CHAPTER 17
COST-VOLUME-PROFIT ANALYSIS
QUESTIONS FOR WRITING AND DISCUSSION
1. CVP analysis allows managers to focus on
prices, volume, costs, profits, and sales mix.
Many different “what-if” questions can be
asked to assess the effect on profits of
changes in key variables.
9. Sales mix is the relative proportion sold of
each product. For example, a sales mix of
4:1 means that, on average, of every five
units sold, four are of the first product and
one is of the second product.
2. The units-sold approach defines sales volume in terms of units of product and gives
answers in these same terms. The salesrevenue approach defines sales volume in
terms of revenues and provides answers in
these same terms.
3. Break-even point is the level of sales activity
where total revenues equal total costs, or
where zero profits are earned.
4. At the break-even point, all fixed costs are
covered. Above the break-even point, only
variable costs need to be covered. Thus,
contribution margin per unit is profit per unit,
provided that the unit selling price is greater
than the unit variable cost (which it must be
for break-even to be achieved).
10.
Packages of products, based on the expected sales mix, are defined as a single
product. Price and cost information for this
package can then be used to carry out CVP
analysis.
11.
A multiple-product firm may not care about
the individual product break-even points. It
may feel that some products can even lose
money as long as the overall picture is profitable. For example, a company that produces
a full line of spices may not make a profit on
each one, but the availability of even the
more unusual spices in the line may persuade grocery stores to purchase from the
company.
12.
Income taxes do not affect the break-even
point at all. Since taxes are a percentage of
income, zero income will generate zero taxes. However, CVP analysis is affected by income taxes in that a target profit must be figured in before-tax income since the CVP
equations do not include the income tax rate.
13.
A change in sales mix will change the contribution margin of the package (defined by the
sales mix) and, thus, will change the units
needed to break even.
14.
Margin of safety is the sales activity in excess of that needed to break even. Operating
leverage is the use of fixed costs to extract
higher percentage changes in profits as
sales activity changes. It is achieved by raising fixed costs and lowering variable costs.
The greater the degree of operating leverage, the more that changes in sales activity
will affect profits. As the margin of safety increases, risk decreases. Increases in leverage raise risk.
15.
Activity-based costing reminds managers
that costs may vary with respect to variables
other than units. Some costs vary according
to the number of batches or number of prod-
5. The contribution margin is very likely negative (variable costs are greater than revenue). When this happens, increasing sales
volume just means increasing losses.
6. Variable cost ratio = Variable costs/Sales.
Contribution margin ratio = Contribution margin/Sales. Also, Contribution margin ratio = 1
– Variable cost ratio. Basically, contribution
margin and variable costs sum to sales.
Therefore, if contribution margin accounts for
a particular percentage of sales, variable
costs account for the rest.
7. The increase in contribution margin ratio
means that the amount of every sales dollar
that goes toward covering fixed cost and
profit has just gone up. As a result, the
break-even point will go down.
8. No. The increase in contribution is $9,000
(0.3 × $30,000), and the increase in advertising is $10,000. This is an important example
because the way the problem is phrased influences us to compare increased revenue
with increased fixed cost. This comparison is
irrelevant. The important comparison is between contribution margin and fixed cost.
379
ucts. This insight prevents a single-minded
focus on unit-based costs, to the exclusion of
factors which might change fixed costs.
EXERCISES
17–1
1.
Contribution margin = Price – Variable costs = $55 – $37 = $18
2.
Break-even in units = $41,400/$18 = 2,300 purses
3.
Sales ($55  6,000)
Less: Variable costs ($37  6,000)
Contribution margin
Less: Fixed costs
Operating income
$330,000
222,000
$108,000
41,400
$ 66,600
17–2
1.
Break-even in units = $270,000/($50 – $23) = 10,000 refrigerators
2.
Sales ($50  16,000)
Less: Variable costs ($23  16,000)
Contribution margin
Less: Fixed costs
Operating income
3.
New break-even in units = $270,000/($50 – $20)
= 9,000 refrigerators
$800,000
368,000
$432,000
270,000
$162,000
17–3
1.
Break-even in units = $4,325/($6.50 – $4.00)
= 1,730 pieces of pottery
2.
Number of units to earn $7,000 profit:
= ($4,325 + $7,000)/($6.50 – $4.00)
= 4,530 pieces of pottery
Sales ($6.50  4,530)
Less: Variable costs ($4  4,530)
Contribution margin
Less: Fixed costs
Operating income
$29,445
18,120
$11,325
4,325
$ 7,000
380
17–4
1.
