CHAPTER 11
COST-VOLUME-PROFIT ANALYSIS:
A MANAGERIAL PLANNING TOOL
QUESTIONS FOR WRITING AND DISCUSSION
1. CVP analysis allows managers to focus on
selling 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.
$30,000/$25 = 1,200 packages, or 2,400
units of A and 1,200 units of B.
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).
5. Profit = $7.00 × 5,000 = $35,000
12.
Profit = 0.60($200,000 – $100,000) =
$60,000
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. The
higher the margin of safety, the lower the
risk.
15.
Operating leverage is the use of fixed costs
to extract higher percentage changes in
profits as sales activity changes. It is
achieved by increasing fixed costs while lowering variable costs. Therefore, increased
leverage implies increased risk, and vice
versa.
16.
Sensitivity analysis is a “what if” technique
that examines the impact of changes in underlying assumptions on an answer. A company can input data on selling prices, variable costs, fixed costs, and sales mix and set
up formulas to calculate break-even points
and expected profits. Then, the data can be
varied as desired to see what impact
changes have on the expected profit.
17.
By specifically including the costs that vary
with nonunit drivers, the impact of changes
in the nonunit drivers can be examined. In
traditional CVP, all nonunit costs are lumped
together as “fixed costs.” While the costs are
fixed with respect to units, they vary with respect to other drivers. ABC analysis reminds
us of the importance of these nonunit drivers
and costs.
6. Variable cost ratio = Variable costs/Sales.
Contribution margin ratio = Contribution
margin/Sales. Contribution margin ratio = 1
– Variable cost ratio.
7. Break-even revenues = $20,000/0.40 =
$50,000
8. No. The increase in contribution is $9,000
(0.30 × $30,000), and the increase in advertising is $10,000.
9. Sales mix is the relative proportion sold of
each product. For example, a sales mix of
3:2 means that three units of one product
are sold for every two of the second product.
10.
Packages of products, based on the expected sales mix, are defined as a single
product. Selling price and cost information
for this package can then be used to carry
out CVP analysis.
11.
Package contribution margin: (2 × $10) + (1
× $5) = $25. Break-even point =
347
18.
JIT simplifies the firm’s cost equation since
more costs are classified as fixed (e.g., direct labor). Additionally, the batch-level variable is gone (in JIT, the batch is one unit).
Thus, the cost equation for JIT includes
fixed costs, unit variable cost times the
number of units sold, and unit product-level
cost times the number of products sold (or
related
cost
driver). JIT means that CVP analysis approaches the standard analysis with fixed
and unit-level costs only.
348
EXERCISES
11–1
1.
Direct materials
Direct labor
Variable overhead
Variable selling expenses
Variable cost per unit
$3.90
1.40
2.10
1.00
$ 8.40
2.
Price
Variable cost per unit
Contribution margin per unit
3.
Contribution margin ratio = $5.60/$14 = 0.40 or 40%
4.
Variable cost ratio = $8.40/$14 = 0.60 or 60%
5.
Total fixed cost = $44,000 + $47,280 = $91,280
6.
Breakeven units = (Fixed cost)/Contribution margin
= $91,280/$5.60
= 16,300
$14.00
8.40
$5.60
349
11–2
1.
Price
Less:
Direct materials
Direct labor
Variable overhead
Variable selling expenses
Contribution margin per unit
$12.00
$1.90
2.85
1.25
2.00
8.00
$4.00
2.
Breakeven units = (Fixed cost)/Contribution margin
= (44,000 + $37,900)/$4.00
= 20,475
3.
Units for target
4.
Sales (22,725 × $12)
Variable costs (22,725 × $8)
Contribution margin
Fixed costs
Operating income
= (44,000 + $37,900 + $9,000)/$4
= $90,900/$4
= 22,725
$ 272,700
181,800
$ 90,900
81,900
$ 9,000
Sales of 22,725 units does produce operating income of $9,000.
11–3
1.
Units = Fixed cost/Contribution margin
= $37,500/($8 – $5)
= 12,500
2.
Sales (12,500 × $8)
Variable costs (12,500 × $5)
Contribution margin
Fixed costs
Operating income
3.
Units = (Target income + Fixed cost)/Contribution margin
= ($37,500 + $9,900)/($8 – $5)
= $47,400/$3
= 15,800
$100,000
62,500
$ 37,500
37,500
$
0
350
11–4
1.
