Solutions for Problems in Chapter 3

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95

Chapter 3 Cost-Volume-Profit Analysis SOLUTIONS LEARNING OBJECTIVES Chapter 3 addresses the following learning objectives: LO1 LO2 LO3 LO4 LO5 LO6

Explain the concepts of cost-volume-profit (CVP) analysis in decision making Apply CVP calculations for a single product Apply CVP calculations multiple products Describe the assumptions and limitations that mangers consider when using CVP analysis Assess operational risk using margin of safety and operating leverage Analyze the difference between contribution margin and gross margin

These learning objectives (LO1 through LO6) are cross-referenced in the textbook to individual exercises and problems.

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QUESTIONS 3.1

A mixed cost function includes both fixed and variable costs. If there are fixed costs in the cost function, then total costs will increase at a smaller rate than the increase in total sales 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 in variable 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 performing CVP analysis for multiple products. There are two ways to calculate it: (1) Calculate the total contribution of all products by subtracting total variable costs from total revenues. Then calculate the weighted average contribution margin per unit by dividing the total contribution margin by the total number of units (the sum of units for all products). (2) Calculate the sales mix for each product by dividing the number of units sold for that product by the total number of units sold for all products. Calculate the contribution margin per unit for each product by subtracting that product’s variable cost from its revenues and dividing the result by that product’s number of units sold. Then calculate the weighted average contribution margin per unit by summing the following computation for all products: Each product’s sales mix percentage times its contribution margin per unit.

3.3

The firm has only variable costs and no fixed costs. If there were fixed costs, income would 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 of revenue remain constant, selling prices per unit remain constant, the sales mix remains constant, and operations are within a relevant range where all of these assumptions are met. These are very strong assumptions. There is always some variation in fixed costs because 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 unit may change at high volumes. However, results using these assumptions are accurate enough for general planning and decision making purposes.

3.6

The margin of safety percentage and degree of operating leverage are related as follows. Margin of Safety Percentage =

1 Degree of Operating Leverage

Degree of Operating Leverage =

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1 Margin of Safety Percentage

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As the degree of operating leverage gets larger (a higher proportion of fixed costs), the margin 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 volume discounts, 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. The level of operations must be matched with the appropriate part of the function. Each piece can be considered as a separate relevant range, and the estimated level of activity needs to be matched with the appropriate relevant range. Otherwise, the analysis will either understate or overstate variable costs.

3.8

Sales mix is the specific proportion of total sales of each type of good or service that is sold. A simple example was presented in the chapter for an ice cream store. Usually about 15% of revenue was from beverages and the rest from ice cream products. As the proportion of specific products sold changes, the contribution margin ratio changes because 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 includes the notion of breakeven. Breakeven is more narrowly constructed; it focuses on only one outcome—the single point at which total revenue equals total cost.

3.10

By definition, the margin of safety is the difference between expected unit sales and breakeven unit sales. If expected unit sales are below breakeven unit sales, the margin of safety 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. It can also help with monitoring operations, and analyzing the operating leverage of an organization.

3.12

To make decisions about advertising costs, accountants predict the amount of cost to be incurred and predict the increase in sales. CVP analysis is then used to determine whether the increase in cost is equal to or greater than the increase in contribution margin from additional units sold.

3.13

Good managers are likely to always ask for sensitivity analysis because uncertainty about sales volumes and other factors always exists. However, when unanticipated changes in the business environment or consumer preferences arise, managers will be even more interested in sensitivity analysis. By analyzing a variety of scenarios, managers can respond more quickly to unanticipated changes.

3.14

The optimism bias is people’s tendency to be overly optimistic about the success of their plans. The overestimations will bias the CVP analysis (e.g. breakeven is lower than realistic) and can lead to sub-optimal decisions based on the CVP analysis. Estimates of sales volumes (revenues) will be unrealistically high (i.e., overestimated) and estimates of costs will be unrealistically low (i.e., underestimated).

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3.15

Cost Management

When average costs are used in CVP analysis and actual volumes are higher than the volume used to calculate the average, fixed costs will be overestimated. When actual volumes are lower than the volume used to calculate the average, fixed costs will be underestimated.

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MULTIPLE CHOICE QUESTIONS 3.16. If total fixed costs doubled and contribution margin per unit was cut in half, what would happen to the break-even point? a) b) c) d)

It would decrease by half. It would double. It would triple. It would quadruple.

Ans: D 3.17. What is BioTec’s contribution margin ratio? a) b) c) d)

60% 40% 30% 20%

Ans: B 3.18. What is the variable cost if the sale price per unit is $40? a) b) c) d)

$ 8.00 $16.00 $24.00 $40.00

Ans: C 3.19. What is the degree of operating leverage if the sales volume is 2,000 units? a) 16 b) 8 c) 4 d) 1 Ans: A 3.20. What are the sales needed to obtain earnings before tax of $6,000? a) b) c) d)

$ 60,000 $ 90,000 $120,000 $180,000

Ans: B © 2012 John Wiley and Sons Canada, Ltd.

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Cost Management

EXERCISES 3.21

Target Profit, Not-For-Profit Breakeven

A. Information is given on a per unit basis, so use the following equation: profit = (S-V)Q – F $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 organizations provide 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 type of organization in the problem to help them solve it. This problem is a breakeven problem 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 the company loses money on each unit it sells. In a not-for-profit, it may be appropriate to sell services at a loss, as long as another source of funds covers the loss. In this problem, the centre receives a grant from the city, so there is “fixed” revenue in addition to the fees collected. Taking the grant into account, the breakeven is: 0 = ($4.64 - $7.64)*Q + $460,000 grant - $236,000 fixed cost 0 = $-3*Q +$224,000 Solving for Q: 3Q = $224,000 Q = 74,667 child visits

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 101 3.22

CVP Graph

A. CVP Graph 3.22(A)

Total Revenue Total Cost

$15,000 $12,000 $9,000 Dollars

$6,000 $3,000 $0 0

500

1,000

1,500

2,000

Number of Gift Baskets

The revenue line is $7 times number of baskets and represents total revenue from units sold. The cost line intersects the intercept at $5,000 reflecting the fixed cost. The slope is 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. CVP Graph 3.22(B)

Total Revenue Total Cost

$1,600,000 $1,200,000 $800,000

Dollars

$400,000 $0 0

37,500

75,000 112,500 150,000

Number of Child Visits

© 2012 John Wiley and Sons Canada, Ltd.

102

Cost Management Total revenue is the sum of the grant plus child visit fees. Unlike most CVP graphs, the breakeven point is the maximum volume before the centre incurs a loss. The grant exceeds fixed costs, so the centre has a surplus up to the breakeven point. Because the entree’s contribution margin is negative, the surplus decreases by $3 per child visit. After the breakeven point of 74,667 child visits, the centre incurs losses.

3.23

Cost Function, Breakeven

A. This problem gives information in units, so use the formula TC = v*q + F to determine variable cost. The average cost must first be turned into total cost: Total cost for 1,200 units is $234*1,200 = $280,800 Total cost for 1,400 units is $205*1,400 = $287,000 Use the two-point method (change in cost divided by change in volume) to determine the variable cost: Variable cost = (287,000 – 280,800)/(1,400 – 1,200) V = $31 B. Turn sales into units and use profit = (S-V)*Q – F. Calculate the number of units sold: Revenue / Selling price per unit = Number of units $10,600/$0.25 per unit =42,400 units Variable cost is $0.12 plus selling costs of $0.02 = $0.14 per unit. Use the breakeven equation, and then solve for the unknown amount of fixed costs: 0 = ($0.25 - $0.14)*42,400 – F 0 = $4,664 – F F = $4,664 C. There can only be one breakeven point within the relevant range, so the breakeven point is first calculated for the first range. If the result is within that range, no additional calculations are needed. However, if the breakeven point is not in the first range, then calculations must be made for the next range.

