module 15 solutions

Module 15

Cost-Volume-Profit Analysis and Planning

DISCUSSION QUESTIONS

Q3-1. Cost-volume-profit analysis is a technique used to examine the relationships among the total volume of some independent variable, total costs, total revenues, and profits during a time period. It is particularly useful in the early stages of planning when it provides a framework for discussing planning issues.

Q3-2. The important assumptions that underlie cost-volume-profit analysis are:

1. All costs are classified as fixed or variable with unit-level activity cost drivers.

2. The total cost function is linear within the relevant range.3. The total revenue function is linear within the relevant range.4. The analysis is for a single product, or the sales mix of multiple

products is constant.5. There is only one activity cost driver: unit or dollar sales

volume.

Q3-3. The use of a single variable in cost-volume-profit analysis is most reasonable when analyzing the profitability of a specific event or the profitability of an organization that produces a single product or service on a continuous basis.

©Cambridge Business Publishers, 2013

Solutions Manual, Module 15 15-1

Q3-4. In a contribution income statement, costs are classified according to behavior as variable or fixed, and the contribution margin (the difference between total revenues and total variable costs) that goes toward covering fixed costs and providing a profit is emphasized. In a functional income statement, costs are classified according to function (rather than behavior), such as manufacturing and selling and administrative. This is the type of income statement typically included in corporate annual reports.

Q3-5. The unit contribution margin is equal to the difference between the unit selling price and the unit variable costs. In computing the unit break-even point, the fixed costs are divided by the unit contribution margin.

Q3-6. The contribution margin ratio is the portion of each dollar of sales revenue contributed toward covering fixed costs and earning a profit. It is especially useful in situations involving several products or when unit sales information is not available.

Q3-7. The desired profit is added to the fixed costs, increasing the sales volume required to cover both.

Q3-8. A profit-volume graph contains only one line showing the relationship between volume and profits, while a cost-volume-profit graph contains two lines – one for total revenues and one for total costs. A profit-volume graph is most likely to be used when management is primarily interested in the impact on profits of changes in sales volume and less interested in the related revenues and costs.

Q3-9. Income taxes increase the sales volume required to earn a desired after-tax profit.

Q3-10. Other things being equal, the higher the degree of operating leverage, the greater the opportunity for profit with increases in sales. Conversely, a higher degree of operating leverage magnifies the risk of large losses with a decrease in sales.


15-2 Financial & Managerial Accounting for MBAs, 3rd Edition

MINI EXERCISES

M15-11

a. Break-even point = $120,000/(1 0.40) = $200,000

b. Margin of safety = $240,000 $200,000 = $40,000

c. Sales volume for desired profit = ($120,000 + $70,000) = $316,667(1 0.40)

M15-12

a. 1. Total variable costs2. Total revenue3. Total costs4. Variable costs5. Fixed costs6. Total costs7. Contribution margin8. Break-even unit sales volume9. Loss area10. Profit area

b. Line CC Line OR Break-Even Point1. Shift downward No change Shift left (decrease)2. No change Increase slope Shift left (decrease)3. Increase slope No change Shift right (increase)4. Shift upward Decrease slope Shift right (increase)5. Shift downward and No change Shift left (decrease)

decrease slope



M15-13

a. 1. Loss area2. Profit area3. Break-even point4. Axis on which profit and loss are measured5. Fixed costs6. Profit at volume E

b. Line CF Break-Even Point1. Increase slope Shift left (decrease)2. Decrease slope Shift right (increase)3. Shift upward Shift left (decrease)4. Shift downward and Shift right (increase) decrease slope5. Shift upward and Can't tell; the two changes

decrease slope have opposite effects.

M15-14

a.



M15-14 (concluded)

b.

c. It is most appropriate to use a profit-volume graph when management is primarily interested in the impact on profits of changes in sales volume and less interested in the related revenues and costs.



M15-15

a. Selling price $5.00 per hot dogVariable costs 3.50 per hot dogContribution margin $1.50

Break-even point = $750,000/$1.50 = 500,000 hot dogs

b.

c.

d. It is easier to determine profit or loss at any volume with a profit-volume graph than with a cost-volume-profit graph. This is especially true in situations, such as this, where the unit contribution margin is small and the scale of activity is large. Although a profit-volume graph provides a clear illustration of profits, it does not illustrate revenues and costs. Hence, a manager using a profit-volume graph does not see the relationship between revenues, costs, and profits.