Contribution margin per unit = $8 – $5 = $3
Contribution margin ratio = $3/$8 = 0.375, or 37.5%
2.
Variable cost ratio = $75,000/$120,000 = 0.625, or 62.5%
3.
Revenue = Fixed cost/Contribution margin ratio
= $37,500/0.375
= $100,000
4.
Revenue = (Target income + Fixed cost)/Contribution margin ratio
= ($37,500 + $9,900)/0.375
= $126,400
11–5
1.
Break-even units = Fixed costs/(Price – Variable cost)
= $180,000/($3.20 – $2.40)
= $180,000/$0.80
= 225,000
2.
Units = ($180,000 + $12,600)/($3.20 – $2.40)
= $192,600/$0.80
= 240,750
3.
Unit variable cost = $2.40
Unit variable manufacturing cost = $2.40 – $0.32 = $2.08
The unit variable cost is used in cost-volume-profit analysis, since it includes
all of the variable costs of the firm.
351
11–6
1.
Before-tax income = $25,200/(1 – 0.40) = $42,000
Units = ($180,000 + $42,000)/$0.80
= $222,000/$0.80
= 277,500
2.
Before-tax income = $25,200/(1 – 0.30) = $36,000
Units = ($180,000 + $36,000)/$0.80
= $216,000/$0.80
= 270,000
3.
Before-tax income = $25,200/(1 – 0.50) = $50,400
Units = ($180,000 + $50,400)/$0.80
= $230,400/$0.80
= 288,000
11–7
1.
Contribution margin per unit = $15 – ($3.90 + $1.40 + $2.10 + $1.60) = $6
Contribution margin ratio = $6/$15 = 0.40 or 40%
2.
Breakeven Revenue = Fixed cost/Contribution margin ratio
= ($52,000 + $37,950)/0.40
= $224,875
3.
Revenue = (Target income + Fixed cost)/Contribution margin ratio
= ($52,000 + $37,950 + $18,000)/0.40
= $269,875
4.
Breakeven units = $224,875/$15 = 14,992 (rounded)
Or
Breakeven units = $89,950/$6 = 14,992 (rounded)
5.
Units for target income = $269,875/$15 = 17,992 (rounded)
Or
Units for target income = $107,950/$6 = 17,992 (rounded)
352
11–8
1.
Sales mix is 2:1 (Twice as many videos are sold as equipment sets.)
2.
Product
Videos
Equipment sets
Total
Price
$12
15
Variable
–
Cost
$4
6
=
CM
$8
9
×
Sales
Mix
2
1
= Total CM
$16
9
$25
Break-even packages = $70,000/$25 = 2,800
Break-even videos
= 2 × 2,800 = 5,600
Break-even equipment sets = 1 × 2,800 = 2,800
3.
Switzer Company
Income Statement
For Last Year
Sales ...........................................................................................
Less: Variable costs .................................................................
Contribution margin..................................................................
Less: Fixed costs ......................................................................
Operating income ................................................................
$ 195,000
70,000
$ 125,000
70,000
$ 55,000
Contribution margin ratio = $125,000/$195,000 = 0.641, or 64.1%
Break-even sales revenue = $70,000/0.641 = $109,204
353
11–9
1.
Sales mix is 2:1:4 (Twice as many videos will be sold as equipment sets, and
four times as many yoga mats will be sold as equipment sets.)
2.
Product
Videos
Equipment sets
Yoga mats
Total
Price
$12
15
18
–
Variable
Cost
$4
6
13
=
CM
$8
9
5
×
Sales
Mix
2
1
4
= Total CM
$16
9
20
$45
Break-even packages = $118,350/$45 = 2,630
Break-even videos
= 2 × 2,630 = 5,260
Break-even equipment sets = 1 × 2,630 = 2,630
Break-even yoga mats
= 4 × 2,630 = 10,520
3.
Switzer Company
Income Statement
For the Coming Year
Sales ...........................................................................................
Less: Variable costs .................................................................
Contribution margin..................................................................
Less: Fixed costs ......................................................................
Operating income ................................................................
