 200,000 units are sold, mix is:

Units sold to new customers (60% 200,000) 120,000Units sold to upgrade customers (40% 200,000) 80,000

Revenues ($210 120,000; $120 80,000) $34,800,000Variable costs ($90 120,000; $40 80,000) 14,000,000Contribution margin 20,800,000Fixed costs 14,000,000

Operating income $ 6,800,000

3a. Let S = Number of units sold to upgrade customersthen S = Number of units sold to new customers

[$210S + $120S] – [$90S + $40S] – $14,000,000 = OI330S – 130S = $14,000,000

200S = $14,000,000S = 70,000 units sold to upgrade customersS = 70,000 units sold to new customers

140,000 units

CheckRevenues ($210 70,000; $120 70,000) $23,100,000Variable costs ($90 70,000; $40 70,000) 9,100,000Contribution margin 14,000,000Fixed costs 14,000,000Operating income $ 0

3b. Let S = Number of units sold to upgrade customersthen 9S = Number of units sold to new customers[$210 (9S ) + $120S] – [$90 (9S ) + $40S] – $14,000,000 = OI

2,010S – 850S = $14,000,0001,160S = $14,000,000

S = 12,069 units sold to upgrade customers9S = 108,621 units sold to new customers

120,690 units

CheckRevenues ($210 108,621; $120 12,069) $24,258,690Variable costs ($90 108,621; $40 12,069) 10,258,650Contribution margin 14,000,040Fixed costs 4,000,000Operating income (subject to rounding) $ 0

3-15

3-28 (Cont’d.)

3c. As Zapo increases its percentage of new customers, which have a higher contribution margin per unit than upgrade customers, the number of units required to break even decreases:

New Customers Upgrade Customers Breakeven PointRequirement 3(a)Requirement 1Requirement 3(b)

50%6090

50%4010

140,000134,616120,690

3-29 (25-30 min.) Athletic scholarships, CVP analysis.

1. Variable costs per scholarship offer:Scholarship amount $20,000Operating costs 2,000Total variable costs $22,000

Let the number of scholarships be denoted by Q

$22,000 Q = $5,000,000 – $600,000$22,000 Q = $4,400,000 Q = $4,400,000 ÷ $22,000 = 200 scholarships

2. Total budget for next year = $5,000,000 × (1.00 – 0.22) = $3,900,000

Then $22,000 Q = $3,900,000 – $600,000 = $3,300,000 Q = $3,300,000 ÷ $22,000 = 150 scholarships

3. Total budget for next year from above = $3,900,000Fixed costs 600,000Variable costs for scholarships $3,300,000

If the total number of scholarships is to remain at 200: Variable cost per scholarship $3,300,000 ÷ 200 $16,500Variable operating cost per scholarship 2,000Amount per scholarship $14,500

3-30 (20 min.) CVP analysis, multiple cost drivers.

1a. = Revenues

= ($45 40,000) ($30 40,000) ($60 1,000) $240,000= $1,800,000 $1,200,000 $60,000 $240,000 = $300,000

1b. = ($45 40,000) ($30 40,000) ($60 800) $240,000 = $312,000

3-30 (Cont’d.)

3-16

2. Denote the number of picture frames sold by Q, then$45Q $30Q – 500 $60 $240,000 = 0$15Q = $30,000 + $240,000 = $270,000

Q = $270,000 $15 = 18,000 picture frames

3. Suppose Susan had 1,000 shipments. $45Q $30Q (1000 $60) $240,000 = 015Q = $300,000

Q = 20,000 picture frames

The breakeven point is not unique because there are two cost drivers—quantity of picture frames and number of shipments. Various combinations of the two cost drivers can yield zero operating income.

3-31 (20 min.) Gross margin and contribution margin.

1a. Cost of goods sold $1,600,000Fixed manufacturing costs 500,000Variable manufacturing costs $1,100,000

Variable manufacturing costs per unit = $1,100,000 200,000 = $5.50 per unit

1b. Total marketing and distribution costs $1,150,000Variable marketing and distribution (200,000 $4) 800,000Fixed marketing and distribution costs $ 350,000

2. Selling price = $2,600,000 200,000 units = $13 per unit

=

= $13 $5.50 $4.00 = $3.50

Operating income =

= ($3.50 230,000) $500,000 $350,000= $45,000

Foreman has confused gross margin with contribution margin. He has interpreted gross margin as if it was all variable, and interpreted marketing and distribution costs as all fixed. In fact, the manufacturing costs, subtracted from sales to calculate gross margin, and marketing and distribution costs contain both fixed and variable components.

3-17

3-31 (Cont’d.)

3. Breakeven point in units =

= = 242,858 units (rounded up)

Breakeven point in revenues = 242,858 $13 = $3,157,154.

3-32 (15–20 min.)Uncertainty, CVP analysis.

1. King pays Foreman $2 million plus $4 (25% of $16) for every home purchasing the pay-per-view. The expected value of the variable component is:

Demand (1)

Payment(2) = (1) $4

Probability(3)

Expected Payment(4)

100,000200,000300,000400,000500,000

1,000,000

$ 400,000800,000

1,200,0001,600,0002,000,0004,000,000

0.050.100.300.350.150.05

$ 20,00080,000

360,000560,000300,000

200,000 $1,520,000

The expected value of King's payment is $3,520,000 ($2,000,000 fixed fee + $1,520,000).

