ch03 - breakeven solution

8/11/2019 Ch03 - Breakeven Solution

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nChapter 3

Cost-Volume-Profit Analysis

LEARNING OBJECTIVES

Chapter 3 addresses the following questions:

Q1 What is cost-volume-profit (CVP) analysis, and how is it used for decision making?Q2 How are CVP calculations performed for a single product?Q3 How are CVP calculations performed for multiple products?Q4 What is the breakeven point?Q5 What assumptions and limitations should managers consider when using CVP analysis?Q6 How are margin of safety and operating leverage used to assess operational risk?

These learning questions (Q1 through Q6) are cross-referenced in the textbook to individualexercises and problems.

COMPLEXITY SYMBOLS

The textbook uses a coding system to identify the complexity of individual requirements in theexercises and problems.

Questions Having a Single Correct Answer:

No Symbol This question requires students to recall or apply knowledge as shown in thetextbook.

e This question requires students to extend knowledge beyond the applicationsshown in the textbook.

Open-ended questions are coded according to the skills described in Steps for Better Thinking(Exhibit 1.10):

Step 1 skills (Identifying) Step 2 skills (Exploring) Step 3 skills (Prioritizing)

Step 4 skills (Envisioning)


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3-2 Cost Management

QUESTIONS

3.1 A mixed cost function includes both fixed and variable costs. If there are fixed costs inthe cost function, then total costs will increase at a smaller rate than the increase in totalsales volume. If there are variable costs in the cost function, then total costs will increase

with total sales volume. When there is a combination of fixed and variable costs, a 10%volume increase will increase total costs by less than 10% because only the increase invariable cost is proportionate to volume; the fixed cost does not change with volume.

3.2 Theweighted average contribution margin per unit is calculated only when performingCVP analysis for multiple products. There are two ways to calculate it:

(1) Calculate the total contribution of all products by subtracting total variable costs fromtotal revenues. Then calculate the weighted average contribution margin per unit bydividing the total contribution margin by the total number of units (the sum of unitsfor all products).

(2) Calculate the sales mix for each product by dividing the number of units sold for thatproduct by the total number of units sold for all products. Calculate the contributionmargin per unit for each product by subtracting that products variable cost from itsrevenues and dividing the result by that products number of units sold. Thencalculate the weighted average contribution margin per unit by summing thefollowing computation for all products: Each products sales mix percentage times itscontribution margin per unit.

3.3 The firm has only variable costs and no fixed costs. If there were fixed costs, incomewould increase by more than 20% when sales increase by 20%.

3.4 None. The firm does not pay income taxes at the breakeven point.

3.5 Assumptions: Fixed costs remain fixed, variable costs per unit or as a percentage ofrevenue remain constant, selling prices per unit remain constant, the sales mix remainsconstant, and operations are within a relevant range where all of these assumptions aremet. These are very strong assumptions. There is always some variation in fixed costsbecause they include costs such as electricity that varies with weather. In addition,organizations often get or give volume discounts, so variable costs and prices per unitmay change at high volumes. However, results using these assumptions are accurateenough for general planning and decision making purposes.

3.6 The margin of safety percentage and degree of operating leverage are related as follows.

LeverageOperatingofDegree

1PercentageSafetyofMargin

PercentageSafetyofMargin

1LeverageOperatingofDegree


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Chapter 3: Cost-Volume-Profit Analysis 3-3

As the degree of operating leverage gets larger (a higher proportion of fixed costs), themargin of safety percentage gets smaller, and vice versa.

3.7 The cost function is assumed to be linear over a relevant range. If there are volumediscounts, the cost function becomes piece-wise linear and the range of operations within

which the organization is performing must be taken into account in CVP analysis. Thelevel of operations must be matched with the appropriate part of the function. Each piececan be considered as a separate relevant range, and the estimated level of activity needs tobe matched with the appropriate relevant range. Otherwise, the analysis will eitherunderstate or overstate variable costs.

3.8 Sales mix is the specific proportion of total sales of each type of good or service that issold. A simple example was presented in the chapter for an ice cream store. Usuallyabout 15% of revenue was from beverages and the rest from ice cream products. As theproportion of specific products sold changes, the contribution margin ratio changesbecause the contribution per unit is different for the different products in the sales mix.

3.9 CVP refers to changes in income over the relevant range of activity; as such, it includesthe notion of breakeven. Breakeven is more narrowly constructed; it focuses on only oneoutcomethe single point at which total revenue equals total cost.

3.10 By definition, the margin of safety is the difference between expected unit sales andbreakeven unit sales. If expected unit sales are below breakeven unit sales, the margin ofsafety will be negative.

3.11 CVP analysis can be used for planning purposes such as budgets, product emphasis,setting prices, setting activity levels, setting work schedules, purchasing raw materials,setting levels for discretionary costs such as advertising and research and development. Itcan also help with monitoring operations, and analyzing the operating leverage of anorganization.

3.12 To make decisions about advertising costs, accountants predict the amount of cost to beincurred and predict the increase in sales. CVP analysis is then used to determinewhether the increase in cost is equal to or greater than the increase in contribution marginfrom additional units sold.

3.13 Good managers are likely to always ask for sensitivity analysis because uncertainty aboutsales volumes and other factors always exists. However, when unanticipated changes inthe business environment or consumer preferences arise, managers will be even moreinterested in sensitivity analysis. By analyzing a variety of scenarios, managers canrespond more quickly to unanticipated changes.


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3-4 Cost Management

EXERCISES

3.14 Target Profit, Not-For-Profit Breakeven

A. Information is given on a per unit basis, so use the following equation:

profit = (p-v)qF$1,000 = ($7 per gift basket$2 per gift basket)*Q - $5,000$6,000 = ($5 per gift basket)*Q

Q = $6,000/$5 per gift basket = 1,200 gift baskets

B. This problem is about a not-for-profit organization. Many not-for-profit organizationsprovide services or sell products at a loss and use donations or grants to cover the losses.As students approach problems in this textbook, they should think briefly about the typeof organization in the problem to help them solve it. This problem is a breakevenproblem with a unit cost of $7.64 and unit revenue of $4.64, or a unit contribution margin

(loss) of $(3.00). In a for-profit organization, these numbers would indicate that thecompany loses money on each unit it sells. In a not-for-profit, it may be appropriate tosell services at a loss, as long as another source of funds covers the loss. In this problem,the clinic receives a grant from the city, so there is fixed revenue in addition to the feescollected.

Taking the grant into account, the breakeven is:

0 = ($4.64 - $7.64)*Q + $460,000 grant - $236,000 fixed cost0 = $-3*Q +$224,000

Solving for Q:

3Q = $224,000

Q = 74,667 patients


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3.15 CVP Graph

A.

The revenue line is $7 times number of baskets and represents total revenue from unitssold. The cost line intersects the intercept at $5,000 reflecting the fixed cost. The slopeis 2, which represents the variable cost. The breakeven occurs at 1,000 gift baskets.Total revenues exceed total costs by $1,000 at 1,200 gift baskets.

B.

Total revenue is the sum of the grant plus patient fees. Unlike most CVP graphs, thebreakeven point is the maximumvolume before the clinic incurs a loss. The grant

CVP Graph 3.15(A)

$0

$3,000

$6,000

$9,000

$12,000

$15,000

0 500 1,000 1,500 2,000

Number of Gift Baskets

Dollars

Total Revenue

Total Cost

CVP Graph 3.15(B)

$0

$400,000

$800,000

$1,200,000

$1,600,000

0 37,500 75,000 112,500 150,000

Number of Patient Visits

Dollars

Total Revenue

Total Cost


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In the relevant range 200 < Q, the breakeven point is calculated as:

0 = $100*Q - $36,000

Q = 360 unitsThis result is in the relevant range, so it is the breakeven point.