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 103 In the relevant range 0 < Q < 200, the breakeven point is calculated as: 0 = ($300 - $200)*Q - $24,000 0 = $100 *Q - $24,000 $24,000 = $100*Q Q = $24,000/$100 Q = 240 units This result is outside of the relevant range, so it is not a feasible solution. In the relevant range 200 < Q, the breakeven point is calculated as: 0 = $100*Q - $36,000 $36,000 = $100*Q Q = $36,000/$100 Q = 360 units This result is in the relevant range, so it is the breakeven point. 3.24

Profit, Price for Target Profit - 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: S* 1,000,000 - $4.50(1,000,000) - $600,000 = $25,000 S * 1,000,000 – $4,500,000 - $600,000 = $25,000 S * 1,000,000= $25,000 + $4,500,000 + $600,000 S * 1,000,000 = $5,125,000 S = $5.125 The firm needs to have an average selling price of $5.125 to earn $25,000 on sales of 1,000,000 units. This problem can be used to raise the issue of predatory pricing versus aggressive competition.

© 2012 John Wiley and Sons Canada, Ltd.

104 3.25

Cost Management CVP, Solve for Unknowns

Calculations: Part A Variable Costs CM% = (S – V)/S; 60% = ($3,000 – VC) / $3,000 60% = ($3,000/$3,000) – (VC/$3,000) 60% = 1 – (VC/$3,000) (VC/$3,000) = 1- 60% VC = (1- 60%) x $3,000 VC = $1,200

Part A Total Costs FC + VC = Total Costs $1,300 + $1,200 = $2,500 Part A Operating Income Sales – Total Costs = OI. $3,000 - $2,500 = $500

Part B Variable Costs Total Costs – FC = VC $4,000-$2,800 = $1,200

Part B Operating Income Sales – Total Costs = OI $4,000 – $4,000 = $0

Part B Contribution Margin % CM%= (S – V)/ S CM% = ($4,000 - $1,200)/$4,000 CM% = 70%

Part C Total Costs S – TC = OI $6,000 – TC = $600 TC = $6,000 - $600 TC = $5,400

Part C Variable Costs Total Costs – FC = VC $5,400 - $900 = $4,500

Part C Contribution Margin % CM%= (S – V)/ S CM%= ($6,000 - $4,500) / $6,000 CM%=25%

Part D Fixed Costs FC + VC = Total Costs FC + $1,000 = $1,600 FC = $1,600 - $1,000 FC = $600

Part D Sales Sales – Total Costs = OI S - $1,600 = $2,400 S = $2,400 + $1,600 S = $4,000

Part D Contribution Margin % CM%= (S – V)/ S CM%= ($4,000 - $1,000) / $4,000 CM%=75%

Summary: Part A. B. C. D.

Sales $3,000 $4,000 $6,000 $4,000

Fixed Costs $1,300 $2,800 $900 $600

© 2012 John Wiley and Sons Canada, Ltd.

Variable Costs $1,200 $1,200 $4,500 $1,000

Total Costs $2,500 $4,000 $5,400 $1,600

Contributio n Margin % 60% 70% 25% 75%

Operating Income $500 $0 $600 $2,400

Chapter 3: Cost-Volume-Profit Analysis 105 3.26

CV, Before and After Tax, Return on Sales – Canterman Company

A. The contribution margin per unit is calculated as follows: Total variable costs = $10,000 manufacturing + $5,000 nonmanufacturing = $15,000 Variable cost per unit = $15,000 total variable costs/500 units = $30 per unit Selling Price per unit = $110 Contribution margin per unit = $110 – $30 = $80 B. Contribution margin ratio = CM per unit/Selling Price per unit = $80/$110 = 73% C. The breakeven point in units is calculated as follows: Fixed costs = $12,500 + $7,500 = $20,000 Number of units at breakeven = $20,000/$80 = 250 units D. First set up the algebraic expression for target profit: Target profit = (1 – tax rate) × [S- (VC ratio * S)– F)] Identify the values of the variables: Desired after-tax profit =0.22×Sales Tax rate = 0.28 Fixed cost = $20,000 Variable cost ratio = $30/$110 = 0.27 Substituting the values into the target profit equation: 0.22*S = (1–0.28) * (S– 0.27*S– $20,000) 0.22*S = 0.72 * (0.73*S – $20,000) 0.22*S = 0.5256*S - $14,400 $14,400 = 0.3056*S S = $14,400/0.3056 S = $47,120 Check calculations: Expected profit = 0.22*S = 0.22*$47,120 = $10,366 Total profit = ($47,120 – $20,000 – 0.27*47,120) * (1–0.28) = $10,366 E. The accountant may be affected by the optimism bias, which is people’s tendency to be overly optimistic about the success of their plans. Estimates of sales volumes and/or selling prices (i.e., revenues) could be unrealistically high, and estimates of costs (fixed costs, variable costs, and tax rates) could be unrealistically low.

© 2012 John Wiley and Sons Canada, Ltd.

106 3.27

Cost Management Profit, Price for Target Profit – Gift4U Units

Sales VC: Materials Labour Total VC CM

Per Unit

Total

2,000

$120

$240,000

2,000 2,000

36 48 84 $36

72,000 96,000 168,000 $72,000

% 100.00 %

70.00% 30.00%

A. Contribution Margin is $36. B. Contribution Margin ratio is 30%. C. Sales break-even: Total fixed costs: Factory Rent Depreciation Expense Utilities Insurance

$43,40 0 12,000

22,000 8,400 $85,80 0 $85,800 / $36 = 2,383.33 units or 2,384 units to break-even. D. To earn a target income of $12,000: EBT: $12,000 / (1-0.2) = $15,000 EBT + FC = $15,000 + $85,800 = $100,800 $100,800 ÷ $36 = 2,800 units 2,800 units x $120 = $336,000 Total Sales Degree of Operating Leverage: Contribution Margin / EBT = $100,800 / $15,000 = 6.72 Margin of Safety in Units: In Units: Target Sales – Sales Breakeven = 2,800 – 2,384 = 416 units

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 107 E. To earn a target income after tax that is 8% of sales: EAT = EBT – TAX 8%*S = EBT * (1-0.2) 8%*S = EBT * 0.8 EBT = 8%S /0.8 EBT = 10%S VC ratio = 70%S S – 0.7S - $85,800 = 0.1S 0.3S - $85,800 = 0.1S 0.2S = $85,800 S = $429,000 $429,000 / $120 = 3,575 units Gift4U needs to increase by 1,575 units: 3,575 – 2,000 = 1,575 3.28

Cost Function, Breakeven - RainBeau Salon

A. Cost Hair dresser salaries Manicurist salaries Supplies Utilities Rent Miscellaneous Total

Fixed $18,000 16,000 0 400 1,000 2,963 $38,363

Variable $0.500 0.325 $0.825

TC = $38,363 + $0.825*appointments Explanations: Salaries: The amount of salaries in May is used to predict the next month because there was a cost-of-living increase. Supplies:An examination of the pattern in supplies costs reveals that for April and May supply cost was $0.50 per appointment. The cost was higher in March, but it is best to use 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 no fixed costs. Utilities: Because weather probably drives most of utilities cost for this business, this solution uses the prior month’s utilities to predict next month’s cost. © 2012 John Wiley and Sons Canada, Ltd.