2. SP = $16VCU = $ 6 ($4 payment to Foreman + $2 variable cost)CMU= $10FC = $2,000,000 + $1,000,000 = $3,000,000

Q =

=

= 300,000 homes

If 300,000 homes purchase the pay-per-view, King will break even.

3-33 (15-20 min.) CVP analysis, service firm.

1. Revenue per package $4,000Variable cost per package 3,600Contribution margin per package $ 400

Breakeven (units) = Fixed costs ÷ Contribution margin per package

3-33 (Cont’d.)

3-18

= = 1,200 tour packages

2. Contribution margin ratio = = = 10%

Revenue to achieve target income = (Fixed costs + target OI) ÷ Contribution margin ratio

= = $5,800,000, or

Number of tour packages to earn $100,000 operating income:

= 1,450 tour packages

Revenues to earn $100,000 OI = 1,450 tour packages × $4,000 = $5,800,000.

3. Fixed costs = $480,000 + $24,000 = $504,000

Breakeven (units) =

Contribution margin per unit =

= = $420 per tour package

Desired variable cost per tour package = $4,000 – $420 = $3,580

Because the current variable cost per unit is $3,600, the unit variable cost will need to be reduced by $20 to achieve the breakeven point calculated in requirement 1.

Alternate Method: If fixed cost increases by $24,000, then total variable costs must be reduced by $24,000 to keep the breakeven point of 1,200 tour packages.

Therefore the variable cost per unit reduction = $24,000 ÷ 1,200 = $20 per tour package.

3-19

3-34(30 min.) CVP, target income, service firm.

1. Revenue per child $600Variable costs per child 200Contribution margin per child $400

Breakeven quantity =

= = 14 children

2. Target quantity =

= = 40 children

3. Increase in rent ($3,000 – $2,000) $1,000Field trips 1,000Total increase in fixed costs $2,000Divide by the number of children enrolled ÷ 40Increase in fee per child $ 50

Therefore the fee per child will increase from $600 to $650.Alternatively,

New contribution margin per child = = $450

New fee per child = Variable costs per child + New contribution margin per child = $200 + $450 = $650

3-35(20-25 min.) CVP analysis, CMA adapted.

1. Selling price $16.00Variable costs per unit:

Purchase price $10.00Shipping and handling 2.00 12.00

Contribution margin per unit (CMU) $ 4.00

Breakeven point in units = = = 150,000 units

3-20

3-25 (Cont’d.)

2. Since Galaxy is operating above the breakeven point, any incremental contribution margin will increase operating income dollar for dollar.

Increase in units sales = 10% × 200,000 = 20,000Incremental contribution margin = $4 × 20,000 = $80,000

Therefore, the increase in operating income will be equal to $80,000. Galaxy’s operating income in 2003 would be $200,000 + $80,000 = $280,000.

3. Selling price $16.00Variable costs:

Purchase price $10 × 130% $13.00 Shipping and handling 2.00 15.00Contribution margin per unit $ 1.00

Target sales in units = = = 800,000 units

Target sales in dollars = $16 × 800,000 = $12,800,000

3-36 (30-40 min.) CVP analysis, income taxes.

1. Revenues – Variable costs – Fixed costs =

Let X = Net income for 2003

20,000($25.00) – 20,000($13.75) – $135,000 =

$500,000 – $275,000 – $135,000 =

$300,000 – $165,000 – $81,000 = X X = $54,000

Alternatively,Operating income = Revenues – Variable costs – Fixed costs

= $500,000 – $275,000 – $135,000 = $90,000 Income taxes = 0.40 × $90,000 = $36,000 Net income = Operating income – Income taxes

= $90,000 – $36,000 = $54,000

2. Let Q = Number of units to break even

$25.00Q – $13.75Q – $135,000 = 0Q = $135,000 $11.25 = 12,000 units

3-21

3-36 (Cont’d.)

3. Let X = Net income for 2004

22,000($25.00) – 22,000($13.75) – ($135,000 + $11,250) =

$550,000 – $302,500 – $146,250 =

$101,250 =

X = $60,750

4. Let Q = Number of units to break even with new fixed costs of $146,250

$25.00Q – $13.75Q – $146,250 = 0Q = $146,250 $11.25 = 13,000 units

Breakeven revenues = 13,000 $25.00 = $325,000

5. Let S = Required sales units to equal 2003 net income$25.00S – $13.75S – $146,250 =

$11.25S = $236,250S = 21,000 units

Revenues = 21,000 units $25.00 = $525,000

6. Let A = Amount spent for advertising in 2004

$550,000 – $302,500 – ($135,000 + A) =

$550,000 – $302,500 – $135,000 – A = $100,000$550,000 – $537,500 = A

A = $12,500

3-37 (20 min.) CVP analysis, decision making.

1. Tocchet’s current operating income is as follows:

Revenues, $105 × 40,000 $4,200,000Variable costs, $55 × 40,000 2,200,000Contribution margin 2,000,000Fixed costs 1,400,000Operating income $ 600,000

3-22

3-37 (Cont’d.)

Let the fixed marketing and distribution costs be F. We calculate F when operating income = $600,000 and the selling price is $99.

($99 × 50,000) – ($55 × 50,000) – F = $600,000 $4,950,000 – $2,750,000 – F = $600,000

F = $4,950,000 – $2,750,000 – $600,000 F = $1,600,000

Hence, the maximum increase in fixed marketing and distribution costs that will allow Tocchet to reduce the selling price and maintain $600,000 in operating income is $200,000 ($1,600,000 – $1,400,000).

