Post on 20-Jan-2023
Chapter 3
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CHAPTER 3
COST‐VOLUME‐PROFIT ANALYSIS
SHORT‐ANSWER QUESTIONS
3‐1 The assumptions underlying CVP analysis are:
1. Changes in the sales volume and production volume are identical. The ending
balances of inventories are zero.
2. All costs are classified as fixed or variable with no mixed costs.
3. All cost behavior is linear within the relevant volume range.
4. The unit selling price, unit variable costs, fixed costs and sales volume are known.
5. Either the product sold or the product mix remains constant although the volume
changes.
6. All revenues and costs can be added and compared without taking into account
the time value of money.
3‐2 Operating income is total revenues from operations for the accounting period
minus total costs from operations:
Operating income = Total revenues from operations – Total costs from operations
Net income is operating income plus non‐operating revenues (such as interest
revenue) minus non‐operating costs (such as interest cost) minus income taxes.
3‐3 CVP certainly is simple, with its assumption of a single revenue driver, a single
cost driver, and linear revenue and cost relationships. Whether these assumptions make it
simplistic depends on the decision context. In some cases, these assumptions may be
sufficiently accurate for CVP to provide useful insights.
3‐4 An increase in the income tax rate does not affect the breakeven point. Operating
income at the breakeven point is zero and thus no income taxes will be paid at this point.
3‐5 Sensitivity analysis is a “what‐if” technique that examines how a result will
change if the original predicted data are not achieved or if an underlying assumption
changes. The advent of spreadsheet software has greatly increased the ability to explore
the effect of alternative assumptions at minimal cost. CVP is one of the most widely used
software applications in the management accounting area.
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3‐6 Examples include:
• Manufacturing—substituting a robotic machine for hourly wage workers.
• Marketing—changing a sales force compensation plan from a percentage of
sales dollars to a fixed salary.
• Customer service—hiring a subcontractor to do customer repair visits on an
annual retainer basis rather than a per visit basis.
3‐7 Examples include:
• Manufacturing—subcontracting a component to a supplier on a per unit basis
to avoid purchasing a machine with a high fixed amortization cost.
• Marketing—changing a sales compensation plan from a fixed salary to a
percentage of sales dollars basis.
• Customer service—hiring a subcontractor to do customer service on a per visit
basis rather than an annual retainer basis.
3‐8 Operating leverage describes the effects that fixed costs have on changes in
operating income as changes occur in units sold and hence in contribution margin.
Knowing the degree of operating leverage at a given level of sales helps managers
calculate the effect of fluctuations in sales on operating incomes.
3‐9 A company with multiple products can compute a breakeven point by assuming
there is a constant mix of products at different levels of total revenue.
EXERCISES
3‐10 (10 min.) Terminology
1. capital intensive
2. Cost‐volume‐profit analysis
3. breakeven point
4. Operating leverage
5. Risk‐loving
6. contribution margin
7. contribution margin percentage
8. gross margin
9. sales mix
10. Risk aversion
11. margin of safety
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3‐11 (15 min.) CVP analysis computations.
Case Revenues
Variable
Costs
Fixed
Costs
Total
Costs OI CM (S) CM%
a $3,000 $2,290 $250 $2,540 $460 $710 23.67%
b
18,500 7,400 1,300 8,700 9,800 11,100 60.00%
c $10,600 7,420 3,200 10,620 (20) 3,180 30.00%
d
9,450 5,670 2,500 8,170 1,280 3,780 40.00%
Case a: Revenues ‐ Total Costs = Operating Income
$3,000 ‐ Total Costs = $460, Total Costs = $2,540
Total Costs = $2,540 = Variable Costs + Fixed Costs
$2,540 = $250 + Variable Costs, Variable Costs = $2,290
CM = Revenues – Variable Costs = $3,000 ‐ $2,290 = $710
CM % = CM/Revenues = $710 ÷ $3,000 = 23.67%
Case b: Total Costs = Variable Costs + Fixed Costs
$8,700 = $7,400 + Fixed Costs, Fixed Costs = $1,300
Revenue ‐ Total Costs = OI
Revenue ‐ $8,700 = $9,800, Revenue = $18,500
CM = Revenues ‐ Variable Costs = $18,500 ‐ $7,400 = $11,100
CM % = CM/Revenues = $11,100 ÷ $18,500= 60.00%
Case c: CM % = CM/Revenues
30% = CM/$10,600, CM = $3,180
CM = Revenues ‐ Variable Costs
$3,180 = $10,600 ‐ Variable Costs, Variable Costs = $7,420
Total Costs = Variable Costs + Fixed Costs
Total Costs = $7,420 + $3,200 = $10,620
OI = Revenues ‐ Total Costs = $10,600 ‐ $10,620 = ($20)
Case d: Total Costs = Variable Costs + Fixed Costs
$8,170 = Variable Costs + $2,500, Variable Costs = $5,670
OI = Revenues ‐ Total Costs = $9,450 ‐ $8,170 = $1,280
CM = Revenues ‐ Variable Costs = $9,450 ‐ $5,670 = $3,780
CM % = CM/Revenues = $3,780 ÷ $9,450= 40.00%
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3‐12 (15 min.) CVP analysis computations.
Case
Unit Selling
Price
Unit
VC
Units
Sold TCM Fixed Costs OI
A $70 $25
20,000 $900,000 $700,000 $200,000
B
87 62 15,000 375,000 250,000 125,000
C 250 100
30,000 4,500,000 3,600,000 900,000
D 150 78
24,000 1,728,000 1,500,000 228,000
a. TCM = Q (USP ‐ UVC)
$900,000 = Q ($70 ‐ $25)
Q = 20,000
TFC = TCM ‐ OI
= $900,000 ‐ $200,000 = $700,000
b. OI = TCM ‐ TFC
$125,000 = TCM ‐ $250,000
TCM = $375,000
TCM = Q (USP ‐ UVC)
$375,000 = 15,000 (USP ‐ $62)
$25 = (USP ‐ $62)
USP = $87
c. OI = TCM ‐ TFC
$900,000 = $4,500,000 ‐ TFC
TFC = $3,600,000
TCM = Q (USP ‐ UVC)
$4,500,000 = 30,000 ($250 ‐ UVC)
$150 = $250 ‐ UVC
UVC = $100
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3‐12 (cont’d)
d. OI = TCM ‐ TFC
OI = $1,728,000 ‐ $1,500,000
OI = $228,000
TCM = Q (USP ‐ UVC)
$1,728,000 = 24,000 ($150 ‐ UVC)
$72 = $150 ‐ UVC
UVC = $78
3‐13 (10 min.) CVP computations.
1a. Sales ($30 per unit × 200,000 units) $6,000,000
Variable costs ($25 per unit × 200,000 units) 5,000,000
Contribution margin $1,000,000
1b. Contribution margin (from above) $1,000,000
Fixed costs 800,000
Operating income $ 200,000
2a. Sales (from above) $6,000,000
Variable costs ($16 per unit × 200,000 units) 3,200,000
Contribution margin $2,800,000
2b. Contribution margin $2,800,000
Fixed costs 2,400,000
Operating income $ 400,000
3. Operating income is expected to increase by $200,000 if Ms. Schoenen’s proposal
is accepted.
The management would consider other factors before making the final decision.
It is likely that product quality would improve as a result of using state of the art
equipment. Due to increased automation, probably many workers will have to be laid
off. Patel’s management will have to consider the impact of such an action on employee
morale. In addition, the proposal increases the company’s fixed costs dramatically. This
will increase the company’s operating leverage and risk.
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3‐14 (10 min.) CVP analysis, income taxes.
1. Monthly fixed costs = $60,000 + $70,000 + $10,000 = $140,000
Contribution margin per unit = $26,000 ‐ $22,000 ‐ $500 = $3,500
Breakeven units per month = Monthly fixed costs
Contribution margin per unit =
$140,000
$3,500 per car = 40 cars
2. Tax rate = 40%
Target net income = $63,000
Target operating income =Target net income $63,000 $63,000
1 - tax rate (1 0.40) 0.60
$105,000
Quantity of output unitsrequired to be sold =
Fixed costs + Target operating income $140,000 $105,000
Contribution margin per unit $3,500
70 cars
3‐15 (10 min.) CVP analysis, income taxes
1. Monthly fixed costs = $28,000 + $45,000 + $5,600 + $1,200 = $79,800
CM per unit = $16,000 ‐ $12,200 = $3,800
Breakeven = Monthly Fixed Costs ÷ UCM
= $79,800 ÷ $3,800 = 21 mowers
2. OI = Target Net Income ÷ [1 ‐ tax rate]
OI = $42,750 ÷ [1 ‐ 0.25]
OI = $57,000
Q = Fixed Costs + Target OI
Unit CM
Q = [$79,800 + $57,000] ÷ $3,800
= 36 mowers
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3‐16 (20 min.) CVP analysis, income taxes.
1. Variable cost percentage is $3.20 $8.00 = 40%
Let R = Revenues needed to obtain target net income
R ‐ 0.40R ‐ $450,000 = 30.01
000,105$
0.60R = $450,000 + $150,000
R = $600,000 0.60 R = $1,000,000
Proof: Revenues $1,000,000
Variable costs (at 40%) 400,000
Contribution margin 600,000
Fixed costs 450,000
Operating income 150,000
Income taxes (at 30%) 45,000
Net income $ 105,000
2.a. Customers needed to earn net income of $105,000:
Total revenues Sales check per customer: $1,000,000 $8 = 125,000 customers
b. Customers needed to break even:
Contribution margin per customer = $8.00 ‐ $3.20 = $4.80
Breakeven number of customers = Fixed costs Contribution margin per customer
= $450,000 $4.80 per customer
= 93,750 customers
3. Using the shortcut approach:
Change in net income =
Change in
number of customers
Unit
contribution
margin (1 ‐ Tax rate)
= (150,000 ‐ 125,000) $4.80 (1 ‐ 0.30) = $120,000 0.7 = $84,000 New net income = $84,000 + $105,000 = $189,000
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3‐16 (cont’d)
The alternative approach is:
Revenues, 150,000 $8.00 $1,200,000
Variable costs at 40% 480,000
Contribution margin 720,000
Fixed costs 450,000
Operating income 270,000
Income tax at 30% 81,000
Net income $ 189,000
3‐17 (15 min.) Gross margin and contribution margin.
1.
Ticket sales ($20 500 attendees) $10,000
Variable cost of dinner ($10a500 attendees) $5,000
Variable invitations and paperwork ($1b 500) $500
Contribution margin 4,500
Fixed cost of dinner 6,000
Fixed cost of invitations and paperwork 2,500 8,500
Operating profit (loss) $ (4,000)a $5,000/500 attendees = $10/attendee b $500/500 attendees = $1/attendee
2.
Ticket sales ($20 1,000 attendees) $20,000
Variable cost of dinner ($10a1,000 attendees)
$10,000
Variable invitations and paperwork ($1b
1,000) $1,000
Contribution margin 9,000
Fixed cost of dinner 6,000
Fixed cost of invitations and paperwork 2,500 8,500
Operating profit (loss) $ 500
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3‐18 (20 min.) Scholarships, CVP analysis.