3.17 The Martell Company

A. Profit (loss) before taxes is:

$5(1,000,000) - $4.50(1,000,000) -$ 600,000= $500,000 - $600,000

= $(100,000)

B. Solving for price at target profit of $25,000:

1,000,000*P - $4.50(1,000,000) - $600,000 = $25,0001,000,000*P = $5,125,000P = $5.125

The firm needs to have an average selling price of $5.125 to earn $25,000 on sales of1,000,000 units.

This problem can be used to raise the issue of predatory pricing versus aggressivecompetition.

3.18 RainBeau Salon

A.

Cost Fixed Variable

Hair dresser salaries $18,000

Manicurist salaries 16,000

Supplies 0 $0.500

Utilities 400

Rent 1,000

Miscellaneous 2,963 0.325

Total $38,363 $0.825

TC = $38,363 + $0.825*appointments

Explanations:

Salaries: The amount of salaries in May is used to predict the next month because therewas a cost-of-living increase.


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3-8 Cost Management

Supplies: An examination of the pattern in supplies costs reveals that for April and Maysupply cost was $0.50 per appointment. The cost was higher in March, but it is best touse the most current information. Students may have averaged the three months for$0.52 per month, or they could have used the high-low method which gives $0.50 with nofixed costs.

Utilities: Because weather probably drives most of utilities cost for this business, thissolution uses the prior months utilities to predict next monthscost.

Miscellaneous: An examination of miscellaneous costs reveals that while it increases asvolumes increase, it does not do so proportionately (as did supplies). For this solution thehigh-low method is used. Variable cost = $0.325 [($3,580 - $3,450)/(1,9001,500)].Using TC = F +VC*Q and solving for F gives a fixed cost of $2,963 [$3,450 = F +($0.325*1,500)].

B. 0 = ($25.00 - $0.825)Q - $38,363

0 = $24.175*Q - $38,363Q = 1,587 appointments

3.19 Madden Company

A. Divide sales and variable costs by 160,000 to get the per-unit selling price of $50 and thevariable cost per unit of $12.50.

Then breakeven formula is

$50*Q - $12.50*Q - $3,000,000 = $0$37.5*Q = $3,000,000

Q = 80,000 units

B. Variable costs are $12.50 per unit/$50.00 per unit = 25% of revenue

Breakeven in sales, where TR = total revenue:

TR - 0.25*TR - $3,000,000 = $4,500,0000.75*TR= $7,500,000

TR = $10,000,000

C. Target after-tax profit

0.10*$36,000,000 = $3,600,000

After-tax income = (1-0.40)*before tax income


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Combining these calculations:

$3,600,000 = 0.60*before tax incomeBefore-tax income = $6,000,000

CVP calculation:

TR- 0.25*TR - $3,000,000 = $6,000,0000.75*TR = $9,000,000

TR = $12,000,000

3.20 Laraby Company

A. Selling price per unit

= $625,000/25,000 units= $25/unit

Variable cost per unit

= $375,000/25,000 units= $15/unit

Breakeven point

$25*Q$15*Q - $150,000 = $0

Q = 15,000 units

B. Adjust the after-tax income target to a before-tax income target.

Income before tax*(1 - .45) = $77,000Income before tax*0.55 = $77,000Income before tax = $140,000

Then solve for units at target profit:

$25Q- 15Q - 150,000 = $140,000

Q = 29,000 units

C. Current variable cost $15.00 Current fixed cost $150,000Less old component (2.50) Plus depreciation onPlus new component 4.50 new machine $18,000/6 3,000New variable cost $17.00 New fixed cost $153,000

Solve for breakeven where

$25*Q$17*Q - $153,000 = $0

Q = 19,125 units


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3-10 Cost Management

D. Solve for target profit where:

$25*Q$17*Q - $153,000 = $100,000 (before tax)

Q = 31,625 units

E. Current contribution margin ratio = ($25$15)/$25 = 40%

New price:

P - $17 = 0.40*P

Rearrange terms:

0.60*P = $17P = $28.33

3.21 Dalton Brothers

A. First determine the pretax income necessary to obtain the $150,000 target net income.The company is subject to two income tax rates. The first $40,000 of taxable income istaxed at 15%, and income over that amount is taxed at 40%. Thus, after-tax income iscalculated after subtracting two tax amounts. Assume = Target pretax income.

- [0.15 x $40,000 + 0.40*( - $40,000)] = $150,000 - (6,000 + 0.4 - 16,000) = $150,0000.6 + 10,000 = $150,000

= $233,333.33

Now total revenue (TR) can be calculated:

TR - 0.60*TR - $250,000 = $233,333.330.40*TR = $483,333.33TR = $1,208,333.33


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B.

3.22 All-Day Candy Company

A. $4*Q - $2.40*Q - $440,000 = $0

Q = 275,000 boxes to break even

B. Current contribution margin ratio = ($4.00-$2.40)/$4.00 = 40%

Estimated variable costs next period (only the candy costs increase)

$2.00 x 1.15 + $0.40 = $2.70

Selling price needed to maintain 40% contribution margin ratio:

P - $2.70 = 0.40*P0.60*P = $2.70

P = $4.50

CVP Graph 3.21(B)

$0

$290,000

$580,000

$870,000

$1,160,000

$1,450,000

$1,740,000

$2,030,000

$0 $435,000 $870,000 $1,305,000 $1,740,000

Revenues

Dollars

Total Revenue

Total Cost


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C. Current pretax income = $4.00*390,000 units - $2.40*390,000 units - $440,000= $184,000

Required sales in units to maintain $184,000 in pretax income:

$4Q - 2.70Q - 440,000 = $184,000$1.30xQ= $624,000Q= 480,000 boxes

Dollar sales= 480,000 boxes @ $4 = $1,920,000

3.23 Junior Achievement Group

A. Breakeven for option 1:

$5,600/($20$6) = 400 sets

Breakeven for option 2:

New variable cost = 0.10*$20 = $2

$5,600/($20 - $6 - $2) = 317 sets

Breakeven for option 3:

There are no fixed costs, so the breakeven point = 0 sets; if no units are sold, no

fee is paid.

B. The cost function for option 1 has the highest proportion of fixed cost, so it has thehighest operating leverage.

C. Lowest operating risk is option 3 because no fees are paid unless there are sales.

D. To find the indifference point, the two cost equations are set equal to each other asfollows:

$5,600 = $3,800 + 10%TR

$1,800 = 10%TRTR = $18,000

When total revenues are below $18,000, option 2 is more profitable. Above

$18,000, option 1 is more profitable.


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E. Option 1 profit = ($20-$6)*1,000 - $5,600 = $8,400

Option 2 profit = ($20-$6-$2)*1,000 - $3,800 = $8,200

Option 3 profit = ($20-$20*0.15)*1,000= $11,000

The highest profit at sales of 1,000 sets is $11,000 for option 3, so this is probably the

best choice. (This answer ignores possible other factors that might influence the

decision.)