2. Let the selling price be P.

We calculate P for which, after increasing fixed manufacturing costs by $100,000 to $900,000 and variable manufacturing cost per unit by $2 to $47, operating income = $600,000

$40,000 P – ($47 × 40,000) – ($10 × 40,000) – $900,000 – $600,000 = $600,000$40,000 P – $1,880,000 – $400,000 – $900,000 – $600,000 = $600,000$40,000 P = $600,000 + $1,880,000 + $400,000 + $900,000 + $600,000$40,000 P = $4,380,000

P = $4,380,000 ÷ 40,000 = $109.50

Tocchet will consider adding the new features provided the selling price is at least $109.50 per unit.

3-38 (10-15 min.) Margin of safety.

1. Selling price ($1,000,000 $10,000) $100Variable cost per unit ($600,000 $10,000) 60Contribution margin $ 40

Breakeven point in units =

= = 6,250 footballs

Breakeven point in dollars = 6,250 × $100 = $625,000

2. Margin of safety in units = 10,000 – 6,250 = 3,750 footballs

Margin of safety in dollars = $100 × 3,750 = $375,0003-38 (Cont’d.)

3-23

3. Contribution margin ratio = = = 40%

Incremental operating income = 40% × $200,000 = $80,000

3-39 (20–30 min.)CVP analysis, shoe stores.

1. Contribution margin per pair = selling price – Variable costs per pair = $30 – $21 = $9 a pair

Breakeven point in number of pairs:

= = 40,000 pairs

Breakeven points in revenues:

= = $1,200,000

2. Revenues, $30 35,000 $1,050,000Variable costs, $21 35,000 735,000Contribution margin 315,000Fixed costs 360,000Operating income (loss) $ (45,000)

An alternative approach is that 35,000 units is 5,000 units below the breakeven point, and the unit contribution margin is $9.00:

$9.00 5,000 = $45,000 below breakeven

3. Fixed costs: $360,000 + $81,000 = $441,000Contribution margin per pair = $30 – $19.50 = $10.50

a. Breakeven point in units = = 42,000 pairs

b. Breakeven point in revenues = $30 42,000 = $1,260,000

3-24

3-39 (Cont’d.)

4. Fixed costs = $360,000Contribution margin per pair = $30 – $21 – $0.30 = $8.70

a. Breakeven point in units = = 41,380 pairs (rounded up)

b. Breakeven point in revenues = $30 41,380 = $1,241,400

5. Breakeven point = 40,000 pairsStore manager receives commission on 10,000 pairs.Cost of commission = $0.30 10,000 = $3,000

Revenues, $30 50,000 $1,500,000Variable costs:

Cost of shoes $975,000Salespeople commission 75,000Manager commission 3,000 1,053,000

Contribution margin 447,000Fixed costs 360,000Operating income $ 87,000

An alternative approach is 10,000 pairs $8.70 contribution margin per pair = $87,000.

3-25

3-39 (Cont’d.)

3-39 Excel Application

Cost-Volume-Profit AnalysisWalk Rite Shoe Company

Original DataUnit Variable Data:Selling price $30.00 Cost of shoes $19.50 Sales commissions 1.50Total variable costs 21.00Annual Fixed Costs:Rent $60,000 Salaries 200,000 Advertising 80,000 Other fixed costs 20,000 Total fixed costs $360,000

Problem 1Contribution margin per unit $9.00 a. Breakeven units 40,000 b. Breakeven revenues $1,200,000

Problem 2Revenues $1,050,000 Cost of shoes 682,500 Sales commissions 52,500 Total variable costs 735,000Contribution margin $315,000Total fixed costs 360,000 Operating income (Loss) $(45,000)

Problem 3Total fixed costs $441,000 Contribution margin per unit $10.50 a. Breakeven units 42,000 b. Breakeven revenues $1,260,000

Problem 4Total variable cost per unit $21.30 Contribution margin per unit $8.70 a. Breakeven units 41,380 b. Breakeven revenues $1,241,409

Problem 5Revenues $1,500,000 Cost of shoes 975,000 Sales commissions 75,000 Manager’s commission 3,000 Total variable costs 1,053,000 Contribution margin $447,000Total fixed costs 360,000 Operating Income (Loss) $87,000

3-26

3-40 (20–25 min.)CVP analysis, shoe stores (continuation of 3-39).

1. Because the unit sales level at the point of indifference would be the same for each plan, the revenue would be equal. Therefore, the unit sales level sought would be that which produces the same total costs for each plan.

Let Q = unit sales level$19.50Q + $360,000 + $81,000 = $21.00Q + $360,000

$81,000 = $1.50QQ = 54,000 pairs

2. Commission Plan Salary Plan           Sales in units 50,000 60,000 50,000 60,000Revenues at $30.00 $1,500,000 $1,800,000 $1,500,000 $1,800,000Variable costs at

$21.00 and at $19.50 1,050,000 1,260,000 975,000 1,170,000Contribution margin 450,000 540,000 525,000 630,000Fixed costs 360,000 360,000 441,000 441,000Operating income $ 90,000 $ 180,000 $ 84,000 $ 189,000

The decision regarding the plans will depend heavily on the unit sales level that is generated by the fixed salary plan. For example, as part (1) shows, at identical unit sales levels in excess of 54,000 units, the fixed salary plan will always provide a more profitable final result than the commission plan.