Break-even in units = $2,380/($60 – $25) = 68 jobs per month
2.
Sales..........................................
Less: Variable cost ..................
Contribution margin ............
Less: Fixed expenses ..............
Operating income................
65 Jobs
$ 3,900
1,625
$ 2,275
2,380
$ (105)
100 Jobs
$ 6,000
2,500
$ 3,500
2,380
$ 1,120
At 100 jobs, the profit is $1,120; at 65 jobs, the loss is $105.
3.
Break-even in units = $2,380/($75 – $25) = 47.6 or 48 jobs per month
17–5
0.06($65,000)X
$3,900X
$2,600X
X
Monthly revenue
= $1,500(20) + 0.02($65,000)X
= $30,000 + $1,300X
= $30,000
= 11.5385 cars per month
= 11.5385($65,000)
= $750,003
Note: Think of this as average monthly revenue. That is, while you cannot sell a
part of a car, some months you might sell 11 cars and other months you might
sell 12 or 13.
17–6
1.
Contribution margin ratio = 1 – ($5,066,600/$10,780,000) = 0.53
Break-even sales revenue = $2,194,200/0.53 = $4,140,000
2.
Margin of safety = Sales – Break-even sales
= $10,780,000 – $4,140,000 = $6,640,000
3.
Contribution margin from increased sales = ($150,000)(0.53) = $79,500
Cost of proposal = $140,000
No, the proposal is not a good idea, the company’s operating income will decrease by $60,500.
381
17–7
1.
Break-even units = $100,000/($400 – $200) = 500 units
2.
First, convert after-tax profit to before-tax profit.
Before-tax profit = $240,000/(1 – 0.4) = $400,000
Let X equal the number of units which must be sold to yield before-tax profit
of $400,000.
$400,000 = $400X – $200X – $100,000
X = 2,500
3.
Alternative A is best, as shown by the following calculations:
Alternative A:
Revenue = $400(350) + $360(2,700) = $1,112,000
Variable cost = $200(3,050) = $610,000
Operating profit = $1,112,000 – $610,000 – $100,000 = $402,000
After-tax profit = $402,000(1 – 0.4) = $241,200
Alternative B:
Revenue = $400(350) + $370(2,200) = $954,000
Variable cost = $200(350) + $175(2,200) = $455,000
Operating profit = $954,000 – $455,000 – $100,000 = $399,000
After-tax profit = $399,000(1 – 0.4) = $239,400
Alternative C:
Revenue = $400(350) + $380(2,000) = $900,000
Variable cost = $200(2,350) = $470,000
Operating profit = $900,000 – $470,000 – $90,000 = $340,000
After-tax profit = $340,000(1 – 0.4) = $204,000
4.
Four assumptions underlying CVP analysis are as follows:
All costs can be divided into fixed and variable elements.
Total variable costs are directly proportional to volume over the relevant
range.
Selling prices are to be unchanged.
Volume is the only relevant factor affecting cost.
382
17–8
1.
Sales (17,800  $35)
Variable expenses (17,800  $23.10)
Contribution margin
Fixed expenses
Operating income
Income taxes (@ 40%)
Net income
2.
Break-even revenue = $23,800/0.34 = $70,000
3.
Units = ($23,800 + $214,200)/($35.00 – $23.10) = 20,000
4.
Before-tax income = $214,200/(1 – 0.40) = $357,000
Units = ($23,800 + $357,000)/($35.00 – $23.10) = 32,000
$623,000
411,180
$211,820
23,800
$188,020
75,208
$112,812
17–9
1.
Sales..................................................
Less variable expenses:
Direct materials ..........................
Direct labor .................................
Variable overhead ......................
Variable selling & admin. ..........
Contribution margin .........................
$1,500,000
$ 250,000
150,000
80,000
300,000
780,000
$ 720,000
Contribution margin ratio = $720,000/$1,500,000 = 0.48
Break-even revenue = Fixed expenses/Contribution margin ratio
= ($100,000 + $250,000)/0.48
= $729,167
2.
Next year’s data:
Fixed expenses = $100,000 + $250,000 + $45,000 = $395,000
Sales = $1,500,000
Variable expenses = $780,000(1.1) = $858,000
Contribution margin ratio = ($1,500,000 – $858,000)/$1,500,000
= 0.428
Break-even point = $395,000/0.428 = $922,897
383
17–10
1.
d
2.
b
3.
a
Original sales ......................
Less: Variable cost .............
Contribution margin ............
Less: Fixed cost ..................
Operating income................