1. Full course load = 30 credits
Tuition fees for full course load = 30 credits x $400 = $12,000
Let the number of scholarships be denoted by Q.
Then, $600,000 + $12,000Q = $4,500,000
$12,000Q = $4,500,000 ‐ $600,000
$12,000Q = $3,900,000
Q = 325 scholarships
2. Total budget for next year = $4,500,000 (1 ‐ 0.20) = $4,500,000 x 0.80
= $3,600,000
Then, 600,000 + $12,000Q = $3,600,000
$12,000Q = $3,600,000 ‐ $600,000
Q = $3,000,000 ÷ $12,000 = 250 scholarships
3. Let the scholarship award per student per year be denoted by V.
Then, $600,000 + 325V = $3,600,000
325V = $3,600,000 ‐ $600,000
V = $3,000,000 ÷ 325 = $9,230.77
3‐19 (35–40 min.) CVP analysis, changing revenues and costs.
1a. SP = 8% × $1,000 = $80 per ticket
UVC = $35 per ticket
UCM = $80 ‐ $35 = $45 per ticket
FC = $22,000 a month
Q = UCM
FC =
per ticket $45
$22,000= 489 tickets (rounded up)
1b. Q = UCM
TOI FC =
per ticket $45
$10,000 $22,000 =
per ticket $45
$32,000= 712 tickets (rounded up)
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3‐19 (cont’d)
2a. SP = $80 per ticket
VCU = $29 per ticket
UCM = $80 ‐ $29 = $51 per ticket
FC = $22,000 a month
Q = UCM
FC =
per ticket $51
$22,000= 432 tickets (rounded up)
2b. Q = UCM
TOI FC =
per ticket $51
$10,000 $22,000 =
per ticket $51
$32,000= 628 tickets (rounded up)
3a. SP = $48 per ticket
VCU = $29 per ticket
CMU = $48 ‐ $29 = $19 per ticket
FC = $22,000 a month
Q = UCM
FC =
per ticket $19
$22,000= 1,158 tickets (rounded up)
3b. Q = UCM
TOI FC =
per ticket $19
$10,000 $22,000 =
per ticket $19
$32,000= 1,685 tickets (rounded up)
4a. The $5 delivery fee can be treated as either an extra source of revenue (as done
below) or as a cost offset. Either approach increases CMU $5:
SP = $53 ($48 + $5) per ticket
VCU = $29 per ticket
CMU = $53 ‐ $29 = $24 per ticket
FC = $22,000 a month
Q = CMU
FC =
per ticket $24
$22,000= 917 tickets (rounded up)
4b. Q = CMU
TOI FC =
per ticket $24
$10,000 $22,000 =
per ticket $24
$32,000= 1,334 tickets (rounded up)
The $5 delivery fee results in a higher contribution margin, which reduces both
the breakeven point and the tickets sold to attain operating income of $10,000.
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3‐20 (20 min.) Contribution margin, gross margin and margin of safety.
1.
Mirabel Cosmetics
Operating Income Statement, June 2012
Units sold 10,000
Revenues $100,000
Variable costs
Variable manufacturing costs $ 55,000
Variable marketing costs 5,000
Total variable costs 60,000
Contribution margin 40,000
Fixed costs
Fixed manufacturing costs $ 20,000
Fixed marketing & administration costs 10,000
Total fixed costs 30,000
Operating income $ 10,000
2. Contribution margin per unit = $40,000
$4 per unit10,000 units
Breakeven quantity = Fixed costs $30,000
7,500 unitsContribution margin per unit $4 per unit
Selling price = Revenues $100,000
$10 per unitUnits sold 10,000 units
Breakeven revenues = 7,500 units $10 per unit = $75,000
Alternatively,
Contribution margin percentage = Contribution margin $40,000
40%Revenues $100,000
Breakeven revenues = Fixed costs $30,000
$75,000Contribution margin percentage 0.40
3. Margin of safety = 10,000 units ‐ 7,500 units = 2,500 units
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3‐20 (cont’d)
4. Units sold 8,000
Revenues (Units sold Selling price = 8,000 $10) $80,000
Contribution margin (Revenues CM percentage = $80,000 40%) $32,000
Fixed costs 30,000
Operating income 2,000
Taxes (30% $2,000) 600
Net income $ 1,400
3‐21 CVP computations.
1. (a) 5,000,000 ($0.60 ‐ $0.36) ‐ $1,080,000 = $120,000
(a) 1,080,000 ÷ [($0.60 ‐ $0.36) ÷ $0.60] = $2,700,000
2. 5,000,000 ($0.60 ‐ $0.408) ‐ $1,080,000 = $(120,000)
3. [5,000,000 (1.1) ($0.60 ‐ $0.36)] ‐ [$1,080,000 (1.1)] = $132,000
4. [5,000,000 (1.4) ($0.48 ‐ $0.324)] ‐ [$1,080,000 (0.8)] = $228,000
5. $1,080,000 (1.1) ÷ ($0.60 ‐ $0.36) = 4,950,000 units
6. ($1,080,000 + $24,000) ÷ ($0.66 ‐ $0.36) = 3,680,000 units
3‐22 (15 min.) CVP exercises.
1. Total CM = $3,240,000 48% = $1,555,200 CM = Revenues ‐ Variable Costs
$1,555,200 = $3,240,000 ‐ Variable Costs, VC = $1,684,800
Units Sold = $3,240,000 ÷ $36 = 90,000
Per Unit Dollars %
Revenues @ $36/unit (given) $36.00 $3,240,000 100%
Variable Costs $18.72 $1,684,800 52%
Contribution Margin $17.28 $1,555,200 48%
Fixed Costs (given) $730,000
Budgeted Operating Income $825,200
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3‐22 (cont’d)
2. New Fixed Costs = $730,000 ‐ ($730,00015%) = $620,500
New unit CM = 42% $36 = $15.12
Per Unit Dollars %
Revenues @ $36/unit (given) $36.00 $3,240,000 100%
Variable Costs $20.88 $1,879,200 58%
Contribution Margin $15.12 $1,360,800 42%
Fixed Costs (given) $620,500
Budgeted Operating Income $740,300
3. New Selling Price = $36 1.1 = $39.60 New Volume = 90,000 .95 = 85,500 VC = 85,500 $18.72 = $1,600,560
Per Unit Dollars
Revenues $39.60 $3,385,800
Variable Costs $18.72 $1,600,560
Contribution Margin $20.88 $1,785,240
Fixed Costs (given) $730,000
Budgeted Operating Income $1,055,240
4. Increasing the selling price results in the highest budgeted operating income of the
alternatives suggested. However, this higher income is based on an assumption that
volume will only be reduced by 5% if the price is increased. The company may want to
perform additional sensitivity analysis on the volume.
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3‐23 (25 min.) Operating leverage.
1. Let Q denote the quantity of bracelets sold
a. Breakeven point under Option 1
$125Q ‐ $80Q = ($435 3) $45Q = $1,305
Q = 29 bracelets
b. Breakeven point under Option 2
$125Q ‐ $80Q ‐ (0.12 $125Q) = 0 $30Q = 0
Q = 0
All costs are variable and therefore can be avoided.
2. Operating income under Option 1 = $45Q ‐ $1,305
Operating income under Option 2 = $30Q
Find Q such that $45Q ‐ $1,305 = $30Q
$15Q = $1,305
Q = 87
87 is the mathematical point of indifference.
Option 1: $125(87) ‐ $80(87) ‐ ($435 3) = $2,610 Option 2: $125(87) ‐ $80(87) ‐ $15(87) = $2,610
3. a. For Q > 87, say, 88,
Option 1 gives operating income = $45 88 ‐ $1,305 = $2,655 better Option 2 gives operating income = $30 88 = $2,640 Rothman will prefer Option 1.
3. b. For Q < 87, say, 86,
Option 1 gives operating income = $45 86 ‐ $1,305 = $2,565 Option 2 gives operating income = $30 86 = $2,580 better Rothman will prefer Option 2.
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3‐23 (cont’d)
4. Degree of operating leverage = CM ÷ Operating Income
Under Option 1, the total CM = $45 150 units = $6,750
Operating Income = $6,750 ‐ $1,305 = $5,445
The Degree of Operating Leverage (Opt 1) = $6,750 ÷ $5,445 = 1.24
Under Option 2, the total CM = OI = $30 150 = $4,500 The Degree of Operating Leverage (Opt 2) = $4,500 ÷ $4,500 = 1.00
5. The calculations in requirement 4 indicate that, when sales are 150 units, a
percentage change in sales and contribution margin will result in 1.24 times that
percentage change in operating income for Option 1, but the same percentage change in
operating income for Option 2. The degree of operating leverage at a given level of sales
helps managers calculate the effect of fluctuations in sales on operating incomes.
3‐24 (15 min.) Gross margin and contribution margin, making decisions.
1. Revenues $800,000
Deduct variable costs:
Cost of goods sold $384,000
Sales commissions 96,000
Other operating costs 32,000 512,000
Contribution margin $288,000
2. Contribution margin percentage = %00.36000,800$
000,288$
3. Incremental revenue (25% $800,000) $200,000
Incremental contribution margin (36% $200,000) 72,000
Incremental fixed costs (advertising) 24,300
Incremental operating income $47,700
If Mr. Saunders increases his advertising, the operating income will increase by
$47,700 converting an operating loss of $44,700 to an operating income of $3,000.
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3‐24 (cont’d)
Proof (Optional):
Variable Other Operating Costs = $32,000 ÷ $800,000 = 4% of sales
Revenues (125% $800,000) $1,000,000
Cost of goods sold (48% of sales) 480,000
Gross margin 520,000
Operating costs:
Store rent $61,200
Salaries and wages 212,000
Sales commissions (12% of sales) 120,000
Amortization of equipment and fixtures 19,200
Other operating costs:
Variable (4% of sales) 40,000
Fixed 64,600 517,000
Operating income $ 3,000
3‐25 (20 min.) CVP, revenue mix.
1.
Men’s Dominator Ladies Luxury
Selling Price $750 $640
Variable Cost $475 $390
Sales Commission $25 $21
Unit CM $250 $229
2. Weighted Average CM = (70% $250) + (30% $229) = $175 + $68.70 = $243.70
3. Units required = Fixed Costs + Target OI
Weighted Average CM
= ($180,000 + $115,000) ÷ $243.70
= 1,210.5 or 1,211 total units
Men’s Dominator = 70% 1,211 = 848 units (rounded up) Ladies Luxury = 30% 1,211 = 363 units (rounded down)
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3‐25 (cont’d)
Proof:
Men’s Dominator Ladies Luxury
Unit CM $250 $229
Units Sold 848 363
Total CM $212,000 $83,127
Total CM – Fixed Costs = Operating Income
($212,000 + $83,127) ‐ $180,000 = $115,127 (difference is due to rounding of units)
3‐26 (30 min.) CVP, international cost structure differences.
1a. India China Canada
Selling Price $ 47.50 $ 47.50 $ 47.50
VC‐Manufacturing $ 5.20 $ 9.50 $ 19.30
VC‐Distribution $ 21.80 $ 18.40 $ 6.20
Total Variable Costs $ 27.00 $ 27.90 $ 25.50
Unit CM $ 20.50 $ 19.60 $ 22.00
Fixed Costs $6,400,000 $4,400,000 $10,200,000
B/E point b/a (units) 312,196 224,490 463,637
1b.