3.24 Borg Controls

A. Expected pretax income:

1,700,000 - 0.60*1,700,000 - 321,000 = 359,000

Converted to dollars:

359,000/1.2 per $= $299,167

ROI = $299,167/$2,680,000 = 11%

B. Target pretax income in dollars:

0.15*$2,680,000 = $402,000

Converted to Euros

$402,000 x 1.2 per $ = 482,400

Required revenue

TR - 0.60*TR - 321,000= 482,4000.40*TR = 803,400TR = 2,008,500


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3.25 NewberrysNutrition

A. Categorize costs

Cost Fixed Variable

Direct materials $300,000

Direct labor 200,000Fixed factory overhead $100,000

Variable factory overhead 150,000

Marketing and Administration 110,000 50,000

Totals $210,000 $700,000

Variable cost per unit = $700,000/100,000 units = $7.00 per unit

Price per unit = $1,000,000/100,000 units = $10.00 per unit

Target pretax income = $120,000/(1-.40) = $200,000

CVP calculation:

($10.00 - $7.00)Q - $210,000 = $200,000$410,000 = $3.00*QQ = 136,667 units.

B. Before calculating the margin of safety, it is necessary to calculate the breakeven point:

($10.00 - $7.00)Q - $210,000 = $0Q = $210,000/$3 = 70,000 units

In revenue: 70,000 units * $10 per unit = $700,000

Margin of safety in units

100,000 units70,000 units = 30,000 units

Margin of safety in revenues

30,000 units * $10 = $300,000

Double-check computation:$1,000,000 - $700,000 = $300,000

C. Degree of operating leverage = 1/Margin of safety percentage= 1/(30,000 units/100,000 units) = 3.33

Double-check calculation:Degree of operating leverage = (Fixed costs/Expected pretax income) + 1= ($210,000/$90,000) + 1 = 3.33


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D. Degree of operating leverage = contribution margin/pretax income= ($9,600 - $3,200)/$800 = 8.0

An alternative calculation for degree of operating leverage is:

1/margin of safety percentage= 1/0.125 = 8.0

3.27 Vines and Daughter

A. Estimated sales in number of swimsuits = $2,000,000/$40 = 50,000 swimsuits

Variable cost per unit = $1,100,000/50,000 swimsuits = $22 per swimsuit

Contribution margin = $40-$22 = $18 per swimsuit

Breakeven in units:

$765,000/$18 = 42,500 swimsuits

B. Margin of safety is 50,00042,500 = 7,500 swimsuits

C. If the margin of safety was 5,000 swimsuits in 2004 and increases to 7,500 swimsuits in2005 (calculated in Part B), then operations will be less risky in 2005. A larger margin ofsafety means that the company is operating further beyond the breakeven point; swimsuit

sales can drop by a larger amount before the company incurs a loss.

D. Contribution margin ratio = $18/$40 = 0.45

Breakeven in revenues:

$765,000/0.45 = $1,700,000

E. Margin of safety in revenue = $2,000,000 - $1,700,000 = $300,000

F. An increase in revenues of $200,000 is expected to increase pretax profits by $90,000 in

profits ($200,000 x 0.45 contribution margin ratio) because fixed costs have been coveredat this point. Total pretax is estimated to be:

$135,000 + $90,000 = $225,000

G. Pretax profit = $180,000/(1-.30) = $257,143

CVP calculation:

($765,000+$257,143)/$18 = 56,786 swimsuits


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PROBLEMS

3.28 Oysters Away

[Note about problem complexity: Item A is coded as Extend instead of Step 2 because judgment

is minimal and students can use chapter examples for help.]

A.

Cost Fixed Variable

Wages $100,000

Packing materials 20,000

Rent and Insurance $25,000

Admin and selling 45,000

Total costs $70,000 $120,000

Wages are classified as variable because employees are paid an hourly wage and can be

laid off when there is no work. Packing materials would vary with the number of casesof oysters packed. Rent and insurance are fixed. No information is given about whetheradministrative and selling is fixed or variable. It is categorized above as fixed, but itcould be a mixed cost. In the absence of additional information, this solution assumes thecost is fixed.

Variable cost per case: $120,000/2,000 cases = $60

Cost function: TC = $70,000 + $60*Q

B. Breakeven calculation:

$0 = ($100 - $60)*Q$70,000Q = $70,000/$40 per caseQ = 1,750 cases

C. Pretax profit = ($100-$60)*3,000 cases - $70,000= $120,000 - $70,000 = $50,000

After-tax profit = $50,000 * (1-0.20) = $40,000

D. If only 2,000 cases have been harvested and sold each of the past several years, it is

unlikely that 3,000 cases will be sold next year unless there is some change in operations.In the absence of information about a change, the quality of the income estimate in Part Cis probably low. In addition, any change in operations major enough to increase sales by50% might change the cost function (see Part E). So, even if the manager anticipatesexpanding the size of operations, the quality of the income estimate is low.

E. It is possible that the costs for workers or packing materials would change above 2,000cases. If the company does not have enough space to handle all of the oysters, rent wouldneed to increase. The company might have to pay workers overtime or hire additional


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workers at a higher or lower rate than current workers (depending on skill levels andsupply of workers). With the additional volume, the company might get a discount onpacking materials, so that cost might be smaller. Administrative costs might or might notincrease with the volume of operations. A 50% increase in volume is very significant,which might require additional administrative costs such as staff, supplies, or fixed

assets.

3.29 Francesca

A.

Quantitative information

Cart lease $800 per month: This is relevant because this is a cost that will beincurred if Francesca leases the cart, but will not be incurred otherwise.

City license $20 per month: This is relevant for the same reason as the cartlease.

Lessor records showing average gross revenues of $32 per hour: Thisinformation is relevant if Francesca thinks she will sell about the sameamount as the lessor. However, the lessors records might not bereliable.

Ingredients 40% of revenue: This is relevant because this cost will be incurredonly if Francesca sells coffee.

Last years income tax rate of 25%: Assuming that the income tax rate is notdifferent for operating the coffee cart, the tax rate is irrelevant toFrancescas decision. The income tax rate will reduce earnings for bothoptions.

Condo rent of $1,000 per month and 20% of condo cost for garage: This cost is

not relevant because it will be the same under both options; it isunavoidable.

Current income $2,400 per month: This is relevant as the opportunity cost ifFrancesca decides to operate the coffee cart instead of continuing hercurrent work.

B. This question calls for calculating the hours Francesca should work to earn a target profitequal to her current earnings of $2,400 per month. Before this computation can beperformed, the cost function for the coffee cart must be determined:

Fixed Variable

Cart lease $800City license 20

Ingredients 0.40*Revenue

Total $820 0.40*Revenue

The monthly cost function is estimated as: TC = $820 + 0.40* Revenue


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Target profit calculation (assuming that revenue is $32 per hour):

$2,400 = ($32 - 0.40*$32)*Hours per month - $820$3,220 = $19.2*Hours per monthHours per month = 168

Assuming that she is willing to work 30 days per month, total hours per month are 168.Then, the average hours that must be worked per day to earn a target profit of $2,400 is:

168 hours per month/30 days per month = 5.6 hours per day

C. This problem requires students to perform the same calculation as when determining theselling price needed to achieve a target profit.

Total hours per month = 25 days x 4 hours per day = 100 hours per month

Target profit calculation:

$2,400 = (Revenue per hour - 0.40*Revenue per hour)*100 hours - $820$3,220 = 60*Revenue per hourRevenue per hour = $53.67

D. As mentioned in Part A above, Francesca cannot be certain that the information shereceived from the lessor is reliable. In addition, revenues are likely to fluctuate based onweather, the economy, competition, and consumer preferences.

