Jawapan MA 12th ed- Chapter 3

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, and/or fixed costs of a product.


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 separated into a fixed component that does not vary with the output level and a component that is variable with respect to the output level.

3. When represented graphically, the behavior of total revenues and total costs are linear (represented as a straight line) in relation to output units within a per unit relevant range and time period.

4. The selling price, variable cost per unit, 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 cost of goods sold and operating costs (excluding income taxes):

Operating income
= Total revenues from operations –
....(Cost of goods sold + Operating cost [excluding income tax])

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 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. In the first two methods, the breakeven units are calculated by dividing total fixed costs by contribution margin per unit.


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 no income taxes are paid at this point.


3-9

Sensitivity analysis is a "what-if" technique that managers use to examine how a result will change if the original predicted data are not achieved or if an underlying assumption changes. The advent of the electronic spreadsheet 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 CVP computations.




3-17 CVP analysis, changing revenues and costs.

1a.
SP = 8% × $1,000 = $80 per ticket
VCU = $35 per ticket
CMU = $80 – $35 = $45 per ticket per ticket
FC = $22,000 a month
Q = FC ÷ CMU = $22,000 ÷ $45 per ticket
...= 489 tickets (rounded up)

1b.
Q = (FC + TOI) ÷ CMU= ($22,000 + $10,000) ÷ $45 per ticket
...= $32,000 ÷ $ 45 per ticket
...= 712 tickets (rounded up)

2a.
SP = $80 per ticket
VCU = $29 per ticket
CMU = $80 – $29 = $51 per ticket
FC = $22,000 a month
Q = FC ÷ CMU = $22,000 ÷ $51 per ticket
...= 432 tickets (rounded up)

2b.
Q = (FC + TOI) ÷ CMU= ($22,000 + $10,000) ÷ $51 per ticket
...= $32,000 ÷ $51 per ticket
...= 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 = FC ÷ CMU = $22,000 ÷ $19 per ticket
...= 1,158 tickets (rounded up)

3b.
Q = (FC + TOI) ÷ CMU= ($22,000 + $10,000) ÷ $19 per ticket
...= $32,000 ÷ $19 per ticket
...= 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:


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 UCM by $5:

SP = $53 ($48 + $5) per ticket
VCU = $29 per ticket CMU = $53 – $29 = $24 per ticket
FC = $22,000 a month
Q = FC ÷ CMU= $22,000 ÷ $24 per ticket
...= 917 tickets (rounded up)

4b.
Q = (FC + TOI) ÷ CMU= ($22,000 + $10,000) ÷ $24 per ticket
...= $32,000 ÷ $24 per ticket
...= 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.


3-18 CVP exercises.

1a.
[Unit’s sold (Selling price – Variable costs)] – Fixed costs = Operating income
[5,000,000 ($0.50 – $0.30)] – $900,000 = $100,000

1b.
Fixed costs ÷ Contribution margin per unit = Breakeven units
$900,000 ÷ [($0.50 – $0.30)] = 4,500,000 units

Breakeven units × Selling price = Breakeven revenues
4,500,000 units × $0.50 per unit = $2,250,000
or,
Fixed costs ÷ Contribution margin ratio = Breakeven revenues
$900,000 ÷ 0.40 = $2,250,000

Contribution margin ratio = (Selling price - Variable costs) ÷ Selling price
= ($0.50 - $0.30) ÷ $0.50 = 0.40

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


3-19 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 = $105,000 ÷ (1 - 0.30)
0.60R = $450,000 + $150,000
.......R = $600,000 ÷ 0.60
.......R = $1,000,000
or,


Proof:


2a.
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) x (Unit contribution margin)
.. x (1 – Tax rate)
= (150,000 – 125,000) x $4.80 x (1 – 0.30)
= $120,000 x 0.7 = $84,000

New net income
= $84,000 + $105,000
= $189,000

The alternative approach is:



3-20 CVP analysis, sensitivity analysis.

1.
SP = $30.00 x (1 – 0.30 margin to bookstore)
.....= $30.00 x 0.70 = $21.00

VCU = $ 4.00 variable production and marketing cost
.............3.15 variable author royalty cost (0.15 x $30.00 x 0.70)
..........$ 7.15

CMU = $21.00 – $7.15 = $13.85 per copy

FC = $ 500,000 fixed production and marketing cost
........3,000,000 up-front payment to Washington
......$3,500,000

Exhibit 3-20A shows the PV graph.