4. c
$ 300,000
240,000
$ 60,000
40,000
$ 20,000
100%
80%
20%
If sales increase by 20%, then revised sales equal $360,000, and the revised
income statement is as follows:
Revised sales ......................
Less: Variable cost .............
Contribution margin ............
Less: Fixed cost ..................
Operating income................
5.
$ 360,000
288,000
$ 72,000
40,000
$ 32,000
100%
80%
20%
a
Price = $3.50/0.7 = $5.00
Added profit
(0.10)($5)(50,000)
$25,000
Added fixed cost
6.
= Added contribution margin – Added fixed cost
= $1.50(50,000) – Added fixed cost
= $75,000 – Added fixed cost
= $50,000
c
8,500 = $297,500/(P – $140)
P = $175
17–11
1.
Contribution margin per unit = $3.60 – $2.88* = $0.72
*Variable unit cost
= $0.75 + $0.38 + $0.35 + $1.15 + $0.25
= $2.88
Contribution margin ratio = $0.72/$3.60 = 0.20
2.
Break-even in units = ($12,000 + $6,720)/$0.72 = 26,000 bottles
Break-even in sales = 26,000 × $3.60 = $93,600
or
= ($12,000 + $6,720)/0.20 = $93,600
384
17–11 Concluded
3.
Sales ($3.60 × 35,000) ..............................
Variable costs ($2.88 × 35,000) ...............
Contribution margin ............................
Fixed costs ...............................................
Operating income................................
$126,000
100,800
$ 25,200
18,720
$ 6,480
4.
Margin of safety = $126,000 – $93,600 = $32,400
or 35,000  26,000 = 9,000 units
5.
Break-even in units = $18,720/($4.00 – $2.88)
= 16,714.3, or 16,715 if rounded to whole units
New operating income = $4(30,400) – $2.88(30,400) – $18,720
= $121,600 – $87,552 – $18,720
= $15,328
Yes, operating income will increase by $8,848 ($15,328 – $6,480).
17–12
1.
Trimax:
Quintex:
$250,000/$50,000 = 5
$400,000/$50,000 = 8
2.
Trimax, Inc.
X = $200,000/0.5*
X = $400,000
Quintex, Inc.
X = $350,000/0.8*
X = $437,500
*$250,000/$500,000 = 0.5; $400,000/$500,000 = 0.8.
Quintex must sell more than Trimax in order to break even because it must
cover $150,000 more in fixed expenses. (It is more highly leveraged.)
3.
Trimax:
Quintex:
5 × 50% = 250%
8 × 50% = 400%
The percentage increase in profits for Quintex is higher than Trimax’s increase due to Quintex’s higher degree of operating leverage (i.e., it has a
larger amount of fixed expenses in proportion to variable costs than Trimax).
Once fixed expenses are covered, additional revenue must only cover variable costs, and 50% of Quintex’s revenue above break-even is profit, whereas
only 20% of Trimax’s revenue above break-even is profit.
385
17–13
1.
Variable
Units in
Package
Product
Price* –
Cost
= CM ×
Mix
=
CM
Miniphone
$25
$12
$13
1
$ 13
Netphone
60
50
10
3
30
Total .............................................................................................. $ 43
*$5,000,000/200,000 = $25
$36,000,000/600,000 = $60
Break-even = $3,440,000/$43
= 80,000
80,000 miniphones (1 × 80,000)
240,000 netphones (3 × 80,000)
2.
Revenue = $3,440,000/($8,600,000/$41,000,000) = $16,400,000
7–14
1.
Before-tax income = $24,000/(1 – 0.4)
= $40,000
Number of pairs of touring model skis to earn $24,000 after-tax income:
= ($316,800 + $40,000)/($80.00 – $52.80)
= 13,118 pairs
2.
Let X = Number of pairs of mountaineering skis
and Y = Number of pairs of touring skis
$88X – $52.80X – $369,600 = $80Y – $52.80Y – $316,800
$88X – $52.80X – $52,800 = $80Y – $52.80Y
$88X – $52.80X – $52,800 = $80(88/80)X – $52.80(88/80)X*
$5.28X = $52,800
X = 10,000 pairs
Revenue = $88 × 10,000 = $880,000
*If total revenue is the same, then 88X = 80Y, or Y = (88/80)X and (88/80)X can
be substituted for Y.
386
7–14
3.
Concluded
Siberian Ski Company would produce and sell 12,000 pairs of the mountaineering skis because they are more profitable.
Sales .......................................
Less: Variable expenses ......
Contribution margin .........
Less: Fixed expenses ...........
Operating income.............