B/E point in revenues (Units $47.50) $14,829,310 $10,663,275 $22,022,757
2. Volume 1,350,000 1,350,000 1,350,000
Total CM (Volume UCM) $ 27,675,000 $ 26,460,000 $ 29,700,000
Less Fixed Costs $6,400,000 $4,400,000 $10,200,000
Forecasted OI $ 21,275,000 $ 22,060,000 $ 19,500,000
China has the lowest breakeven point—it has the lowest fixed costs ($4,400,000) and
its variable cost per unit ($27.90) is only marginally higher than India. While Canada has
a higher per unit CM, the fixed costs are more than double those of China. The higher
fixed costs add risk to operating in Canada (leverage).
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3‐26 (cont’d)
3. China’s OI = $19.60 per unit less Fixed Costs of $4,400,000
Canada’s OI = $22.00 per unit less Fixed Costs of $10,200,000
$19.60X ‐ $4,400,000 = $22.00X ‐ $10,200,000
$5,800,000 = $2.40X
X = 2,416,666.667 (or 2,416,667)
Proof and India’s Operating Income at same sales volume
India China Canada
Unit CM $ 20.50 $ 19.60 $ 22.00
Volume 2,416,666.667 2,416,666.667 2,416,666.667
Total CM (Volume UCM) $49,541,667 $ 47,366,667 $ 53,166,667
Less Fixed Costs $6,400,000 $4,400,000 $10,200,000
Forecasted OI $43,141,667 $ 42,966,667 $ 42,966,667
(Note: India’s forecasted OI is slightly higher at this volume)
3‐27 (25 min.) CVP, Not for profit
1. Contributions $19,000,000
Fixed costs 1,000,000
Cash available to purchase land $18,000,000
Divided by cost per hectare to purchase land ÷3,000
Hectares of land SG can purchase 6,000 hectares
2. Contributions ($19,000,000 ‐ $5,000,000) $14,000,000
Fixed costs 1,000,000
Cash available to purchase land $13,000,000
Divided by cost per hectare ($3,000 ‐ $1,000) ÷2,000
Hectares of land SG can purchase 6,500 hectares
On financial considerations alone, SG should take the subsidy because it can
purchase 500 more hectares (6,500 ‐ 6,000).
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3‐27 (cont’d)
3. Let the decrease in contributions be$x . Cash available to purchase land = $19,000,000 ‐ $x ‐ $1,000,000
Cost to purchase land = $3,000 ‐ $1,000 = $2,000
To purchase 6,000 hectares, we solve the following equation for x .
19,000,000 1,000,0006,000
2,000
18,000,000 6,000 2,000
18,000,000 12,000,000$6,000,000
x
x
xx
SG will be indifferent between taking the government subsidy or not if
contributions decrease by $6,000,000.
3‐28 (30 min.) CVP, revenue mix
Zyrcon
1. Alien Predators
Vegas
Pokermatch
Revenue $89 $59
Variable Manufacturing Costs 18 12
Variable Marketing Costs 27 16
Total Variable Costs 45 28
Unit CM $44 $31
Sales Mix 40% 60%
Weighted CM $17.60 $18.60
Weighted CM = $17.60 + $18.60 = $36.20
Breakeven in total units = Fixed Costs ÷ Weighted CM
= $18,750,000 ÷ $36.20
= 517,956 units
40% of 517,596 = 207,183 units of Alien Predators
60% of 517,596 = 310,773 units of Vegas Pokermatch
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-76 Copyright © 2013 Pearson Canada Inc.
3‐28 (cont’d)
Proof:
OI = Total CM ‐ Fixed Costs
OI = ($44 207,183) + ($31 310,773) ‐ $18,750,000 OI = $9,116,052 + $9,633,963 ‐ $18,750,000
OI = $15 (difference due to rounding of units)
2. Alien Predators Vegas Pokermatch
Revenue $89 $59
Variable Manufacturing Costs 18 12
Variable Marketing Costs 27 16
Total Variable Costs 45 28
Unit CM $44 $31
Sales Mix 25% 75%
Weighted CM $11.00 $23.25
Weighted CM = $11.00 + $23.25 = $34.25
Breakeven in total units = Fixed Costs ÷ Weighted CM
= $18,750,000 ÷ $34.25
= 547,446 units
25% of 547,446 = 136,862 units of Alien Predators
75% o‐f 547,446 = 410,584 units of Vegas Pokermatch
Proof:
OI = Total CM ‐ Fixed Costs
OI = ($44 136,862) + ($31 410,584) ‐ $18,750,000 OI = $6,021,928 + $12,728,104 ‐ $18,750,000
OI = $32 (difference due to rounding of units)
3. 40%/60% Mix 25%/75% Mix
Weighted CM $36.20 $34.25
Unit Sales 750,000 750,000
Total CM $27,150,000 $25,687,500
Fixed Costs 18,750,000 18,750,000
OI $8,400,000 $6,937,500
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-77
3‐29 (40 min.) Alternative cost structures, uncertainty, and sensitivity analysis.
1. Contribution margin assuming fixed rental arrangement = $50 ‐ $30 = $20 per
bouquet
Fixed costs = $5,000
Breakeven point = $5,000 ÷ $20 per bouquet = 250 bouquets
Contribution margin assuming $10 per arrangement rental agreement
= $50 ‐ $30 ‐ $10 = $10 per bouquet
Fixed costs = $0
Breakeven point = $0 ÷ $10 per bouquet = 0
2. Let x denote the number of bouquets EB must sell for it to be indifferent
between the fixed rent and royalty agreement.
To calculate x we solve the following equation.
$50 x ‐ $30 x ‐ $5,000 = $50 x ‐ $40 x $20 x ‐ $5,000 = $10 x $10 x = $5,000 x = $5,000 ÷ $10 = 500 bouquets
For sales between 0 to 500 bouquets, EB prefers the royalty agreement because in
this range, $10 x > $20 x ‐ $5,000. For sales greater than 500 bouquets, EB prefers the fixed rent agreement because in this range, $20 x ‐ $5,000 > $10 x .
3. If we assume the $5 savings in variable costs applies to both options, we solve
the following equation for x .
$50 x ‐ $25 x ‐ $5,000 = $50 x ‐ $35 x $25 x ‐ $5,000 = $15 x $10 x = $5,000 x = $5,000 ÷ $10 per bouquet = 500 bouquets
The answer is the same as in Requirement 2, that is, for sales between 0 to 500
bouquets, EB prefers the royalty agreement because in this range, $15 x > $25 x ‐ $5,000. For sales greater than 500 bouquets, EB prefers the fixed rent agreement because in this
range, $25 x ‐ $5,000 > $15 x .
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-78 Copyright © 2013 Pearson Canada Inc.
3‐29 (cont’d)
4. Fixed rent agreement:
Bouquets
Sold
(1)
Revenue
(2)
Fixed
Costs
(3)
Variable
Costs
(4)
Operating
Income
(Loss)
(5)=(2)–(3)–(4) Probability
(6)
Expected
Operating
Income
(7)=(5) (6)200 200$50=$10,000 $5,000 200$30=$ 6,000 $ (1,000) 0.20 $ ( 200)
400 400$50=$20,000 $5,000 400$30=$12,000 $ 3,000 0.20 600
600 600$50=$30,000 $5,000 600$30=$18,000 $ 7,000 0.20 1,400
800 800$50=$40,000 $5,000 800$30=$24,000 $11,000 0.20 2,200
1,000 1,000$50=$50,000 $5,000 1,000$30=$30,000 $15,000 0.20 3,000
Expected value of rent agreement $7,000
Royalty agreement:
Bouquets
Sold
(1)
Revenue
(2)
Variable
Costs
(3)
Operating
Income
(4)=(2)–(3)
Probability
(5)
Expected Operating
Income
(6)=(4) (5) 200 200$50=$10,000 200$40=$ 8,000 $2,000 0.20 $ 400
400 400$50=$20,000 400$40=$16,000 $4,000 0.20 800
600 600$50=$30,000 600$40=$24,000 $6,000 0.20 1,200
800 800$50=$40,000 800$40=$32,000 $8,000 0.20 1,600
1,000 1,000$50=$50,000 1,000$40=$40,000 $10,000 0.20 2,000
Expected value of royalty agreement $6,000
EB should choose the fixed rent agreement because the expected value is higher
than the royalty agreement. EB will lose money under the fixed rent agreement if EB
sells only 200 bouquets but this loss is more than made up for by high operating
incomes when sales are high.
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-79
3‐30 (20 min.) CVP analysis, multiple cost drivers.
1. 350,000 pens sold, order size 100
2. 350,000 pens sold, order size 250
Per 100 Each Pen
Costs to buy pens $ 95.00 $ 0.95
Imprinting Costs $ 35.00 $ 0.35
Total Variable Costs $130.00 $ 1.30
Revenues 350,000 $4.50 $1,575,000
Variable Costs 350,000 $1.30 $455,000
Contribution
Margin $1,120,000
Setups (350,000/100) $120 $420,000
Product Margin $700,000
Fixed Costs $275,000
OI $425,000
Revenues 350,000 $4.50 $1,575,000
Variable Costs 350,000 $1.30 $455,000
Contribution
Margin $1,120,000
Setups (350,000/250) $120 $168,000
Product Margin $952,000
Fixed Costs $275,000
OI $677,000
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-80 Copyright © 2013 Pearson Canada Inc.
3‐30 (cont’d)
3. Unit Margins, Breakevens & Setups at various order sizes
Order Size 50 units/order 100 units/order 250 units/order 500 units/order
Setup Costs $120.00 $120.00 $120.00 $120.00
Setup/unit $2.40 $1.20 $0.48 $0.24
VC/Unit $1.30 $1.30 $1.30 $1.30
Subtotal $3.70 $2.50 $1.78 $1.54
Revenues $4.50 $4.50 $4.50 $4.50
Unit Margin $0.80 $2.00 $2.72 $2.96
Fixed Costs $275,000 $275,000 $275,000 $275,000
Breakeven
FC/Unit Marg
343,750 units 137,500 units 101,103 units 92,906 units
Number of setups
at breakeven point
6,875 setups 1,375 setups 404 setups 186 setups
The breakeven point is not unique because there are two cost drivers—quantity of
pens and number of setups. Various combinations of the two cost drivers can yield zero
operating income.
3‐31 (15‐20 min.) Uncertainty, CVP.
1. King pays Couture $3.2 million plus $6.75 (25% of $27.00) for every home
purchasing the pay‐per‐view. The expected value of the variable component is:
Demand Payment Probability Expected payment
(1) (2) = (1) $6.75 (3) (4) = (2) (3) 250,000 $ 1,687,500 0.05 $ 84,375
300,000 2,025,000 0.10 202,500
350,000 2,362,500 0.20 472,500
400,000 2,700,000 0.40 1,080,000
500,000 3,375,000 0.15 506,250
1,000,000 6,750,000 0.10 675,000
$3,020,625
The expected value of King’s payment is $6,220,625 ($3,200,000 fixed fee +
$3,020,625).