E. There are many other types of information to consider. Some information might helpFrancesca evaluate the financial viability of the coffee cart, such as local populationtrends, competition, and economic outlook. Additional information relates to Francescasown preferences, such as whether she wants to give up her other occupations and howmuch she would enjoy running a coffee cart in Vail.

3.30 Keener Boomerangs

A. Last month 1,200 regular and 2,400 premium boomerangs were sold. Assuming the salesmix remains constant, two premium boomerangs are sold for each regular boomerang.

B. Total fixed product line costs:Regular: 1,200 units x $8.17 = $9,804Premium: 2,400 units x $24.92 = $59,808

C. Total corporate fixed costs: $5.62 x (1,200 + 2,400) units = $20,232


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D. To calculate the overall breakeven, it is easiest to first calculate the weighted averagecontribution margin ratio using an income statement approach:

Regular Premium TotalUnits 1,200 2,400 3,600Revenue $26,580 $108,720 $135,300

Variable cost 5,172 16,584 21,756Contribution margin $21,408 $ 92,136 $113,544

Weighted average contribution margin ratio ($113,544/$135,300) 83.92%

Overall corporate breakeven (recall that there are three fixed costs):

Revenues = ($9,804 + $59,808 + $20,232)/83.92% = $107,059

Breakeven for Regular based on sales mix in revenues:$107,059*($26,580/$135,300) $ 21,032

Breakeven for Premium based on sales mix in revenues:$107,059*($108,720/$135,300) 86,027

Total corporate sales at breakeven $107,059

E. Breakeven for regular boomerangs ignoring corporate fixed costs:

Revenues = $9,804/[($22.15-$4.31)/$22.15]= $9,804/0.8054= $12,173

F. When regular boomerangs is required to cover only its own fixed costs, the companydoes not need to sell as many units to breakeven. The breakeven revenue for boomerangsis higher when it covers both its own and corporate fixed costs ($21,032) than when itonly covers its own fixed costs ($12,173).

G. Corporate fixed costs are not usually under the control of the individual productmanagers. Therefore, corporate fixed costs generally are not considered when evaluatingindividual product profitability. However, the company as a whole needs to cover all ofits fixed costs, so it is important to take corporate fixed costs into account when planningoverall operations.

H. The actual sales mix can differ from plans for many reasons. For example, customerpreferences can change, altering the number and prices of units. Competitors prices andproducts could affect the sales mix. Consumer buying patterns change when theeconomy changes. Sometimes an unforeseen event will greatly alter consumer behavior.These changes cannot easily be predicted.

I. When the sales mix is more uncertain, the quality of information from CVP analysis islower because the CVP assumptions are more likely to be violated. Therefore, thelikelihood that the sales mix will remain constant must be evaluated. Sensitivity analysis


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should also be performed to examine a larger range of operations that incorporatepossible changes in sales mix. The quality of the CVP analysis is negatively affected byhigher uncertainty about any of the variables used.

3.31 Not-For-Profit After-School Art Program

A.1. Here are several possible costs; students may think of others.

Cost Category

Staff people Fixed (fixed schedule according to # of children)

Art supplies Mixed, some that will be used up, and some (easels) thatwill be fixed

High school help Fixed (fixed schedule according to # of children)

Snack food Variable

2. Snack food is the only completely variable cost and number of snacks served wouldbe a good cost driver. Art supplies have a variable component, and number ofchildren or number of hours of art would be reasonable cost drivers.

B. The cost structure likely has a larger proportion of fixed costs because salaries for staffand supervisors would be much higher per hour than the cost of supplies and snacks.

C. The marginal cost is the variable cost (supplies and snacks) per child for three children.

D. The opportunity cost is the revenue foregone from a fee-paying child.

E. CVP analysis offers the neighbor an opportunity to vary assumptions, such as price andvolume of children served while he is considering various options such as scholarships.A spreadsheet can be set up with an input area for all of the assumptions such as fixedcosts, variable costs, number of children, fees per child, number of fee-paying children,number of scholarships, and so on. Then the CVP calculations would be performed in aseparate part of the spreadsheet, with cell references to the input cells. The neighborcould then modify data in the input cells to analyze the expected financial results underdifferent sets of assumptions.


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3.32 Ersatz

A spreadsheet showing the CVP graph solutions for this problem is available on the Instructorsweb site for the textbook (available at www.wiley.com/college/eldenburg).

A. The variable cost per unit is the same for 1,000 units and for 1,500 units. Therefore, it isreasonable to assume that these variable costs will also apply to a volume of 1,300 units.Variable costs per unit are:

$40 + $10 + $6 = $56 per unit

Fixed costs are:

$10,000 + $11,000 + $20,000 = $41,000

Breakeven is:

$100*Q$56*Q - $41,000 = $0

Q = 932 units to break even

B.

C. At 1,300 units, pretax income is estimated as:

= ($100 - $56) per unit*1,300 units - $41,000 = $16,200

D. Following is a possible solution to this question. Notice that the message is as short aspossible, yet fully answers the shareholders question. The message also avoids use of

$0

$50,000

$100,000

$150,000

$200,000$250,000

0 500 1,000 1,500 2,000

Dollars

Number of Units

CVP Graph 3.32(B) Total Revenue

Total Cost


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highly technical language, but it assumes that the shareholder is familiar with the termsused in the income statement.

Dear Major Shareholder,

You asked why our profits increased by 800% when sales increased by only 50%.When we sell 1,000 units, we are very close to the breakeven pointthe point at whichour revenues exactly cover our costs. As volume increases above this level, our profitincreases by $44 per unit (our selling price of $100 minus variable costs of $56).Hence, when sales increase by 500 units, pretax income goes up by $22,000. This willbe true for any 500 unit change in sales. At 1,000 units our pretax income was only$3,000, so the percentage change when we move from 1,000 units to 1,500 units isvery high.

Please let me know if I can answer any additional questions.

Sincerely,Accountant

E. New breakeven

$100*(1.03)*Q - $56*(1.03)*Q - $41,000 = $0$103*Q - $57.68*Q = $41,000

Q= 905 units

The old contribution margin was $44, and the new contribution margin is $45.32, so thecontribution margin per unit has been increased by 3%, causing breakeven unit sales to

decrease.

F. The two approaches will yield the same cost (and, therefore, the same income) when

$11,000 + $10*Q = $20*Q

Q = 1,100 units


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G.

H. If sales exceed 1,100 units, paying $10,000 per period + $10 per unit (the old payarrangement) will result in lower total selling costs.

I. Sales representatives with high selling volumes would probably like the new systembecause they would be likely to earn more. The opposite would be true for salesrepresentatives with low selling volumes. Sales representatives who dislike risk mightprefer the existing pay system, which guarantees a minimum payment. People oftendislike any change, so there may be resistance regardless of whether sales representativesare better off. Overall, the new pay system might encourage sales representatives toachieve higher sales. It also might lead to higher employee turnover.