Mountaineering Model
$ 1,056,000
633,600
$ 422,400
369,600
$ 52,800
387
Touring Model
$960,000
633,600
$326,400
316,800
$ 9,600
PROBLEMS
17–15
1.
Break-even calculations for the first year of operations:
Fixed expenses:
Advertising .....................................
Rent (6,000 × $28) ..........................
Property insurance ........................
Utilities ............................................
Malpractice insurance ...................
Depreciation ($60,000/4) ................
Wages and fringe benefits:
Regular wagesa .......................
Overtime wagesb .....................
Fringe benefits (@ 40%) .........
Total fixed expenses .............................
$ 500,000
168,000
22,000
32,000
180,000
15,000
403,200
7,500
164,280
$1,491,980
a($25
+ $20 + $15 + $10)(16 hours)(360 days) = $403,200.
b(200 × $15 × 1.5) + (200 × $10 × 1.5) = $7,500.
Break-even point = Revenue – Variable costs – Fixed costs
= $30X + ($2,000)(0.2X)(0.3) – $4X – $1,491,980
= $30X + $120X – $4X – $1,491,980
146X = $1,491,980
X = 10,219.04 or 10,220 clients
2.
Based on the report of the marketing consultant, the expected number of new
clients during the first year is 18,000. Therefore, it is feasible for the law office to break even during the first year of operations as the break-even point
is 10,220 clients (as shown above).
Expected value = (20 × 0.1) + (30 × 0.3) + (55 × 0.4) + (85 × 0.2)
= 50 clients per day
Annual clients = 50 × 360 days
= 18,000 clients per year
388
17–16
1.
a.
Operating income for 2:1 sales mix:
Regular
Sander
Mini-Sander
Sales ..........................................
$ 3,000,000
$ 2,250,000
Less: Variable expenses ..........
1,800,000
1,125,000
Contribution margin .............
$ 1,200,000
$ 1,125,000
Less: Direct fixed expenses.....
250,000
450,000
Product margin .....................
$ 950,000
$ 675,000
Less: Common fixed expenses ...............................................
Operating income .................................................................
b.
Operating income for 1:1 sales mix:
Regular
Sander
Mini-Sander
Sales ..........................................
$ 2,400,000
$ 3,600,000
Less: Variable expenses ..........
1,440,000
1,800,000
Contribution margin .............
$ 960,000
$ 1,800,000
Less: Direct fixed expenses.....
250,000
450,000
Product margin .....................
$ 710,000
$ 1,350,000
Less: Common fixed expenses ...............................................
Operating income .................................................................
c.
Total
$6,000,000
3,240,000
$2,760,000
700,000
$2,060,000
600,000
$1,460,000
Operating income for 1:3 sales mix:
Regular
Sander
Mini-Sander
Sales ..........................................
$ 1,200,000
$ 5,400,000
Less: Variable expenses ..........
720,000
2,700,000
Contribution margin .............
$ 480,000
$ 2,700,000
Less: Direct fixed expenses.....
250,000
450,000
Product margin .....................
$ 230,000
$ 2,250,000
Less: Common fixed expenses ...............................................
Operating income .................................................................
d.
Total
$5,250,000
2,925,000
$2,325,000
700,000
$1,625,000
600,000
$1,025,000
Total
$6,600,000
3,420,000
$3,180,000
700,000
$2,480,000
600,000
$1,880,000
Operating income for 1:2 sales mix:
Regular
Sander
Mini-Sander
Sales ..........................................
$ 1,200,000
$ 3,600,000
Less: Variable expenses ..........
720,000
1,800,000
Contribution margin .............
$ 480,000
$ 1,800,000
Less: Direct fixed expenses.....
250,000
450,000
Product margin .....................
$ 230,000
$ 1,350,000
Less: Common fixed expenses ...............................................
Operating income .................................................................
389
Total
$4,800,000
2,520,000
$2,280,000
700,000
$1,580,000
600,000
$ 980,000
17–16 Concluded
2.
a.
Unit Contribution
Sales
Package
Product
Margin
Mix
Contribution Margin
Regular sander
$40 – $24 = $16
2
$ 32
Mini-sander
$60 – $30 = $30
1
30
Total .......................................................................
$ 62
Break-even packages = $1,300,000/$62 = 20,967.74
Break-even regular sanders = 41,935
Break-even mini-sanders = 20,968
b.
Unit Contribution
Sales
Package
Product
Margin
Mix
Contribution Margin
Regular sander
$40 – $24 = $16
1
$ 16
Mini-sander
$60 – $30 = $30
1
30
Total .......................................................................