Exhibit 3-20A
PV Graph for Media Publishers


2a.
Breakeven (number of unit)
= FC ÷ CMU
= $3,500,000 ÷ $13.85
= 252,708 copies sold (rounded up)

2b.
Target OI
= (FC + OI) ÷ CMU
= ($3,500,000 + $2,000,000) ÷ $13.85
= $5,500,000 ÷ $13.85
= 397,112 copies sold (rounded up)

3a.
Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30 has the following effects:
SP = $30.00 x (1 – 0.20)
.....= $30.00 0.80 = $24.00

VCU =$ 4.00 variable production and marketing cost
..........+ 3.60 variable author royalty cost (0.15 x $30.00 x 0.80)
.........$ 7.60

CMU = $24.00 – $7.60 = $16.40 per copy

Breakeven (number of unit)
= FC ÷ CMU
= $3,500,000 ÷ $16.40
= 213,415 copies sold (rounded)

The breakeven point decreases from 252,708 copies in requirement 2 to 213,415 copies.

3b.
Increasing the listed bookstore price to $40 while keeping the bookstore margin at 30% has the following effects:

SP = $40.00 x (1 – 0.30)
.....= $40.00 x 0.70 = $28.00

VCU = $ 4.00 variable production and marketing cost
..........+ 4.20 variable author royalty cost (0.15 x $40.00 x 0.70)
...........$ 8.20

CMU= $28.00 – $8.20 = $19.80 per copy

Breakeven (number of unit)
= FC ÷ CMU
= $3,500,000 ÷ $19.80
= 176,768 copies sold (rounded)

The breakeven point decreases from 252,708 copies in requirement 2 to 176,768 copies.

3c.
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.


3-21 CVP analysis, margin of safety.

1.
Breakeven point revenues
= Fixed costs ÷ Contribution margin percentage

Contribution margin percentage
= Fixed costs ÷ Breakeven point revenues
= $400,000 ÷ $1,000,000
= 0.40

2.
Contribution margin percentage
= (Selling price - Variable cost per unit) ÷ Selling price
0.40 = (SP - $12) ÷ SP
0.40 SP = SP – $12
0.60 SP = $12
SP = $20

3.



3-22 Operating leverage.

1a.
Let Q denote the quantity of carpets sold

Breakeven point under Option 1
$500Q - $350Q = $5,000
.............$150Q = $5,000
...................Q = $5,000 x $150 = 34 carpets (rounded)

1b.
Breakeven point under Option 2
$500Q - $350Q - (0.10 x $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 x $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 x 101) - $5,000 = $10,150
Option 2 gives operating income = $100 x 101 = $10,100
So Color Rugs will prefer Option 1.

3b.
For Q < style="color: rgb(51, 51, 255);">
Option 1 gives operating income = ($150 x 99) - $5,000 = $9,850
Option 2 gives operating income = $100 x 99 = $9,900
So Color Rugs will prefer Option 2.

4.
Degree of operating leverage
= Contribution margin ÷ Operating income

Under Option 1
= ($150 x 100) ÷ $10,000
= 1.5

Under Option2
= ($100 x 100) ÷ $10,000
= 1.0

5.
The calculation 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 in operating income for Option 2. The degree of operating leverage at a given level of sales helps managers calculate the effect of fluctuation in sales on operating incomes.


3-23 CVP analysis, international cost structure differences.

1.



2.

1($8 + $11) x 800,000
2($5.50 + $11.50) x 800,000
3($13 + $9) x 800,000

Thailand has the lowest breakeven point––it has both the lowest fixed costs ($4,500,000) and the lowest variable cost per unit ($17.00). Hence, for a given selling price, Thailand will always have a higher operating income (or a lower operating loss) than Singapore or the U.S.

The U.S. breakeven point is 1,200,000 units. Hence, with sales of 800,000 units, it has an operating loss of $4,000,000.


3-24 Sales mix, new and upgrade customers.

1.