M15-16

Product

Unit Contribution

MarginSales Mix (units)* Weight

A $1 6 $1 x 6/10 = $0.60B 2 3 2 x 3/10 = 0.60C 3 1 3 x 1/10 = 0.30

10 $1.50

*B = 3C and A = 2B, so A = 3 x 2 = 6

Average unit contribution margin = $1.50

Break-even unit sales volume = $112,500/$1.50 = 75,000 units

Units of A at break-even = 75,000 x 6/10 = 45,000



EXERCISES

E15-17

a.Alberta Company

Contribution Income StatementFor the Month of May 2012

Sales (6,000 x $40) $240,000Less variable costs:

Direct materials (6,000 x $10) $ 60,000Direct labor (6,000 x $2) 12,000Manufacturing overhead (6,000 x $5) 30,000Selling and administrative (6,000 x $5) 30,000 (132,000)

Contribution margin 108,000Less fixed costs:

Manufacturing overhead 40,000Selling and administrative 20,000 (60,000)

Profit $ 48,000

b.

Note: The instructor might extend this assignment in class, computing the break-even point, the margin of safety, and the impact on profits of a change in sales.



E15-18

a. Sales $750,000Variable costs (450,000 ) Contribution margin $300,000

Contribution margin ratio = $300,000/$750,000 = 0.40Annual break-even dollar sales volume = $210,000/0.40 = $525,000

b. Annual margin of safety in dollars:Sales $750,000Break-even sales dollars (525,000)Margin of safety $225,000

c. To determine the variable and total cost lines, it is necessary to compute the variable cost ratio:

Variable cost ratio = Variable costs = $450,000 = 0.60Sales $750,000

At a volume of $1,000,000 sales dollars, variable costs are $600,000.

d. Revised annual break-even dollar sales:

($210,000 + $35,000)/0.40 = $612,500



Fixed costs = $210,000

Profit =$90,000

Variable costs =$450,000

E15-19

a. Contribution margin $ 380,000Sales 1,000,000 Contribution margin ratio 0.38

Break-even point in sales dollars = $285,000/0.38= $750,000

b. Current sales $1,000,000Break-even sales (750,000 ) Margin of safety $ 250,000

c. Current fixed costs $285,000Impact of increase 57,000New fixed costs $342,000

Revised break-even point = $342,000/0.38= $900,000

d. Required before-tax income = $200,000/(1 0.36)= $312,500

Sales volume required to provide an after-tax income of $200,000:($285,000 + $312,500)/0.38 = $1,572,368

e. Sales $1,572,368Variable costs (62% of sales) (974,868 ) Contribution margin (38% of sales) 597,500Fixed costs (285,000 ) Net income before taxes 312,500Income taxes (36%) (112,500 ) Net income after taxes $ 200,000*

*Answer reflects rounding.



E15-20

a. Fixed costs $12,500,000Contribution [($8,000 $1,000) 1,500] $10,500,000Endowments and grants 250,000 (10,750,000 ) Required from other sources $ 1,750,000

b. Break-even price ($30,000/3,000) = $10.00

Revenues (2,700 $10) $27,000Fixed costs (30,000 ) Deficit $ 3,000

c. Cost to city ($20 10,000) = $200,000

d. Contribution [($1.25 $0.75) 5,000] $2,500Fixed costs (500 ) Amount raised $2,000

e. Available funds $20,000Fixed costs (5,000 ) Available for variable costs 15,000Variable costs per present $10 Number of presents 1,500



E15-21

a.Capital-

IntensiveLabor-

IntensiveFixed costs:

Manufacturing overhead

$2,440,000 $ 700,000

Selling 500,000 500,000 Total $2,940,000 $1,200,000

Selling price $ 30.00 $30.00

Variable costs:

Direct materials $5.00 $ 6.00Direct labor 5.00 12.00Manuf. overhead 4.00 2.00Selling 2.00 (16 .00) 2.00 (22 .00) Unit cont. margin $14 .00 $ 8 .00

Fixed costs $2,940,000 $1,200,000Unit cont. margin $14.00 $ 8.00 Unit break-even point 210,000 150,000



E15-21 (concluded)

b. Paper Mate would be indifferent between the two methods at the unit volume, X, where total costs are equal.