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Cost Management

Miscellaneous:An examination of miscellaneous costs reveals that while it increases as volumes increase, it does not do so proportionately (as did supplies). For this solution the high-low method is used. Variable cost = [($3,580 - $3,450)/(1,900 – 1,500)] = $0.325 Fixed costs: TC = F +VC*Q $3,450 = F + ($0.325*1,500) $3,450 = F + $487.50 F = $3,450 - $487.50 F = $2,962.50 rounded to $2,963 B. Estimate the appointments required in June to break even. BE = ($25.00 - $0.825)Q - $38,363 BE = $24.175*Q - $38,363 $38,363 = $24.175*Q Q = $38,363 / $24.175 Q = 1,587 appointments 3.29

Breakeven, Target Profit, ROI Target Profit - Madden Company

A. Divide sales and variable costs by 160,000 to get the per-unit selling price of $50 and the variable 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 = $3,000,000 / $37.5 Q = 80,000 units B. Variable costs are $12.50 per unit/$50.00 per unit = 25% of sales Breakeven in sales, where TS = total sales: TS - 0.25*TS - $3,000,000 = $4,500,000 0.75*TS= $7,500,000 TR = $10,000,000 C. Target after-tax profit 0.10*$36,000,000 = $3,600,000 EAT EAT = (1-0.40)*EBT © 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 109

Combining these calculations: $3,600,000 = 0.60*EBT EBT = $3,600,000/0.60 EBT = $6,000,000 CVP calculation: TS- 0.25*TS - $3,000,000 = $6,000,000 0.75*TS = $9,000,000 TS = $9,000,000 / 0.75 TS = $12,000,000 D. Begin by converting the after-tax earnings to pretaxearnings per unit. EAT = 30%SP*Q EAT = 30%*$50*Q EAT = $15/unit EBT = EAT / (1-40%) EBT per unit = $15/60% EBT per unit = $25 Substitute the Pretax Profit into the Target Profit Breakeven Analysis: SP – VC – FC = Target Profit $50Q – $12.50Q – 3,000,000 = $25Q $37.50Q -$3,000,000 = $25Q $12.50Q = $3,000,000 Q = $3,000,000 / $12.50 Q = 240,000 units Dollar sales = Q * SP = 240,000 * $50 = $12,000,000 Check:

Sales 12,000,000 VC (12.50 * 240,000) 3,000,000 FC 3,000,000 Pretax Profit 6,000,000 After-tax Profit (.6*6,000,000) 3,600,000

Desired Profit (sales * 30%) 12,000,000 * .30

© 2012 John Wiley and Sons Canada, Ltd.

3,600,000

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3.30

Breakeven, Target Profit, Cost Changes, Selling Price - 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 $10*Q - $150,000 = $0 Q = $150,000 / $10 Q = 15,000 units B. Adjust the after-tax earnings target to a before-tax earnings target. EBT*(1 - .45) = $77,000 EBT*0.55 = $77,000 EBT = $77,000/0.55 EBT = $140,000 Then solve for units at target profit: $25Q- 15Q - 150,000 = $140,000 $10Q -$150,000 = $140,000 Q = $290,000/$10 Q = 29,000 units C. Current variable cost Less old component Plus new component New variable cost

$15.00 (2.50) 4.50 $17.00

Solve for breakeven where $25*Q – $17*Q - $153,000 = $0 $8Q - $153,000 = $0 Q = $153,000 / $8 Q = 19,125 units

© 2012 John Wiley and Sons Canada, Ltd.

Current fixed cost $150,000 Plus depreciation on new machine $18,000/6 3,000 New fixed cost $153,000

Chapter 3: Cost-Volume-Profit Analysis 111 D. Solve for target profit where: $25*Q – $17*Q - $153,000 = $100,000 (before tax) $8*Q = $253,000 Q = $253,000/$8 Q = 31,625 units E. Current contribution margin ratio = ($25 – $15)/$25 = 40% New selling price: S - $17 = 0.40*S S – 0.40*S = $17 0.60*S = $17 S = $17/0.60 S = $28.33 3.31

Target Profit, Progressive Income Tax Rates, CVP Graph - 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 is taxed at 15%, and income over that amount is taxed at 40%. Thus, after-tax income is calculated after subtracting two tax amounts. EBT = Target pretax income. EBT - [(0.15 * $40,000) + (0.40*(EBT - $40,000))] = $150,000 EBT – [6,000 + (0.4*EBT–(0.4 *$40,000) = $150,000 EBT – (6,000 + 0.4*EBT – 16,000) = $ 150,000 0.6 EBT + 10,000 = $150,000 EBT = $140,000/0.6 EBT = $233,333.33 Now total sales (TS) can be calculated: TS – TVC – FC = EBT TS - 0.60*TS - $250,000 = $233,333.33 0.40*TS = $483,333.33 TS = $483,333.33 / 0.40 TS = $1,208,333.33

© 2012 John Wiley and Sons Canada, Ltd.

112

Cost Management B.

CVP Graph 3.31(B)

Total Sales Total Cost

$2,030,000 $1,740,000 $1,450,000 $1,160,000

Dollars

$870,000 $580,000 $290,000 $0 $0

$435,000

$870,000

$1,305,000

$1,740,000

Sales

3.32

Breakeven, Selling Price, Target Profit with Price and Cost Changes - All-Day Candy Company

A. $4*Q - $2.40*Q - $440,000 = $0 $1.60*Q = $440,000 Q = $440,000 / $1.60 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: S - $2.70 = 0.40*S 0.60*S = $2.70 S = $4.50

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 113 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 $1.30*Q= $624,000 Q = $624,000 / $1.30 Q= 480,000 boxes Dollar sales = 480,000 boxes @ $4 = $1,920,000 3.33

Breakeven, Operating Leverage, Cost Function Decision - 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 $3,800/($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 the highest 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 as follows: $5,600 = $3,800 + 10%TS $1,800 = 10%TS TS = $18,000 When total sales are below $18,000, option 2 is more profitable. Above $18,000, option 1 is more profitable.

© 2012 John Wiley and Sons Canada, Ltd.

114

Cost Management 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-$6-($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.)

3.34

ROI Target Profit, Foreign Exchange Rates - Borg Controls

A. Expected pretax income: 1,700,000€ - 0.60*1,700,000€ - 321,000€ = 359,000€ Converted to dollars: 359,000€/1.6€ per $= $224,375 ROI = $224,375/$2,680,000 = 8.4% B. Target pretax income in dollars: 0.15*$2,680,000 = $402,000 Converted to Euros $402,000 x 1.6 € per $ = 643,200€ Required revenue TS - 0.60*TS - 321,000€ = 643,200€ 0.40*TS = 964,200€ TS = 964,200€ / 0.40 TS = 2,410,500€

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 115 3.35

Target Profit, Margin of Safety, Operating Leverage, Contribution Margin and Gross Margin - Newberry’s Nutrition

A. Categorize costs Cost Direct materials Direct labour Fixed factory overhead Variable factory overhead Marketing and Administration Totals

Fixed

Variable $300,000 200,000

$100,000 110,000 $210,000

150,000 50,000 $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*Q Q = $410,000 / $3.00 Q = 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 = $0 Q = $210,000/$3 = 70,000 units In revenue: 70,000 units * $10 per unit = $700,000 Margin of safety in units 100,000 units – 70,000 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

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116

Cost Management 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 D. Newberry's Nutrition Contribution Margin Income Statement per unit

Sales (100,000 units) Variable Costs

$ 10.00

Direct Materials

$ 3.00

300,000

Direct Labour Variable Factory Overhead Marketing and Administration

2.00

200,000

1.50

150,000

0.50

50,000

Contribution Margin Fixed Costs Fixed Factory Overhead Marketing and Administration Budgeted Income Before Taxes

© 2012 John Wiley and Sons Canada, Ltd.

