成本会计管理的着重点-第十版-书后习题答案第三章.doc

成本会计：管理的着重点 第十版 书后习题答案第三章
CHAPTER 3
COST-VOLUME-PROFIT ANALYSIS

3-1 Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, and operating income as changes occur in the output level, selling price, variable costs per unit, or fixed costs.

3-2 The assumptions underlying the CVP analysis outlined in Chapter 3 are:

1. Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units produced and sold.
2. Total costs can be divided into a fixed component and a component that is variable with respect to the level of output.
3. When graphed, the behavior of total revenues and total costs is linear (straight-line) in relation to output units within the relevant range.
4. The unit selling price, unit variable costs, and fixed costs are known and constant.
5. The analysis either covers a single product or assumes that the sales mix, when multiple products are sold, will remain constant as the level of total units sold changes.
6. All revenues and costs can be added and compared without taking into account the time value of money.

3-3 Operating income is total revenues from operations for the accounting period minus total costs from operations (excluding income taxes):
Operating income = Total revenues – Total costs

Net income is operating income plus nonoperating revenues (such as interest revenue) minus nonoperating costs (such as interest cost) minus income taxes. Chapter 3 assumes nonoperating revenues and nonoperating costs are zero. Thus, Chapter 3 computes net income as:
Net income = Operating income – Income taxes

3-4 Contribution margin is computed as the difference between total revenues and total variable costs. Contribution margin per unit is the difference between selling price and variable cost per unit. Contribution-margin percentage is the contribution margin per unit divided by selling price.

3-5 Three methods to calculate the breakeven point are the equation method, the contribution margin method, and the graph method.

3-6 Breakeven analysis denotes the study of the breakeven point, which is often only an incidental part of the relationship between cost, volume, and profit. Cost-volume-profit relationship is a more comprehensive term than breakeven analysis.

3-7 CVP certainly is simple, with its assumption of output as the only revenue and 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. The examples in Chapter 3 (the software package context in the text and the travel agency example in the Problem for Self-Study) illustrate how CVP can provide such insights. In more complex cases, the basic ideas of simple CVP analysis can be expanded.

3-8 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.

3-9 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.

3-10 Examples include:
Manufacturing––substituting a robotic machine for hourly wage workers.
Marketing––changing a sales force compensation plan from a percent 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.

3-11 Examples include:
Manufacturing––subcontracting a component to a supplier on a per-unit basis to avoid purchasing a machine with a high fixed depreciation cost.
Marketing––changing a sales compensation plan from a fixed salary to percent of sales dollars basis.
Customer service––hiring a subcontractor to do customer service on a per-visit basis rather than an annual retainer basis.

3-12 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.

3-13 CVP analysis is always conducted for a specified time horizon. One extreme is a very short-time horizon. For example, some vacation cruises offer deep price discounts for people who offer to take any cruise on a day's notice. One day prior to a cruise, most costs are fixed. The other extreme is several years. Here, a much higher percentage of total costs typically is variable.
CVP itself is not made any less relevant when the time horizon lengthens. What happens is that many items classified as fixed in the short run may become variable costs with a longer time horizon.

3-14 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.

3-15 Yes, gross margin calculations emphasize the distinction between manufacturing and nonmanufacturing costs (gross margins are calculated after subtracting fixed manufacturing costs). Contribution margin calculations emphasize the distinction between fixed and variable costs. Hence, contribution margin is a more useful concept than gross margin in CVP analysis.

3-16 (10 min.) CVP computations.

Variable
Fixed
Total
Operating
Contribution
Contribution

Revenues
Costs
Costs
Costs
Income
Margin
Margin %

a.
$2,000
$ 500
$300
$ 800
$1,200
$1,500
75.0%
b.
2,000
1,500
300
1,800
200
500
25.0%
c.
1,000
700
300
1,000
0
300
30.0%
d.
1,500
900
300
1,200
300
600
40.0%

3-17 (10-20 min.) CVP computations.

a. TCM = Q (USP – UVC)
= 70,000 ($30 – $20)
= $700,000
TFC = TCM – OI
= $700,000 - (– $15,000) = $715,000

b. TCM = Q (USP – UVC)
$900,000 = 180,000 ($25 – UVC)
UVC = $20

OI = TCM – TFC
= $900,000 – $800,000 = $100,000

c. TCM = Q (USP – UVC)
$300,000 = 150,000 (USP – $10)
USP = $12

OI = TCM – TFC
= $300,000 – $220,000 = $80,000

d. Q = TCM ÷ (USP – UVC)
= $120,000 ÷ ($20 – $14)
= 20,000

TFC = TCM – OI
= $120,000 – $12,000 = $108,000

3-18 (15–20 min.) CVP analysis, changing revenues and costs.