Let S = Number of units sold to upgrade customers
1.5S = Number of units sold to new customers

Operating income = Revenues – Variable costs – Fixed costs
OI = [$210 (1.5S) + $120S] – [$90 (1.5S) + $40S] – $14,000,000
OI = $435S – $175S – $14,000,000
Breakeven point is 134,616 units when OI = 0


Check


2.
When 200,000 units are sold, mix is:

Units sold to new customers (60% x 200,000) 120,000
Units sold to upgrade customers (40% x 200,000) 80,000


3a.
Let S = Number of units sold to upgrade customers
then S = Number of units sold to new customers


Check


3b.
Let S = Number of units sold to upgrade customers
then 9S = Number of units sold to new customers


Check


3c.
As Zapo increases its percentage of new customers, which have a higher contribution margin per unit than upgrade customers, the number of units required to break even decreases:



3-25 CVP analysis, multiple cost drivers.

1a.
Operating Income=

= ($45 x 40,000) - ($30 x 40,000) - ($60 x 1,000) - $240,000
= $1,800,000 - $1,200,000 - $60,000 - $240,000
= $300,000

1b.
Operating Income =

= ($45 x 40,000) - ($30 x 40,000) - ($60 x 800) - $240,000
= $1,800,000 - $1,200,000 - $48,000 - $240,000
= $312,000

2.
Denote the number of picture frames sold by Q, then
$45Q - $30Q – 500 x $60 - $240,000 = 0
$15Q = $30,000 + $240,000 = $270,000
.....Q = $270,000 x $15
........= 18,000 picture frames

3.
Suppose Susan had 1,000 shipments.
$45Q - $30Q - (1000 x $60) - $240,000 = 0
15Q = $300,000
....Q = 20,000 picture frames

The breakeven point is not unique because there are two cost drivers—quantity of picture frames and number of shipments. Various combinations of the two cost drivers can yield zero operating income.


3-26 Athletic scholarships, CVP analysis.

1.
Variable costs per scholarship offer:


Let the number of scholarships be denoted by Q

$22,000 Q = $5,000,000 – $600,000
$22,000 Q = $4,400,000
.............Q = $4,400,000 ÷ $22,000
................= 200 scholarships

2.
Total budget for next year = $5,000,000 × (1.00 – 0.22) = $3,900,000

Then $22,000 Q = $3,900,000 – $600,000 = $3,300,000
.....................Q = $3,300,000 ÷ $22,000 = 150 scholarships

3.
Total budget for next year from above = $3,900,000
Fixed costs ...............................................600,000
Variable costs for scholarships ..............$3,300,000

If the total number of scholarships is to remain at 200:



3-29 Uncertainty, CVP analysis.

1.
Brady pays Foreman $2 million plus $4 (25% of $16) for every home purchasing the pay-per-view. The expected value of the variable component is:


The expected value of Brady's payment is $3,520,000 ($2,000,000 fixed fee + $1,520,000).

2.
SP = $16
VCU = $ 6 ($4 payment to Foreman + $2 variable cost)
CMU= $10
FC = $2,000,000 + $1,000,000 = $3,000,000
Q = FC ÷ CMU
...= $3,000,000 ÷ $10
...= 300,000 homes

If 300,000 homes purchase the pay-per-view, Brady will break even.


3-30 CVP, target income, service firm.

1.


Breakeven quantity
= FC ÷ CMU
= $5,600 ÷ $400
= 14 children

2.
Target quantity
= (FC + Target OI) ÷ CMU
= ($5,600 + $10,400) ÷ $400
= 40 children

3.

Therefore the fee per child will increase from $600 to $650.

Alternatively,

New contribution margin per child
= ($5,600 + $2,000 + $10,400) ÷ $400 = $450

New fee per child
= Variable costs per child + New contribution margin per child
= $200 + $450
= $650


3-31 CVP analysis, CMA adapted.

1.


Breakeven point in units
= FC ÷ CMU
= $600,000 ÷ $4.00
= 150,000 units

2.
Since Galaxy is operating above the breakeven point, any incremental contribution margin will increase operating income dollar for dollar.

Increase in units sales = 10% × 200,000 = 20,000
Incremental contribution margin = $4 × 20,000 = $80,000

Therefore, the increase in operating income will be equal to $80,000.
Galaxy’s operating income in 2003 would be $200,000 + $80,000 = $280,000.

3.