$16X + $2,940,000 = $22X + $1,200,000$6X = $1,740,000

X = 290,000 units

Identical results are obtained if profit, rather than cost, equations are used.

($30 $16)X – $2,940,000 = ($30 $22)X – $1,200,000$6X = $1,740,000

X = 290,000 units

Paper Mate should use the labor-intensive method if sales are less than 290,000 units and use the capital-extensive method if sales are above 290,000 units.

c. 1. Operating leverage is a measure of the responsiveness of income to changes in sales. The higher a firm's operating leverage, the more sensitive are its profits to changes in sales volume. It is also an indication of an organization's cost structure. The higher the portion of an organization's fixed costs (in comparison with variable costs), the higher its operating leverage.

2. Capital- Labor-

Intensive IntensiveUnit contribution margin $ 14.00 $ 8.00Unit sales volume x 250,000 x 250,000Contribution margin 3,500,000 2,000,000Fixed costs (2,940,000) (1,200,000)Net income $ 560,000 $ 800,000

Contribution margin $3,500,000 $2,000,000Net income 560,000 800,000 Operating leverage 6.25 2.50

3. The capital-intensive method has a higher operating leverage because of the greater use of fixed assets.



E15-22

a.Florida Berry Basket

Contribution Income StatementFor the Year Ended December 31, 2012

Sales (45,000 $90) $4,050,000Variable costs (45,000 $80) (3,600,000 ) Contribution margin 450,000Fixed costs 275,000 ) Net income $ 175,000

b. Operating leverage = Contribution margin/Net income= $450,000/$175,000= 2.57

c. Percentage change in profits = % decrease in sales x Operating leverage= 10 x 2.57= 25.7 percent decrease

Profits should decrease by 25.7 percent to $130,025, computed as: [$175,000 ($175,000 x 0.257)].

d. Contribution margin [45,000 ($90 $77.50)] $ 562,500Fixed costs (375,000 ) Net income $ 187,500

Operating leverage ($562,500/$187,500) 3

The acquisition of the berry-picking machines will reduce variable costs, thereby increasing the contribution margin. It will also increase fixed costs, thereby increasing the difference between the contribution margin and net income. The net effect would be an increase in operating leverage.



E15-23

a. Unit Sales Selling MixProduct Price (units) WeightStandard $ 50 x 1,750/2,500 $35Multiform 125 x 500/2,500 25Complex 250 x 250/2,500 25Average unit selling price $85

Unit Sales Contribution Mix Product Margin (units)* Weight Standard $ 20 x 1,750/2,500 $14Multiform 50 x 500/2,500 10Complex 100 x 250/2,500 10Average unit contribution margin $34

Contribution margin ratio = $34/$85 = 0.40

Break-even sales volume = $45,000/0.40 = $112,500

b. Actual sales volume = 2,500 $85 = $212,500Break-even sales volume 112,500 Margin of safety $100,000

c.



E15-24

Once the following, or a similar, format is established, each case is solved by filling in the given information and working toward the unknowns.

Case 1 Case 2 Case 3 Case 4

Unit sales 1,000 800 4,300?* 3,000 ?*

Sales revenue $20,000 $ 1,600 ? $137,600 ? $60,000Variable costs:

Unit $ 10 $ 1 $ 12 $ 5?Unit sales x 1,000 x 800 x 4,300 x 3,000 ?Total (10,000 ) (800 ) (51,600 ) (15,000 ) ?

Contribution margin $10,000? $ 800 $ 86,000? $45,000?Fixed costs (8,000 ) (400 )? (80,000) (30,000 )?

Net income $ 2,000? $ 400 $ 6,000?# $15,000 ?#

Unit cont. margin:Cont. margin $10,000? $ 800 $86,000? $45,000?Unit sales 1,000 800 4,300 ? 3,000 ?Unit contribution $ 10? $ 1? $ 20 ? $ 15

Break-even point:Fixed costs $8,000 $ 400 $ 80,000 $30,000?

Unit cont. margin

$10 ? $1 ? $20 ? $15 Unit break-even point 800 ? 400 ? 4,000 2,000

Margin of safety (unit sales less unit break- even point) 200 ? 400 ? 300 1,000

*Solved as the unit break-even point plus the margin of safety.#Solved as the unit contribution margin times margin of safety.