3. Let TQ = Target number of units

$30.00TQ – $19.50TQ – $441,000 = $168,000$10.50TQ = $609,000

TQ = $609,000 ÷ $10.50TQ = 58,000 units

$30.00TQ – $21.00TQ – $360,000 = $168,000$9.00TQ = $528,000

TQ = $528,000 ÷ $9.00TQ = 58,667 units (rounded)

The decision regarding the salary plan depends heavily on predictions of demand. For instance, the salary plan offers the same operating income at 58,000 units as the commission plan offers at 58,667 units.

3-27

3-41 (10-20 min.) Sensitivity and inflation (continuation of 3-40).

1. Revenues, $30 48,000 $1,440,000$18 2,000 36,000 $1,476,000

Variable costs:Goods sold $19.50 50,000 975,000Commission, 5% $1,476,000 73,800 1,048,800

Contribution margin 427,200Fixed costs 360,000Operating income $ 67,200

An alternative approach is:

Contribution margin on 48,000 pairs $9.00 $432,000Deduct negative contribution margin on unsold pairs, 2,000 [$18.00 – ($19.50 + $.90* commission)] 4,800Contribution margin 427,200Fixed costs 360,000Operating income $ 67,200

*5% of $18.00 = $0.90

2. Optimal operating income, given perfect knowledge, would be the $432,000 [($30 – $19.50 – $1.50) 48,000] contribution computed above, minus $360,000 fixed costs, or $72,000.

3. The point of indifference is where the operating incomes are equal. Let X = unit cost per pair that would produce the identical operating income of $67,200. Then:

48,000[$30.00 – (X + $1.50)] – $360,000 = $ 67,200 48,000($28.50 – X) – $360,000 = $ 67,200

$1,368,000 – 48,000X – $360,000 = $ 67,20048,000X = $940,800

X = $19.60

Therefore, any rise in purchase cost in excess of $19.60 per pair increases the operating income benefit of signing the long-term contract.

In a shortcut solution, you could take the $4,800 difference between the "ideal" operating income (of $72,000) at the current cost per pair and the operating income under the contract (of $67,200) and divide it by 48,000 units to get 10 cents per pair difference.

3-28

3-42 (30 min.) CVP analysis, income taxes, sensitivity.

1a. In order to break even, Almo Company must sell 500 units. This amount represents the point where revenues equal total costs.

Let Q denote the quantity of canopies sold.Revenue = Variable costs + Fixed costs

$400Q = $200Q + $100,000$200Q = $100,000

Q = 500 units

Breakeven can also be calculated using contribution margin per unit. Contribution margin per unit = Selling price – Variable cost per unit = $400 – $200 = $200

Breakeven = Fixed Costs Contribution margin per unit= $100,000 $200= 500 units

1b. In order to achieve its net income objective, Almo Company must sell 2,500 units. This amount represents the point where revenues equal total costs plus the corresponding operating income objective to achieve net income of $240,000.

Revenue = Variable costs + Fixed costs + [Net income ÷ (1 – Tax rate)] $400Q = $200Q + $100,000 + [$240,000 (1 0.4)] $400 Q = $200Q + $100,000 + $400,000

Q = 2,500 units

2. To achieve its net income objective, Almo Company 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 net income and is the only alternative that equals or exceeds the company’s net income objective. Calculations for the three alternatives are shown below.

Alternative 1Revenues = ($400 350) + ($360a 2,700) = $1,112,000

Variable costs = $200 3,050b = $610,000Operating income = $1,112,000 $610,000 $100,000 = $402,000

Net income = $402,000 (1 0.4) = $241,200 a$400 – $40; b350 units + 2,700 units.

Alternative 2Revenues = ($400 350) + ($370c 2,200) = $954,000

Variable costs = ($200 350) + ($190d 2,200) = $488,000Operating income = $954,000 $488,000 $100,000 = $366,000

Net income = $366,000 (1 0.4) = $219,600 c$400 – $30; d$200 – $10.

3-29

3-42 (Cont’d.)

Alternative 3Revenues = ($400 350) + ($380e 2,000) = $900,000

Variable costs = $200 2,350f = $470,000Operating income = $900,000 $470,000 $90,000g = $340,000

Net income = $340,000 (1 0.4) = $204,000 e$400 – 0.05 $400 = 400 – $20; f350 units + 2,000 units; g$100,000 – $10,000

3-43 (30 min.) Choosing between compensation plans, operating leverage.

1. Variable costs of goods sold as a percentage of revenues = = 45%

Let breakeven revenues be denoted by R, then

R =

R = 0.45R + $2,870,000 + 0.18R + $3,420,000

R 0.45R 0.18R = $2,870,000 + $3,420,000 = $6,290,0000.37R = $6,290,000

R = $6,290,000 0.37 = $17,000,000

2. With its own sales force, Marston’s fixed marketing costs would increase to $3,420,000 + $2,080,000 = $5,500,000.

Variable cost of marketing = 10% of Revenues

Let breakeven revenues be denoted by R, then

R = 0.45R + $2,870,000 + 0.10R + $5,500,000

R 0.45R 0.10R = $2,870,000 + $5,500,000 = $8,370,0000.45R = $8,370,000

R = $8,370,000 0.45 = $18,600,000

3-30

3-43 (Cont’d.)