$555,000
330,000
$225,000
118,350
$106,650
Contribution margin ratio = $225,000/$555,000 = 0.4054, or 40.54%
Break-even revenue = $118,350/0.4054 = $291,934
11–10
1.
Variable cost per unit = $5.60 + $7.50 + $2.90 + $2.00 = $18
Breakeven units = $75,000/($24 – $18) = 12,500
Breakeven Revenue = $24 × 12,500 = $300,000
2.
Margin of safety in sales dollars = ($24 × 14,000) – $300,000 = $36,000
3.
Margin of safety in units = 14,000 units – 12,500 units = 1,500 units
354
11–11
1.
$35,000
$30,000
$25,000
$20,000
$15,000
$10,000
$5,000
$0
0
500
1,000
1,500
2,000
2,500
3,000
3,500
Units Sold
Break-even point = 2,500 units; + line is total revenue and x line is total costs.
355
11–11 Continued
2.
a. Fixed costs increase by $5,000:
$40,000
$35,000
$30,000
$25,000
$20,000
$15,000
$10,000
$5,000
$0
0
500
1,000
1,500
2,000
Units Sold
Break-even point = 3,750 units
356
2,500
3,000
3,500
4,000
11–11 Continued
b. Unit variable cost increases to $7:
$50,000
$40,000
$30,000
$20,000
$10,000
$0
0
500
1,000
1,500
2,000
2,500
Units Sold
Break-even point = 3,333 units
357
3,000
3,500
4,000
11–11 Continued
c. Unit selling price increases to $12:
$50,000
$40,000
$30,000
$20,000
$10,000
$0
0
500
1,000
1,500
2,000
2,500
Units Sold
Break-even point = 1,667 units
358
3,000
3,500
4,000
11–11 Continued
d.
Both fixed costs and unit variable cost increase:
$70,000
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0
0
1,000
2,000
3,000
4,000
5,000
Units Sold
Break-even point = 5,000 units
359
6,000
7,000
8,000
11–11 Continued
3.
Original data:
$10,000
$0
0
500
1,000
1,500
2,000
-$10,000
Break-even point = 2,500 units
360
2,500
3,000
3,500
4,000
11–11 Continued
a. Fixed costs increase by $5,000:
$15,000
$0
0
500
1,000
1,500
2,000
-$15,000
Break-even point = 3,750 units
361
2,500
3,000
3,500
4,000
11–11 Continued
b. Unit variable cost increases to $7:
$10,000
$0
0
500
1,000
1,500
2,000
-$10,000
Break-even point = 3,333 units
362
2,500
3,000
3,500
4,000
11–11 Continued
c. Unit selling price increases to $12:
$10,000
$0
0
500
1,000
1,500
2,000
-$10,000
Break-even point = 1,667 units
363
2,500
3,000
3,500
4,000
11–11 Concluded
d. Both fixed costs and unit variable cost increase:
$15,000
$0
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
-$15,000
Break-even point = 5,000 units
4. The first set of graphs is more informative since these graphs reveal how
costs change as sales volume changes.
364
11–12
1.
Darius: $100,000/$50,000 = 2
Xerxes: $300,000/$50,000 = 6
2.
Darius
X = $50,000/(1 – 0.80)
X = $50,000/0.20
X = $250,000
Xerxes
X = $250,000/(1 – 0.40)
X = $250,000/0.60
X = $416,667
Xerxes must sell more than Darius to break even because it must cover
$200,000 more in fixed costs (it is more highly leveraged).
3.
Darius: 2 × 50% = 100%
Xerxes: 6 × 50% = 300%
The percentage increase in profits for Xerxes is much higher than the increase for Darius because Xerxes has a higher degree of operating leverage
(i.e., it has a larger amount of fixed costs in proportion to variable costs as
compared to Darius). Once fixed costs are covered, additional revenue must
cover only variable costs, and 60 percent of Xerxes revenue above breakeven is profit, whereas only 20 percent of Darius revenue above break-even is
profit.
11–13
1.
Breakeven units = $10,350/($15 – $12) = 3,450
2.
Breakeven sales dollars = $10,350/0.20 = $51,750
3.
Margin of safety in units = 5,000 – 3,450 = 1,550
4.
Margin of safety in sales dollars = $75,000 – $51,750 = $23,250
365
11–14
1.