E15-25

Once the following or similar format is established, each case can be solved by filling in the known amounts and working toward the unknowns.

Case A Case B Case C Case DSales revenue $100,000 $80,000 $50,000 $45,000*

Cont. margin ratio 0.40 ? 0.50 0.40 0.80 ?Contribution margin $ 40,000 $40,000? $20,000 $36,000?Fixed costs ( 30,000) (35,000)? (10,000)? (20,000)?Net income $ 10,000? $ 5,000 $10,000 $16,000?

Variable cost ratio 0.60? 0.50 0.60? 0.20Contribution margin ratio 0.40? 0.50? 0.40 0.80?Total 1.00 1.00 1.00 1.00

Break-even point:Fixed costs $ 30,000 $35,000 $10,000? $20,000?Cont. marg. ratio 0.40 ? 0.50 ? 0.40 0.80 Dollar break-even point $ 75,000? $70,000? $25,000? $25,000

Margin of safety (dollar sales less dollar break-even point) $ 25,000? $10,000? $25,000? $20,000

*Computed as the break-even point plus the margin of safety.



E15-26 A

Weekly contribution per average customer:

$15 sales per visit (1 - 0.80) contribution ratio 1.75 visits = $5.25

Annual contribution per customer = $5.25 52 weeks = $273

Customers required for desired profit = ($80,000 + $40,000)/$273 = 440

Required population = 440 customers / 0.04 customers in population = 11,000

E15-27 A

a. Minimum order size to break even on order = $200 = $2,500(0.10 – 0.02)

b. Annual sales to break-even on average customer = ($200 x 4 orders) + $1,000 = $22,500

(0.10 – 0.02)

c. Average order size = $22,500/4 = $5,625

d. Order-level costs ($200 4 orders 100 customers) $ 80,000Customer-level costs ($1,000 100 customers) 100,000Facility-level costs 60,000Total costs $ 240,000Contribution margin ratio 0.08 Minimum annual sales to break even $3,000,000

e. Average order size = $3,000,000/(4 orders 100 customers) = $7,500

f. Part (a) considers only order-level costs while part (c) also considers customer-level costs, and part (e) adds facility-level costs. In order for a company to break even on an order, it need only cover order-level costs. To break even on a customer, the company must cover order-level and customer-level costs. Finally, to achieve true break-even, all costs must be covered.



PROBLEMS

P15-28

a. Unit contribution margin: $35 $25 = $10

Total contribution (20,000 $10) $200,000Fixed costs 110,000 Net income before taxes 90,000Net income after taxes 54,000 Income taxes 36,000Net income before taxes $90,000 Tax rate 0.40

b. Required before-tax income = $90,000/(1 0.40)= $150,000

Volume required to provide an after-tax income of $90,000:($110,000 + $150,000)/$10 = 26,000 units

c. Contribution marginCurrent $10.00Impact of reduction in variable costs 2 .50 New $12 .50

Fixed costs:Current $110,000Impact of increase in fixed costs 20,000New $130,000

Volume required to provide an after-tax income of $90,000:($130,000 + $150,000)/$12.50 = 22,400 units

The reduction in variable costs was more than enough to offset the increase in fixed costs. Consequently, the volume required to achieve an after-tax profit of $90,000 declined from 26,000 units to 22,400 units.

d. Requirements (a) through (c) assume that taxable income and accounting income are equal and that the tax rate is constant.



P15-29

a.New York Tours

Contribution Income StatementFor the Month of June 2012

Sales (3,000 $90) $270,000Less variable costs:

Admission fees (3,000 $30) $ 90,000Lunch (3,000 $20) 60,000Overhead (3,000 $12) 36,000Selling and administrative (3,000 $8) 24,000 (210,000)


Operations 25,000Selling and administrative 15,000 (40,000)

Before-tax profit 20,000Income taxes ($20,000 × .40) 8,000After-tax profit $ 12,000

b. Monthly break-even point in units.: $40,000/($90 70) = 2,000 units

c. Margin of safety in units:Actual June sales 3,000 unitsBreak even sales 2,000 unitsMargin of safety 1,000 units

d. Sales for an after-tax profit of $15,000:Required before-tax profit = $15,000/(1 0.40) = $25,000Required sales = ($40,000 + $25,000)/($90 70) = 3,250



P15-29 (concluded)

e.