J. Pros of changing the system:

Reduces operating risk by reducing fixed costs Reduces costs if sales are less than 1,100 units May encourage sales representatives to sell more

Cons of changing the system:

Increases costs if sales are greater than 1,100 units

Could have adverse effects on sales representative morale

3.33 King Salmon Sales

A. This question calls for a breakeven calculation, which means that the cost function mustfirst be determined. Costs are categorized as shown in the following table. Labor costsare assumed to be variable because employees work only as needed. Administration cost

$0

$50,000

$100,000

$150,000

$200,000

$250,000

0 500 1,000 1,500 2,000

Dollars

Number of Units

CVP Graph 3.32(G)Total Revenue

Old Costs

New Costs


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is assumed to be fixed because there is no information to suggest that this cost variesproportionately with volume of activity.

Fixed Variable

Fish $200,000

Smoking materials 20,000Packaging materials 30,000

Labor 300,000

Administration $150,000

Sales commission 10,000

Total $150,000 $560,000

If all variable costs vary with pounds of salmon, then variable cost is estimated as:

$560,000/100,000 lbs. = $5.60 per lb.

The cost function is: TC = $150,000 + $5.60 per lb.

If the selling price is the same as last year, it can estimatedbased on last years totalrevenue and total volume:

Price = $800,000/100,000 lbs. = $8.00 per lb.

In this problem, it is best to calculate the breakeven in units because there is a limit on thenumber of pounds of salmon available:

0 = ($8.00$5.60)*Q - $150,000

$150,000 = $2.40*QQ = 62,500 lbs

The company cannot cover its fixed costs, because it cannot acquire enough salmon tobreak even. Therefore, the company should not operate this year. Note: According tothe information in this question, the company will avoid administrative costs if there is nosalmon production. Therefore, there will be zero profit or loss and the company will bebetter off if there is no production.

B. The term breakeven has a slightly different meaning in this question than usual. In thisquestion, breakeven meansbeing at least as well off as the alternative. The loss at the

maximum possible production volume of 50,000 lbs. = ($8.00$5.60)*50,000 lbs.$150,000 =$30,000. If the company incurs administrative costs whether or not itproduces salmon, then the loss with no production would be$150,000. Therefore, thecompany would be better off producing salmon and incurring a smaller loss.

C. Breakeven price:

0 = (P-$5.60)*50,000 lbs. - $150,000

P = $8.60


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D. The managers assume that their cost function is linear (fixed costs remain fixed andvariable costs remain constant) and that they are operating in the relevant range. Theyare also assuming that they can purchase at least 50,000 lbs of salmon and that they cansell the salmon for at least $8.60 per lb.

E. Although the exact values may differ from the assumptions, greater reliance can beplaced on the assumptions about cost than on the other assumptions. For example, fixedcosts of administration will not be exactly $150,000 because they include costs such aselectricity that vary with weather and electricity rates. However, administrative costs arenot likely to vary widely from year to year unless the managers increase or decreasespending on discretionary items, over which they have control. Labor and supplies costsare also likely to remain relatively constant. However, there are a number ofuncertainties about the specific assumptions regarding the cost of salmon, selling prices,and volume. For example, the cost to purchase salmon could increase because of theshortage, but then King Salmons selling price might also increase. If selling prices

increase, demand could drop. King Salmons managers cannot predict perfectly thevolume of salmon that will be available; in some years fish counts are lower than in otheryears, so the volumes could be lower than 50,000 lbs. However, if the company hasoperated for many years, the managers can use prior data to analyze the reasonableness oftheir assumptions.

F. This memo could be composed in a variety of ways. The main points that should becovered include:

A brief explanation of the risk associated with fixed costs compared to variablecosts and how that risk relates to fluctuations in business volume for King

Salmon.

A explanation of how the risk of loss could be reduced by decreasing the amountof fixed costs, and thus reducing the breakeven point.

A statement that many of King Salmons costs are variable, but thatadministrative cost is probably primarily fixed.

An explanation of the size of fixed costs at King Salmon: Last year theproportion of fixed cost was $150,000/$710,000 = 21%.

Suggestions of one or more ways that King Salmon could convert some of itsadministrative costs from fixed to variablee.g., hiring temporary office help.

An offer to work with owner to identify ways to reduce the risk of loss.


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3.34 Joe Davies

A.1.

Relevant Fixed Variable

First clock No; Sunk costEquipment No; Sunk cost

Materials Yes $30 each

Rent space Yes $2,500

Utilities Yes 300

Joes salary Yes 3,000

Sales staff Yes 2,000 7 each

Total $7,800 $37 each

2. Contribution margin = $225 - $37 = $188 per clock

Contribution margin ratio = $188/$225 = 0.8356

3. TC = $7,800 + $37*Q

Breakeven in number of clocks:

$7,800/$188 per clock = 42 clocks

Breakeven in revenues:

$7,800/0.8356 = $9,335

OR: 42 clocks * $225 per clock = $9,450 (difference due to rounding)

4. Number of clocks to achieve target profit:

($7,800 + $4,000)/$188 per clock = 63 clocks

B.1. Joe cannot be certain that the price of wood will remain the same for the next

year. If gasoline costs increase, wood transportation costs could increase. Ifdemand greatly increases or decreases, the purchase cost will change in

response. If there is a natural disaster, such as a fire or flood, supply may belimited and prices could increase. Rent prices increase periodically, and so hisrent could change in the next year. Utility bills could increase or decrease,according to weather, potential shortages, or increased demand due to badweather in other parts of the country. He could have to pay sales people moreor less than he plans, depending on the local economy and the demand forclocks. If there is only small demand for the clocks initially, he may have toincrease salary until demand builds. There are many other answers for thisquestion, too.


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2. It is likely that Joe may need to advertise. He also may need a receptionist inthe office during business hours. He has not included regulatory costs such asbusiness licenses, employment and property taxes, and any local fees forservices. Joe has not considered insurance or employee benefit costs.

Students may have identified other costs as well.

3. Joe cannot be certain that his estimated sales volume is correct because hedoes not know what the local and regional competition might be, and he doesnot know whether most of his sales will happen during holiday seasons.Unanticipated fluctuations are also likely to occur for discretionary productssuch as clocks. Furthermore, he does not have experience selling the clocksfull time, so he might be overestimating demand for the clocks.

C. Because Joe likes to make the clocks, he is biased toward starting this business.Therefore, he is likely to overestimate revenues and underestimate costs. Part B.2

above already identified a number of costs that he has overlooked.

D. Uncertainties and potential biases reduce the quality of the information used as inputs forthe CVP analysis, thus reducing the quality of the CVP information. As a result, anobjective person would be skeptical of the CVP results and would potentially seek higherquality information. For example, market research might be used to increase the qualityof revenue estimates.

E. There is no one answer to this part. Sample solutions and a discussion of typical studentresponses will be included in assessment guidance on the Instructors web site for thetextbook (available at www.wiley.com/college/eldenburg).

3.35 Jasmine Krishnan

A. Usually, sensitivity analysis is performed to determine how sensitive profits are tochanges in assumptions such as estimated prices, costs and volumes of sales. Sensitivityanalysis helps decision makers understand the range of operations that could be expected,both under normal conditions and under best and worst case scenarios.

B. Jasmine is excited about her idea. She probably also believes that setting up these tripswould be quite a lot of fun. Therefore, she may be over-optimistic in her beliefs about

future operations. When people find an alternative in which they are highly interested,they become biased toward that alternative and choose assumptions that are likely to leadto a positive decision about that alternative. In addition, they may interpret results morepositively than if they were not biased. Jasmine would need to underestimate insuranceor other costs or overestimate sales for this business venture to be attractive to investors.If she does this, she is biasing the information.

