Cost-Volume-Profit Analysis SOLUTIONS

Chapter 3: Cost-Volume-Profit Analysis 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.

96 Cost Management 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 = 1 Margin of Safety Percentage

Chapter 3: Cost-Volume-Profit Analysis 97 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).

98 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.

Chapter 3: Cost-Volume-Profit Analysis 99 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

100 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

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

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.

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.

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 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.

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

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.

108 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

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 3,600,000

110 Cost Management 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 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

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

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.

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

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

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 $ 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.

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

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

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.

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

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

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

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

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.

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.

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

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

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.

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

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.

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