Target sales in units
= (FC + Target OI) ÷ CMU
= ($600,000 + $200,000) ÷ $1.00
= 800,000 units

Target sales in dollars = $16 × 800,000 = $12,800,000


3-32 CVP analysis, income taxes.

1.
Revenues – Variable costs – Fixed costs
= Target Net Income ÷ (1 - Tax rate)

Let X = Net income for 2005
20,000($25.00) – 20,000($13.75) – $135,000 = X ÷ (1 - 0.40)
$500,000 – $275,000 – $135,000 = X ÷ 0.60
$300,000 – $165,000 – $81,000 = X
X = $54,000

Alternatively,
Operating income
= Revenues – Variable costs – Fixed costs
= $500,000 – $275,000 – $135,000 = $90,000

Income taxes = 0.40 × $90,000 = $36,000

Net income
= Operating income – Income taxes
= $90,000 – $36,000
= $54,000

2.
Let Q = Number of units to break even

$25.00Q – $13.75Q – $135,000 = 0
Q = $135,000 ÷ $11.25
...= 12,000 units

3.
Let X = Net income for 2006

22,000($25.00)–22,000($13.75)–($135,000+$11,250) = X ÷ (1–0.40)
$550,000 – $302,500 – $146,250 = X ÷ 0.60
$101,250 = X ÷ 0.60
X = $60,750

4.
Let Q = Number of units to break even with new fixed costs of $146,250

$25.00Q – $13.75Q – $146,250 = 0
Q = $146,250 ÷ $11.25 = 13,000 units

Breakeven revenues = 13,000 x $25.00 = $325,000

5.
Let S = Required sales units to equal 2006 net income

$25.00S – $13.75S – $146,250 = $54,000 ÷ 0.60
$11.25S = $236,250
..........S = 21,000 units

Revenues = 21,000 units x $25.00 = $ 525,000

6.
Let A = Amount spent for advertising in 2006

$550,000 – $302,500 – ($135,000 + A) = $60,000 ÷ 0.60
$550,000 – $302,500 – $135,000 – A = $100,000
$550,000 – $537,500 = A
A = $12,500


3-33 CVP analysis, decision making.

1.
Tocchet’s current operating income is as follows:


Let the fixed marketing and distribution costs be F. We calculate F when operating income = $600,000 and the selling price is $99.
($99 × 50,000) – ($55 × 50,000) – F = $600,000
$4,950,000 – $2,750,000 – F = $600,000
F = $4,950,000 – $2,750,000 – $600,000
F = $1,600,000

Hence, the maximum increase in fixed marketing and distribution costs that will allow Tocchet to reduce the selling price and maintain $600,000 in operating income is $200,000 ($1,600,000 – $1,400,000).

2.
Let the selling price be P.

We calculate P for which, after increasing fixed manufacturing costs by $100,000 to $900,000 and variable manufacturing cost per unit by $2 to $47, operating income = $600,000

$40,000P–($47×40,000)–($10×40,000)– $900,000– $600,000=$600,000
$40,000 P – $1,880,000 – $400,000 – $900,000 – $600,000 = $600,000
$40,000 P = $600,000 + $1,880,000 + $400,000 + $900,000 + $600,000
$40,000 P = $4,380,000
............P = $4,380,000 ÷ 40,000
...............= $109.50

Tocchet will consider adding the new features provided the selling price is at least $109.50 per unit.


3-34 CVP analysis, shoe stores.

1.
Contribution margin per pair
= Selling price – Variable costs per pair
= $30 – $21
= $9 a pair

Breakeven point in number of pairs:
= FC ÷ CMU
= $360,000 ÷ $9.00
= 40,000 pairs

Breakeven points in revenues:
= FC ÷ CM% per dollar of sales
= $360,000 ÷ (100%-70%)
= $1,200,000

2.