$ 46
Break-even packages = $1,300,000/$46 = 28,260.87
Break-even regular sanders = 28,261*
Break-even mini-sanders = 28,261*
*Rounded to nearest whole unit.
c.
Unit Contribution
Sales
Package
Product
Margin
Mix
Contribution Margin
Regular sander
$40 – $24 = $16
1
$ 16
Mini-sander
$60 – $30 = $30
3
90
Total .......................................................................
$106
Break-even packages = $1,300,000/$106 = 12,264.15
Break-even regular sanders = 12,264
Break-even mini-sanders = 36,792
d.
Unit Contribution
Sales
Package
Product
Margin
Mix
Contribution Margin
Regular sander
$40 – $24 = $16
1
$ 16
Mini-sander
$60 – $30 = $30
2
60
Total .......................................................................
$ 76
Break-even packages = $1,300,000/$76 = 17,105.26
Break-even regular sanders = 17,105
Break-even mini-sanders = 34,211
390
17–17
Sales ..................................
Less: Variable costs ........
Contribution margin ...
Less: Fixed costs .............
Operating income .......
A
$10,000
8,000
$ 2,000
1,000*
$ 1,000
Units sold ..............................
Price/Unit ..............................
Variable cost/Unit .................
Contribution margin/Unit .....
Contribution margin ratio ....
Break-even in units ..............
B
$15,600*
11,700
$ 3,900
5,000
$ (1,100)*
2,000*
$5
$4*
$1*
20%*
1,000*
1,300
$12*
$9
$3
25%*
1,667*
C
$16,250*
9,750
$ 6,500*
6,100*
$ 400
D
$ 9,000
5,400*
$ 3,600*
750
$ 2,850
125
$130
$78*
$52*
40%
118*
90
$100*
$60*
$40*
40%*
19*
*Designates calculated amount.
Note: When the calculated break-even in units includes a fractional amount, it has
been rounded up to the next whole unit.
17–18
1.
Variable cost ratio = $342,000/$900,000 = 0.38
Contribution margin ratio = $558,000/$900,000 = 0.62
2.
$150,000 × (0.62) = $93,000
3.
Revenue = ($363,537 + 0)/0.62
0.62 × Revenue = $363,537
Revenue = $586,350
Margin of safety = $900,000 – $586,350 = $313,650
391
17–18 Concluded
4.
Revenue = ($363,537 + $200,000)/0.62 = $908,931
Operating income = $120,000/(1 – 0.4)* = $200,000
*$77,785/$194,463 = 0.4 tax rate.
Revenue = ($363,537 + $200,000)/0.62 = $908,931
Sales.....................................................................
Less: Variable expenses ($908,931 × 0.38) .......
Contribution margin .....................................
Less: Fixed expenses .........................................
Profit before taxes ........................................
Taxes ($200,000 × 0.40) ......................................
Net income ....................................................
$908,931
345,394
$563,537
363,537
$200,000
80,000
$120,000
17–19
1.
Contribution margin per unit = $281,250/125,000 = $2.25
Contribution margin ratio = $281,250/$625,000 = 0.45
Break-even units = $180,000/$2.25 = 80,000 units
Break-even revenue = 80,000 × $5 = $400,000
or
Break-even revenue = $180,000/0.45 = $400,000
Margin of safety = $625,000 – $400,000 = $225,000
2.
The break-even point decreases:
Units = $180,000/Contribution margin per unit
= $180,000/($5.50 – $2.75)
= 65,455 units
Revenue = 65,455 × $5.50 = $360,003
3.
The break-even point increases:
Units = $180,000/($5.00 – $3.10)
= 94,737 units
Revenue = 94,737 × $5.00 = $473,685
392
17–19 Concluded
4.
Predictions of increase or decrease of the break-even point can be made
without computation for price changes or for variable cost changes. If both
change, then the unit contribution margin must be known before and after to
predict the effect on the break-even point. Simply giving the direction of the
change for each individual component is not sufficient. For our example, the
unit contribution changes from $2.25 to $2.40, so the break-even point will
decrease.
Units = $180,000/($5.50 – $3.10)
= 75,000 units
Revenue = 75,000 × $5.50 = $412,500
5.
The break-even point will increase as more units will need to be sold to cover
the additional fixed expenses.
Units = $230,000/$2.25
= 102,223 units
Revenue = 102,223 × $5 = $511,115
17–20
1.
$900,000/100,000 = $9 = Unit contribution margin
Units = $765,000/$9 = 85,000 units
Profit = 30,000 × $9 = $270,000
2.