P15-30

a. Prior to solving this problem it is necessary to determine the variable costs per unit, the fixed costs per year, and the unit selling price.

Using the high-low method:Variable costs per unit = ($85,000 $70,000)/(8,000 5,000) = $5

Fixed costs = $85,000 $5(8,000) = $45,000or, = $70,000 $5(5,000) = $45,000

Unit selling price = $65,000/5,000 = $104,000/8,000 = $13

Unit contribution margin = $13 $5 = $8

Break-even point = $45,000/$8 = 5,625 units

b. Sales volume required to earn a profit of $10,000: ($45,000 + $10,000)/$8 = 6,875 units



Variable costs = $210,000

Fixed costs = $40,000

Profit = $20,000

Totalrevenues & Totalcosts

P15-31

a. Contribution ratio = 1.0 0.60 = 0.40

Break-even point = $1,300,000/0.40 = $3,250,000

b. Before-tax profit = $500,000/(1 0.34) = $757,576 (rounded)

Required sales volume = ($1,300,000 + $757,576)/0.40 = $5,143,940

c. Profits of automation = Profits of outsourcing(1 0.54)X ($1,300,000 + $300,000) = (1 0.65)X ($1,300,000 $300,000)0.46X $1,600,000 = 0.35X $1,000,0000.11X = $600,000 X = $5,454,545 (rounded)

d.Automation Outsourcing

Strength: It will provide higher profits if

sales increase. It may provide new

opportunities. It may enhance quality.

Strength: This alternative has less risk

and a lower break-even point. It is preferred at the current

sales volume. It allows focusing on core

competencies.

Weakness: This alternative has higher risk

and a higher break-even point.

Weakness: This alternative will not have

as great a potential for high profits.

It provides less control of operations.



P15-32

a. The break-even point in patient-days equals total fixed costs divided by the contribution margin per patient-day.

Fixed costs: Melford Hospital charges $2,900,000 Salaries 480,000 Total $3,380,000Unit contribution margin:

Revenues per patient-day $300Variable costs per patient-day (100)*Contribution margin per patient-day $200

*$6,000,000 total 2011 revenues/$300 revenue per patient-day equals 20,000 patient-days for 2011.

$2,000,000 total 2011 variable costs / 20,000 patient-days = $100 variable costs per patient-day

Break-even point in patient-days = $3,380,000/$200= 16,900 patient-days

b.Pediatrics

Schedule of Change in Earnings from Rental of 20 Additional BedsFor the Year Ending June 30, 2012

Increase in revenues (20 beds 90 days $300/ day) $ 540,000Increase in expenses:

Fixed charges by Melford Hospital:Annual charge per bed ($2,900,000/60) $ 48,333Number of additional beds 20 Total increase in fixed charges 966,660

Variable charges by Melford Hospital($100/patient-day 90 days 20 beds) 180,000 (1,146,660)

Net decrease in earnings $ (606,660)

(Note that the break-even on the additional 20 beds is 4,834 bed days ($966,660/$200), or 242 days for each of the 20 additional beds. This is an increase of 3,034 bed days (or 152 days for each bed) above the estimated demand of 90 days for each of the 20 beds.)



P15-33

a. Required before-tax profit = $30,000/( 1– 0.40) = $50,000

Required sales for a $30,000 after-tax profit:

Sure Foot = ($280,000* + $50,000)/($80 – 50) = 11,000 pairs

Trail Runner = ($200,000* + $50,000)/($75 – 50) = 10,000 pairs

*Because only one product will be produced the product-level costs and the facility-level costs are combined: $130,000 + $150,000 for Sure Foot and $50,000 + $150,000 for Trail Runner.

b. Required sales for identical before-tax profit:

Sure Foot Profit = Trail Runner Profit($80 – $50)X – $280,000 = ($75 – $50)X – $200,000 $30X – $25X = $80,000 $5X = $80,000 X = 1 6,000 pairs

c. The after-tax profit or loss is the same with either product. Hence, it is only necessary to solve for one product.