3. Using Sales Employing OwnAgents Sales Staff

Revenues $26,000,000 $26,000,000Variable manufacturing costs

$26,000,000 0.45; 0.45 11,700,000 11,700,000Variable marketing costs

$26,000,000 0.18; 0.10 4,680,000 2,600,000Contribution margin 9,620,000 11,700,000Fixed costs

Fixed manufacturing costs 2,870,000 2,870,000Fixed marketing costs 3,420,000 5,500,000

Total fixed costs 6,290,000 8,370,000Operating income $ 3,330,000 $ 3,330,000

= 2.89 = 3.51

The calculations indicate that at sales of $26,000,000, a percentage change in sales and contribution margin will result in 2.89 times that percentage change in operating income if Marston continues to use sales agents and 3.51 times that percentage change in operating income if Marston employs its own sales staff. The higher contribution margin per dollar of sales and higher fixed costs gives Marston more operating leverage, that is greater benefits (increases in operating income) if revenues increase but greater risks (decreases in operating income) if revenues decrease.

4. Variable costs of marketing = 15% of RevenuesFixed marketing costs = $5,500,000

Operating income = Revenues

Denote the revenues required to earn $3,420,000 of operating income by R, thenR 0.45R $2,870,000 0.15R $5,500,000 = $3,330,000

R 0.45R 0.15R = $3,330,000 + $2,870,000 + $5,500,000 0.40R = $11,700,000

R = $11,700,000 0.40 = $29,250,000

3-31

3-44 (15–25 min.)Sales mix, three products.1. Sales of A, B, and C are in ratio 20,000 : 100,000 : 80,000. So for every 1 unit of A, 5 (100,000 ÷ 20,000) units of B are sold, and 4 (80,000 ÷ 20,000) units of C are sold.

Let Q = Number of units of A to break even 5Q = Number of units of B to break even 4Q = Number of units of C to break even

Contribution margin – Fixed costs = Zero operating income

$3Q + $2(5Q) + $1(4Q) – $255,000 = 0$17Q = $255,000

Q = 15,000 ($255,000 ÷ $17) units of A5Q = 75,000 units of B4Q = 60,000 units of C

Total = 150,000 units2. Contribution margin:

A: 20,000 $3 $ 60,000B: 100,000 $2 200,000C: 80,000 $1 80,000 Contribution margin $340,000

Fixed costs 255,000Operating income $ 85,000

3. Contribution marginA: 20,000 $3 $ 60,000B: 80,000 $2 160,000C: 100,000 $1 100,000

Contribution margin $320,000Fixed costs 255,000Operating income $ 65,000

Let Q = Number of units of A to break even 4Q = Number of units of B to break even 5Q = Number of units of C to break even

Contribution margin – Fixed costs = Breakeven point

$3Q + $2(4Q) + $1(5Q) – $255,000 = 0$16Q = $255,000

Q = 15,938 ($255,000 ÷ $16) units of A (rounded)4Q = 63,752 units of B5Q = 79,690 units of C

Total = 159,380 units

Breakeven point increases because the new mix contains less of the higher contribution margin per unit, product B, and more of the lower contribution margin per unit, product C.

3-32

3-45 (30 min.) Multiproduct breakeven, decision making.

1. Breakeven point in 2003 (units) = = = 16,500 units

Breakeven point in 2003 (in revenues) = 16,500 units × $50 = $825,000 in sales revenues

2. Breakeven point in 2004 (in units)Evenkeel expects to sell 3 units of Plumar for every 2 units of Ridex in 2004, so consider a bundle consisting of 3 units of Plumar and 2 units of Ridex.

Unit contribution Margin from Plumar = $50 – $20 = $30Unit contribution Margin from Ridex = $25 – $15 = $10

The contribution margin for the bundle is

$30 × 3 units of Plumar + $10 × 2 units of Ridex = $110

So bundles to be sold to break even = = 4,500 bundles

Breakeven point in 2004 (in units)Plumar, 4,500 × 3 = 13,500 unitsRidex, 4,500 × 2 = 9,000 units

Breakeven point in revenues:

Plumar 13,500 units × $50 per unit = $675,000Ridex 9,000 units × $25 per unit = 225,000Total $900,000

3. Contribution margin percentage in 2003 =

= = 60%

Contribution margin percentage in 2004 =

= = = 55%

The breakeven point in 2004 increases because fixed costs are the same in both years but the contribution margin generated by each dollar of sales revenue at the given product mix decreases in 2004 relative to 2003.3-45 (Cont’d.)

3-33

4. Despite the breakeven sales revenue being higher, Evenkeel should accept Glaston’s offer. The breakeven points are irrelevant because Evenkeel is already above the breakeven sales volume in 2003. By accepting Glaston’s offer, Evenkeel has the ability to sell all the 30,000 units of Plumar in 2004 and make more sales of Ridex to Glaston without incurring any more fixed costs.

Operating income in 2004 with and without Ridex are expected to be as folows:

2004 2004 without Ridex with Ridex Sales $1,500,0001 $2,000,0002

Variable costs 600,0003 900,0004

Contribution margin 900,000 1,100,000Fixed costs 495,000 495,000Operating income $ 405,000 $ 605,000

1$50 × 30,000 units2($50 × 30,000 units) + ($25 × 20,000 units)3$20 × 30,000 units4($20 × 30,000 units) + ($15 × 20,000 units)

3-34

3-46 (20–25 min.)Sales mix, two products.