1. USP = 8% ´ $1,000 = $80
UVC = $35 ($17 + $18)
UCM = $45
FC = $22,000 a month

a. Q = =
= 489 tickets (rounded up)
b. Q = =
=
= 712 tickets (rounded up)

2. USP = $80
UVC = $29 ($17 + $12)
UCM = $51
FC = $22,000 a month
a. Q = =
= 432 tickets (rounded up)
b. Q = =
=
= 628 tickets (rounded up)

3-19 (20 min.) CVP, changing revenues and costs. (Continuation of 3-18)

1. Sunshine charges $1,000 per round-trip ticket. Hence, each ticket will yield only a $48 commission.
USP = $48
UVC = $29 ($17 + $12)
UCM = $19
FC = $22,000

a. Q = =
= 1,158 tickets (rounded up)

b. Q = =
=
= 1,685 tickets (rounded up)
The reduced commission sizably increases the breakeven point and the number of tickets required to yield a target operating income of $10,000:

8%
Old Commission
(3-18 Requirement 2)

Upper Limit on
Commission of $48
Breakeven point
Attain OI of $10,000
432
628
1,158
1,685

2. 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 UCM by $5:
USP = $53 ($48 + $5)
UVC = $29 ($17 + $12)
UCM = $24
FC = $22,000

a. Q = =
= 917 tickets (rounded up)
b. Q = =
= 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.

3-20 (20 min.) CVP exercises.

Revenues

Variable
Costs

Contribution
Margin

Fixed
Costs

Budgeted
Operating
Income
Orig.
$10,000,000G

$8,200,000G

$1,800,000

$1,700,000G

$100,000
1.
10,000,000

8,020,000

1,980,000

1,700,000

280,000
2.
10,000,000

8,380,000

1,620,000

1,700,000

(80,000)
3.
10,000,000

8,200,000

1,800,000

1,785,000

15,000
4.
10,000,000

8,200,000

1,800,000

1,615,000

185,000
5.
10,800,000

8,856,000

1,944,000

1,700,000

244,000
6.
9,200,000

7,544,000

1,656,000

1,700,000

(44,000)
7.
11,000,000

9,020,000

1,980,000

1,870,000

110,000
8.
10,000,000

7,790,000

2,210,000

1,785,000

425,000

Gstands for given.
3-21 (20 min.) CVP exercises.

1.
a.
5,000,000 ($0.50 – $0.30) – $900,000
=
$ 100,000

b.

=

$2,250,000

2.

5,000,000 ($0.50 – $0.34) – $900,000
=
$ (100,000)

3.

[5,000,000 (1.1) ($0.50 – $0.30)] – [$900,000 (1.1)]
=
$ 110,000

4.

[5,000,000 (1.4) ($0.40 – $0.27)] – [$900,000 (0.8)]
=
$ 190,000

5.

$900,000( 1.1) ÷ ($0.50 – $0.30)
=
4,950,000 units

6.

($900,000 + $20,000) ÷ ($0.55 – $0.30)
=
3,680,000 units

3-22 (10–15 min.) CVP analysis, income taxes.

1. Operating income = Net income ÷ (1 – tax rate)
= $84,000 ´ (1 – 0.40) = $140,000

2. Contribution margin – Fixed costs = Operating income
Contribution margin – $300,000 = $140,000
Contribution margin = $440,000

3. Revenues – 0.80 Revenues = Contribution margin
0.20 Revenues = $440,000
Revenues = $2,200,000

4. Breakeven point = Fixed costs ¸ Contribution margin percentage
Breakeven point = $300,000 ÷ 0.20 = $1,500,000
3-23 (20–25 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 =

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. Sales checks to earn net income of $105,000:
$1,000,000 ¸ $8 = 125,000 sales checks

b. Sales checks to break even:

Contribution margin = $8.00 – $3.20 = $4.80
$450,000 ¸ $4.80 = 93,750 sales checks

3. Using the shortcut approach:

Change in net income = ´ ´ (1 – Tax rate)

= (150,000 – 125,000) ´ $4.80 ´ (1 – .30)
= $120,000 ´ 0.7 = $84,000
New net income = $84,000 + $105,000 = $189,000

Proof: 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

3-24 (10 min.) CVP analysis, margin of safety.

