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Communication

CMN 114

Margaret Buckby

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Chapter 3: Cost-Volume-Profit Analy95s
Chapter 3
Cost-Volume-ProfitAnalysis
SOLUTIONS
LEARNING OBJECTIVES
Chapter 3 addresses the following learning objectives:
LO1 Explain the concepts of cost-volume-profit (CVP) analysis in decision making
LO2 Apply CVP calculations for a single product
LO3 Apply CVP calculations multiple products
LO4 Describe the assumptions and limitations that mangers consider when using CVP analysis
LO5 Assess operational risk using margin of safety and operating leverage
LO6 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.
© 2012 John Wiley and Sons Canada, Ltd. 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
1
Degree of Operating Leverage =
Margin of Safety Percentage
© 2012 John Wiley and Sons Canada, Ltd. 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).
© 2012 John Wiley and Sons Canada, Ltd. 98 Cost Management
3.15 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.
© 2012 John Wiley and Sons Canada, Ltd. Chapter 3: Cost-Volume-Profit Analysi99
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) It would decrease by half.
b) It would double.
c) It would triple.
d) It would quadruple.
Ans: D
3.17.What is BioTec’s contribution margin ratio?
a) 60%
b) 40%
c) 30%
d) 20%
Ans: B
3.18.What is the variable cost if the sale price per unit is $40?
a) $ 8.00
b) $16.00
c) $24.00
d) $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) $ 60,000
b) $ 90,000
c) $120,000
d) $180,000
Ans: B
© 2012 John Wiley and Sons Canada, Ltd. 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
© 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
$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.
Total Revenue
CVP Graph 3.22(B)
Total Cost
$1,600,000
$1,200,000
$800,000
$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 Cost Management
3.25 CVP, Solve for Unknowns
Calculations:
Part A Variable Costs Part A Total Costs
CM% = (S – V)/S; FC + VC = Total Costs
60% = ($3,000 – VC) / $3,000 $1,300 + $1,200 = $2,500
60% = ($3,000/$3,000) – (VC/$3,000)
60% = 1 – (VC/$3,000) Part A Operating Income
Sales – Total Costs = OI.
(VC/$3,000) = 1- 60%
VC = (1- 60%) x $3,000 $3,000 - $2,500 = $500
VC = $1,200
Part B Variable Costs Part B Operating Income Part B Contribution Margin %
Total Costs – FC = VC Sales – Total Costs = OI CM%= (S – V)/ S
$4,000-$2,800 = $1,200 $4,000 – $4,000 = $0 CM% = ($4,000 - $1,200)/$4,000
CM% = 70%
Part C Total Costs Part C Variable Costs Part C Contribution Margin %
S – TC = OI Total Costs – FC = VC CM%= (S – V)/ S
$6,000 – TC = $600 $5,400 - $900 = $4,500 CM%= ($6,000 - $4,500) / $6,000
TC = $6,000 - $600 CM%=25%
TC = $5,400
Part D Fixed Costs Part D Sales Part D Contribution Margin %
FC + VC = Total Costs Sales – Total Costs = OI CM%= (S – V)/ S
FC + $1,000 = $1,600 S - $1,600 = $2,400 CM%= ($4,000 - $1,000) / $4,000
FC = $1,600 - $1,000 S = $2,400 + $1,600 CM%=75%
FC = $600 S = $4,000
Summary:
Fixed Variable Total Contributio Operating
Part Sales Costs Costs Costs n Margin % Income
A. $3,000 $1,300 $1,200 $2,500 60% $500
B. $4,000 $2,800 $1,200 $4,000 70% $0
C. $6,000 $900 $4,500 $5,400 25% $600
D. $4,000 $600 $1,000 $1,600 75% $2,400
© 2012 John Wiley and Sons Canada, Ltd. 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 Cost Management
3.27 Profit, Price for Target Profit – Gift4U
Units Per Unit Total %
2,000 $120 $240,000 100.00
Sales %
VC:
Materials 2,000 36 72,000
Labour 2,000 48 96,000
Total VC 84 168,000 70.00%
CM $36 $72,000 30.00%
A. Contribution Margin is $36.
B. Contribution Margin ratio is 30%.
C. Sales break-even:
Total fixed costs:
$43,40
Factory Rent 0
Depreciation
Expense 12,000
Utilities 22,000
Insurance 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 Fixed Variable
Hair dresser salaries $18,000
Manicurist salaries 16,000
Supplies 0 $0.500
Utilities 400
Rent 1,000
Miscellaneous 2,963 0.325
Total $38,363 $0.825
TC = $38,363 + $0.825*appointments
Explanations:
Salaries: The amount of salaries in May is used to predict the next month because 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. 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
© 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 3,600,000
© 2012 John Wiley and Sons Canada, Ltd. 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 $15.00 Current fixed cost $150,000
Less old component (2.50) Plus depreciation on
Plus new component 4.50 new machine $18,000/6 3,000
New variable cost $17.00 New fixed cost $153,000
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. 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.
Total Sales
CVP Graph 3.31(B)
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 Fixed Variable
Direct materials $300,000
Direct labour 200,000
Fixed factory overhead $100,000
Variable factory overhead 150,000
Marketing and Administration 110,000 50,000
Totals $210,000 $700,000
Variable cost per unit = $700,000/100,000 units = $7.00 per unit
Price per unit = $1,000,000/100,000 units = $10.00 per unit
Target pretax income = $120,000/(1-.40) = $200,000
CVP calculation:
($10.00 - $7.00)Q - $210,000 = $200,000
$410,000 = $3.00*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
© 2012 John Wiley and Sons Canada, Ltd. 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 %
10
Sales (100,000 units) $ 10.00 $ 1,000,000 0
Variable
Costs
0.3
Direct Materials $ 3.00 300,000 0
0.2
Direct Labour 2.00 200,000 0
Variable Factory 0.1
Overhead 1.50 150,000 5
Marketing and 0.0
Administration 0.50 50,000 5
0.7
$ 7.00 $ 700,000 0
0.3
Contribution Margin $ 3.00 $ 300,000 0
Fixed Costs
Fixed Factory
Overhead $ 100,000
Marketing and
Administration 110,000
$ 210,000
Budgeted Income
Before Taxes $ 90,000
© 2012 John Wiley and Sons Canada, Ltd. Chapter 3: Cost-Volume-Profit Analysis 117
Newberry's Nutrition
Gross Margin Income Statement
Sales 1,000,000
Cost of Goods Sold
Direct Materials 300,000
Direct Labour 200,000
Variable Factory
Overhead 150,000
Fixed Factory
Overhead 100,000
750,000
Gross Margin 250,000
Non-Manufacturing Expenses
Marketing and
Administration 160,000
Budgeted Income Before Taxes 90,000
3.36 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 Fixed Variable
Wages $100,000
Packing materials 20,000
Rent and Insurance $25,000
Admin and selling 45,000
Total costs $70,000 $120,000
Wages are classified as variable because employees are paid an hourly wage and can be
laid off when there is no work. Packing materials would vary with the number of 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:
Fixed Variable
Cart lease $800
City licence 20
Ingredients 0.40*Sales
Total $820 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) $ 21,032
Breakeven for Premium based on sales mix in revenues:
$107,059*($108,720/$135,300) 86,027
Total corporate sales at breakeven $107,059
E. Breakeven for regular boomerangs ignoring corporate fixed costs:
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 uncertain

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