Variable cost ratio = Variable costs/Sales
= $399,900/$930,000
= 0.43, or 43%
Contribution margin ratio = (Sales – Variable costs)/Sales
= ($930,000 – $399,900)/$930,000
= 0.57, or 57%
2.
Break-even sales revenue = $307,800/0.57 = $540,000
3.
Margin of safety = Sales – Break-even sales
= $930,000 – $540,000 = $390,000
4.
Contribution margin from increased sales = ($7,500)(0.57) = $4,275
Cost of advertising = $5,000
No, the advertising campaign is not a good idea, because the company’s operating income will decrease by $725 ($4,275 – $5,000).
11–15
1.
Income
0
0
$570,000
P
= Revenue – Variable cost – Fixed cost
= 1,500P – $300(1,500) – $120,000
= 1,500P – $450,000 – $120,000
= 1,500P
= $380
2.
$160,000/($3.50 – Unit variable cost) = 128,000 units
Unit variable cost = $2.25
3.
Margin of safety = Actual units – Breakeven units
300 = 35,000 – breakeven units
Breakeven units = 34,700
Breakeven units = Total Fixed Cost/(Price – Variable cost per unit)
34,700 = Total Fixed Cost/($40 – $30)
Total Fixed Cost = $347,000
366
11–16
1.
Contribution margin per unit = $5.60 – $4.20*
= $1.40
*Variable costs per unit:
$0.70 + $0.35 + $1.85 + $0.34 + $0.76 + $0.20 = $4.20
Contribution margin ratio = $1.40/$5.60 = 0.25 = 25%
2.
Break-even in units = ($32,300 + $12,500)/$1.40 = 32,000 boxes
Break-even in sales = 32,000 × $5.60 = $179,200
or
= ($32,300 + $12,500)/0.25 = $179,200
3.
Sales ($5.60 × 35,000)
Variable costs ($4.20 × 35,000)
Contribution margin
Fixed costs
Operating income
4.
Margin of safety = $196,000 – $179,200 = $16,800
5.
Break-even in units = 44,800/($6.20 – $4.20) = 22,400 boxes
$ 196,000
147,000
$ 49,000
44,800
$ 4,200
New operating income = $6.20(31,500) – $4.20(31,500) – $44,800
= $195,300 – $132,300 – $44,800 = $18,200
Yes, operating income will increase by $14,000 ($18,200 – $4,200).
367
11–17
1.
Variable cost ratio = $126,000/$315,000 = 0.40
Contribution margin ratio = $189,000/$315,000 = 0.60
2.
$46,000 × 0.60 = $27,600
3.
Break-even revenue = $63,000/0.60 = $105,000
Margin of safety = $315,000 – $105,000 = $210,000
4.
Revenue = ($63,000 + $90,000)/0.60
= $255,000
5.
Before-tax income = $56,000/(1 – 0.30) = $80,000
Note: Tax rate = $37,800/$126,000 = 0.30
Revenue = ($63,000 + $80,000)/0.60 = $238,333
Sales ................................................................................
Less: Variable expenses ($238,333 × 0.40) ..................
Contribution margin.......................................................
Less: Fixed expenses ....................................................
Income before income taxes .........................................
Income taxes ($80,000 × 0.30) .......................................
Net income ................................................................
368
$ 238,333
95,333
$ 143,000
63,000
$ 80,000
24,000
$ 56,000
11–18
1.
Contribution margin/unit = $410,000/100,000 = $4.10
Contribution margin ratio = $410,000/$650,000 = 0.6308
Break-even units = $295,200/$4.10 = 72,000 units
Break-even revenue = 72,000 × $6.50 = $468,000
or
= $295,200/0.6308 = $467,977*
*Difference due to rounding error in calculating the contribution margin ratio.
2.
The break-even point decreases:
X = $295,200/(P – V)
X = $295,200/($7.15 – $2.40)
X = $295,200/$4.75
X = 62,147 units
Revenue = 62,147 × $7.15 = $444,351
3.
The break-even point increases:
X = $295,200/($6.50 – $2.75)
X = $295,200/$3.75
X = 78,720 units
Revenue = 78,720 × $6.50 = $511,680
4.
Predictions of increases or decreases in 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 $4.10 to $4.40, so the break-even point in
units will decrease.