An alternative approach is that 35,000 units is 5,000 units below the breakeven point, and the unit contribution margin is $9.00:

$9.00 x 5,000 = $45,000 below breakeven

3.
Fixed costs: $360,000 + $81,000 = $441,000
Contribution margin per pair = $30 – $19.50 = $10.50

a. Breakeven point in units = $441,000 ÷ $10.50 = 42,000 pairs

b. Breakeven point in revenues = $30 x 42,000 = $1,260,000

4.
Fixed costs = $360,000
Contribution margin per pair = $30 – $21 – $0.30 = $8.70

a. Breakeven point in units=$360,000÷$8.70=41,380pairs(rounded up)

b. Breakeven point in revenues = $30 x 41,380 = $1,241,400

5.
Breakeven point = 40,000 pairs
Store manager receives commission on 10,000 pairs.
Cost of commission = $0.30 x 10,000 = $3,000


An alternative approach is 10,000 pairs x $8.70 contribution margin per pair = $87,000.


3-38 CVP analysis, income taxes, sensitivity.

1a.
In order to break even, Almo Company must sell 500 units. This amount represents the point where revenues equal total costs.

Let Q denote the quantity of canopies sold.
Revenue = Variable costs + Fixed costs
$400Q = $200Q + $100,000
$200Q = $100,000
.......Q = 500 units

Breakeven can also be calculated using contribution margin per unit.
Contribution margin per unit
= Selling price – Variable cost per unit
= $400 – $200
= $200

Breakeven = Fixed Costs ÷ Contribution margin per unit
= $100,000 ÷ $200
= 500 units

1b.
In order to achieve its net income objective, Almo Company must sell 2,500 units. This amount represents the point where revenues equal total costs plus the corresponding operating income objective to achieve net income of $240,000.

Revenue = Variable costs + Fixed costs + [Net income ÷ (1 – Tax rate)]
$400Q = $200Q + $100,000 + [$240,000 ÷ (1 - 0.4)]
$400 Q = $200Q + $100,000 + $400,000
........Q = 2,500 units

2.
To achieve its net income objective, Almo Company should select the first alternative where the sales price is reduced by $40, and 2,700 units are sold during the remainder of the year. This alternative results in the highest net income and is the only alternative that equals or exceeds the company’s net income objective. Calculations for the three alternatives are shown below.

Alternative 1
Revenues = ($400 x 350) + ($360a x 2,700) = $1,112,000
Variable costs = $200 x 3,050b = $610,000
Operating income = $1,112,000 - $610,000 - $100,000 = $402,000
Net income = $402,000 x (1 - 0.4) = $241,200

a$400 – $40; b350 units + 2,700 units.

Alternative 2
Revenues = ($400 x 350) + ($370c x 2,200) = $954,000
Variable costs = ($200 x 350) + ($190d x 2,200) = $488,000
Operating income = $954,000 - $488,000 - $100,000 = $366,000
Net income = $366,000 x (1 - 0.4) = $219,600

c$400 – $30; d$200 – $10.

Alternative 3
Revenues = ($400 x 350) + ($380e x 2,000) = $900,000
Variable costs = $200 x 2,350f = $470,000
Operating income = $900,000 - $470,000 - $90,000g = $340,000
Net income = $340,000 x (1 - 0.4) = $204,000

e$400 – 0.05 x $400 = 400 – $20;
f350 units + 2,000 units;
g$100,000 – $10,000


3-40 Sales mix, three products.

1.
Sales of A, B, and C are in ratio 20,000 : 100,000 : 80,000. So for every 1 unit of A, 5 (100,000 ÷ 20,000) units of B are sold, and 4 (80,000 ÷ 20,000) units of C are sold.

Let Q = Number of units of A to break even
5Q = Number of units of B to break even
4Q = Number of units of C to break even

Contribution margin – Fixed costs = Zero operating income


2.


3.


Let Q = Number of units of A to break even
...4Q = Number of units of B to break even
...5Q = Number of units of C to break even

Contribution margin – Fixed costs = Breakeven point


Breakeven point increases because the new mix contains less of the higher contribution margin per unit, product B, and more of the lower contribution margin per unit, product C.


3-41 Multiproduct breakeven, decision making.

1.
Breakeven point in 2005 (units)
= FC ÷ CMU
= $495,000 ÷ ($50 - $20)
= 16,500 units

Breakeven point in 2005 (in revenues)
= 16,500 units × $50
= $825,000 in sales revenues

2.
Breakeven point in 2006 (in units)
Evenkeel expects to sell 3 units of Plumar for every 2 units of Ridex in 2006, so consider a bundle consisting of 3 units of Plumar and 2 units of Ridex.