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Copyright © 2013 Pearson Canada Inc. 3-81
3‐31 (cont’d)
2. USP = $27.00
UVC = $9.00 ($6.75 payment to Couture + $2.25 variable cost)
UCM = $18.00
FC = $3,200,000 + $1,300,000 = $4,500,000
Q = FC
UCM = $4,500,000 ÷ $18 = 250,000
If 250,000 homes purchase the pay‐per‐view, King will break even.
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-82 Copyright © 2013 Pearson Canada Inc.
PROBLEMS
3‐32 (20‐30 min.) Effects on operating income, pricing decision.
1. Analysis of special order:
Sales, 5,000 units $98 $490,000
Variable costs:
Direct materials, 5,000 units $48 $240,000
Direct manufacturing labour, 5,000 units $16 80,000
Variable manufacturing overhead, 5,000 units $8 40,000
Other variable costs, 5,000 units $7 35,000
Sales commission, flat rate 9,500
Total variable costs 404,500
Contribution margin $ 85,500
Note that the variable costs, except for commissions, are affected by production
volume, not sales dollars.
If the order is accepted, operating income increases by $85,500.
4. Whether the general manager is making a correct decision depends on many
factors. He is incorrect if the capacity would otherwise be idle and if his objective is to
increase operating income in the short run. If the offer is rejected, Teguchi, in effect, is
willing to invest $85,500 in immediate gains forgone (an opportunity cost) to preserve the
long‐run selling‐price structure. He is correct if he thinks future competition or future
price concessions to customers will hurt Teguchi’s operating income by more than
$85,500.
There is also the possibility that Andrews could become a long‐term customer. In
this case, is a price that covers only short‐run variable costs adequate? Would the sales
representative be willing to accept the lower flat sales commission (as distinguished from
the regular $58,800 = 12% $490,000) on a long term basis?
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-83
3‐33 (20‐30 min.) CVP, executive teaching compensation.
1. (a) Advertising in magazines $5,200
Mailing of brochures 2,500
Administrative labour at UKBS 3,700
Charge for UKBS lecture auditorium 1,800
Airfare and accommodation 3,800
Lecture fee 2,750
Total fixed costs $19,750
Meals and drinks $38
Binders and photocopying 37
Unit variable cost $75
Unit contribution margin = Unit revenues – Unit variable costs
= $350 ‐ $75
= $275
Breakeven point = Fixed costs
Unit contribution margin
= $19,750 ÷ $275
= 71.82 or 72 attendees
(b) Advertising in magazines $5,200
Mailing of brochures 2,500
Administrative labour at UKBS 3,700
Charge for UKBS lecture auditorium 1,800
Total fixed costs $13,200
Unit contribution margin = $275
Breakeven point = Fixed costs
Unit contribution margin
= $13,200 ÷ $275
= 48 attendees
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-84 Copyright © 2013 Pearson Canada Inc.
3‐33 (cont’d)
The breakeven point drops from 72 attendees to 48 attendees—the $6,550 ($3,800 +
$2,750) package to Smith requires 24 attendees with a unit contribution margin of $275 to
be recouped. In the regular compensation package, Hutchison’s expense allowance and
lecture speaking fee of $6,550 is a fixed cost to UKBS. In contrast, with Hutchison’s
suggested compensation package, UKBS has no cost item (either fixed or variable) for
Hutchison up to its breakeven point. Beyond the breakeven point, Hutchison receives 50%
of the operating income from the one‐day program.
2. Operating income to UKBS = $350N ‐ $75N ‐ $13,200
2009 2010 2011
Attendees 60 75 120
Revenues $21,000 $26,250 $42,000
VC 4,500 5,625 9,000
CM 16,500 20,625 33,000
Fixed Costs 13,200 13,200 13,200
OI 3,300 7,425 19,800
Smith’s share
(50%) $1,650 $3,712.50 $9,900
3. This question raises a broad set of issues:
(a) Hutchison has taken a high level of risk with a compensation plan that only pays
him the guaranteed $6,550 under the regular plan. In both 2009 and 2010, he received less
than the $6,550 figure. Hutchison could comment to the Dean that if the UKBS finds the
risk‐sharing program attractive in periods of low demand, it should be willing to share
the revenues in periods of high demand.
(b) Hutchison could stress to UKBS how much they both have gained from the one‐
day seminars. UKBS has made an operating income each year. In addition, only some of
UKBS’s fixed costs are cash outflows. For example, the $1,800 charge for use of the lecture
auditorium is not a cash outflow. If the auditorium would not be otherwise used that
day, UKBS may well view the $1,800 amount as quite different from the cash outlay
items.
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-85
3‐33 (cont’d)
(c) Hutchison could respond to the Dean that the agreement is not really a 50%/50%
profit‐sharing plan. It considers only the UKBS costs. Assume Hutchison pays $3,300 for
airfare/accommodation. Then, in 2009 he actually lost $1,650 ($1,650 ‐ $3,300) for giving
the seminar, while in 2010 he received only $412.50 ($3,712.50 ‐ $3,300).
(d) If Hutchison views the Dean as adamant in wanting to change the formula, he
could consider negotiating with another university or organization to handle the
planning and marketing of the seminar.
3‐34 (20 Min.) CVP computations with sensitivity analysis
1. USP = $36.00 � (1 ‐ 0.30 margin to bookstore)
= $36.00 � 0.70 = $25.20
UVC = $4.80 variable production and marketing cost
3.78 variable author royalty cost (0.15 � $36.00 � 0.70)
$8.58
UCM = $25.20 ‐ $8.58 = $16.62
FC = $600,000 fixed production and marketing cost
3,600,000 up‐front payment to Washington
$4,200,000
(a) Breakeven number in units = $4,200,000 ÷ $16.62 = 252,708 copies sold
(rounded)
(b) Target OI = ($4,200,000 + $2,400,000) ÷ $16.62 = 397,112 copies sold (rounded)
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-86 Copyright © 2013 Pearson Canada Inc.
3‐34 (cont’d)
2. (a) Decreasing the normal bookstore margin to 20% of the listed bookstore price
of $36 has the following effects:
USP = $36.00 � (1 ‐ 0.20)
= $36.00 � 0.80 = $28.80
UVC = $4.80 + $4.32 (0.15 � $36.00 � 0.80) = $9.12
UCM = $28.80 ‐ $9.12 = $19.68
Breakeven number of units = $4,200,000 ÷ $19.68 = 213,415 copies sold (rounded)
(b) Increasing the listed bookstore price to $48 while keeping the bookstore margin
at 30% has the following effects:
USP = $48.00 � (1 ‐ 0.30)
= $36.00 � 0.70 = $33.60
UVC = $4.80 + $5.04 (0.15 � $48.00 � 0.70) = $9.84
UCM = $33.60 ‐ $9.84 = $23.76
Breakeven number of units = $4,200,000 ÷ $23.76 = 176,768 copies sold (rounded)
3‐35 (15‐20 min.) CVP analysis, service firm.
1. Revenue per package $9,200
Variable cost per package 6,340
Contribution margin per package $2,860
Breakeven (units) = Fixed costs ÷ Contribution margin per package
= $1,287,000 ÷ $2,860 = 450 package tours
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-87
3‐35 (cont’d)
2. Contribution margin ratio = Contribution margin per package
Selling price = $2,860 ÷ $9,200
=31.09%
Units needed to achieve target income = (Fixed costs + target OI) ÷ UCM
= ($1,287,000 + $214,500) ÷ $2,860 = 525 packages
Revenues to earn $214,500 OI = 525 tour packages $9,200= $4,830,000
or
Revenue to achieve target income = (Fixed costs + target OI) ÷ CM ratio
= ($1,287,000 + $214,500) ÷ .3109
= $4,829,527 (rounding difference)
3. Fixed costs = $1,287,000 + $40,500 = $1,327,500
Breakeven (units) = Fixed costs
Contribution margin per unit
Contribution margin per unit = $1,327,500 ÷ 450
= $2,950 per tour package
Desired variable cost per tour package = $9,200 – $2,950 = $6,250
Because the current variable cost per unit is $6,340 the unit variable cost will need to
be reduced by $90 to achieve the breakeven point calculated in requirement 1.
Alternate Method: If fixed cost increases by $40,500 then total variable costs must be
reduced by $40,500 or $40,500/450 or $90 per package tour.
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-88 Copyright © 2013 Pearson Canada Inc.
3‐36 (30 min.) CVP, target operating income and net income
1. Selling price to break even
(USP ‐ UVC) Q ‐ Fixed Costs = $0
(USP ‐ $24.75) 80,000 ‐ $800,000 = $0
(USP ‐ $24.75) = $800,000 ÷ 80,000
USP ‐ $24.75 = $10
USP = $34.75
2.
[USP ‐ $24.75] 60,000 = (0.20USP 60,000) + Fixed Costs 60,000USP ‐ $1,485,000 = 12,000USP + $800,000
48, 000USP = $2,285,000
USP = $47.61
3. Offer should be rejected. The proposed variable cost to purchase of $28 exceeds
the variable manufacturing costs of $24.75. The company would lose $3.25 ($28.00 ‐
$24.75) per unit.
Cost Item Total Cost Unit Cost
Total Variable Costs:
Direct Material $600,000 $7.50
Direct Labour 400,000 5.00
Variable Overhead 720,000 9.00
Variable Selling 260,000 3.25
Total Variable Costs $1,980,000 $24.75
Total Fixed Costs
Fixed Overhead $400,000
Fixed Selling 250,000
Fixed Administration 150,000 $800,000
Chapter 3
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3‐36 (cont’d)
4. Desired after tax profit = $350,000
Before tax profit = After‐tax profit ÷ (1‐tax rate)
Before tax profit = $350,000 ÷ (1‐0.30)
Before tax profit (OI) = $500,000
(USP ‐ $24.75) 80,000 ‐ $800,000 = $500,000
(USP ‐ $24.75) = ($500,000 + $800,000) ÷ 80,000
USP ‐ $24.75 = $16.25
USP = $41.00
3‐37 (30 min.) CVP, target income, service firm.
1. Revenue per child $600
Variable costs per child 200
Contribution margin per child $400
Breakeven quantity = Fixed Costs ÷ Contribution margin/child
= $400
$5,600 = 14 children
2. Target quantity = (Fixed costs + Target operating income) ÷ Contribution
margin/child
= $400
10,400$ $5,600 = 40 children
3. Increase in rent ($3,000 – $2,000) $1,000
Field trips 1,000
Total increase in fixed costs $2,000
Divide by the number of children enrolled ÷40
Increase in fee per child $50
Therefore, the fee per child will increase from $600 to $650.
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-90 Copyright © 2013 Pearson Canada Inc.
3‐37 (cont’d)
Alternatively,
New contribution margin per child = 40
10,400$000,2$ $5,600 = $450
New fee per child = Variable costs per child + New contribution margin per child
= $200 + $450 = $650
3‐38 (20 min.) CVP and income taxes.