CM ratio = $900,000/$2,000,000 = 0.45
Break-even sales = $765,000/0.45 = $1,700,000
Profit = ($200,000 × 0.45) + $135,000 = $225,000
3.
Margin of safety = $2,000,000 – $1,700,000 = $300,000
4.
$900,000/$135,000 = 6.667 (Operating leverage)
6.667 × 20% = 1.3333
1.3333 × $135,000 = $180,000
New profit level = $180,000 + $135,000 = $315,000
5.
0.10($20) × Units = ($20 × Units) – ($11 × Units) – $765,000
$2 × Units = ($9 × Units) – $765,000
Units = 109,286
6.
Operating income = $180,000/(1 – 0.4) = $300,000
Units = ($765,000 + $300,000)/$9 = 118,334
393
17–21
1.
Unit contribution margin = $4,050,000/120,000 = $33.75
Break-even point = $3,375,000/$33.75 = 100,000
CM ratio = $4,050,000/$7,500,000 = 0.54
Break-even point = $3,375,000/0.54 = $6,250,000
2.
Sales.............................................
Variable expenses .......................
Contribution margin ...............
Fixed expenses ...........................
Operating income...................
$8,500,000
4,213,450*
$4,286,550
3,475,000
$ 811,550
*Unit variable cost = $3,450,000/120,000 = $28.75 Variable cost ratio =
28.75/58 = 0.4957. Thus, variable expenses = 0.4957 × $8,500,000 =
$4,213,450.
The company would gain $136,550 if the proposal is implemented.
3.
$540,000 × 0.54 = $291,600
4.
Operating income = $1,254,000/(1 – 0.34) = $1,900,000
Units = ($3,375,000 + $1,900,000)/$33.75
= 156,297 units
5.
Margin of safety = $7,500,000 – $6,250,000 = $1,250,000
6.
Operating leverage = $4,050,000/$675,000 = 6
Profit increase = 20% × 6 = 120%
17–22
1.
CM ratio = $372,429/$802,429 = 0.464
2.
Revenue = $154,750/0.464
= $333,513
3.
1.06($217,679)
$230,740
0.4372Revenue
Revenue
$895,883 – $802,429
$93,454/$802,429
= [1 – 1.05(0.536)]Revenue – 1.04($154,750)
= 0.4372Revenue – $160,940
= $391,680
= $895,883
= $93,454 (increase in revenues needed)
= 11.6% increase in bid prices
Kline should raise prices approximately 11.6% for a 6% income increase.
394
17–22 Concluded
4.
Income = $175,000/(1 – 0.34) = $265,152
Revenue = ($265,152 + $160,940)/0.4372
= $974,593
17–23
1.
Break-even units = $300,000/$20.30* = 14,778
*$406,000/20,000 = $20.30.
Break-even dollars = 14,778 × $60.90** = $899,980
or
= $300,000/0.3333 = $900,090
The difference is due to rounding error.
**$1,218,000/20,000 = $60.90.
2.
Margin of safety = $1,218,000 – $900,090 = $317,910
3.
Sales ..................................................................
Variable costs ($1,218,000 × 0.45) ..................
Contribution margin ....................................
Fixed costs .......................................................
Net income ...................................................
$1,218,000
548,100
$ 669,900
550,000
$ 119,900
Break-even units = $550,000/$33.495* = 16,420
Break-even sales dollars = $550,000/0.55** = $1,000,000
*$669,900/20,000 = $33.495.
**$669,900/$1,218,000 = 55%.
395
17–24
1.
Unit variable cost = $18 + (Var. OH/Total DLH)Unit DLH
= $18 + ($120,000/30,000)1 = $22
Break-even units = $18,000/($26 – $22) = 4,500
Additional profit = $4 × (20,000 – 4,500) = $62,000
2.
Unit-based variable costs:
Materials handling.........
Power .............................
Machine costs ...............
Total ..........................
Machine hours* .............
Pool rate ....................
$ 18,000
22,000
80,000
$ 120,000
÷ 20,000
$
6.00
*Since all three activities have the same consumption ratio, kilowatt-hours or
material moves could also be used as cost drivers.
Overhead ($6 × 10,000/20,000) ................
Prime cost .................................................
Total unit variable cost .......................