Sure Foot: [($80 – $50)16,000 – $280,000] × (1 – 0.40) = $120,000

Trail Runner: [($75 – $50)16,000 – $200,000] × (1 – 0.40) = $120,000

d. Without further analysis it is apparent that at a volume of 13,000 pairs the Trail Runner is preferred. Trail Runner requires fewer sales to achieve a $30,000 after-tax profit and the profits of both products are not identical until a total of 16,000 pairs of either product are sold. This answer can also be demonstrated analytically:

Sure Foot: [($80 – $50)13,000 – $280,000] × (1 – 0.40) = $66,000

Trail Runner: [($75 – $50)13,000 – $200,000] × (1 – 0.40) = $75,000



P15-33 (concluded)

e. Required Sure Foot variable costs for identical profit at 13,000 pairs:

Because before-tax and after-tax profits will be the same for either product, it is simpler to develop a solution based on identical before-tax profits with X representing the required Sure Foot variable costs per pair.

Sure Foot Profit = Trail Runner Profit ($80 – X)13,000 – $280,000 = ($75 – $50)13,000 – $200,000 $1,040,000 – 13,000X – $280,000 = $325,000– $200,000 –13,000X = – $635,000 X = $48.85 (rounding)

The variable costs of Sure Foot must decline $1.15 ($50.00 – $48.85) to $48.85.

Sure Foot Profit with reduced variable costs = [($80 – $48.85)13,000 – $280,000] × (1 – 0.40) = $74,970 (with rounding error)



P15-34

a. Cost-estimating equation:Variable cost ratio = $1,243,155 $1,113,567 = 0.8134

$1,364,661 $1,205,340Annual fixed costs = $1,243,155 – ($1,364,661 x 0.8134) = $133,139.7 (thousand)

Total cost (in thousands) = $133,139.7 + 0.8134XWhere X is revenue in thousands of dollars.

Note the high variable cost ratio, as discussed in the chapter opening.

b. Annual break-even point:Contribution margin ratio = 1 – 0.8134 = 0.1866Break-even point = ($133,139.7/0.1866) = $713,503.2 (thousand)

c. Predicted 2009 operating profit:Revenues $1,670,269.0Less:Variable costs (1,670,269 × 0.8134) 1,358,596.8Fixed costs 133,139 .7 Operating profit $ 178,532 .5

d. The equations assume linear cost behavior, stable prices, and a stable cost structure.

Netflix reported a 2009 operating profit of $191,939,000, $13,406,500 more than the amount predicted using equations based on 2007 and 2008 data, an error of approximately 7 percent. This under-prediction likely occurred because of changes in Netflix’s cost structure, higher fixed costs and lower variable costs, as the number of Netflix customers increase with greater use of streaming video. See the opening vignette for Chapter 3.



P15-35 A

a. Annual break-even point in sales dollars:Break-even point = $360,000/(1 0.75 0.05) = $1,800,000

b. Annual break-even point in units:Break-even point = $360,000/{$120 [$120(0.75 + 0.05)]} = 15,000 units(or $1,800,000/$120 = 15,000)

c. On new books the contribution to other costs is 25 percent (1.00 less 0.75 to the publisher) of the suggested retail price. On used books the contribution to other costs is 50 percent of the suggested retail price (0.75 less 0.25 cost of the book). Shifting towards more used books and fewer new books will increase bookstore profitability with the same unit sales.

d. Publisher project break-even point:Note: Solution is in terms of wholesale price to bookstore, not retail price to final buyer.

Project break-even point = $325,000/(1 0.20 0.15) = $500,000

e. Profitability analysis of sales of 8,000 new books:1. Bookstore’s unit-level contribution

Final retail sales $120 8,000 $960,000Less unit-level costs (0.75 + 0.05) (768,000 ) Bookstore’s unit-level contribution $192,000

2. Publisher’s project-level contribution:Sales to bookstores $120 0.75 8,000 $720,000Unit-level costs (0.20 + 0.15) (252,000)Project-level costs (325,000 ) Publisher’s project contribution $143,000

3. Author’s royalties: $720,000 net to publisher 0.15 $108,000



P15-36

a. Current break-even point in sales dollars:

Contribution margin ratio = $400,000/$1,050,000 = 0.38095

Break-even point = $240,000/0.38095 = $630,004

b. Unit contribution margin and break-even point:

Average unit contribution margin = $400,000/2,500 = $160

Unit break-even point = $240,000/$160 = 1,500 units

c. The current average unit contribution margin is $160.