Unit contribution Margin from Plumar = $50 – $20 = $30
Unit contribution Margin from Ridex = $25 – $15 = $10

The contribution margin for the bundle is
$30 × 3 units of Plumar + $10 × 2 units of Ridex = $110

So bundles to be sold to breakeven
= $495,000 ÷ $110
= 4,500 bundles

Breakeven point in 2006 (in units)
Plumar, 4,500 × 3 = 13,500 units
Ridex, 4,500 × 2 = 9,000 units

Breakeven point in revenues:


4.
Despite the breakeven sales revenue being higher, Evenkeel should accept Glaston’s offer. The breakeven points are irrelevant because Evenkeel is already above the breakeven sales volume in 2003. By accepting Glaston’s offer, Evenkeel has the ability to sell all the 30,000 units of Plumar in 2004 and make more sales of Ridex to Glaston without incurring any more fixed costs.

Operating income in 2004 with and without Ridex are expected to be as folows:

1 $50 x 30,000 units
2 ($50 x 30,000 units) + ($25 x 20,000)
3 $20 x 30,000 units
4 ($20 x 30,000 units) + ($15 x 20,000)


3-42 Sales mix, two products.

1.
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

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)
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.


3-44 Ethics, CVP analysis.

1.
Contribution margin percentage
= (Revenue - Variable costs) ÷ Revenue
= ($5,000,000 - $3,000,000) ÷ $5,000,000
= $2,000,000 ÷ $5,000,000
= 40%

Breakeven revenues
= FC ÷ CM%
= $2,160,000 ÷ 0.40
= $5,400,000

2.
If variable costs are 52% of revenues, contribution margin percentage equals 48% (100% - 52%)

Breakeven revenues
= FC ÷ CM%
= $2,160,000 ÷ 0.48
= $4,500,000

3.


4.
Incorrect reporting of environmental costs with the goal of continuing operations is unethical. In assessing the situation, the specific “Standards of Ethical Conduct for Management Accountants” (described in Exhibit 1-7) that the management accountant should consider are listed below.

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 Bush to not 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. Bush may be tempted to report lower environmental costs to please Lemond and Woodall and save the jobs of his colleagues. This action, however, violates the responsibility for integrity. The Standards of Ethical Conduct require the management accountant to communicate favorable as well as unfavorable information.

Objectivity
The management accountant’s Standards of Ethical Conduct 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.

Bush should indicate to Lemond that estimates of environmental costs and liabilities should be included in the analysis. If Lemond still insists on modifying the numbers and reporting lower environmental costs, Bush should raise the matter with one of Lemond’s superiors. If after taking all these steps, there is continued pressure to understate environmental costs, Bush should consider resigning from the company and not engage in unethical behavior.


3-45 Deciding where to produce.

1.
The annual breakeven point in units at the Peoria plant is 73,500 units and at the Moline plant is 47,200 units, calculated as follows.

Contribution margin per unit calculation:


Fixed costs calculation:
Total fixed costs
= (Fixed manufacturing costs per unit + Fixed marketing and distribution costs per unit) × Production rate per day × Normal working days

Peoria = ($30.00 + $19.00) × 400 × 240 = $4,704,000

Moline = ($15.00 + $14.50) × 320 × 240 = $2,265,600

Breakeven calculation:

Breakeven units = Fixed costs ÷ Contribution margin per unit

Peoria = $4,704,000 ÷ $64 = 73,500 units

Moline = $2,265,600 ÷ $48 = 47,200 units

2.
The operating income that would result from the division production manager’s plan to produce 96,000 units at each plant is $3,628,800. The normal capacity at the Peoria plant is 96,000 units (400 × 240); however, the normal capacity at the Moline plant is 76,800 units (320 × 240). Therefore, 19,200 units (96,000 – 76,800) will be manufactured at Moline at a reduced contribution margin of $40.00 per unit ($48 – $8).

3.
The optimal production plan is to produce 120,000 units at the Peoria plant and 72,000 units at the Moline plant. The full capacity of the Peoria plant, 120,000 units (400 units × 300 days), should be utilized as the contribution from these units is higher at all levels of production than the contribution from units produced at the Moline plant.


The contribution margin is higher when 120,000 units are produced at the Peoria plant and 72,000 units at the Moline 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.


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