$ 3
18
$ 21
Non-unit-based variable costs (assumes costs vary strictly with each cost
driver with no fixed components; in reality, fixed components could exist for
each activity and some method of separating fixed and variable costs should
be used):
Product-level: Engineering (X2) = $100,000/5,000 = $20/hour
Batch-level:
Inspection (X3) = $40,000/2,100 = $19/inspection hour
Setups (X4) = $60,000/60 = $1,000/setup
Break-even units (where X1 equals units):
$26X1 = $18,000 + $21X1 + $20X2 + $19X3 + $1,000X4
X1 = ($18,000 + $20X2 + $19X3 + $1,000X4)/5
X1 = 20,920
The above analysis assumes that the expected engineering hours, inspection
hours, and setups are realized. If the levels of these three activities vary, then
the break-even point will vary. The analysis also assumes that depreciation is
a fixed cost. In an activity-based costing system, this cost may be converted
into a variable cost by using the units-of-production method. If this were
done, assuming that the $18,000 represents straight-line depreciation with no
salvage value and that the annual expected production of 20,000 units is
achieved, then the variable cost per unit would increase by $0.90
396
17-24 Concluded
($18,000/20,000). In the above analysis, this change decreases the numerator
by $18,000 and the denominator by $0.90.
Then, X1 = $86,600/$4.10 = 21,122 units.
3.
The CVP analysis in Requirement 2 is more accurate because it recognizes
that adding a product will increase the cost of support activities like inspection, engineering, and setups. In the conventional analysis, these costs are
often ignored because they are viewed as fixed. Activity costing also tries to
identify cost behavior more carefully than conventional costing. This may
produce more accurate cost relationships and a better analysis. For example,
for Salem Electronics, the break-even point appears to be much higher than
the original analysis indicated. The difference is significant enough that the
decision is clearly opposite of what was signaled by the conventional analysis. As a result, the use of the more accurate ABC analysis is recommended.
17–25
1.
Variable
Contribution
Sales
Price
Cost
Margin
Mix
Rose .......... $100
$67.92
$32.08
5
Violet .........
80
56.60
23.40
1
Total .........................................................................................
Total
Contribution
Margin
$160.40
23.40
$183.80
Rose variable cost = $50 + $10 + [$11* × (36,000/50,000)] = $67.92
Violet variable cost = $43 + $7 + [$11* × (6,000/10,000)] = $56.60
*$462,000/42,000 DLH = $11 per direct labor hour.
Break-even packages = $550,000/$183.80 = 2,992
Cases of Rose = 5 × 2,992 = 14,960
Cases of Violet = 2,992
397
17–25 Concluded
2.
Unit-based variable costs:
Prime costs ...............
Benefitsa....................
Machine costsb .........
Total .....................
× Units in mix............
Package ...............
Rose
$ 60.00
3.43
4.03
$ 67.46
×
5
$ 337.30
+
Violet
$ 50.00
2.86
6.05
$ 58.91
×
1
$ 58.91
=
$396.21
a$200,000/42,000
= $4.762/hour
Per unit of Rose: $4.762(36,000/50,000) = $3.43
Per unit of Violet: $4.762(6,000/10,000) = $2.86
b$262,000/13,000
= $20.15/machine hour
Per unit of Rose: $20.15(10,000/50,000) = $4.03
Per unit of Violet: $20.15(3,000/10,000) = $6.05
Non-unit-based variable costs (assumes strictly variable behavior for each
cost driver with no fixed component):
Receiving: $225,000/75 = $3,000/receiving order
Packing:
$125,000/150 = $833/packing order
CVP analysis:
Let
X1 = Number of packages
X2 = Number of receiving orders
X3 = Number of packing orders
Packages = ($200,000 + $3,000X2 + $833X3)/$183.79*
*Sales revenue per package [($100 × 5) + ($80 × 1)] – Variable cost per package ($396.21).
Assume X2 = 75 and X3 = 150.
Packages = $550,000/$183.79 = 2,993
Break-even cases of Rose = 5 × 2,993 = 14,965
Break-even cases of Violet = 2,993
The answer is the same as the conventional response. The responses will
differ only if the levels of the non-unit-based variables change.
398
17–26
1.
Revenue = $157,500/0.35* = $450,000
*CM ratio = $210,000/$600,000 = 0.35.
2.
Of total sales revenue, 40% is produced by jay-flex machines and 60% by free
weight sets.
$240,000/$200 = 1,200 units
$360,000/$75 = 4,800 units
Thus, the sales mix is 1 to 4.
Variable
Contribution
Sales
Price
Cost*
Margin
Mix
Jay-flex .............. $200
$130.00
$70.00
1
Free weights .....
75
48.75
26.25
4
Package ................................................................................................