C. If the brochure contains biased information, the quality of information is low. Potentialinvestors who rely on the brochure would be given misleading information. Thus, the


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quality of potential investor decisions would be low unless they seek and obtain moreobjective sources of information.

D. The ethical problem is that the biased information misleads potential investors to believethat the new venture has a higher probability of success than it actually has. Some

investors may rely on Jasmine to return their investments in the future, but she may notsucceed and may not be able to return the investment or any return on it. Most investorshave a range of choices and consider both the investment return and risk as they comparetheir choices. By biasing the information, Jasmine would also bias the decision makingprocess for her potential investors; they may invest in a project that is more risky thantheir other investments without realizing the potential consequences of this decision.This is unfair to them and unethical.

E. Jasmine needs to present the most objective set of assumptions possible in hercalculations so that her investors can make the best decisions for their own welfare.Sensitivity analysis showing realistic best and worst case scenarios will help investors

identify more accurately the risk they are undertaking by investing in this venture. Thequality of their decision making will be greatly improved.

3.36 Small Business Owners

A. Many small business owners have no business experience or education. They do notknow any of the techniques needed for high quality decisions.

B. Because risk of loss for small businesses is the risk of loss of their personal cash flows,owners need to fully understand the consequences of their choices on profits. In addition,

a large proportion of new businesses fail. Therefore, CVP analysis is highly useful. CVPanalysis can help owners more thoroughly consider the quality of information they use toestimate future results and recognize the risks of their decisions. They are also able toperform sensitivity analysis to reduce elements of surprise from changes in future plansand results. They can respond more quickly to changes in their operating environment,increasing their chances of success.

C. Student answers to this question will vary depending on the web sites they locate andexplore.

D. Student memos will vary, but they should include the following in simple, clear

language:

Developing CVP analysis forces decision makers to estimate future revenues,costs, and volumes, which is good for small businesses because of the uncertaintyin their operating environments.

Using sensitivity analysis increases the ability of owners to identify risk andrespond to changes in their operating environment.


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CVP analysis also acts as a budget or plan for future operations. Small businessowners may not believe they need a plan, but most businesses do need to plan.

Provide an overview of the process of using CVP analysis, includingidentification of the estimates that must be developed, the formulas used, and the

types of sensitivity analysis that could be performed.

Recommendations for setting up a spreadsheet to perform CVP analysis.

3.37 Wildcat Lair

[Note: This problem contains the same data is problem 2.28 in Chapter 2, which requiresstudents to determine a cost function. The cost function computations shown in Part A below areidentical to the solution for problem 2.28.]

A. Before calculating the breakeven points and degree of operating leverage, it is firstnecessary to create the cost function. The Lairs costs are categorized as follows:

Fixed VariablePurchases of prepared food $ $21,000Serving personnel 30,000Cashier 5,500Administration 10,000University surcharge 7,000Utilities 1,500 _______

Totals $47,000 $28,000

Total revenue is the most likely cost driver for both variable costs. Food costs arelikely to vary proportionately with sales, and the University surcharge isspecifically based on sales.

Because revenue is the cost driver for both variable costs, total revenue (TR)instead of quantity (Q) can be used in the cost function:

Variable cost = $28,000/$70,000 = 0.40, or 40% or revenue

Combining fixed and variable costs, the cost function is:

TC = $47,000 + 40%*Total revenue

Given the cost function, the universitys breakeven point is:

$47,000/($42,000/$70,000) = $47,000/0.6 = $78,333


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Wildcat Lairs breakeven point is:

$47,000/(49,000/$70,000) = $47,000/0.7 = $67,143

B. For July, the degree of operating leverage (without the University surcharge) is:

1Profit

F = [$47,000/($-5,000 + $7,000)] + 1 = 24.5

C. The university surcharge is irrelevant. If the university closes the restaurant it will lose$2,000, which is the current contribution margin ($5,000 + $7,000).

D. The fixed costs consist mostly of serving personnel and cashiers. Personnel could workon a more variable basis, with more employees scheduled for busier times. Employeescould be called in or sent home when volumes fluctuate. During slow periods, servingpersonnel could also serve as cashiers.

E. Reducing the reliance on fixed costs reduces the risk of losses during periods whenvolume is low. When volumes decrease, for example between semesters and through thesummer, the fixed costs would be lower and easier to cover.

F. There is no one answer to this part. Sample solutions and a discussion of typical studentresponses will be included in assessment guidance on the Instructors web site for thetextbook (available at www.wiley.com/college/eldenburg). Following is a brief summaryof some pros and cons:

If the club is closed, the university foregoes $2,000 current contribution. In addition,

students may leave campus for food that is now prepared on campus, and it is likely thatthere are economies of scale at food services, so food for other outlets could increase incost. On the other hand, the facility currently being used by the Lair could potentially beused for some other purpose. If the Lair is not widely used, then it might not provide animportant service to the university community.

G. There is no one answer to this part. Sample solutions and a discussion of typical studentresponses will be included in assessment guidance on the Instructors web site for thetextbook (available at www.wiley.com/college/eldenburg).

3.38 The Elder Clinic

A.The cost function is:

TC = $19,736 + $6.07*patient-visits.

For more details about developing the cost function, see problem 2.36 in Chapter 2.


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Breakeven, solving for price:

$0 = (P - $6.29) * 940 patient-visits - $19,285940*P = $25,197.6P = $26.81 per patient-visit

The average patient fee during March-July was:

$16,545/3,290 patient-visits = $5.03 per patient-visit

The actual fees charged are far below the levels needed to break even.

B. Many patients may not be able to afford this fee. Since many of elderly patients are onfixed incomes, they may have to make trade-offs between other living expenses and theirmedical expenses. They may also forego needed medical services.

C. If the fee is raised, volumes are likely to go down. That means that fees may need to beraised again, causing further declines in volume. This is called the Death Spiral (thistopic is explicitly addressed in Chapter 13).

D. If possible, the clinic could try to substitute cheaper labor for expensive labor. If aphysicians assistant or specially trained nurse can see some portion of patients instead ofa physician, this would reduce some of the fixed cost. Analysis of other costs that can bereduced is needed. There may be grants that would offset some fixed costs, or it ispossible that donors can be found to offset some costs. An annual fund raising eventmight be held.

3.39 Elinas Stained Glass

A spreadsheet showing the solution for this problem is available on the Instructors web siteforthe textbook (available at www.wiley.com/college/eldenburg).

A. Below is one solution for the cost function. This solution involves a number ofjudgments about cost classification and choice of estimation methods. Other reasonablesolutions are possible, particularly for raw materials and supplies and miscellaneous.

Labor and rent costs are most likely fixed. Rent is usually a fixed cost, and labor appears

to be fixed for this company because the employees work regular schedules. Both ofthese costs are estimatedbased on the most recent months information. This procedurewill incorporate the apparent rent increase that took place in September and the mostrecent employee schedules and pay rates. Therefore, the rent cost is estimated at 2,200,and the labor cost is estimated at 4,282.

Raw materials and supplies for a manufacturing organization are most likely to bevariable. No information is provided about alternative cost drivers, so this solutionestimates raw materials and supplies as a percentage of revenue. This treatment isreasonable because these types of costs and revenues both tend to vary with the size of


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window. If raw material and supply costs change over time, then it is best to use the mostrecent information available. Therefore, this variable cost is estimated using the mostrecent months data:

4,029/16,116 = 25% of revenue

No information is provided about the nature of the miscellaneous cost. Miscellaneousmight include direct costs such as packing materials for the windows and indirect costsfor supplies used in the office. Also, this cost appears to have increased along with theincreases in revenues over the four months presented. The scatter plot shown below isused to further analyze the relationship.