1. Revenues – Variable costs ‐ Fixed costs = Target net income ÷ (1 ‐ tax rate)
Let X = Net income for 2012
20,000($30.00) ‐ 20,000($16.50) ‐ $162,000 = X ÷ (1‐0.40)
$600,000 ‐ $330,000 ‐ $162,000 = X ÷ 0.60
X = $64,800
2. Let Q = Number of unit to break even $30.00Q ‐ $16.50Q ‐ $162,000 = 0 Q = $162,000 ÷ $ 13.50 = 12,000 units
3. Let X = Net income for 2013
22,000($30.00) ‐ 22,000($16.50) ‐ ($162,000 + $13,500) = X ÷ (1‐0.40)
$297,000 ‐ $175,500 = X ÷ 0.60
X = $72,900
4. Let Q = Number of units to break even with new fixed costs of $175,500
$30.00Q ‐ $16.50Q ‐ $175,500 = 0
Q = $175,500 ÷ $ 13.50 = 13,000 units
Revenues = 13,000($30.00) = $390,000
Alternatively, the computation could be $175,500 divided by the contribution margin percentage of 45% to obtain $390,000.
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-91
3‐38 (cont’d)
5. Let S = Required sales units to equal 2012 net income
$30.00S ‐ $16.50S ‐ $175,500 = $64,800 ÷ 0.60
$13.50S = $283,500
S = 21,000 units
Revenues = 21,000 units � $30.00 = $630,000
6. Let A = Amount spent for advertising in 2013
$660,000 ‐ $363,000 ‐ ($162,000 + A) = $72,000 ÷ 0.6
$297,000 ‐ $162,000 ‐ A = $120,000
A = $15,000
3‐39 (20‐25 min.) CVP income taxes, manufacturing decisions.
1.
Total Per Unit
Sales $1,350,000 $54.00
Variable Costs $742,500 $29.70
CM $607,500 $24.30
Fixed Costs $375,000
Operating Income $232,500
Income Taxes (40%) $93,000
Net Income $139,500
Breakeven point = Fixed Costs ÷ Unit CM = $375,000 ÷ $24.30
= 15,433 units (rounded)
Breakeven point ($) = 15,433 $54 = $833,382
or Alternate calculation:
CM Percentage = $24.30 ÷ $54.00 = 45%
Breakeven point ($) = Fixed Costs ÷ CM% = $375,000 ÷ 0.45
= $833,333
Margin of Safety = Sales ‐ Breakeven Sales
= $1,350,000 ‐ $833,333 = $516,667
or = $1,350,000 ‐ $833,382 = $516,618
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-92 Copyright © 2013 Pearson Canada Inc.
3‐39 (cont’d)
2.
Operating Income = After Tax Income ÷ (1‐tax rate)
= $225,000 ÷ (1‐0.40)
= $375,000
Units needed = (Fixed Costs + Target OI) ÷ Unit CM
= ($375,000 + $375,000) ÷ $24.30
= 30,865 units (rounded)
3.
Change in CM = $9.80 ‐ $7.50 = $2.30 decrease in unit CM
New CM = $24.30 ‐ $2.30 = $22.00
Change In Annual Fixed Costs = Increased Amortization Charges
= ($25,000 ‐ $0) ÷ 5 = $5,000
New Fixed Costs = $375,000 + $5,000 = $380,000
New Breakeven Point = New Fixed Costs ÷ New Unit CM
= $380,000 ÷ $22 = 17,273 units (rounded)
Units Needed for Target OI = (New Fixed Costs + Target OI) ÷ New Unit CM
= ($380,000 + $232,500) ÷ $22.00
= 27,841 units (rounded)
4. Variable Costs of New Product = $29.70 1.6 = $47.52
Old Product New Product Total
Units 30,000 20,000 50,000
Sales $1,620,000 $1,900,000 $3,520,000
VC ($891,000) ($950,400) ($1,841,400)
CM $729,000 $949,600 $1,678,600
CM% 45% 49.98% 47.6875%
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-93
3‐39 (cont’d)
New Breakeven Point in Sales $ = Fixed Costs ÷ Weighted CM %
= $375,000 ÷ 47.6875% = $786,370*
Alternate Calculation: Sales mix is 3:2
Weighted Average CM = [3 $24.3] + [2 $47.48]
= $72.90 + $94.96
= $167.86
Breakeven Point (packages) = $375,000 ÷ $167.86
= 2,235 packages
2,235 3 = 6,705 units of Old 2,235 2 = 4,470 of New
Total Revenues = [6,705 $54] + [4,470 $95] = $362,070 + $424,650
= $786,720* *difference due to rounding of units
3‐40 (20 min.) CVP, shoe stores.
1. UCM (SP ‐ UVC = $30 ‐ $21) $9.00
a. Breakeven units (FCUCM = $360,000 $9 per unit) 40,000
b. Breakeven revenues (Breakeven units SP = 40,000 units $30 per unit)$1,200,000
2. Pairs sold 35,000
Revenues, 35,000 $30 $1,050,000
Total cost of shoes, 35,000 $19.50 682,500
Total sales commissions, 35,000 $1.50 52,500
Total variable costs 735,000
Contribution margin 315,000
Fixed costs 360,000
Operating income (loss) $ (45,000)
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-94 Copyright © 2013 Pearson Canada Inc.
3‐40 (cont’d)
3. Unit variable data (per pair of shoes)
Selling price $ 30.00
Cost of shoes 19.50
Sales commissions 0
Variable cost per unit $ 19.50
Annual fixed costs
Rent $ 60,000
Salaries, $200,000 + $81,000 281,000
Advertising 80,000
Other fixed costs 20,000
Total fixed costs $ 441,000
UCM, $30 ‐ $19.50 $ 10.50
a. Breakeven units, $441,000$10.50 per unit 42,000
b. Breakeven revenues, 42,000 units $30 per unit $1,260,000
4. Unit variable data (per pair of shoes)
Selling price $ 30.00
Cost of shoes 19.50
Sales commissions 1.80
Variable cost per unit $ 21.30
Total fixed costs $ 360,000
UCM, $30 ‐ $21.30 $ 8.70
a. Break even units = $360,000$8.70 per unit 41,380 (rounded up)
b. Break even revenues = 41,380 units $30 per unit $1,241,400
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3‐40 (cont’d)
5. Pairs sold 50,000
Revenues (50,000 pairs $30 per pair) $1,500,000
Total cost of shoes (50,000 pairs $19.50 per pair) $ 975,000
Sales commissions on first 40,000 pairs (40,000 pairs $1.50 per pair) 60,000
Sales commissions on additional 10,000 pairs:
[10,000 pairs ($1.50 + $0.30 per pair)] 18,000
Total variable costs $1,053,000
Contribution margin $ 447,000
Fixed costs 360,000
Operating income $ 87,000
Alternative approach:
Breakeven point in units = 40,000 pairs
Store manager receives commission of $0.30 on 10,000 (50,000 ‐ 40,000) pairs.
Contribution margin per pair beyond breakeven point of 10,000 pairs = $8.70 ($30 ‐ $21 ‐ $0.30) per
pair.
Operating income = 10,000 pairs $8.70 contribution margin per pair = $87,000.
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3-96 Copyright © 2013 Pearson Canada Inc.
3‐41 (30 min.) CVP, shoe stores (continuation of 3‐40).
Salaries + Commission Plan Higher Fixed Salaries Only
No. of
units sold
CM
per Unit CM
Fixed
Costs
Operating
Income
CM
per Unit CM
Fixed
Costs
Operating
Income
Difference in
favour of higher‐
fixed‐salary‐only
(1) (2) (3)=(1) (2) (4) (5)=(3)–(4) (6) (7)=(1) (6) (8) (9)=(7)–(8) (10)=(9)–(5)
40,000 $9.00 $360,000 $360,000 0 $10.50 $420,000 $441,000 $ (21,000) $(21,000)
42,000 9.00 378,000 360,000 18,000 10.50 441,000 441,000 0 (18,000)
44,000 9.00 396,000 360,000 36,000 10.50 462,000 441,000 21,000 (15,000)
46,000 9.00 414,000 360,000 54,000 10.50 483,000 441,000 42,000 (12,000)
48,000 9.00 432,000 360,000 72,000 10.50 504,000 441,000 63,000 (9,000)
50,000 9.00 450,000 360,000 90,000 10.50 525,000 441,000 84,000 (6,000)
52,000 9.00 468,000 360,000 108,000 10.50 546,000 441,000 105,000 (3,000)
54,000 9.00 486,000 360,000 126,000 10.50 567,000 441,000 126,000 0
56,000 9.00 504,000 360,000 144,000 10.50 588,000 441,000 147,000 3,000
58,000 9.00 522,000 360,000 162,000 10.50 609,000 441,000 168,000 6,000
60,000 9.00 540,000 360,000 180,000 10.50 630,000 441,000 189,000 9,000
62,000 9.00 558,000 360,000 198,000 10.50 651,000 441,000 210,000 12,000
64,000 9.00 576,000 360,000 216,000 10.50 672,000 441,000 231,000 15,000
66,000 9.00 594,000 360,000 234,000 10.50 693,000 441,000 252,000 18,000
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-97
3‐41 (cont’d)
1. See preceding table. The new store will have the same operating income under
either compensation plan when the volume of sales is 54,000 pairs of shoes. This can
also be calculated as the unit sales level at which both compensation plans result in the
same total costs:
Let Q = unit sales level at which total costs are same for both plans:
$19.50Q + $360,000 + $81,000 = $21Q + $360,000
$1.50 Q = $81,000
Q = 54,000 pairs
2. When sales volume is above 54,000 pairs, the higher‐fixed‐salaries plan results in
lower costs and higher operating incomes than the salary‐plus‐commission plan. So, for
an expected volume of 55,000 pairs, the owner would be inclined to choose the higher‐
fixed‐salaries‐only plan. But it is likely that sales volume itself is determined by the
nature of the compensation plan. The salary‐plus‐commission plan provides a greater
motivation to the salespeople, and it may well be that for the same amount of money paid
to salespeople, the salary‐plus‐commission plan generates a higher volume of sales than
the fixed‐salary plan.
3. Let TQ = Target number of units
For the salary‐only plan:
$30.00TQ ‐ $19.50TQ ‐ $441,000 = $168,000
$10.50TQ = $609,000
TQ = $609,000 ÷ $10.50
TQ = 58,000 units
For the salary‐plus‐commission plan:
$30.00TQ ‐ $21.00TQ ‐ $360,000 = $168,000
$9.00TQ = $528,000
TQ = $528,000 ÷ $9.00
TQ = 58,667 units (rounded up)
The decision regarding the salary plan depends heavily on predictions of
demand. For instance, the salary plan offers the same operating income at 58,000 units
as the commission plan offers at 58,667 units.
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3-98 Copyright © 2013 Pearson Canada Inc.
3‐41 (cont’d)
4.
WalkRite Shoe Company
Operating Income Statement, 2008
Revenues (48,000 pairs $30) + (2,000 pairs $18) $1,476,000
Cost of shoes, 50,000 pairs $19.50 975,000
Commissions = Revenues 5% = $1,476,000 0.05 73,800
Contribution margin 427,200
Fixed costs 360,000
Operating income $ 67,200
3‐42 (30 min.) Uncertainty and expected costs.