Current unit contribution margin of individual products:Cozy Kitchen $100,000/1,000 units $100All-House $300,000/1,500 units $200

Shifting the mix to 80:20 will change the average unit contribution margin:

($100 0.80) + ($200 0.20) = $120

Contribution with proposed plan = 3,000 units $120 = $360,000

The current contribution margin is $400,000. The contribution margin with a shift in the mix, even with a 500-unit sales increase, is only $360,000. Hence, profits will decrease if the projected shift occurs. In the absence of capacity constraints, sales reps should emphasize increased sales of the product with the higher unit contribution margin.



P15-37

a. 1. Current contribution:Fixed costs $21,000Profit + 9,000Contribution $30,000

Contribution margin ratio = $30,000/$50,000 = 0.60Current break-even point = $21,000/0.60 = $35,000

2. Super SuperBurgers Chickens

Selling price $2.50 $3.00Variable costs -1.00* -1.80Unit contribution $1.50 $1.20

*$2.50 × (1.0 – 0.60)

Short-run Volume Mix

Super Burgers 10,000 0.50Super Chickens 10,000 0.50

UnitContribution Mix Weight

Super Burgers $1.50 0.50 $0.75Super Chickens 1.20 0.50 0.60Average unit contribution $1.35

Short-run monthly profit:Contribution (20,000 units × $1.35) $27,000Less fixed costs ($21,000 + 7,760) (28,760 ) Profit (loss) $ (1,760 )

Short-run contribution ratio:Contribution margin 27,000Revenue [(10,000 × $2.50) + (10,000 × $3.00)] ÷55,000Contribution ratio 0.4909

Short-run break-even point = $28,760/0.4909 = $58,586



P15-37 (concluded)

3. Long-run Volume Mix

Super Burgers 30,000 2/3Super Chickens 15,000 1/3

UnitContribution Mix Weight

Super Burgers $1.50 2/3 $1.00Super Chickens 1.20 1/3 0.40Average unit contribution $1.40

Long-run monthly profit:Contribution (45,000 units × $1.40) $63,000Less fixed costs ($21,000 + 7,760) (28,760 ) Profit $34,240

Long-run contribution ratio:Contribution margin $ 63,000Revenue [(30,000 × $2.50) + (15,000 × $3.00)] ÷120,000Contribution ratio 0.525

Long-run break-even point = $28,760/0.525 = $54,781

b. Answers to requirement (b) will vary. Two possible recommendations are as follows:

Do not introduce the sandwich. There is too much risk. Introducing the sandwich causes a short-run loss, a permanent decline in the contribution ratio, and an increase in the break-even point. If the predicted increase in sales does not occur, the company will be in serious difficulty. Also, it is unclear what the time period is for the short run.

Introduce the sandwich. While there is a short-run loss, a permanent decline in the contribution ratio, and an increase in the break-even point, these negatives are more than offset by the long-run increase in volume. Introducing the sandwich is taking the business to the next level of size and profitability.



P15-38 A

a. AccuMeterContribution Income Statement

For the Year 2012Sales $2,000,000Less variable costs:

Direct materials $500,000Processing 750,000Setup 200,000Batch movement 40,000Order filling 20,000 (1,510,000)


Manufacturing overhead 800,000Selling and administrative 300,000 (1,100,000)

Net income (loss) $ (610,000)

b. AccuMeterMulti-Level Contribution Income Statement

For the Year 2012Sales $2,000,000Less unit-level costs:

Direct materials $500,000Processing 750,000 (1,250,000)

Unit-level contribution 750,000Less lot-level costs:

Setup 200,000Batch movement 40,000Order filling 20,000 (260,000)

Lot-level contribution 490,000Less facility-level costs:

Manufacturing overhead 800,000Selling and administrative 300,000 (1,100,000)

Net income (loss) $ (610,000)



P15-38 A (concluded)

c. Sales (500 at $40) $20,000Less unit and lot-level costs:

Direct materials (500 at $10) $5,000Processing (500 at $15) 7,500Setup 2,000Batch movement 400Order filling 200 (15,100)Contribution per lot $ 4,900

d. Unit contribution margin:Selling price $60Less unit-level costs:

Direct materials $12Processing 15 (27)

Unit contribution $33

Lot-level costs:Setup $2,000Movement 400Order filling 200Total $2,600

Lot-level costs $2,600Desired contribution 700 $3,300Unit contribution $33 Required lot size 100 units



MANAGEMENT APPLICATIONS

MA15-39

It is important for senior management to set the ethical climate for the organization. In this case, perhaps out of a true concern for employees, or perhaps out of a desire for a “big bonus,” the plant manager is proposing an unethical (illegal?) speedup of the assembly line.