The scatter plot seems to confirm a positive relationship between miscellaneous costs andrevenues. Therefore, regression analysis will be used to estimate the cost function formiscellaneous costs, with revenues as the independent variable. Portions of theregression output are shown below.

Regression Statistics

Multiple R 0.93615673R Square 0.876389423

Adjusted R Square 0.814584134

Standard Error 50.45858562

Observations 4

CoefficientsStandard

Error t Stat P-value

Intercept 334.0982722 98.20792106 3.401948 0.076609

X Variable 1 0.030302406 0.008047137 3.765614 0.063843

Scatter Plot 3.39(A)

$0

$100

$200

$300

$400

$500

$600

$700$800

$900

$0 $5,000 $10,000 $15,000 $20,000

Revenues

MiscellaneousCosts


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Based on the regression results, the miscellaneous cost function is estimated as:

TC = 334 + 3% of revenues

Given the following summary of individual cost functions, the total cost function forElina's is TC = 6,816 + 28% of total revenue.

Cost Category Fixed Variable

Raw materials and supplies 0 25% of total revenue

Labor 4,282

Rent 2,200

Miscellaneous 334 3% of total revenue

Total 6,816 28% of total revenue

B.The monthly amount of revenues needed to generate profit of $10,000 per month is:

Revenue F Profit

CMR356,23

28.01

000,10816,6

C. The degree of operating leverage for September was:

[16,116*(1-0.28)]/4,813 = 2.41

D. If sales decrease by 10%, profit decreases by about 24% (10% * 2.41). Elinas coststructure includes a large proportion of fixed costs.

E.

CVP Graph 3.39(E)

$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

$0 $5,372 $10,744 $16,116 $21,488 $26,860

Revenues

D

ollars

Total Revenue

Total Cost

Margin of Safety

Breakeven Point TargetProfit


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F. There are many different ways to write a memo to Elina. Following are points thatshould be covered in the memo.

The CVP analysis indicates that Elina must achieve a substantial increase in revenues

to achieve targeted profit of 10,000 per month. Revenue would have to increase by7,240 over September's level, or 45% (23,356-16,116)/16,116 = 0.45).

The CVP graph and degree of operating leverage indicate that fixed costs are a largeportion of total costs. If Elina believes that this is too much risk, she will need to finda way to increase revenue without increasing fixed costs.

Here are a few possible recommendations for increasing revenues, students may havethought of others. She could offer classes in the evening to develop a larger clientelefor her work. She could sell stained glass pieces and supplies to people taking classesand to others who produce stained glass for hobby purposes. Both of these plans are

unlikely to increase fixed costs by much since employees are currently idle part of thetime. (However, she would need to invest in higher inventories.)

3.40 Toddler Toy Company

A sample spreadsheet for this problem is available on the Instructors web site for the textbook(available at www.wiley.com/college/eldenburg).

A. See the sample spreadsheet.

B. When the volume of doll sales increases to 225,000, total company profit increases from$347,500 to $383,750.

Manual check: The profit should have increased by the contribution margin for dollstimes the increase in volume of doll sales:

(225,000 dolls200,000 dolls) x ($3.50 price per doll - $2.05 variable cost perdoll)

= 25,000 dolls x $1.45 per doll = $36,250

The profit increase is added to the original profit, and the revised profit agrees

with the spreadsheet:

Original profit $347,500Increase in profit (calculated above) 36,250Revised profit $383,750

C. The expected pretax profit decreases from $347,500 to $288,500.


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D. The expected pretax profit would increase from $347,500 to $375,000.

Note about rounding in the following solutions. The spreadsheet template available on theWeb for this problem does not include any roundingi.e., the spreadsheet allows partialunits of product and prices with more than 3 decimal places. Because CVP is an estimation

technique involving uncertain future revenues and costs, the authors do not believe that itwould be useful for the spreadsheet to round units to whole numbers or to round prices to 2decimal places. Additional precision in the calculations would not improve decision making.

E. The new breakeven point is a total of 668,919 units(243,243 dolls, 152,027 bears, and273,649 cars) and revenue of$1,705,135.

F. The expected pretax profit is $485,363.

G. The spreadsheet shows total units as follows for different levels of target income:

Target Income Total Units$100,000 239,050$150,000 275,827$2,000,000 x 10% = $200,000 312,604

H.1. All of these cash flows and quantities are subject to change depending on things like

consumer preferences, the economic environment, capacity constrains, unusualsituations like electricity disruptions due to weather, labor strikes, and other factorsthat are not predictable.

2. Sensitivity analysis provides managers a model best-case, worst-case, and averagescenarios. This can help them reduce risk in operations as they make decisions. Forexample, if there is a down turn in the economy, sales are likely to be affected.Sensitivity analysis can help managers determine whether the organization will profiteven if sales decrease. In addition, each product can be analyzed separately todetermine which product is most profitable and should be emphasized.

3. Managers are often biased toward an optimistic view of the future. They may believethat their decisions will always turn out well, or they may wish to report favorableexpectations to superiors. They may support one particular product based on theirown preferences. They may favor a product designed or manufactured by employeeswho are also good friends. These types of biases often cause them to overestimatesales volumes and prices and to underestimate costs. Alternatively, they may bebiased against products because they do not like them or because someone they donot like developed or manufactures them. These types of biases cause managers tounderestimate sales volumes and prices and to overestimate costs.


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3.41 Pet Palace

A sample spreadsheet for this problem is available on the Instructors web site for the textbook(available at www.wiley.com/college/eldenburg).

A. See the sample spreadsheet.

B. The breakeven point is revenue of $900,442. Revenue needed for an after-tax targetincome of $100,000 is $1,118,732.

C. Expected after-tax income under the original assumptions is $11,250. Below is asummary of the expected after-tax income if each product were emphasized in anadvertising campaign:

Product Emphasized After-Tax ProfitPets $ 4,875

Food 26,250Toys 11,250Other 15,000

This answer contradicts the previous answer. Based on the expected after-tax profit, thecompany would benefit most from emphasizing Food in an advertising campaign.Other products have the highest contribution margin; each additional dollar of revenuefor Other products contributes more to profits than an additional dollar of revenue forFood, Toys, or Pets products. However, estimated revenues for Food are much higherthan for the other products. Therefore, a 10% increase in revenue for Food has a muchlarger positive effect on profit than a 10% increase in revenue for any of the other

products.

D. There are many possible answers to this question. Managers may increase advertising toincrease brand recognition. If some products are unique to a particular outlet, managersmay want to promote them because there is no competition for those products. Managersmay also choose to advertise products that are on sale to bring customers into the store.


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BUILD YOUR PROFESSIONAL COMPETENCIES

3.42 Focus on Professional Competency: Decision Modeling

A.

1. Chapter 3 addressed any type of decision that might be affected by the relationshipsbetween a companys revenues and costs. The chapter included examples of thefollowing types of decisions: Which products or services to emphasize, the amount tobudget for revenues or costs, and whether to incur a discretionary cost such asadvertising. Additional examples are provided in Exhibit 3.6.