1. Monthly Number of
Orders Cost of Current System
300,000 $1,000,000 + $40(300,000) = $13,000,000
400,000 $1,000,000 + $40(400,000) = $17,000,000
500,000 $1,000,000 + $40(500,000) = $21,000,000
600,000 $1,000,000 + $40(600,000) = $25,000,000
700,000 $1,000,000 + $40(700,000) = $29,000,000
Monthly Number of
Orders Cost of Partially Automated System
300,000 $5,000,000 + $30(300,000) = $14,000,000
400,000 $5,000,000 + $30(400,000) = $17,000,000
500,000 $5,000,000 + $30(500,000) = $20,000,000
600,000 $5,000,000 + $30(600,000) = $23,000,000
700,000 $5,000,000 + $30(700,000) = $26,000,000
Monthly Number of
Orders Cost of Fully Automated System
300,000 $10,000,000 + $20(300,000) = $16,000,000
400,000 $10,000,000 + $20(400,000) = $18,000,000
500,000 $10,000,000 + $20(500,000) = $20,000,000
600,000 $10,000,000 + $20(600,000) = $22,000,000
700,000 $10,000,000 + $20(700,000) = $24,000,000
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-99
3‐42 (cont’d)
2. Current System Expected Cost:
$13,000,000 × 0.1 = $ 1,300,000
17,000,000 × 0.25 = 4,250,000
21,000,000 × 0.40 = 8,400,000
25,000,000 × 0.15 = 3,750,000
29,000,000 × 0.10 = 2,900,000
$ 20,600,000
Partially Automated System Expected Cost:
$14,000,000 × 0.1 = $ 1 ,400,000
17,000,000 × 0.25 = 4,250,000
20,000,000 × 0.40 = 8,000,000
23,000,000 × 0.15 = 3,450,000
26,000,000 × 0.10 = 2,600,000
$19,700,000
Fully Automated System Expected Cost:
$16,000,000 × 0.1 = $ 1,600,000
18,000,000 × 0.25 = 4,500,000
20,000,000 × 0.40 = 8,000,000
22,000,000 × 0.15 = 3,300,000
24,000,000 × 0.10 = 2,400,000
$19,800,000
3. Dawmart should consider the impact of the different systems on its relationship
with suppliers. The interface with Dawmart’s system may require that suppliers also
update their systems. This could cause some suppliers to raise the cost of their
merchandise. It could force other suppliers to drop out of Dawmart’s supply chain
because the cost of the system change would be prohibitive. Dawmart may also want to
consider other factors such as the reliability of different systems and the effect on
employee morale if employees have to be laid off as it automates its systems.
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3-100 Copyright © 2013 Pearson Canada Inc.
3‐43 (25 min.) CVP analysis, decision making.
1. Unit selling price $148
Variable manufacturing costs per unit 63
Variable marketing and distribution costs per unit 15
Contribution margin per unit $ 70
Fixed manufacturing costs $ 1,012,000
Fixed marketing and distribution costs 780,000
Total fixed costs $1,792 ,000
Breakeven point in units = Total fixed costs
Contribution margin per unit
= $1,792,000 ÷ $70
= 25,600 units
Breakeven point in revenues = 25,600 units $148 per unit = $3,788,800
2. Tocchet’s current operating income is as follows:
Revenues, $148 60,000 $8,880,000
Variable costs, $78 60,000 4,680,000
Contribution margin 4,200,000
Fixed costs 1,792,000
Operating income $ 2,408,000
Let the fixed costs be $F. We calculate $F when operating income = $2,408,000 and
the selling price is $140.
($140 70,000) ‐ ($78 70,000) – $F = $2,408,000 $9,800,000 ‐ $5,460,000 – $F = $2,408,000
$F = $1,932,000
Hence the maximum increase in fixed costs for which Tocchet will prefer to reduce the
selling price is $140,000 ($1,932,000 ‐ $1,792,000).
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-101
3‐43 (cont’d)
3. Let the selling price be P.
We calculate P for which, after increasing fixed manufacturing costs by $150,000 to
$1,942,000 and variable manufacturing cost per unit by $3.20 to $66.20, operating income
= $2,408,000
60,000P ‐ ($66.20 60,000) ‐ ($15 60,000) ‐ $1,942,000 = $2,408,000 60,000P ‐ $3,972,000 ‐ $900,000 ‐ $1,942,000 = $2,408,000
60,000P = $9,222,000
P = $153.70
Tocchet will consider adding the new features provided the selling price is at least
$153.70 per unit.
Proof: New CM = $153.70 ‐ $66.20 ‐ $15 = $72.50
OI = (60,000 $72.50) ‐ $1,942,000 = $2,408,000
3‐44 (20–25 min.) Sales mix, two products.
1. Sales of standard and deluxe carriers are in the ratio of 150,000:50,000. So for
every 1 unit of deluxe, 3 (150,000 ÷ 50,000) units of standard are sold.
Contribution margin of the bundle = 3 $6 + 1 $12 = $18 + $12 = $30
Breakeven point in bundles = $1,200,000
$30= 40,000 bundles
Breakeven point in units is:
Standard
carrier:
40,000 bundles × 3 units per
bundle 120,000 units
Deluxe carrier: 40,000 bundles × 1 unit per bundle 40,000 units
Total number of units to breakeven 160,000 units
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3‐44 (cont’d)
Alternatively,
Let Q = Number of units of Deluxe carrier to break even
3Q = Number of units of Standard carrier to break even
Revenues – Variable costs – Fixed costs = Zero operating income
$20(3Q) + $30Q ‐ $14(3Q) ‐ $18Q ‐ $1,200,000 = 0
$60Q + $30Q ‐ $42Q ‐ $18Q = $1,200,000
$30Q = $1,200,000
Q = 40,000 units of Deluxe
3Q = 120,000 units of Standard
The breakeven point is 120,000 Standard units plus 40,000 Deluxe units, a total of
160,000 units.
2a. Unit contribution margins are: Standard: $20 ‐ $14 = $6; Deluxe: $30 ‐ $18 = $12
If only Standard carriers were sold, the breakeven point would be:
$1,200,000 $6 = 200,000 units.
2b. If only Deluxe carriers were sold, the breakeven point would be:
$1,200,000 $12 = 100,000 units 3. Operating income = Contribution margin of Standard + Contribution margin of Deluxe - Fixed costs
= 180,000($6) + 20,000($12) ‐ $1,200,000
= $1,080,000 + $240,000 ‐ $1,200,000
= $120,000
Sales of standard and deluxe carriers are in the ratio of 180,000: 20,000. So for
every 1 unit of deluxe, 9 (180,000 ÷ 20,000) units of standard are sold.
Contribution margin of the bundle = 9 $6 + 1 $12 = $54 + $12 = $66
Breakeven point in bundles = $1,200,000
$66= 18,182 bundles (rounded up)
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-103
3‐44 (cont’d)
Breakeven point in units is:
Standard
carrier:
18,182 bundles × 9 units per
bundle 163,638 units
Deluxe carrier: 18,182 bundles × 1 unit per bundle 18,182 units
Total number of units to breakeven 181,820 units
Alternatively,
Let Q = Number of units of Deluxe product to break even
9Q = Number of units of Standard product to break even
$20(9Q) + $30Q ‐ $14(9Q) ‐ $18Q ‐ $1,200,000 = 0
$180Q + $30Q ‐ $126Q ‐ $18Q = $1,200,000
$66Q = $1,200,000
Q = 18,182 units of Deluxe (rounded up)
9Q = 163,638 units of Standard
The breakeven point is 163,638 Standard + 18,182 Deluxe, a total of 181,820 units.
The major lesson of this problem is that changes in the sales mix change
breakeven points and operating incomes. In this example, the budgeted and actual total
sales in number of units were identical, but the proportion of the product having the
higher contribution margin declined. Operating income suffered, falling from $300,000
to $120,000. Moreover, the breakeven point rose from 160,000 to 181,820 units.
3‐45 (15 min.) CVP, movie production.
1. Fixed costs = $22,000,000 (production cost)
Unit variable cost = (4% +4% + 8% + 8% + 12%) = 36% of revenues
Unit contribution margin = 100% ‐ 36% = 64% of revenues or $0.64 per $1
(a) Breakeven point in revenues = Fixed costs
Unit contribu tion margin per $1 revenue
= $22,000,000/$0.64
= $34,375,000
(b) Panther receives 65% of box‐office receipts.
Required box‐office receipts = $34,375,000 ÷ 0.65 = $52,884,616 (rounded)
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3‐45 (cont’d)
2. Revenues, 0.65 $320,000,000 $208,000,000
Variable costs, 0.36 $208,000,000 74,880,000
Contribution margin 133,120,000
Fixed costs 22,000,000
Operating income $111,120,000
3‐46 (20 min.) CVP, cost structure differences, movie production (continuation of 3‐
45).
1. Contract A
Fixed costs for Contract A:
Production costs $32,000,000
Fixed salary 50,000,000
Total fixed costs $82,000,000
Unit variable cost = 8% + 8% + 18% = 34% or $0.34 per $1 revenue marketing fee
Unit contribution margin = $0.66 per $1 revenue
(a) Breakeven point in revenues =
Fixed costs
Unit contribu tion margin per $1 revenue
= $82,000,000 ÷ $0.66
= $124,242,425 (rounded)
Breakeven point in box office sales = $124,242,425 ÷ 0.65
= $191,142,192 (rounded)
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-105
3‐46 (cont’d)
Contract B
Fixed costs for Contract B:
Production costs $32,000,000
Fixed salary 8,000,000
Total fixed costs $40,000,000
Unit variable cost = $0.18 per $1 revenue fee to Parimont Productions
[3%+3%+8%+8%] $0.22 per $1 revenue residual to directors/actors
$0.40 per $1 revenue
Unit contribution margin = $0.60 per $1 revenue
Breakeven point in revenues = $40,000,000/$0.60 = $66,666,667 (rounded)
Breakeven point in box office sales = $66,666,667/0.65
= $102,564,103 (rounded)
Difference in Breakeven Points
Contract A has a higher fixed cost and a lower variable cost per sales dollar. In
contrast, Contract B has a lower fixed cost and a higher variable cost per sales dollar. In
Contract B, there is more risk‐sharing between Panther and the actors that lowers the
breakeven point, but results in Panther receiving less operating income if the film is a
mega‐success.
2.
Contract A:
Revenues, 0.65 $280,000,000 $182,000,000
Variable costs, 0.34 $182,000,000 61,880,000
Contribution margin 120,120,000
Fixed costs 82,000,000
Operating income $38,120,000
Contract B:
Revenues, 0.65 $280,000,000 $182,000,000
Variable costs, 0.4 $182,000,000 72,800,000
Contribution margin 109,200,000
Fixed costs 40,000,000
Operating income $69,200,000
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-106 Copyright © 2013 Pearson Canada Inc.
3‐46 (cont’d)
Contract A has a higher breakeven point than Contract B, because it has a higher
level of fixed costs and a lower unit contribution margin. This means after breakeven is
reached, under Contract A, $0.66 of every additional revenue dollar will contribute to OI,
but under Contract B only $0.60 of every additional revenue dollar will contribute to OI.