1. Let Q = Number of units of Deluxe carrier to break even 3Q = Number of units of Standard carrier to break even

Revenues – Variable costs – Fixed costs = Zero operating income

$20(3Q) + $30Q – $14(3Q) – $18Q – $1,200,000 = 0$60Q + $30Q – $42Q – $18Q = $1,200,000

$30Q = $1,200,000Q = 40,000 units of Deluxe

3Q = 120,000 units of Standard

The breakeven point is 120,000 Standard units plus 40,000 Deluxe units, a total of 160,000 units.

2a. Unit contribution margins are: Standard: $20 – $14 = $6; Deluxe: $30 – $18 = $12If only Standard carriers were sold, the breakeven point would be:$1,200,000 $6 = 200,000 units.

2b. If only Deluxe carriers were sold, the breakeven point would be:$1,200,000 $12 = 100,000 units

3. Operating income = Contribution margin of Standard + Contribution margin of Deluxe – Fixed costs = 180,000($6) + 20,000($12) – $1,200,000 = $1,080,000 + $240,000 – $1,200,000 = $120,000

Let Q = Number of units of Deluxe product to break even 9Q = Number of units of Standard product to break even

$20(9Q) + $30Q – $14(9Q) – $18Q – $1,200,000 = 0$180Q + $30Q – $126Q – $18Q = $1,200,000

$66Q = $1,200,000Q = 18,182 units of Deluxe (rounded)

9Q = 163,638 units of Standard

The breakeven point is 163,638 Standard + 18,182 Deluxe, a total of 181,820 units.

The major lesson of this problem is that changes in the sales mix change breakeven points and operating incomes. In this example, the budgeted and actual total sales in number of units were identical, but the proportion of the product having the higher contribution margin declined. Operating income suffered, falling from $300,000 to $120,000. Moreover, the breakeven point rose from 160,000 to 181,820 units.

3-35

3-47 (15 min.) CVP analysis under uncertainty.

1. Both products have the same unit contribution margin:

Unit contribution margin = Selling price per unit Variable costs per unit= $10 $8 = $2

Breakeven point =

=

= 200,000 units for each product

2. The expected demand for the two umbrellas is:

Event Emerald Green Shocking Pink (1) Demand

(2)Probability

(1) (2)Units

(3)Probability

(1) (3)Units

50,000100,000200,000300,000400,000500,000

Expected demand

0.00.10.20.40.20.11.0

10,00040,000

120,00080,000

50,000

300,000

0.10.10.10.20.40.11.0

5,00010,00020,00060,000

160,000 50,000

305,000

Expected operating income of Emerald Green umbrellas:$2 (300,000) $400,000 = $200,000

Expected operating income of Shocking Pink umbrellas:$2 (305,000) $400,000 = $210,000

The Shocking Pink umbrellas should be chosen because they have the higher expected operating income.

3. The expected operating income from the two products would be identical. If the choice criterion is to maximize expected operating income, the company will be indifferent between Emerald Green and Shocking Pink umbrellas. However, assume that management considers risk factors. Emerald Green umbrellas, for example, have a 10% chance of selling only 100,000 units, which would result in a net operating loss of $200,000. Also, there is a 30% chance that sales of Emerald Green will exceed 300,000 units. If this event happens, the operating income of Emerald Green umbrellas will be higher than the operating income of Shocking Pink umbrellas. If management is reluctant to take risks, it would prefer selling the 300,000 units of Shocking pink.3-47 (Cont’d.)

3-36

The expected values are important, but the dispersion of the probability distribution is also important. Normally, the wider the dispersion, the greater the risk. Knowledge of the entire probability distribution helps management assess the risk before reaching a decision.

3-48 (30 min.) Ethics, CVP analysis.

1. Contribution margin percentage =

=

= = 40%

Breakeven revenues =

= = $5,400,000

2. If variable costs are 52% of revenues, contribution margin percentage equals 48% (100% 52%)

Breakeven revenues =

= = $4,500,000

3. Revenues $5,000,000Variable costs (0.52 $5,000,000) 2,600,000Fixed costs 2,160,000Operating income $ 240,000

4. Incorrect reporting of environmental costs with the goal of continuing operations is unethical. In assessing the situation, the specific “Standards of Ethical Conduct for Management Accountants” (described in Exhibit 1-7) that the management accountant should consider are listed below.

CompetenceClear reports using relevant and reliable information should be prepared. Preparing reports on the basis of incorrect environmental costs in order to make the company’s performance look better than it is violates competence standards. It is unethical for Bush to not report environmental costs in order to make the plant’s performance look good.

3-37

3-48 (Cont’d.)

IntegrityThe management accountant has a responsibility to avoid actual or apparent conflicts of interest and advise all appropriate parties of any potential conflict. Bush may be tempted to report lower environmental costs to please Lemond and Woodall and save the jobs of his colleagues. This action, however, violates the responsibility for integrity. The Standards of Ethical Conduct require the management accountant to communicate favorable as well as unfavorable information.

ObjectivityThe management accountant’s Standards of Ethical Conduct require that information should be fairly and objectively communicated and that all relevant information should be disclosed. From a management accountant’s standpoint, underreporting environmental costs to make performance look good would violate the standard of objectivity.

Bush should indicate to Lemond that estimates of environmental costs and liabilities should be included in the analysis. If Lemond still insists on modifying the numbers and reporting lower environmental costs, Bush should raise the matter with one of Lemond’s superiors. If after taking all these steps, there is continued pressure to understate environmental costs, Bush should consider resigning from the company and not engage in unethical behavior.

3-49 (35 min.) Deciding where to produce.