Break-even units = $295,200/($7.15 – $2.75) = 67,091
Now, let’s look at the break-even point in revenues. We might expect that it,
too, will decrease. However, that is not the case in this particular example.
Here, the contribution margin ratio decreased from about 63 percent to just
over 61.5 percent. As a result, the break-even point in revenues has gone up.
Break-even revenue = 67,091 × $7.15 = $479,701
369
11–18 Concluded
5.
The break-even point will increase because more units will need to be sold to
cover the additional fixed expenses.
Break-even units = $345,200/$4.10 = 84,195 units
Revenue = $547,268
370
PROBLEMS
11–19
1.
Operating income
(0.20)Revenue
(0.20)Revenue
(0.40)Revenue
Revenue
= Revenue(1 – Variable cost ratio) – Fixed cost
= Revenue(1 – 0.40) – $24,000
= (0.60)Revenue – $24,000
= $24,000
= $60,000
Sales ................................................................................
Variable expenses ($60,000 × 0.40) ..............................
Contribution margin.......................................................
Fixed expenses ..............................................................
Operating income .....................................................
$ 60,000
24,000
$ 36,000
24,000
$ 12,000
$12,000 = $60,000 × 20%
2.
If revenue of $60,000 produces a profit equal to 20 percent of sales and if the
price per unit is $10, then 6,000 units must be sold. Let X equal number of
units, then:
Operating income
0.20($10)X
$2X
$4X
X
0.25($10)X
$2.50X
$3.50X
X
= (Price – Variable cost) – Fixed cost
= ($10 – $4)X – $24,000
= $6X – $24,000
= $24,000
= 6,000 buckets
= $6X – $24,000
= $6X – $24,000
= $24,000
= 6,857 buckets
Sales (6,857 × $10) .........................................................
Variable expenses (6,857 × $4) .....................................
Contribution margin.......................................................
Fixed expenses ..............................................................
Operating income .....................................................
$68,570
27,428
$41,142
24,000
$17,142
$17,142* = 0.25 × $68,570 as claimed
*Rounded down.
Note: Some may prefer to round up to 6,858 units. If this is done, the operating income will be slightly different due to rounding.
371
11–19 Concluded
3.
Net income = 0.20Revenue/(1 – 0.40)
= 0.3333Revenue
0.3333Revenue
0.3333Revenue
0.2667Revenue
Revenue
= Revenue(1 – 0.40) – $24,000
= 0.60Revenue – $24,000
= $24,000
= $89,989
11–20
1.
Unit contribution margin = $1,060,000/50,000 = $21.20
Break-even units = $816,412/$21.20 = 38,510 units
Operating income = 30,000 × $21.20 = $636,000
2.
CM ratio = $1,060,000/$2,500,000 = 0.424 or 42.4%
Break-even point = $816,412/0.424 = $1,925,500
Operating income = ($200,000 × 0.424) + $243,588 = $328,388
3.
Margin of safety = $2,500,000 – $1,925,500 = $574,500
4.
$1,060,000/$243,588 = 4.352 (operating leverage)
4.352 × 20% = 0.8704
0.8704 × $243,588 = $212,019
New operating income level = $212,019 + $243,588 = $455,607
5.
Let X = Units
0.10($50)X = $50.00X – $28.80X – $816,412
$5X = $21.20X – $816,412
$16.20X = $816,412
X = 50,396 units
6.
Before-tax income = $180,000/(1 – 0.40) = $300,000
X = ($816,412 + $300,000)/$21.20 = 52,661 units
372
11–21
1.
Unit contribution margin = $825,000/110,000 = $7.50
Break-even point = $495,000/$7.50 = 66,000 units
CM ratio = $7.50/$25 = 0.30
Break-even point
= $495,000/0.30 = $1,650,000
or
= $25 × 66,000 = $1,650,000
2.
Increased CM ($400,000 × 0.30)
Less: Increased advertising expense
Increased operating income
3.
$315,000 × 0.30 = $94,500
4.
Before-tax income = $360,000/(1 – 0.40) = $600,000
Units = ($495,000 + $600,000)/$7.50
= 146,000
5.
Margin of safety = $2,750,000 – $1,650,000 = $1,100,000
or
= 110,000 units – 66,000 units = 44,000 units
6.