However, the fixed costs for Contract A are significantly higher than for Contract B.
At the predicted level of box office receipts, Contract B is the more lucrative contract.
The point of indifference (in terms of revenue to Panther) (not required in question)
($1.00R ‐ $0.34R) ‐ $82,000,000 = ($1.00R ‐ $0.40R) ‐ $40,000,000
$0.66R ‐ $0.60R = $42,000,000
R = $700,000,000
It seems highly unlikely the film will gross enough box office receipts to generate
$700 million of revenue to Panther. Panther should select Contract B.
3‐47 (30 min.) Multi‐product breakeven, decision making.
1. Unit CM = USP ‐ UVC = $600 ‐ $210 ‐ $60 = $330
Breakeven point in 2011 (units) = Fixed Costs ÷ Unit CM
= $2,574,000 ÷ $330
= 7,800 units
Breakeven point in 2011 (in revenues) = 7,800 units $600 = $4,680,000 in sales revenues or CM % = UCM ÷ USP = $330 ÷ $600 = 55%
Breakeven point in 2011 in revenues = $2,574,000 ÷ 55% = $4,680,000
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-107
3‐47 (cont’d)
2. Breakeven point in 2012 (in units)
Bonavista expects to sell 2.5 units of Surrey for every 1 unit of Shilo (10,000 ÷ 4,000)
Unit Contribution Margin from Surrey = $600 ‐ $270 = $330
Unit Contribution Margin from Shilo = $350 ‐ $180 = $170
The contribution margin for the bundle is ($330 2.5 units) + ($170) = $995
Breakeven point = Fixed Costs ÷ Package CM
= $2,574,000 ÷ $995
= 2,587 bundles or packages consisting of 2.5 Surrey and 1 Shilo
Surrey 2.5 2,587 = 6,468 Shilo 1 2,587 = 2,587
Total = 9,055
3. Contribution margin percentage in 2011 = 55% (as calculated above)
Contribution margin percentage in 2012 = CM per bundle/Revenue per bundle
CM % in 2012 = $995 ÷ [(2.5 $600) + ($350)] = $995 ÷ $1,850 = 53.78%
The breakeven point in 2012 increases because fixed costs are the same in both years
but the contribution margin generated by each dollar of sales revenue at the given
product mix decreases in 2012 relative to 2011.
4. Despite the breakeven sales revenue being higher, I would advise the president to
accept Dover’s offer. The breakeven points per se are irrelevant because I do not expect
the company to operate in the region of the breakeven dollars. By accepting the offer,
Bonavista can sell all the original Surrey model and sell the Shilo as well without
incurring any more fixed costs.
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3-108 Copyright © 2013 Pearson Canada Inc.
3‐47 (cont’d)
Profits in 2012 with and without Shilo are expected to be as follows:
Surrey Shilo Total
Selling Price $600 $350
Units 10,000
4,000 14,000
Total Sales $6,000,000 $1,400,000 $7,400,000
Variable
Costs $2,700,000 $720,000 $3,420,000
CM $3,300,000 $680,000 $3,980,000
Fixed Costs $ 2,574,000 $ – $2,574,000
OI $ 726,000 $ 680,000 $ 1,406,000
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-109
3‐48 (30 min.) Choosing between compensation plans, operating leverage.
1. We can recast Marston’s income statement to emphasize contribution margin,
and then use it to compute the required CVP parameters.
Marston Corporation
Income Statement
For the Year Ended December 31, 2011
Using Sales Agents Using Own Sales Force
Revenues $26,000,000 $26,000,000
Variable Costs
Cost of goods sold—variable $11,700,000 $11,700,000
Marketing commissions 4,680,000 16,380,000 2,600,000 14,300,000
Contribution margin $9,620,000 $11,700,000
Fixed Costs
Cost of goods sold—fixed 2,870,000 2,870,000
Marketing—fixed 3,420,000 6,290,000 5,500,000 8,370,000
Operating income $3,330,000 $ 3,330,000
Contribution margin
percentage
($9,620,00026,000,000; $11,700,000$26,000,000)
37% 45%
Breakeven revenues
($6,290,0000.37; $8,370,0000.45) $17,000,000 $18,600,000
Degree of operating leverage
($9,620,000$3,330,000; $11,700,000$3,330,000)
2.89
3.51
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3‐48 (cont’d)
2. The calculations indicate that at sales of $26,000,000, a percentage change in sales
and contribution margin will result in 2.89 times that percentage change in operating
income if Marston continues to use sales agents and 3.51 times that percentage change
in operating income if Marston employs its own sales staff. The higher contribution
margin per dollar of sales and higher fixed costs gives Marston more operating
leverage, that is, greater benefits (increases in operating income) if revenues increase
but greater risks (decreases in operating income) if revenues decrease. Marston also
needs to consider the skill levels and incentives under the two alternatives. Sales agents
have more incentive compensation and hence may be more motivated to increase sales.
On the other hand, Marston’s own sales force may be more knowledgeable and skilled
in selling the company’s products. That is, the sales volume itself will be affected by
who sells and by the nature of the compensation plan.
3. Variable costs of marketing = 15% of Revenues
Fixed marketing costs = $5,500,000
Operating income = Revenues costs manuf.Variable costs manuf.
Fixed costs
marketingVariable
costs
marketingFixed
Denote the revenues required to earn $3,330,000 of operating income by R, then:
R ‐ 0.45R ‐ $2,870,000 ‐ 0.15R ‐ $5,500,000 = $3,330,000
R ‐ 0.45R ‐ 0.15R = $3,330,000 + $2,870,000 + $5,500,0
0.40R = $11,700,000
R = $11,700,000 0.40 = $29,250,000
Chapter 3
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3‐49 (20‐25 min.) Special‐order decision.
1. Time spent on manufacturing bottles = 750,000 bottles ÷ 100 bottles per hour = 7,500
hours
So 10,000 ‐ 7,500 = 2,500 hours available for toys.
Moulded plastic toy requires: 100,000 units ÷ 40 units per hour = 2,500 hours, so
MPC has enough capacity to accept the toys order. Additional income from accepting the
order is:
Revenue $3.40 100,000 $340,000
Variable costs 2.70 100,000 270,000
Contribution margin 70,000
Fixed costs 24,000
Additional income $ 46,000
So MPC should accept the order since it has enough excess capacity to make the
100,000 toys.
2. Time spent on manufacturing bottles = 850,000 ÷ 100= 8,500 hours
So 10,000 ‐ 8,500 = 1,500 hours available for toys.
From requirement 1, the moulded plastic toy requires 2,500 hours and generates
$46,000 in operating income.
So if the toy offer is accepted, 1,000 hours (2,500 hours required ‐ 1,500 hours
available) of bottle making will be forgone, equal to 100,000 bottles (100 bottles/hr. 1,000 hrs.):
Operating income from accepting $46,000
Forgone contribution margin (100,000 bottles $0.30)* 30,000
Increase in operating income $16,000
So MPC should accept the special order.
*CM = $0.55 ‐ $0.25 = $0.30
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3‐49 (cont’d)
Without considering the fixed costs for the toy mould, the contribution per
machine‐hour of the constrained resource for bottles and the special toy are as follows:
Bottles Toys
Contribution margin per unit $0.30 $0.70
Multiplied by units made in 1 machine‐hour 100 40
Contribution margin per machine‐hour $30 $ 28
This suggests that MPC should make as many bottles as it can rather than the
special toys, because bottles generate a higher contribution margin per machine‐hour.
So if MPC used the 1,500 hours available to it for making toys after using the 8,500
hours to make bottles, it would be able to make 1,500 40 = 60,000 toys and earn operating income of:
Contribution margin 60,000 $0.70 $42,000
Fixed mould costs 24,000
Increase in operating income $18,000
The contribution margin earned covers the fixed costs of the mould, so MPC should
make 850,000 bottles and 60,000 toys.
3. Time spent on manufacturing bottles = 900,000 ÷ 100 = 9,000 hours
So 10,000 ‐ 9,000 = 1,000 hours available for toys.
So if the toy offer is accepted, then 1,500 hours (2,500 hours required ‐ 1,000 hours
available) of bottle capacity will be forgone = 150,000 bottles
Contribution from accepting toy offer $ 46,000
Forgone profits on bottles 150,000 $0.30 (45,000)
Increase (decrease) in operating income $ 1,000
So accept the special order.
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-113
3‐50 (25 min.) CVP, sensitivity analysis.
Contribution margin per corkscrew = $4 ‐ 3 = $1
Fixed costs = $6,000
Units sold = Total sales ÷ Selling price = $40,000 ÷ $4 per corkscrew = 10,000 corkscrews
1. Sales increase 10%
Sales revenues 10,000 1.10 $4.00 $44,000
Variable costs 10,000 1.10 $3.00 33,000
Contribution margin 11,000
Fixed costs 6,000
Operating income $ 5,000
2. Increase fixed costs $2,000; Increase sales 50%
Sales revenues 10,000 1.50 $4.00 $60,000
Variable costs 10,000 1.50 $3.00 45,000
Contribution margin 15,000
Fixed costs ($6,000 + $2,000) 8,000
Operating income $ 7,000
3. Increase selling price to $5.00; Sales decrease 20%
Sales revenues 10,000 0.80 $5.00 $40,000
Variable costs 10,000 0.80 $3.00 24,000
Contribution margin 16,000
Fixed costs 6,000
Operating income $10,000
4. Increase selling price to $6.00; Variable costs increase $1 per corkscrew
Sales revenues 10,000 $6.00 $60,000
Variable costs 10,000 $4.00 40,000
Contribution margin 20,000
Fixed costs 6,000
Operating income $14,000
Alternative 4 yields the highest operating income. If TOP is confident that unit sales
will not decrease despite increasing the selling price, it should choose alternative 4.
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3-114 Copyright © 2013 Pearson Canada Inc.
3‐51 (15‐25 min.) Nonprofit institution.
1. Let Q = Number of visits
Revenues ‐ Variable costs ‐ Fixed costs = 0
$850,000 ‐ $16Q ‐ $500,000 = 0
$16Q = $350,000
Q = 21,875 visits
Revenues ‐ Variable costs ‐ Fixed costs = 0
$765,000 ‐ $16Q ‐ $500,000 = 0
$16Q = $265,000
Q = 16,562 visits
The reduction in service is more than the 10% reduction in the budget. Without
restructuring operations, the quantity of service units must be reduced by 24.29% [(21,875
‐ 16,562) ÷ 21,875] to stay within the budget.
3. Let V = Variable cost per visit
$765,000 ‐ 21,875V ‐ $500,000 = 0
21,875V = $265,000
V = $12.11 ($12.114285)*
Percentage drop: ($16 ‐ $12.114285*) ÷ $16 = 24.29%
Regarding requirements 2 and 3, note that the decrease in service can be measured by a
formula:
% reduction in service = (% budget change) ÷ (% variable cost)
The variable cost percentage is ($16 21,875) ÷ $850,000 = $350,000 ÷ $850,000 = 41.1765%*
% reduction in service = 10% ÷ 41.1765% = 24.29%
*The extra decimal places are used to minimize the rounding difference. Most will
round to two decimals for the money and to 24%.