1. The annual breakeven point in units at the Peoria plant is 73,500 units and at the Moline plant is 47,200 units, calculated as follows.

Contribution margin per unit calculation:

Peoria Moline Selling price $150.00 $150.00Less variable costs:

Manufacturing 72.00 88.00Marketing and distribution 14.00 14.00

Contribution margin per unit $ 64.00 $ 48.00

Fixed costs calculation:Total fixed costs = (Fixed manufacturing costs per unit + Fixed marketing and distribution

costs per unit) × Production rate per day × Normal working days

Peoria = ($30.00 + $19.00) × 400 × 240 = $4,704,000

Moline = ($15.00 + $14.50) × 320 × 240 = $2,265,600

3-38

3-49 (Cont’d.)

Breakeven calculation:

Breakeven units = Fixed costs ÷ Contribution margin per unit

Peoria = $4,704,000 ÷ $64 = 73,500 units

Moline = $2,265,600 ÷ $48 = 47,200 units

2. The operating income that would result from the division production manager’s plan to produce 96,000 units at each plant is $3,628,800. The normal capacity at the Peoria plant is 96,000 units (400 × 240); however, the normal capacity at the Moline plant is 76,800 units (320 × 240). Therefore, 19,200 units (96,000 – 76,800) will be manufactured at Moline at a reduced contribution margin of $40.00 per unit ($48 – $8).

Contribution margin per plant:Peoria, 96,000 × $64 $ 6,144,000Moline, 76,800 × $48 3,686,400Moline, 19,200 × $40 768,000

Total contribution margin $10,598,400Deduct total fixed costs, $4,704,000 + $2,265,600 6,969,600Operating income $ 3,628,800

3. The optimal production plan is to produce 120,000 units at the Peoria plant and 72,000 units at the Moline plant. The full capacity of the Peoria plant, 120,000 units (400 units × 300 days), should be utilized as the contribution from these units is higher at all levels of production than the contribution from units produced at the Moline plant.

Contribution margin per plant:Peoria, 96,000 × $64 $ 6,144,000Peoria 24,000 × $64 – $3 1,464,000Moline, 72,000 × $48 3,456,000

Total contribution margin $11,064,000Deduct total fixed costs 6,969,600Operating income $ 4,094,400

The contribution margin is higher when 120,000 units are produced at the Peoria plant and 72,000 units at the Moline plant. As a result, operating income will also be higher in this case since total fixed costs for the division remain unchanged regardless of the quantity produced at each plant.

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Chapter 3 Internet Exercise

The Internet exercise is available to students only on the Prentice Hall Companion Website www.prenhall.com/horngren. Students can click on Cost Accounting, 11th ed., and access the Internet Exercise for the chapter, which links to the Web site of a company or organization. The Internet Exercise on the Web will be updated periodically so that it is current with the latest information available on the subject organization's Web site. A printout copy of the Internet exercise for this chapter as of early 2002 appears below.

The solution to the Internet exercise, which will also be updated periodically, is available to instructors from the Companion Website's faculty view. To access the solution, click on Cost Accounting, 11th ed., Faculty link, and then register once to obtain your password through the online form. After the initial registration, you will have a personal login ID and password to use to log in. A printout of the solution to the Internet exercise for this chapter as of early 2002 follows. The exercise and solution provide instructors with an idea of the content of the Internet exercise for this chapter.

Internet Exercise

Southwest Airlines is the nation's fifth largest domestic carrier. It serves 57 cities with a fleet of 352 Boeing 737s. Southwest just marked its twenty-eighth consecutive year of profitability, and enjoys the distinction of having the lowest operating cost structure in the domestic airline industry. In this exercise you will examine factors that contribute to Southwest's success.

Go to www.iflyswa.com/, and click on the "About SWA" link, followed by the "Investor Relations" link. From here you can access Southwest's 2000 annual report in Adobe Acrobat pdf format. Use Southwest's 2000 annual report to answer the following questions:

1. Skim Southwest Airline's annual report, pages 7-15, and explain how each of the following factors contributes to its low operating cost structure: a. Load factor.b. Type of aircraft.c. Choice of markets, flights, in-flight service, and aircraft boarding procedures.d. Method of ticketing.

2a. Go to Southwest's income statement and examine Southwest's 2000 operating expenses. Identify each expense as either a fixed, variable, or mixed cost (a combination of fixed and variable costs).

Operating Expense Type

2b. In the short run are Southwest's labor costs predominantly fixed or variable? Explain your answer.

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Internet Exercise (Cont’d.)

3. Identify potential cost drivers for the following expenses: salaries, fuel and oil, maintenance materials and repairs, agency commissions, aircraft rentals, landing fees, and depreciation.

Operating Expense Potential Cost Drivers

4. In the year 2000, Southwest reported passenger revenues of $5,467,965,000 on 42,215,162,000 passenger-miles. Ignoring freight and other revenues calculate Southwest's breakeven point for operating income in revenues and passenger-miles assuming:

Aircraft rentals, depreciation, and other operating expenses, which totaled $1,337,415,000, are 100% fixed.

Salaries, fuel, maintenance, agency commissions, and landing fees, which totaled $3,291,000,000, are 90% variable.

5. In light of your analysis in questions 1-4, discuss the strategy of Priceline.com. At Priceline.com you can purchase airline tickets, hotel rooms, and rental cars at 40% or more off the lowest published prices provided you are flexible about your flight plans and can travel at short notice.