*($390,000 × 0.40)/1,200 units = $130.00 per unit
($390,000 × 0.60)/4,800 units = $48.75 per unit
Packages = $157,500/$175
= 900
Jay-flex: 1 × 900 = 900 machines
Free weights: 4 × 900 = 3,600 sets
3.
Operating leverage = Contribution margin/Operating income
= $210,000/$52,500
= 4.0
Percentage change in net income = 4 × 40% = 160%
399
Total
$ 70
105
$ 175
17–26 Concluded
4.
The new sales mix is 1 jay-flex:8 free weight sets:1 jay-rider.
Variable
Contribution
Sales
Price
Cost
Margin
Mix
Jay-flex .............. $200
$130.00
$70.00
1
Free weights .....
75
48.75
26.25
8
Jay-rider ............
180
140.00
40.00
1
Package ................................................................................................
Total
$ 70
210
40
$320
Packages = ($157,500 + $5,700)/$320 = 510
Jay-flex: 1 × 510 = 510 machines
Free weights: 8 × 510 = 4,080 sets
Jay-rider: 1 × 510 = 510 machines
No, in the coming year, the addition of the jay-rider will result in a lower operating income.
Decreased contribution margin from loss of jay-flex sales ............
Increased fixed costs .........................................................................
Increased contribution margin from jay-rider sales.........................
Decrease in operating income ......................................................
$(42,000)
(5,700)
24,000
$(23,700)
Ironjay might still choose to introduce the jay-rider if it believes the following:
Sales for the jay-rider will grow, sales of the jay-flex will stabilize, and the variable costs of the jay-rider (which are quite high) can be reduced. Then, income in future years will be higher.
COLLABORATIVE LEARNING EXERCISE
17–27
Part I
1.
a.
b.
c.
Overhead = $3,868 + $108.95 setups ..........................................
Overhead = –$516 + $9.64 machine hours ................................
Overhead = $1,264 + $4.73 machine hours + $89.42 setups ....
R2 = 0.867
R2 = 0.510
R2 = 0.962
The multiple regression equation is best. It has the highest R2, the signs on
the variables make sense, and both independent variables are significant at
the 0.01 level.
400
17–27 Continued
2.
To compute the break-even units, we need total fixed costs and the contribution margin per unit.
Fixed overhead (Regression intercept × 12) ...............
Setup costs ($89.42 × 160 setups last year) ...............
Fixed selling and administrative expense ..................
Total fixed costs.....................................................
$ 15,168
14,307
180,000
$ 209,475
Direct materials .............................................................
Direct labor ....................................................................
Variable overhead ($4.73/100 boxes) ..........................
Total unit variable cost ..........................................
$ 0.35
0.25
0.05
$ 0.65
Unit contribution margin = $0.90 – $0.65 = $0.25
Break-even units = $209,475/$0.25 = 837,900 boxes
Part II
1.
Contribution margin per jar of sauce:
Price ..........................................
Less:
Direct materials .................
Direct labor ........................
Variable overhead*............
Contribution margin .................
$ 2.00
(0.75)
(0.50)
(0.09)
$ 0.66
*Variable overhead = $4.73/50 jars = $0.09 per jar.
Contribution
Sales
Margin
Mix
Pasta ..........
$0.25
2
Sauce .........
0.66
1
Total ...............................................
Total
Contribution
Margin
$0.50
0.66
$1.16
Break-even packages = ($180,000 + $15,168 + $14,307)/$1.16 = 180,582
Break-even boxes of pasta = 2 × 180,582 = 361,164
Break-even jars of sauce = 180,582
401
17–27
2.
Concluded
If setups double, then the new setup cost = 2 × $14,307 = $28,614.
New break-even packages = ($180,000 + $15,168 + $28,614)/$1.16
= 192,916
Break-even boxes of pasta = 2 × 192,916 = 385,832
Break-even jars of sauce = 192,916
3.
Uncertainty in the cost estimates and sales mix naturally leads to some
uncertainty in the break-even estimates. The fixed and variable costs were
estimated using regression. These estimates are heavily reliant on the assumptions of regression. To the extent that Sorrentino Company data do not
conform to regression assumptions, the estimates are wrong. The sales mix
of two boxes of pasta to one jar of sauce is the company’s best guess. If relatively more sauce is sold, the break-even point will go down. If relatively more
pasta is sold, the break-even point will go up.
The activity-based costing does give Sorrentino Company a better idea of its
cost structure. Setups are an important activity, but they are not variable with
respect to units. The ABC approach, which specifically separates various levels of cost, focuses management attention on batch-level and product-level
costs.
17–28 Answers will vary.
402