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-115
3‐52 (30 min.) CVP, nonprofit event planning.
1. Computation of fixed costs.
Hotel University
Rental cost of venue $2,700 $ 7,000
Permits 0 500
Chamber administration/marketing 5,000 5,000
Entertainment 4,000 4,000
$11,700 $16,500
Computation of contribution margin per person:
Hotel University
Selling (ticket) price per person $175 $175
Catering cost per person 110 75
Contribution margin per person $65 $100
Breakeven point = Fixed costs
Unit contribution margin
Breakeven point for Hotel venue = $11,700 ÷ $65 = 180 tickets
Breakeven point for University venue = $16,500 ÷ $100 = 165 tickets
2. Operating Income Projections with 100 attendees and 250 attendees
Hotel
Attendees 100 250
Ticket Price $175 $175
Total Revenues $17,500 $43,750
VC @ $110 11,000 27,500
CM 6,500 16,250
Fixed Costs 11,700 11,700
Operating Income $(5,200) $4,550
University
Attendees 100 250
Ticket Price $175 $175
Total Revenues $17,500 $43,750
VC @ $75 7,500 18,750
CM 10,000 25,000
Fixed Costs 16,500 16,500
Operating Income $(6,500) $8,500
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-116 Copyright © 2013 Pearson Canada Inc.
3‐52 (cont’d)
The Hotel venue has higher variable costs per person and lower fixed costs. In
contrast, the University venue has lower variable costs per person and higher fixed costs.
3. Requirement 2 gives the operating income equation for each venue. Setting these
two equations equal and solving for Q gives the level of ticket sales at which the
operating incomes for the two venues are equal:
$175Q ‐ $110Q ‐ $11,700 = $175Q ‐ $75Q ‐ $16,500
$100Q ‐ $65Q = $16,500 ‐ $11,700
$35Q = $4,800
Q = 137 (rounded)
Proof:
Hotel University
Attendees 137.14286 137.14286
Ticket Price 175 175
Total Revenues 24,000 24,000
VC @ $110; $75 15,086 10,286
CM 8,914 13,714
Fixed Costs 11,700 16,500
Operating Income (2,786) (2,786)
Above 137, the University venue will yield higher operating income (or a lower
operating loss) than the hotel venue.
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-117
3‐53 (20‐30 min.) CVP under uncertainty.
1. (a) At a selling price of $120, the unit contribution margin is ($120 ‐ $60) = $60, and
it will require the sale of ($240,000 ÷ $60) = 4,000 units to break even. The sales in dollars
are $480,000 and there is a 2/3 probability of equaling or exceeding this sales level—that
is, that 2/3 of the area under the graph exists between $480,000 and $720,000.
(b) At a selling price of $84, the unit contribution margin is ($84 ‐ $60) = $24, and it
will require the sale of ($240,000 ÷ $24) = 10,000 units to break even. At the lower price,
the sales in dollars are $840,000 and there is a 2/3 probability of equaling or exceeding this
sales volume.
Therefore, if you seek to maximize the probability of showing an operating income,
you are indifferent between the two strategies.
2.
Expected ExpectedSelling Variable Fixedoperating sales price per unit cost per unit costsincome level
At a selling price of $120:
Expected revenues = $540,000 ($120 4,500) Expected operating income = [($120 ‐ $60) 4,500] ‐ $240,000
= $30,000
At a selling price of $84:
Expected revenues = $900,000 ($84 10,715) Expected operating income = [($84 ‐ $60) 10,715] ‐ $240,000 = $17,160
A selling price of $120 will maximize the expected operating income.
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-118 Copyright © 2013 Pearson Canada Inc.
3‐54 (30 min.) Governance, CVP analysis.
1. Contribution margin percentage = Revenues – Variable costs
Revenues
= ($8,000,000 ‐ $4,320,000) ÷ $8,000,000
= $3,680,000 ÷ $8,000,000
= 46%
Breakeven revenues = Fixed Costs/CM Percentage
= $3,900,000 ÷ .46 = $8,478,261 (rounded)
2. If variable costs are 48% of revenues, CM percentage equals 52% (100% ‐ 48%).
Breakeven revenues = Fixed costs
Contribu tion margin percentage
= $3,900,000 ÷ .52 = $7,500,000
3. Revenues $8,000,000
Variable costs (0.48 $8,000,000) 3,840,000
Fixed costs 3,900,000
Operating income $ 260,000
4. Incorrect reporting of environmental costs with the goal of continuing operations is
unethical.
The management accountant could consider the following issues:
Competence
Clear reports using relevant and reliable information should be prepared. Preparing
reports on the basis of incorrect environmental costs in order to make the company’s
performance look better than it is violates competence standards. It is unethical for
Walton not to report environmental costs in order to make the plant’s performance look
good.
Integrity
The management accountant has a responsibility to avoid actual or apparent
conflicts of interest and advise all appropriate parties of any potential conflict. Walton
may be tempted to report lower environmental costs to please Bell and Klein and save
the jobs of her colleagues. This action, however, violates the responsibility for integrity.
Chapter 3
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3‐54 (cont’d)
Objectivity
The management accountant should require that information should be fairly and
objectively communicated and that all relevant information should be disclosed. From a
management accountant’s standpoint, underreporting environmental costs to make
performance look good would violate the standard of objectivity.
Walton should indicate to Bell that estimates of environmental costs and liabilities
should be included in the analysis. If Bell still insists on modifying the numbers and
reporting lower environmental costs, Walton should raise the matter with one of Bell’s
superiors. If, after taking all these steps, there is continued pressure to understate
environmental costs, Walton should consider resigning from the company and not
engage in unethical behaviour.
Walton can also argue the sustainability issue, that is, companies should act with a
view to sustainable operations, from all perspectives, environmental, social responsibility,
and economic.
3‐55 (20‐25 min.) Governance, CVP, cost analysis.
1. (a) USP = $68
UVC = $28.50 ($19.25 + $9.25)
UCM = $39.50
FC = $25,000,000
Q = FC ÷ UCM
= $25,000,000 ÷ $39.50
= 632,912 monthly treatments (rounded up)
(b) USP = $68
UVC = $19.25
UCM = $48.75
FC = $25,000,000
Q = FC ÷ UCM
= $25,000,000 ÷ $48.75
= 512,821 monthly treatments (rounded up)
Instructor’s Solutions Manual for Cost Accounting, 6Ce
3-120 Copyright © 2013 Pearson Canada Inc.
3‐55 (cont’d)
2. Diba believes that the $9.25 per monthly visit should be included in the variable
costs per visit. His argument is that a product like “Vital Hair” has a positive probability
of attracting product litigation. By excluding any allowance for the possible event, the
assumption is that it will be zero.
Diba faces an integrity issue. His report to the Executive Committee will understate
his expected cost estimates when he takes Kelly’s advice.
One possibility Diba should have explored is reporting the $19.25 per treatment
variable cost in the breakeven computations as well as including qualifications in the
report about possible product litigation costs.
3. Diba likely has been placed in a compromised situation. He may feel Kelly
deliberately set him up to avoid the $9.25 amount being reported to the Executive
Committee. At a minimum, he should directly confront Kelly with his concerns. If she is
unresponsive, he faces a very tough dilemma. His options are:
(a) Stay in his current position and be more determined next time to have his concerns
registered.
(b) Report his concerns to Kelly’s immediate superior.
(c) Resign.
If he selects (a), it would be useful to show Kelly the Code of Professional Ethics and
stress how her behaviour has put him in a difficult ethical situation.
Chapter 3
Copyright © 2013 Pearson Canada Inc. 3-121
3‐56 (35 min.) Deciding where to produce.
Peona Modine
Selling price $150.00 $150.00
Variable cost per unit
Manufacturing $72.00 $88.00
Marketing and distribution 14.00 86.00 14.00 102.00
Contribution margin per unit (CMU) 64.00 48.00
Fixed costs per unit
Manufacturing 30.00 15.00
Marketing and distribution 19.00 49.00 14.50 29.50
Operating income per unit $ 15.00 $ 18.50
CMU of normal production $64 $48
CMU of overtime production
($64 – $3; $48 – $8) 61 40
1.
Annual fixed costs:
P ‐ ($49.00 400 units 240 days) M ‐ ($29.50 320 units 240 days) $4,704,000 $2,265,600
Breakeven volume:
P ‐ ($4,704,000 $64) M ‐ ($2,265,600 $48)
73,500 units
47,200 Units
2.
Units produced and sold 96,000 96,000
Normal annual volume (units)
(400 × 240; 320 × 240) 96,000 76,800
Units over normal volume (overtime) 0 19,200
CM from normal production units
(normal annual volume CMU normal
production)
(96,000 × $64; 76,800 × $48) $6,144,000 $3,686,400
CM from overtime production units
(0; 19,200 $40) 0 768,000
Total contribution margin 6,144,000 4,454,400
Total fixed costs 4,704,000 2,265,600
Operating income $1,440,000 $2,188,800
Total operating income $3,628,800
Instructor’s Solutions Manual for Cost Accounting, 6Ce
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3‐56 (cont’d)
3. The optimal production plan is to produce 120,000 units at the Peona plant and
72,000 units at the Modine plant. The full capacity of the Peona plant, 120,000 units (400
units × 300 days), should be used because the contribution from these units is higher at
all levels of production than is the contribution from units produced at the Modine
plant.
Contribution margin per plant:
Peona, 96,000 × $64 $ 6,144,000
Peona 24,000 × ($64 ‐ $3) 1,464,000
Modine, 72,000 × $48 3,456,000
Total contribution margin 11,064,000
Deduct total fixed costs 6,969,600
Operating income $ 4,094,400
The contribution margin is higher when 120,000 units are produced at the Peona
plant and 72,000 units at the Modine plant. As a result, operating income will also be
higher in this case since total fixed costs for the division remain unchanged regardless
of the quantity produced at each plant.
COLLABORATIVE LEARNING PROBLEM
3‐57 (25 Min.) (CVP analysis and revenue mix)
1. Let A = Number of units of A to break even
5A = Number of units of B to break even
4A = Number of units of C to break even
$3.60A + $2.40(5A) + $1.20(4A) ‐ $306,000 = 0
A = 15,000 units of A
5A = 75,000 units of B
4A = 60,000 units of C
Total = 150,000 units
Chapter 3
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3‐57 (cont’d)
2. Contribution margin:
A: 20,000 � $3.60 = $72,000
B: 100,000 � $2.40 = $240,000
C: 80,000 � $1.20 = $96,000
$408,000
Operating Income = $408,000 ‐ $306,000 = $102,000
3. Contribution margin:
A: 20,000 � $3.60 = $72,000
B: 80,000 � $2.40 = $192,000
C: 100,000 � $1.20 = $120,000
$384,000
Operating Income = $384,000 ‐ $306,000 = $78,000
Let A = Number of units of A to break even
4A = Number of units of B to break even
5A = Number of units of C to break even
$3.60A + $2.40(4A) + $1.20(5A) ‐ $306,000 = 0
A = 15,938 units of A
5A = 63,752 units of B
4A = 79,690 units of C
Total = 159,380 units