1. Breakeven point revenues =
Contribution margin percentage = = 0.40
2. Contribution margin percentage =
0.40 =
0.40 USP = USP – $12
0.60 USP = $12
USP = $20
3. Revenues, 80,000 units ´ $20 $1,600,000
Breakeven revenues 1,000,000
Margin of safety $ 600,000

3-25 (25 min.) Operating leverage.

1. Let Q denote the quantity of carpets sold

a. Breakeven point under Option 1
$500Q - $350Q = $5,000
$150Q = $5,000
Q = $5,000 ¸ $150 = 34 carpets (rounded)
b. Breakeven point under option 2
$500Q - $350Q - (0.10 ´ $500Q) = 0
100Q = 0
Q = 0

2. Operating income under Option 1 = $150Q - $5,000
Operating income under Option 2 = $100Q

Find Q such that $150Q - $5,000 = $100Q
$50Q = $5,000
Q = $5,000 ¸ $50 = 100 carpets

For Q = 100 carpets, operating income under both Option 1 and Option 2 = $10,000

3a. For Q > 100, say, 101 carpets,
Option 1 gives operating income = $150 ´ 101 - $5,000 = $10,150
Option 2 gives operating income = $100 ´ 101 = $10,100
So Color Rugs will prefer Option 1.

3b. For Q < 100, say, 99 carpets,
Option 1 gives operating income = $150 ´ 99 - $5,000 = $9,850
Option 2 gives operating income = $100 ´ 99 = $9,900
So Color Rugs will prefer Option 2.

3-25 (Cont’d.)

4. Degree of operating leverage =

Under option 1, Degree of operating leverage = = 1.5

Under option 2, Degree of operating leverage = = 1.0

5. The calculations in requirement 4 indicate that when sales are 100 units, a percentage change in sales and contribution margin will result in 1.5 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.

3-26 (30 min.) CVP analysis, sensitivity analysis.

1. USP = $30.00 ´ (1 – 0.30 margin to bookstore)
= $30.00 ´ 0.70 = $21.00
UVC = $ 4.00 variable production and marketing cost
3.15 variable author royalty cost (0.15 ´ $30.00 ´ 0.70)
$ 7.15
UCM = $21.00 – $7.15 = $13.85
FC = $ 500,000 fixed production and marketing cost
3,000,000 up-front payment to Washington
$3,500,000

3-26 (Cont’d.)

Exhibit 3-26A shows the PV graph.
EXHIBIT 3-26A
PV Graph for Media Publishers

2. a. =
=
= 252,708 copies sold (rounded up)
b. Target OI =
=
=
= 397,112 copies sold (rounded up)
3-26 (Cont’d.)
3. a. Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30 has the following effects:
USP = $30.00 ´ (1 – 0.20)
= $30.00 ´ 0.80 = $24.00
UVC = $ 4.00 variable production and marketing cost
+ 3.60 variable author royalty cost (0.15 ´ $30.00 ´ 0.80)
$ 7.60

UCM = $24.00 – $7.60 = $16.40
=
=
= 213,415 copies sold (rounded)
The breakeven point decreases from 252,708 copies in requirement 2 to 213,415 copies.
b. Increasing the listed bookstore price to $40 while keeping the bookstore margin at 30% has the following effects:
USP = $40.00 ´ (1 – 0.30)
= $40.00 ´ 0.70 = $28.00
UVC = $ 4.00 variable production and marketing cost
+ 4.20 variable author royalty cost (0.15 ´ $40.00 ´ 0.70)
$ 8.20
UCM = $28.00 – $8.20 = $19.80

=
= 176,768 copies sold (rounded)
The breakeven point decreases from 252,708 copies in requirement 2 to 176,768 copies.
c. The answer to requirements 3a and 3b decreases the breakeven point relative to requirement 2 because in each case fixed costs remain the same at $3,500,000 while contribution margin per unit increases.

3-27 (10 min.) CVP analysis, international cost structure differences.

1.

Annual Fixed Costs
(1)

Selling Price
(2)