Solution to Internet Exercise

1a. One of the most important factors influencing profitability is an airline's load factor. Airlines don't make money flying empty planes. Load factor refers to the proportion of a plane's seats that are occupied on each flight. Southwest consistently has the highest load factor in the industry. Its load factor was a record 70.5% in 2000. Southwest's choice of aircraft and operating strategy contributes to its high load factor.

1b. Southwest flies only Boeing 737s. Its commitment to a single type of aircraft simplifies its operations in terms of maintenance, scheduling, staffing, and training. Pilots can fly any plane, mechanics can service any plane, and flight crews can staff any flight. This minimizes training costs and spare part inventories, and minimizes the time that aircraft spend at the gate.

1c. Southwest provides short haul point-to-point service. This enables Southwest to avoid the cost of providing in-flight meals, and more importantly avoid the ground time required to load and unload meals from aircraft. In addition, Southwest utilizes open seating (first come, first served) for aircraft boarding. This minimizes the ground time for aircraft at the gate and results in higher aircraft and airport utilization.

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Internet Exercise (Cont’d.)

1d. Southwest reduces ticketing costs by selling over 70% of its seats through its Web site or phone calls to reservation agents versus an industry average of 20% to 25%. In addition to lowering commission costs, this results in a greater use of e-tickets (electronic tickets). E-tickets speed check-in times and reduce paper and back-office processing costs.

2a.

Operating Expense TypeSalaries, wages, and benefits MixedFuel and oil VariableMaintenance materials and repairs MixedAgency commissions VariableAircraft rentals Fixed*Landing fees VariableDepreciation Fixed

*Refer to footnotes to the financial statements. Aircraft rentals are primarily long-term fixed commitments.

2b. In the short run Southwest's labor costs are predominantly fixed. While pilots, mechanics, flight attendants, and administrators may be compensated for overtime, base salaries are generally fixed. In the long run labor costs are variable. Southwest can layoff employees if business slows or hire additional employees to meet increased demand.

3.Operating Expense Potential Cost DriversSalaries, wages, and benefits Number of flights, passengers, flight milesFuel and Oil Flight milesMaintenance materials and repairs Flight miles and timeAgency commissions # of tickets, passenger revenuesAircraft rentals Number of flights, passengers, flight miles,

Number of breakdowns by aircraftLanding fees Number of flights, passengersDepreciation Flight miles, cost of planes*

* If the unit of production method of deprecation is used, the expense is a function of aircraft cost and usage.

4. Revenue per passenger mile $0.1295 ($5467,965,000 ÷ 42,215,162,000)Variable cost per passenger mile $0.0702 [(0.90 × $3,291,000,000) ÷ 42,215,162,000]

Contribution margin per mile $0.0593

Breakeven miles = Fixed cost / Contribution margin per mile Breakeven miles = ($1,337,415,000 + $329,100,000 / $0.0593 = 28,103, 119,000 miles

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Internet Exercise (Cont’d.) Breakeven revenues = $28,103,119,000 × .1295 = $3,639,353,900

5. The variable cost of flying an additional passenger is very low. (How much can it possibly cost to prepare an airline meal?) Thus, airlines value the ability to price discriminate and offer low-priced tickets on empty flights to travelers with flexible flight plans.

Chapter 3 Video Case

The video case can be discussed using only the case writeup in the chapter. Alternatively, instructors can have students view the videotape of the company that is the subject of the case. The videotape can be obtained by contacting your Prentice Hall representative. The case questions challenge students to apply the concepts learned in the chapter to a specific business situation.

STORE 24: COST-VOLUME-PROFIT ANALYSIS

1. Customers who might be attracted to money order services include those new to the location who don’t have a bank checking account, or those who do not wish to establish a relationship with a bank for financial services. In the Northeast, Store 24 operates in neighborhoods with large immigrant populations, whose members have yet to open bank checking accounts. These customers are also likely to buy Store 24’s other products once they are in the store.

2. Contribution margin per unit:

Selling price: 69.0 centsDeduct:Direct labor 22.5 cents ($9.00 per hour/60 minutes) × 1.5 minutesProcessing fee 5.0 centsContribution margin 41.5 cents per unit

3. Equation method formula: Revenues – Variable costs – Fixed costs (FC) = Operating income (OI)Where(Unit selling price × quantity (Q)) – (Unit variable costs × Q) – Fixed costs = OI

(0.69Q) – ((0.225 +0.05)Q) – $25.00 = $0 0.415Q – $25.00 = $0

0.415Q = $25.00Q = $25.00/0.415 = 60.24 money orders (approx. 2 per day)

Contribution margin method: $25.00/0.415 cents per unit = 60.24 units

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Video Case (Cont’d.)

4. Revenues – Variable costs – Fixed costs (FC) = Operating income (OI)

(0.69Q) – ((0.225 +.05)Q) – $25.00 = $100 0.415Q – $25.00 = $100

0.415Q = $100 + 25.00Q = $125.00/0.415 = 301.2 money orders (approx.10 per day)

5. Since it takes three times as long for a clerk to complete a money order transaction versus a typical product sale (90 seconds versus 30 seconds), customers who are not purchasing money orders will have to wait while the money order transaction is being completed. Some customers may choose not to wait, thereby costing the store those sales. It is impossible to calculate the exact cost since the number of customers who might leave and the contribution margin for the average $3.00 sale is not known. Students may try to calculate the cost using the gross margin percentage of 30%, but this percentage does not consider variable operating costs such as the labor of the store clerk.

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