$825,000/$330,000 = 2.5 (operating leverage)
20% × 2.5 = 50% (profit increase)
373
$ 120,000
40,000
$ 80,000
11–22
1.
Sales mix:
Squares: $300,000/$30 = 10,000 units
Circles: $2,500,000/$50 = 50,000 units
Product
Squares
Circles
Package
P
$30
50
–
V*
$10
10
=
P–V
$20
40
×
Sales
Mix
1
5
=
Total
CM
$ 20
200
$220
*$100,000/10,000 = $10
$500,000/50,000 = $10
Break-even packages = $1,628,000/$220 = 7,400 packages
Break-even squares = 7,400 × 1 = 7,400
Break-even circles = 7,400 × 5 = 37,000
2.
Contribution margin ratio = $2,200,000/$2,800,000 = 0.7857
0.10Revenue = 0.7857Revenue – $1,628,000
0.6857Revenue = $1,628,000
Revenue = $2,374,216
3.
New mix:
Product
Squares
Circles
Package
P
$30
50
–
V
$10
10
=
P–V
$20
40
×
Sales
Mix
3
5
Break-even packages = $1,628,000/$260 = 6,262 packages
Break-even squares = 6,262 × 3 = 18,786
Break-even circles = 6,262 × 5 = 31,310
CM ratio = $260/$340* = 0.7647
*(3)($30) + (5)($50) = $340 revenue per package
0.10Revenue = 0.7647Revenue – $1,628,000
0.6647Revenue = $1,628,000
Revenue = $2,449,225
374
=
Total
CM
$ 60
200
$260
11–22 Concluded
4.
Increase in CM for squares (15,000 × $20)
Decrease in CM for circles (5,000 × $40)
Net increase in total contribution margin
Less: Additional fixed expenses
Increase in operating income
$ 300,000
(200,000)
$ 100,000
45,000
$ 55,000
Gosnell would gain $55,000 by increasing advertising for the squares.
This is a good strategy.
11–23
1.
Product
Scientific
Business
Total
Price* –
$25
20
Variable
Cost
=
$12
9
*$500,000/20,000 = $25
$2,000,000/100,000 = $20
X = ($1,080,000 + $145,000)/$68
X = $1,225,000/$68
X = 18,015 packages
18,015 scientific calculators (1 × 18,015)
90,075 business calculators (5 × 18,015)
2.
Revenue = $1,225,000/0.544* = $2,251,838
*($1,360,000/$2,500,000) = 0.544
375
CM
$13
11
×
Units in
Mix
1
5
=
Package
CM
$13
55
$68
11–24
1.
Currently:
Sales (830,000 × $0.36)
Variable expenses
Contribution margin
Fixed expenses
Operating income
$ 298,800
224,100
$ 74,700
54,000
$ 20,700
New contribution margin = 1.5 × $74,700 = $112,050
$112,050 – promotional spending – $54,000 = 1.5 × $20,700
Promotional spending = $27,000
2.
Here are two ways to calculate the answer to this question:
a. The per-unit contribution margin needs to be the same:
Let P* represent the new price and V* the new variable cost.
(P – V) = (P* – V*)
$0.36 – $0.27 = P* – $0.30
$0.09 = P* – $0.30
P* = $0.39
b. Old break-even point = $54,000/($0.36 – $0.27) = 600,000
New break-even point = $54,000/(P* – $0.30) = 600,000
P* = $0.39
The selling price should be increased by $0.03.
3.
Projected contribution margin (700,000 × $0.13)
Present contribution margin
Increase in operating income
$91,000
74,700
$16,300
The decision was good because operating income increased by $16,300.
(New quantity × $0.13) – $54,000 = $20,700
New quantity = 574,615
Selling 574,615 units at the new price will maintain profit at $20,700.
376
11–25
1.
Contribution margin ratio = $487,548/$840,600 = 0.58
2.
Revenue = $250,000/0.58 = $431,034
3.
Operating income
0.08R/(1 – 0.34)
0.1212R
0.4588R
R
4.
$840,600 × 110% =
$353,052 × 110% =
= CMR × Revenue – Total fixed cost
= 0.58R – $250,000
= 0.58R – $250,000
= $250,000
= $544,900
$924,660
388,357
$536,303
CMR = $536,303/$924,660 = 0.58
The contribution margin ratio remains at 0.58.
5.