$ 1,000,000

$ 7.00

$

700,000

$ 3.00

$

300,000

$

100,000

$

110,000 210,000

$

90,000

% 10 0 0.3 0 0.2 0 0.1 5 0.0 5 0.7 0 0.3 0

Chapter 3: Cost-Volume-Profit Analysis 117

Newberry's Nutrition Gross Margin Income Statement Sales Cost of Goods Sold Direct Materials Direct Labour Variable Factory Overhead Fixed Factory Overhead

1,000,000 300,000 200,000 150,000

Gross Margin

100,000 750,000 250,000

Non-Manufacturing Expenses Marketing and Administration

160,000

Budgeted Income Before Taxes

3.36

90,000

Breakeven, Target Profit, Margin of Safety, Operating Leverage - Pike Street Taffy

A. It is first necessary to determine the cost function: Assuming that the cost of ingredients varies with the amount of taffy produced, the variable cost per kilogram is: $3,200/2,000 kgs = $1.60/kg. The rent is assumed to be fixed. The wages are also fixed because employees work standard shifts. Total fixed costs are: $800+$4800 = $5,600 Breakeven point in kilograms: $5,600/($4.80 - $1.60) = 1,750 kgs.

© 2012 John Wiley and Sons Canada, Ltd.

118

Cost Management Breakeven point in revenues: 1,750 kgs * $4.80 per kg. = $8,400 B. Calculate the pretax income needed for an after-tax income of $3,000: $3,000/(1-20%)=$3,750 Units needed to earn a pretax income of $3,750: ($5,600 + $3,750)/($4.80 -$1.60) = 2,922 kgs. Revenues needed to earn a pretax income of $3,750: 2,922 kgs * $4.80 per kg. = $14,026 Check calculation using contribution margin ratio formula: Contribution margin ratio = ($4.80-$1.60)/$4.80 = 66.6667% ($5,600 + $3,750)/66.6667% = $14,025 (difference due to rounding) C. The margin of safety is current total sales less total sales at breakeven: =$9,600 - $8,400 = $1,200 The margin of safety percentage = $1,200/$9,600 = 0.125 = 12.5% (Revenues are 12.5% above the breakeven point) 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

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 119 3.37

Breakeven, Target Profit, Margin of Safety - 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 50,000 – 42,500 = 7,500 swimsuits C. If the margin of safety was 5,000 swimsuits in 2012and increases to 7,500 swimsuits in 2013(calculated in Part B), then operations will be less risky in 2013. A larger margin of safety 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 covered at 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 3.38

CVP Analysis with Taxes, Margin of Safety – Pineridge Kennels

A. Expected after-tax profit at 8,400 dog-days: Contribution margin = $32 Fee - $5 Variable cost = $27 per dog-day [($27×8,400) – $160,000]× (1-.30) = $46,760 © 2012 John Wiley and Sons Canada, Ltd.

120

Cost Management B. First calculate the breakeven point in dog-days. 0 = $27 × dog days - $160,000 Dog days = $160,000 / $27 Breakeven point = 5,926 dog-days Then calculate margin of safety at 7,200 dog-days: Margin of safety = 7,200 – 5,926 = 1,274 dog-days C. Dog-days needed to achieve after-tax profit of $108,000 Pretax profit = $108,000/(1-.30) = $154,286 Target pretax profit + Fixed costs = $154,286 + $160,000 = $314,286 Dog days needed = $314,286/$27 CM per dog-day = 11,640 dog-days D. Percentage increase = (11,640 – 8,400) /8,400 = 38.6% This large an increase could mean that the volume is out of the relevant range and fixed costs could change. We do not know the capacity of the kennel. If capacity is less than 11,640 days, new dog enclosures would need to be built and other fixed costs, such as staffing, might increase. In addition, variable costs could increase if overtime would be needed or more expensive help would be hired. We need to know the relevant range of the current cost function, which is, the point at which fixed and/or variable costs would change. We would also need to know whether a market exists for the additional volume at current prices, and whether additional fixed costs would be needed for advertising or other promotional costs to achieve the higher volume.

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 121

PROBLEMS 3.39

Cost Function, Breakeven, Quality of Information, Relevant Range – Premier Lobsters

A. Cost Wages Packing materials Rent and Insurance Admin and selling Total costs

Fixed $25,000 45,000 $70,000

Variable $100,000 20,000 $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 cases of oysters packed. Rent and insurance are fixed. No information is given about whether administrative and selling is fixed or variable. It is categorized above as fixed, but it could be a mixed cost. In the absence of additional information, this solution assumes the cost 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 – $70,000 $0 = $40*Q - $70,000 $40*Q = $70,000 Q = $70,000/$40 per case Q = 1,750 cases C. EBT = ($100-$60)*3,000 cases - $70,000 EBT = $120,000 - $70,000 = $50,000 After-tax profit = $50,000 * (1-0.20) = $40,000 D. If only 2,000 cases have been packed 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 C is probably low. In addition, any change in operations major enough to increase sales by 50% might change the cost function (see Part E). So, even if the manager anticipates expanding 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 2,000 cases. If the company does not have enough space to handle all of the lobsters, rent would need to increase. The company might have to pay workers overtime or hire © 2012 John Wiley and Sons Canada, Ltd.

122

Cost Management additional workers at a higher or lower rate than current workers (depending on skill levels and supply of workers). With the additional volume, the company might get a discount on packing materials, so that cost might be smaller. Administrative costs might or might not increase 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.

3.40

Relevant Information, Breakeven, Target Profit, Business Risk - Francesca

A. Quantitative information Cart lease $800 per month: This is relevant because this is a cost that will be incurred if Francesca leases the cart, but will not be incurred otherwise. City licence $20 per month: This is relevant for the same reason as the cart lease. Lessor records showing average gross revenues of $32 per hour: This information is relevant if Francesca thinks she will sell about the same amount as the lessor. However, the lessor’s records might not be reliable. Ingredients 40% of revenue: This is relevant because this cost will be incurred only if Francesca sells coffee. Last year’s income tax rate of 25%: Assuming that the income tax rate is not different for operating the coffee cart, the tax rate is irrelevant to Francesca’s decision. The income tax rate will reduce earnings for both options. 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 is unavoidable. Current income $2,400 per month: This is relevant as the opportunity cost if Francesca decides to operate the coffee cart instead of continuing her current work. B. This question calls for calculating the hours Francesca should work to earn a target profit equal to her current earnings of $2,400 per month. Before this computation can be performed, the cost function for the coffee cart must be determined: Cart lease City licence Ingredients Total

Fixed $800 20 $820

Variable 0.40*Sales 0.40*Sales

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

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 123 Target profit calculation (assuming that revenue is $32 per hour): $2,400 = ($32 - 0.40*$32)*Hours per month - $820 $3,220 = $19.20*Hours per month Hours per month = $3,220/$19.20 = 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 the selling 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 = (Sales per hour - 0.40*Sales per hour)*100 hours - $820 $3,220 = 0.60*Sales per hour *100 $3,220 = 60*Sales per hour Sales per hour = $3,220/60 Sales per hour = $53.67 D. As mentioned in Part A above, Francesca cannot be certain that the information she received from the lessor is reliable. In addition, revenues are likely to fluctuate based on weather, the economy, competition, and consumer preferences. E. There are many other types of information to consider. Some information might help Francesca evaluate the financial viability of the coffee cart, such as local population trends, competition, and economic outlook. Additional information relates to Francesca’s own preferences, such as whether she wants to give up her other occupations and how much she would enjoy running a coffee cart in Whistler. 3.41

Sales Mix, Multiple-Product Breakeven, Business Risk, Quality of Information Keener

A. Last month 1,200 regular and 2,400 premium boomerangs were sold. Assuming the sales mix remains constant, two premium boomerangs are sold for each regular boomerang. B. Total fixed product line costs: Regular: 1,200 units x $8.17 = $9,804 Premium: 2,400 units x $24.92 = $59,808 C. Total corporate fixed costs: $5.62 x (1,200 + 2,400) units = $20,232 © 2012 John Wiley and Sons Canada, Ltd.