2. The quantitative analyses in Chapter 3 address decisions including calculation of:

Breakeven point in number of units or revenues Volume of units or revenues needed to achieve a targeted level of pretax or

after-tax income

Sensitivity of results to changes in assumptions about volumes, prices, and

costs. Development of a cost function, including techniques such as analysis at the

account level, regression, and the high-low method

3. Quantitative results were not the only information used by decision makers in Chapter3. They also used several qualitative (i.e., non-quantitative) factors. For example, thestore manager of The Spotted Cow Creamery considered the effects of weather on icecream sales. The Spotted Cow Creamery owner considered ways to motivateemployee work effort. In the Small Animal Clinic example, the manager wasconcerned about the risk of loss if she increased the clinics fixed costs. Qualitativefactors are useful in decision making because some relevant information cannot be

quantified.

4. Following is one example from Chapter 3 where data, knowledge, and insights werelinked together; students may think of others. In The Spotted Cow Creamery (Part 2),the owner knew that beverages had a much higher contribution margin than icecream. The owner combined this knowledge with insight to hypothesize thatdifferences in profitability between store locations might be driven by differences insales mix. The owner then obtained data about the sales mix at the different stores toevaluate whether his hypothesis was true.

5. Following is one example from Chapter 3 where improvement in analysis led to

improved decision making; students may think of others. In The Spotted CowCreamery (Parts 1 and 2), the store manager (Holger) originally believed that his storesales would increase the following month. However, he did not have any reasonableevidence to suggest how or why profits would improve. After the owner provided thestore manager with information about the sales mix and its effect on profitability atother stores, Holger performed CVP analysis and began to investigate specific waysto achieve higher profits. These new analyses were more focused on relevantinformation and were less biased, leading to higher quality decisions.


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B. CVP analysis is a method to calculate quantitative information; it is used to estimateprofit and also to estimate activity levels that would lead to targeted income. Solutionsare tested with CVP analysis through calculations of expected outcomes. For example,CVP analysis reveals the profit effects of an advertising expenditure. In addition, CVPsensitivity analyses helps decision makers identify the assumptions that are the most

influential to the quantitative results, or determine the effects of fluctuations in volumes,revenues, and costs on profitability.

C.1. CVP sensitivity analysis is the use of quantitative and qualitative information to study

how volumes, revenues, costs, and profits would change with changes in variousassumptions. If profitability changes little as changes in assumptions are made,managers have more confidence in the likelihood that outcomes will be similar toplans. However, if profitability changes a great deal with small changes inassumptions, managers have less confidence that outcomes will be similar to plans.

2. The degree of operating leverage is an index of the extent to which the cost functionincludes fixed costs. Organizations having a higher degree of operating leveragehave greater volatility in earnings from changes in sales volumes than companieshaving a lower degree of operating leverage. Thus, the degree of operating leverageis a quantitative measure of how profitability is likely to change under differentscenarios. It can also be used as a measure of risk. The higher the operatingleverage, the more risky operations are, from a financial perspective.

D.1. CVP analysis requires the following types of data: volumes, revenues, cost function

(fixed and variable costs), target profit, income tax rate. For CVP analysis ofmultiple products, volume, revenue, and cost data are also needed for each product.

2. Knowledge about the organization improves the abilities to develop reasonable CVPassumptions, perform meaningful sensitivity analyses, and appropriately interpret theresults. Many types of organizational knowledge are useful for CVP analysis,including knowledge about individual products and product lines, cost behavior,relationships between selling prices and volumes, and income tax rates.

3.43 Integrating Across the Curriculum: Economics and Marketing

[Note: This problem requires familiarity with elementary microeconomics and the ability todifferentiate a simple function.]A. Recall the equation for total revenue: TR = P*Q

Substituting the demand function (1,0002*P) for Q:

TR = P*(1,0002*P)

TR =1,000*P2*P2


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B. Total cost = TC = ($24,000 + $6,000) + ($75 + $25)*Q = $30,000 + $100*Q

Substituting the demand function (1,0002*P) for Q:

TC = $30,000+$100*(1,0002*P) = $30,000+$100,000-$200*P

TC = $130,000-$200*P

C. First set the revenue function equal to the cost function and algebraically convert theequation to quadratic form (AP2+ BP + C = 0):

TR = TC1,000*P2*P2 = 130,000 - 200*P2*P2- 1,200*P + 130,000 = 0

Using a quadratic equation calculator, there are two values of P that solve this equation(i.e., there are two breakeven points):

P1= $458.12 (rounded up)P2= $141.89 (rounded up)

Note: The above solution was obtained using the quadratic equation calculators atwww.1728.com/quadratc.htm andwww.math.com/students/calculators/source/quadratic.htm. These calculatorswere located by entering quadratic equationcalculator in the Google searchengine. The results can be double-checked by verifying that profit is zero at thetwo breakeven points:

Breakeven Point_______P=$458.12 P=$141.89

Total revenue (1,000*P2*P2) $38,372.14 $101,624.46Total cost ($130,000-$200*P) 38,376.00 101,622.00

Profit $ (3.86) $ 2.46(nonzero profits due to rounding)

D. Because the revenue and cost functions both depend on the selling price (P), it isnecessary to calculate price before a graph can be created. The demand function can beused to solve for P:

Q = 1,0002*PP = (1,000Q) / 2


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Now a hypothetical data table can be created for units, price, revenues, and costs. Thedata table is used to create a CVP graph for Q between zero and 1,000 units.

Units Price Revenues Costs0 $500 $ 0 $ 30,000

125 438 54,688 42,500250 375 93,750 55,000375 313 117,188 67,500500 250 125,000 80,000625 188 117,188 92,500750 125 93,750 105,000875 63 54,688 117,500

1,000 0 0 130,000

Break even occurs at the following two points:

Q1 = 1,0002*P1 = 1,0002*458.12 = 83.76 units

Q2 = 1,0002*P2 = 1,0002*141.89 = 716.22 units

E. Profit is maximized at the selling price where marginal revenue equals marginal cost.Marginal revenue and marginal cost are calculated by differentiating each function withrespect to price:

Marginal revenue:

TR = 1,000*P2*P2

First derivative of TR = 1,0004*P

CVP Graph 3.43(D)

$0

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

$140,000

0 125 250 375 500 625 750 875 1,000

Number of Units

Dollars

Total Revenue

Total Cost

Breakeven Point


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Marginal cost:

TC = 130,000 - 200*P

First derivative of TC = -200

Set marginal revenue equal to marginal cost and solve for P:

1,0004*P = -2004*P = 1,200

P = $300 per unit

Based on a selling price of $300 per regulator, the company should sell all of theregulators that are demanded at that price:

1,0002*P = 1,0002*300 = 1,000600 = 400 regulators

F. In this situation, total revenue is a nonlinear function; the selling price does not remainconstant at different levels of activity. The total revenue function is consistent withmicroeconomic theory, which assumes that quantities sold (i.e., the quantity demanded)will decline as the price increases.

G. If the companys sales have varied between 375 and 425 regulators per year at a price of$300, then this range of activity can is assumed to be a relevant range of operations. Inturn, this means that it is reasonable to assume that the selling price will remain constantin the future within this range of operations (assuming there are no other factors thatmight influence the price)i.e., the total revenue function is approximately linear withinthe range of 375 to 425 regulators per year. Given this assumption, it would beappropriate to use CVP analysis to estimate profits within the relevant range of 375 to425 regulators per year.

ch03 - breakeven solution

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