We do not know if New City Automotive has a code of ethics. If it does, Art Conroy should refer to it for guidance. Because Art is a management accountant, he should also refer to the Standards of Ethical Conduct for Management Accountants, published by the Institute of Management Accountants.

Art has followed these standards so far. Faced with an issue that concerned him, he went to the appropriate company official. At this point, he should follow the procedures for resolution of ethical conflict. In particular, he needs to further discuss the situation with Paula, expressing his concern about what may happen if the speedup is detected (strikes, legal action, mistrust, plant closure) and what he believes are the advantages of facing the situation directly.

He might recommend a general meeting with all employees and suggest that in this meeting financial information be shared. Employees should be made aware of the likelihood of closing the plant if financial performance is not improved. They should also be shown how a small increase in productivity will make a big difference in financial performance. They might even be invited to offer their own suggestions for increasing productivity. They should be treated as team members, rather than as adversaries. Finally Art might conclude his comments by noting how the careers of all plant employees, including management, will be adversely affected if the speedup is detected or if productivity is not improved. In this case, including employees in the decision is less risky than the alternative.



MA15-40

a. Using a unit-level analysis, develop a graph with two lines, (1) representing Homestead Telephone’s cost structure in the 1940s and (2) representing Homestead Telephone’s cost structure in the late 1990s. Be sure to label the axes and lines.

b. With sales revenue as the independent variable, the likely impact of the changed cost structure on Homestead Telephone’s:

Contribution margin percent: Because variable costs decrease, the contribution margin percent will INCREASE

Break-even point With an increase in fixed costs and a decrease in variable costs, the impact on the break-even point CANNOT BE DETERMINED. If there is a change, the BEP will likely increase because of downward pressure on prices.

c. The shift from human operators to mechanical devices increased Homestead’s operating leverage, which means that if sales increase, the percentage increase in before-tax profits will exceed the percentage increase in sales. Conversely, if sales decrease, the percentage decrease in profits will exceed the percentage decrease in sales.



MA15-41

a. To determine the break-even point, you must first find the contribution margin as a percent of sales and the fixed costs per period. Because there are no taxes at the break-even point, our analysis is based on before-tax information:

Variable costs as a percent of sales =

Change in total costs = $4,857,900 $4,430,000 = 0.823Change in Sales $5,520,000 $5,000,000

Fixed costs = $4,430,000 ($5,000,000 0.823) = $315,000

Break-even point = $315,000 / (1 – 0.823) = $1,779,661

b. Sales volume required to earn an after-tax profit of $480,000:

Required before-tax profit = $480,000/(1 – 0.40) = $800,000

Required sales = ($315,000 + $800,000)/(1 – 0.823) = $6,299,435

c. Regional Distribution, Inc.Contribution Income Statement

For the Year 2012

Sales $6,000,000Variable costs ($6,000,000 0.823) (4,938,000 ) Contribution margin 1,062,000Fixed costs (315,000 ) Before-tax profits 747,000Income taxes at 40 percent (298,800 ) After-tax profit $ 448,200



MA15-41 (concluded)

d. The method used for determining the cost equation for Regional Distribution with the available data was the high-low method, which used only two data points. There was not sufficient information to determine whether those two data points were representative of the larger population of data points. Also, it was not possible to determine the possible effects of inflation on the data from 2010 to 2011. Also, if Regional Distribution has multiple products and or departments that have varying cost structures, using aggregate data for the company as a whole to estimate its costs and break-even point may not produce accurate results. The cost-volume-profit model works best when there is a single cost driver and all costs are either variable or fixed with respect to that cost driver. For that reason, the model is generally more effective for analyzing smaller segments of a business, such as a particular product line.



module 15 solutions

Documents

total volume

profitvolume graph

unit variable costs

fixed costs

profit analysis

dollar sales volume

total revenues

profit graph