124

Cost Management D. To calculate the overall breakeven, it is easiest to first calculate the weighted average contribution margin ratio using an income statement approach: Regular Premium Total Units 1,200 2,400 3,600 Sales $26,580 $108,720 $135,300 Variable cost 5,172 16,584 21,756 Contribution 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): BE in Sales = ($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) Breakeven for Premium based on sales mix in revenues: $107,059*($108,720/$135,300) Total corporate sales at breakeven

$ 21,032 86,027 $107,059

E. Breakeven for regular boomerangs ignoring corporate fixed costs: BE in Sales = $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 company does not need to sell as many units to breakeven. The breakeven revenue for boomerangs is higher when it covers both its own and corporate fixed costs ($21,032) than when it only covers its own fixed costs ($12,173). G. Corporate fixed costs are not usually under the control of the individual product managers. Therefore, corporate fixed costs generally are not considered when evaluating individual product profitability. However, the company as a whole needs to cover all of its fixed costs, so it is important to take corporate fixed costs into account when planning overall operations. H. The actual sales mix can differ from plans for many reasons. For example, customer preferences can change, altering the number and prices of units. Competitor’s prices and products could affect the sales mix. Consumer buying patterns change when the economy 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 is lower because the CVP assumptions are more likely to be violated. Therefore, the © 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 125 likelihood that the sales mix will remain constant must be evaluated. Sensitivity analysis should also be performed to examine a larger range of operations that incorporate possible changes in sales mix. The quality of the CVP analysis is negatively affected by higher uncertainty about any of the variables used. 3.42

Cost Function, Marginal Cost, Opportunity Cost, Usefulness of CVP - Not-ForProfit After-School Art Program

A. 1. Here are several possible costs; students may think of others. Cost Staff people Art supplies High school help Snack food

Category Fixed (fixed schedule according to # of children) Mixed, some that will be used up, and some (easels) that will be fixed Fixed (fixed schedule according to # of children) Variable

2. Snack food is the only completely variable cost and number of snacks served would be a good cost driver. Art supplies have a variable component, and number of children 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 staff and 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 contribution margin foregone from a fee-paying child. E. CVP analysis offers the neighbor an opportunity to vary assumptions, such as price and volume 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 fixed costs, 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 a separate part of the spreadsheet, with cell references to the input cells. The neighbor could then modify data in the input cells to analyze the expected financial results under different sets of assumptions.

© 2012 John Wiley and Sons Canada, Ltd.

126

Cost Management

3.43

Breakeven, CVP, Potential Cost Structure Change, Employee Reaction - Ersatz

A spreadsheet showing the CVP graph solutions for this problem is available on the Instructor’s web site for the textbook (available at www.wiley.com/canada/eldenburg). A. The variable cost per unit is the same for 1,000 units and for 1,500 units. Therefore, it is reasonable 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: $0= $100*Q – $56*Q - $41,000 $0 = $44*Q -$41,000 Q = $41,000 / $44 Q = 932 units to break even B.

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 127 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 as possible, yet fully answers the shareholder’s question. The message also avoids use of highly technical language, but it assumes that the shareholder is familiar with the terms used 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 point; the point at which our revenues exactly cover our costs. As volume increases above this level, our profit increases 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 will be 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 is very 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 $45.32Q = $41,000 Q = $41,000/$45.32 Q= 905 units The old contribution margin was $44, and the new contribution margin is $45.32, so the contribution 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 $11,000 = $20*Q - $10*Q $11,000 = $10*Q Q = $11,000 / $10 Q = 1,100 units

© 2012 John Wiley and Sons Canada, Ltd.

128

Cost Management G.

H. If sales exceed 1,100 units, paying $10,000 per period + $10 per unit (the old pay arrangement) will result in lower total selling costs. I. Sales representatives with high selling volumes would probably like the new system because they would be likely to earn more. The opposite would be true for sales representatives with low selling volumes. Sales representatives who dislike risk might prefer the existing pay system, which guarantees a minimum payment. People often dislike any change, so there may be resistance regardless of whether sales representatives are better off. Overall, the new pay system might encourage sales representatives to achieve 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

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 129 3.44

CVP Analysis, Bonus, Taxes – J & J Products

A. Amount of pretax bonus required to receive $36,000 after taxes: (1 – tax rate)×Pretax bonus = $36,000 0.70*Pretax bonus = $36,000 Pretax bonus =$36,000 / .70 = $51,429 B. Amount of after-tax earnings J & J will need to pay the bonus in Part A, assuming that the bonus is 10% of after-tax earnings: EAT* 10% = $51,429 EAT = $51,429/0.10 = $514,290 With a tax rate of 35%, pretax income must be: $514,290/(1-.35) = $791,215 pretax income C. First determine the amount of pretax income needed to achieve after-tax income of $514,290: Pretax income × (1 – tax rate) = $514,290 Pretax income = $514,290/(1–0.35) = $791,215 Then determine the number of units (Q) needed to achieve pre-bonus and pretax income of $791,215: Sales– Variable costs – Fixed costs = $791,215 $30*Q– $10*Q – $200,000 = $791,215 $20*Q = $991,215 Q = 49,560.75 units Rounding up, units sold = 49,561 D. The bonus should help to align Sally’s goals with the goals of J & J because the bonus will increase as company profits increase. However, the bonus could possibly motivate unethical behavior such as encouraging customers to move scheduled purchases from one period to another to achieve personal gain.

© 2012 John Wiley and Sons Canada, Ltd.

130

Cost Management

3.45

Contribution Margin vs. Gross Margin – FongFone Ltd. A. 1. Sales in dollar Sales – SalesBE = MOS Sales – $250 * 2,700 = $75,000 Sales – $675,000 = $75,000 Sales = $675,000 + $75,000 Sales = $750,000 2. Variable Selling and Administrative Expenses Sales – VC = CM CM = 30% of Sales Sales – VC = 30% Sales VC = 70% of Sales Total VC = 70% of Total Sales Total VC = 70% * $750,000 Total VC = $525,000 Total VC = DL + DM + VMOH + VS&A $525,000 = $170,000 + $210,000 + $80,000 + VS&A $525,000 = $460,000 + VS&A VS&A = $65,000 3. Fixed Manufacturing Overhead Gross Margin = 22.5% of Sales Sales – COGS = Gross Margin $750,000 – COGS = 22.5% *$750,000 $750,000 – COGS = $168,750 COGS = $581,250 COGS = DL + DM + VMOH +FMOH $581,250 = $170,000 + $210,000 + $80,000 + FMOH FMOH = $121,250 4. Fixed Selling and Administrative Expenses FC = FMOH + FS&A SalesBE = FC / CM% $675,000 = FC / 30% FC = $675,000 * 30% = $202,500 $202,500 = $121,250 + FS&A FS&A = $81,250 5. Earnings (Income) Before Taxes S – VC – FC = EBT

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 131 $750,000 – $525,000 – $202,500 = $22,500 B. 1. Sales volume in dollars and in units to earn a $36,000 income after taxes. Target EBT =Target EAT / (1-Tax rate) = $36,000 / 0.75 = $48,000 Target CM = FC + Target EBT = $202,500 + $48,000 = $250,500 Target Sales = CM / CM% = $250,500 / 30% = $835,000 Target Units = $835,000/ $250 = 3,340 2. Calculate the degree of operating leverage. If sales increase by 8%, what is the impact on the operating income? CM / EBT = $250,500 / $48,000 = 5.219 8% * 5.219 = 41.75% 3.46

Breakeven, Avoidable Fixed Costs, Price, CVP Assumptions, Operating Risk - King Salmon Sales

A. This question calls for a breakeven calculation, which means that the cost function must first be determined. Costs are categorized as shown in the following table. Labour costs are assumed to be variable because employees work only as needed. Administration cost is assumed to be fixed because there is no information to suggest that this cost varies proportionately with volume of activity. Fixed Fish Smoking materials Packaging materials Labour Administration Sales commission Total

Variable $200,000 20,000 30,000 300,000

$150,000 $150,000

10,000 $560,000

If all variable costs vary with kilograms of salmon, then variable cost is estimated as: $560,000/100,000 kgs. = $5.60 per kg. The cost function is: TC = $150,000 + $5.60 per kg.

© 2012 John Wiley and Sons Canada, Ltd.

132

Cost Management If the selling price is the same as last year, it can be estimated based on last year’s total revenue and total volume: Price = $800,000/100,000 kgs. = $8.00 per kg. In this problem, it is best to calculate the breakeven in units because there is a limit on the number of kilograms of salmon available: $0 = ($8.00 – $5.60)*Q - $150,000 $150,000 = $2.40*Q Q = 62,500 kgs The company cannot cover its fixed costs, because it cannot acquire enough salmon to break even. Therefore, the company should not operate this year. Note: According to the information in this question, the company will avoid administrative costs if there is no salmon production. Therefore, there will be zero profit or loss and the company will be better off if there is no production. B. The term “breakeven” has a slightly different meaning in this question than usual. In this question, “breakeven” means being at least as well off as the alternative. The loss at the maximum possible production volume of 50,000 kgs. = ($8.00 – $5.60)*50,000 kgs. – $150,000 = –$30,000. If the company incurs administrative costs whether or not it produces salmon, then the loss with no production would be –$150,000. Therefore, the company would be better off producing salmon and incurring a smaller loss. C. Breakeven selling price: $0 = (SP -$5.60)*50,000 kgs. - $150,000 $0 = SP*50,000 - $280,000 – 150,000 $430,000 = SP*50,000 SP = $430,000/50,000 SP = $8.60 D. The managers assume that their cost function is linear (fixed costs remain fixed and variable costs remain constant) and that they are operating in the relevant range. They are also assuming that they can purchase at least 50,000 kgs of salmon and that they can sell the salmon for at least $8.60 per kg. E. Although the exact values may differ from the assumptions, greater reliance can be placed on the assumptions about cost than on the other assumptions. For example, fixed costs of administration will not be exactly $150,000 because they include costs such as electricity that vary with weather and electricity rates. However, administrative costs are not likely to vary widely from year to year unless the managers increase or decrease spending on discretionary items, over which they have control. Labour and supplies costs are also likely to remain relatively constant. However, there are a number of uncertainties about the specific assumptions regarding the cost of salmon, selling prices, and volume. For example, the cost to purchase salmon could increase because of the

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 133 shortage, but then King Salmon’s selling price might also increase. If selling prices increase, demand could drop. King Salmon’s managers cannot predict perfectly the volume of salmon that will be available; in some years fish counts are lower than in other years, so the volumes could be lower than 50,000 kgs. However, if the company has operated for many years, the managers can use prior data to analyze the reasonableness of their assumptions. F. This memo could be composed in a variety of ways. The main points that should be covered include:

3.47

•

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

•

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

•

A statement that many of King Salmon’s costs are variable, but that administrative cost is probably primarily fixed.

•

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

•

Suggestions of one or more ways that King Salmon could convert some of its administrative costs from fixed to variable—e.g., hiring temporary office help.

•

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

Cost Function, Breakeven, Target Profit, Business Risk and Bias, Interpretation Joe

A. 1. First clock Equipment Materials Rent space Utilities Joe’s salary Sales staff Total

© 2012 John Wiley and Sons Canada, Ltd.

Relevant No; Sunk cost No; Sunk cost Yes Yes Yes Yes Yes

Fixed

Variable $30 each

$2,500 300 3,000 2,000 $7,800

7 each $37 each

134

Cost Management 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 = 41.49 round up to 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 =62.77 rounded up to 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. If demand 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 be limited and prices could increase. Rent prices increase periodically, and so his rent could change in the next year. Utility bills could increase or decrease, according to weather, potential shortages, or increased demand due to bad weather in other parts of the country. He could have to pay sales people more or less than he plans, depending on the local economy and the demand for clocks. If there is only small demand for the clocks initially, he may have to increase salary until demand builds. There are many other answers for this question, too. 2. It is likely that Joe may need to advertise. He also may need a receptionist in the office during business hours. He has not included regulatory costs such as business licenses, employment and property taxes, and any local fees for services. 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 he does not know what the local and regional competition might be, and he does not know whether most of his sales will happen during holiday seasons. Unanticipated fluctuations are also likely to occur for discretionary products such as clocks. Furthermore, he does not have experience selling the clocks full time, so he might be overestimating demand for the clocks.

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 135 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 abovealready identified a number of costs that he has overlooked. D. Uncertainties and potential biases reduce the quality of the information used as inputs for the CVP analysis, thus reducing the quality of the CVP information. As a result, an objective person would be skeptical of the CVP results and would potentially seek higher quality information. For example, market research might be used to increase the quality of revenue estimates. E. There is no one answer to this part. Sample solutions and a discussion of typical student responses will be included in assessment guidance on the Instructor’s web site for the textbook (available at www.wiley.com/canada/eldenburg). 3.48

CVP Sensitivity Analysis, Bias, Quality of Information - Jasmine Krishnan

A. Usually, sensitivity analysis is performed to determine how sensitive profits are to changes in assumptions such as estimated prices, costs and volumes of sales. Sensitivity analysis 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 trips would 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 lead to a positive decision about that alternative. In addition, they may interpret results more positively than if they were not biased. Jasmine would need to underestimate insurance or 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. Potential investors who rely on the brochure would be given misleading information. Thus, the quality of potential investor decisions would be low unless they seek and obtain more objective sources of information. D. The ethical problem is that the biased information misleads potential investors to believe that 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 not succeed and may not be able to return the investment or any return on it. Most investors have a range of choices and consider both the investment return and risk as they compare their choices. By biasing the information, Jasmine would also bias the decision making process for her potential investors; they may invest in a project that is more risky than their other investments without realizing the potential consequences of this decision. This is unfair to them and unethical.

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Cost Management E. Jasmine needs to present the most objective set of assumptions possible in her calculations 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. The quality of their decision making will be greatly improved.

3.49

Small Business Owners, CVP Research on the Internet

A. Many small business owners have no business experience or education. They do not know 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. CVP analysis can help owners more thoroughly consider the quality of information they use to estimate future results and recognize the risks of their decisions. They are also able to perform sensitivity analysis to reduce elements of surprise from changes in future plans and 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 and explore. 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 uncertainty in their operating environments.

•

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

•

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

•

Provide an overview of the process of using CVP analysis, including identification 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.

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 137 3.50

Cost Function, Target Profit, Operating Leverage, CVP Graph, Owner Goals Elina’s Stained Glass A spreadsheet showing the solution for this problem is available on the Instructor’s web site for the textbook (available at www.wiley.com/canada/eldenburg). A. Below is one solution for the cost function. This solution involves a number of judgments about cost classification and choice of estimation methods. Other reasonable solutions are possible, particularly for “raw materials and supplies” and “miscellaneous.” Labour and rent costs are most likely fixed. Rent is usually a fixed cost, and labour appears to be fixed for this company because the employees work regular schedules. Both of these costs are estimated based on the most recent month’s information. This procedure will incorporate the apparent rent increase that took place in September and the most recent employee schedules and pay rates. Therefore, the rent cost is estimated at €2,200, and the labour cost is estimated at €4,282. Raw materials and supplies for a manufacturing organization are most likely to be variable. No information is provided about alternative cost drivers, so this solution estimates raw materials and supplies as a percentage of revenue. This treatment is reasonable because these types of costs and revenues both tend to vary with the size of window. If raw material and supply costs change over time, then it is best to use the most recent information available. Therefore, this variable cost is estimated using the most recent month’s data: €4,029/€16,116 = 25% of revenue No information is provided about the nature of the miscellaneous cost. Miscellaneous might include direct costs such as packing materials for the windows and indirect costs for supplies used in the office. Also, this cost appears to have increased along with the increases in revenues over the four months presented. The scatter plot shown below is used to further analyze the relationship.

© 2012 John Wiley and Sons Canada, Ltd.

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The scatter plot seems to confirm a positive relationship between miscellaneous costs and revenues. Therefore, regression analysis will be used to estimate the cost function for miscellaneous costs, with revenues as the independent variable. Portions of the regression output are shown below. Regression Statistics Multiple R 0.873015438 R Square 0.762155955 Adjusted R Square 0.643233932 Standard Error 69.99280477 Observations 4

Intercept X Variable 1

Coefficients 288.5314984 0.033136813

Standard Error 162.9787289 0.013089407

t Stat 1.770363 2.531575

P-value 0.218684 0.126985

Based on the regression results, the miscellaneous cost function is estimated as: TC = €289 + 3% of revenues Given the following summary of individual cost functions, the total cost function for Elina's is TC = €6,771 + 28% of total revenue. © 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 139 Cost Category Raw materials and supplies Labour Rent Miscellaneous Total

Fixed € 0 4,282 2,200 289 €6,771

Variable 25% of total revenue 3% of total revenue 28% of total revenue

B. The monthly amount of revenues needed to generate profit of $10,000 per month is: F + P r o f i t 6,771 +10,000 = = 23,293 R e v e n u e = 1 − 0.28 C M R

C. The degree of operating leverage for September was: [€16,116*(1-0.28)]/€4,812 = 2.41 D. If sales decrease by 10%, profit decreases by about 24% (10% * 2.41). Elina’s cost structure includes a large proportion of fixed costs. E.

Target Profit

Breakeven Point

Margin of Safety

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Cost Management F. There are many different ways to write a memo to Elina. Following are points that should 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 by €7,177 over September's level, or 45% (€23,293-€16,116)/€16,116 = 0.45).

•

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

•

Here are a few possible recommendations for increasing revenues, students may have thought of others. She could offer classes in the evening to develop a larger clientele for her work. She could sell stained glass pieces and supplies to people taking classes and 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 the time. (However, she would need to invest in higher inventories.)

3.51 Building and Using a CVP financial Model – Toddler Toy Company A sample spreadsheet for this problem is available on the Instructor’s web site for the textbook (available at www.wiley.com/canada/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 dolls times the increase in volume of doll sales: (225,000 dolls – 200,000 dolls) * ($3.50 price per doll - $2.05 variable cost per doll) = 25,000 dolls * $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 Increase in profit (calculated above) Revised profit C. The expected pretax profit decreases from $347,500 to $288,500. © 2012 John Wiley and Sons Canada, Ltd.

$347,500 36,250 $383,750

Chapter 3: Cost-Volume-Profit Analysis 141 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 the Web for this problem does not include any rounding—i.e., the spreadsheet allows partial units 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 it would be useful for the spreadsheet to round units to whole numbers or to round prices to 2 decimal 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, and 273,649 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 $100,000 $150,000 $2,000,000 x 10% = $200,000

Total Units 239,050 275,827 312,604

H. 1. All of these cash flows and quantities are subject to change depending on things like consumer preferences, the economic environment, capacity constraints, unusual situations like electricity disruptions due to weather, labour strikes, and other factors that are not predictable. 2. Sensitivity analysis provides managers model best-case, worst-case, and average scenarios. This can help them reduce risk in operations as they make decisions. For example, 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 profit even if sales decrease. In addition, each product can be analyzed separately to determine which product is most profitable and should be emphasized. 3. Managers are often biased toward an optimistic view of the future. They may believe that their decisions will always turn out well, or they may wish to report favorable expectations to superiors. They may supportone particular product based on their own preferences. They may favor a product designed or manufactured by employees who are also good friends. These types of biases often cause them to overestimate sales volumes and prices and to underestimate costs. Alternatively, they may be biased against products because they do not like them or because someone they do not like developed or manufactures them. These types of biases cause managers to underestimate sales volumes and prices and to overestimate costs.

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3.52

Building and Using a CVP Financial Model - Pet Palace

A sample spreadsheet for this problem is available on the Instructor’s web site for the textbook (available at www.wiley.com/canada/eldenburg). A. See the sample spreadsheet. B. The breakeven point is revenue of $900,442. (See Base Case worksheet) Revenue needed for an after-tax target income of $100,000 is $1,118,732. C. Expected after-tax income under the original assumptions is $11,250. (See Base Case worksheet). Below is a summary of the expected after-tax income if each product were emphasized in an advertising campaign: Product Emphasized Pets Food Toys Other

After-Tax Profit $ 4,875 26,250 11,250 15,000

Based on the expected after-tax profit, the company would benefit most from emphasizing Food in an advertising campaign. Other products have the highest contribution margin; each additional dollar of revenue for Other products contributes more to profits than an additional dollar of revenue for Food, Toys, or Pets products. However, estimated revenues for Food are much higher than for the Other products. Therefore, a 10% increase in revenue for Food has a much larger 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 to increase brand recognition. If some products are unique to a particular outlet, managers may want to promote them because there is no competition for those products. Managers may also choose to advertise products that are on sale to bring customers into the store.

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 143

MINI-CASES 3.53

Cost Function, Operating Leverage, Keeping or Dropping a Business - Wildcat Lair

[Note: This problem contains the same data is problem 2.46 in Chapter 2, which requires students to determine a cost function. The cost function computations shown in Part A below are identical to the solution for problem 2.46.] A. Before calculating the breakeven points and degree of operating leverage, it is first necessary to create the cost function. The Lair’s costs are categorized as follows: Fixed Purchases of prepared food Serving personnel Cashier Administration University surcharge Utilities Totals

Variable $21,000

$30,000 5,500 10,000 1,500 $47,000

7,000 _______ $28,000

Total sales is the most likely cost driver for both variable costs. Food costs are likely to vary proportionately with sales, and the University surcharge is specifically based on sales. Because sales is the cost driver for both variable costs, total sales (TS) 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 Sales Wildcat Lair’s breakeven point is: $47,000/[70,000-21,000)/70,000] $47,000/($49,000/$70,000) $47,000/0.7 = $67,143 Given the cost function, the university’s breakeven point is: $47,000/[($70,000 - $28,000)/$70,000] $47,000/($42,000/$70,000) $47,000/0.6 = $78,333 © 2012 John Wiley and Sons Canada, Ltd.

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Cost Management

B. For July, the degree of operating leverage (without the University surcharge) is: F +1 = [$47,000/($-5,000 + $7,000)] + 1 = 24.5 Profit

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 work on a more variable basis, with more employees scheduled for busier times. Employees could be called in or sent home when volumes fluctuate. During slow periods, serving personnel could also serve as cashiers. E. Reducing the reliance on fixed costs reduces the risk of losses during periods when volume is low. When volumes decrease, for example between semesters and through the summer, 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 student responses will be included in assessment guidance on the Instructor’s web site for the textbook (available at www.wiley.com/canada/eldenburg). Following is a brief summary of 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 that there are economies of scale at food services, so food for other outlets could increase in cost. On the other hand, the facility currently being used by the Lair could potentially be used for some other purpose. If the Lair is not widely used, then it might not provide an important service to the university community. G. There is no one answer to this part. Sample solutions and a discussion of typical student responses will be included in assessment guidance on the Instructor’s web site for the textbook (available at www.wiley.com/canada/eldenburg).

© 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 145 3.54

Not For Profit Breakeven Price, Budget Alternatives - The Little Beaver Daycare Centres

A. The cost function is: Daycare staff salaries Daycare supplies used Administrative salaries Rent Utilities Other expenses Total Costs

Fixed $ 14,115 219 3,412 1,100 226 702 $ 19,774

Variable $ 3.49

2.53 $ 6.02

Daycare supplies used: Use high low method to estimate FC and VC VC = ($3,182- $2,934)/(849-778) = $3.49 FC = TC – VC = $3,182 – (849 * $3.49) = $219 TC = $19,774 + $6.02*children attending. Note: Ch 2 solution to 2.56 is based on Other expense $664 + $2.58 * children attending resulting in cost formula TC = $19,736 + $6.07*number of children Breakeven, solving for sale price: $0 = (S - $6.02) * 940 children - $19,774 $0 = 940*S- $5,658.8 – $19,774 940*S = $25,432.8 S = $27.06 per child OR $0 = (S – 6.07) * 940 - $19,736 $0 = 940*S - $5,705.8 - $19,736 940*S = $25,441.8 S = $27.07 per child The average daycare fee during March-July was: $16,545/3,290 children = $5.03 per child The actual fees charged are far below the levels needed to break even. B. Many families may not be able to afford this fee. Since many of the families are on fixed incomes, they may have to make trade-offs between other living expenses and their © 2012 John Wiley and Sons Canada, Ltd.

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Cost Management daycare expenses. They may also forego needed daycare services or look elsewhere for less expensive daycare. C. If the fee is raised, volumes are likely to go down. That means that fees may need to be raised again, causing further declines in volume. This is called the “Death Spiral” (this topic is explicitly addressed in Chapter 13). D. If possible, the centre could try to substitute cheaper labour for expensive labour. If a daycare provider assistant or specially trained helper can care for the children instead of a fully qualified provider, this would reduce some of the fixed cost. Analysis of other costs that can be reduced is needed. There may be grants that would offset some fixed costs, or it is possible that donors can be found to offset some costs. An annual fund raising event might be held.

3.55

Integrating Across the Curriculum: Economics and Marketing – Hollis Company

[Note: This problem requires familiarity with elementary microeconomics and the ability to differentiate a simple function.] A. Recall the equation for total revenue: TR = P*Q Substituting the demand function (1,000 – 2*P) for Q: TR = P*(1,000 – 2*P) TR =1,000*P – 2*P2 B. Total cost = TC = ($24,000 + $6,000) + ($75 + $25)*Q = $30,000 + $100*Q Substituting the demand function (1,000 – 2*P) for Q: TC = $30,000+$100*(1,000–2*P) TC = $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 the equation to quadratic form (AP2 + BP + C = 0): TR = TC 1,000*P – 2*P2 = 130,000 - 200*P 2*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) © 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 147

Note: The above solution was obtained using the quadratic equation calculators at www.1728.com/quadratc.htm and www.math.com/students/calculators/source/quadratic.htm. These calculators were located by entering “quadratic equation calculator” in the Google search engine. The results can be double-checked by verifying that profit is zero at the two breakeven points:

Total revenue (1,000*P – 2*P2) Total cost ($130,000-$200*P) Profit

Breakeven Point_______ P=$458.12 P=$141.89 $38,372.14 $101,624.46 38,376.00 101,622.00 $ (3.86) $ 2.46 (nonzero profits due to rounding)

D. Because the revenue and cost functions both depend on the selling price (P), it is necessary to calculate price before a graph can be created. The demand function can be used to solve for P: Q = 1,000 – 2*P P = (1,000 – Q) / 2 Now a hypothetical data table can be created for units, price, revenues, and costs. The data table is used to create a CVP graph for Q between zero and 1,000 units. Units 0 125 250 375 500 625 750 875 1,000

Price $500 438 375 313 250 188 125 63 0

© 2012 John Wiley and Sons Canada, Ltd.

Revenues $0 54,688 93,750 117,188 125,000 117,188 93,750 54,688 0

Costs $30,000 42,500 55,000 67,500 80,000 92,500 105,000 117,500 130,000

148

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CVP Graph 3.55(D)

Total Cost

$140,000 $120,000 $100,000 $80,000

Dollars

$60,000 $40,000

Breakeven Point

$20,000 $0 0

125

250

375

500

625

750

875

1,000

Number of Units

Break even occurs at the following two points: Q1 = 1,000 – 2*P1 = 1,000 – 2*458.12 = 83.76 units Q2 = 1,000 – 2*P2 = 1,000 – 2*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 with respect to price: Marginal revenue: TR = 1,000*P – 2*P2 First derivative of TR = 1,000 – 4*P Marginal cost: TC = 130,000 - 200*P First derivative of TC = -200 Set marginal revenue equal to marginal cost and solve for P: 1,000 – 4*P = -200 4*P = 1,200 P = $300 per unit © 2012 John Wiley and Sons Canada, Ltd.

Chapter 3: Cost-Volume-Profit Analysis 149 Based on a selling price of $300 per regulator, the company should sell all of the regulators that are demanded at that price: 1,000 – 2*P = 1,000 – 2*300 = 1,000 – 600 = 400 regulators F. In this situation, total revenue is a nonlinear function; the selling price does not remain constant at different levels of activity. The total revenue function is consistent with microeconomic theory, which assumes that quantities sold (i.e., the quantity demanded) will decline as the price increases. G. If the company’s 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. In turn, this means that it is reasonable to assume that the selling price will remain constant in the future within this range of operations (assuming there are no other factors that might influence the price)—i.e., the total revenue function is approximately linear within the range of 375 to 425 regulators per year. Given this assumption, it would be appropriate to use CVP analysis to estimate profits within the relevant range of 375 to 425 regulators per year.

© 2012 John Wiley and Sons Canada, Ltd.