Additional variable expense = $840,600 × 0.03 = $25,218
New contribution margin = $487,548 – $25,218 = $462,330
New CM ratio = $462,330/$840,600 = 0.55
Break-even point = $250,000/0.55 = $454,545
The effect is to increase the break-even point.
6.
Present contribution margin
Projected contribution margin ($920,600 × 0.55)
Increase in contribution margin/profit
$ 487,548
506,330
$ 18,782
Fitzgibbons should pay the commission because profit would increase by
$18,782.
377
11–26
1.
One package, X, contains three Grade I and seven Grade II cabinets.
0.3X($3,400) + 0.7X($1,600) = $1,600,000
X = 748 packages
Grade I: 0.3 × 748 = 224 units
Grade II: 0.7 × 748 = 524 units
2.
Product
Grade I
Grade II
Package
P
$3,400
1,600
–
Direct fixed costs—Grade I
Direct fixed costs—Grade II
Common fixed costs
Total fixed costs
V
$2,686
1,328
=
P–V
$714
272
×
Mix
3
7
=
Total CM
$2,142
1,904
$4,046
P–V
$956
392
×
Mix
3
7
=
Total CM
$2,868
2,744
$5,612
$ 95,000
95,000
35,000
$ 225,000
$225,000/$4,046 = 56 packages
Grade I: 3 × 56 = 168; Grade II: 7 × 56 = 392
3.
Product
Grade I
Grade II
Package
Package CM
Package CM
$21,400X
X
P
$3,400
1,600
–
V
$2,444
1,208
=
= 3($3,400) + 7($1,600)
= $21,400
= $1,600,000 – $600,000
= 47 packages remaining
141 Grade I (3 × 47) and 329 Grade II (7 × 47)
Additional contribution margin:
141($956 – $714) + 329($392 – $272)
Increase in fixed costs
Increase in operating income
$73,602
44,000
$29,602
Break-even: ($225,000 + $44,000)/$5,612 = 48 packages
144 Grade I (3 × 48) and 336 Grade II (7 × 48)
378
11–26 Concluded
The new break-even point is a revised break-even for 2004. Total fixed costs
must be reduced by the contribution margin already earned (through the first
five months) to obtain the units that must be sold for the last seven months.
These units are then be added to those sold during the first five months:
CM earned = $600,000 – (83* × $2,686) – (195* × $1,328) = $118,102
*224 – 141 = 83; 524 – 329 = 195
X = ($225,000 + $44,000 – $118,102)/$5,612 = 27 packages
In the first five months, 28 packages were sold (83/3 or 195/7). Thus, the revised break-even point is 55 packages (27 + 28)—in units, 165 of Grade I and
385 of Grade II.
4.
Product
Grade I
Grade II
Package
P
$3,400
1,600
New sales revenue
–
V
$2,686
1,328
=
P–V
$714
272
×
Mix
1
1
=
Total CM
$714
272
$986
$1,000,000 × 130% = $1,300,000
Package CM = $3,400 + $1,600
$5,000X = $1,300,000
X = 260 packages
Thus, 260 units of each cabinet will be sold during the rest of the year.
Effect on profits:
Change in contribution margin [$714(260 – 141) – $272(329 – 260)]
Increase in fixed costs [$70,000(7/12)]
Increase in operating income
$66,198
40,833
$25,365
X = F/(P – V)
= $295,000/$986
= 299 packages (or 299 of each cabinet)
The break-even point for 2006 is computed as follows:
X = ($295,000 – $118,102)/$986
= $176,898/$986
= 179 packages (179 of each)
To this, add the units already sold, yielding the revised break-even point:
Grade I:
83 + 179 = 262
Grade II: 195 + 179 = 374
379
11–27
1.
R = F/(1 – VR)
= $150,000/(1/3)
= $450,000
2.
Of total sales revenue, 60 percent is produced by floor lamps and 40 percent
by desk lamps.
$360,000/$30 = 12,000 units
$240,000/$20 = 12,000 units
Thus, the sales mix is 1:1.
Product
Floor lamps
Desk lamps
Package
P
$30.00
20.00
–
V*
$20.00
13.33
=
P–V
$10.00
6.67
×
Mix
1
1
=
Total CM
$10.00
6.67
$16.67
X = F/(P – V)
= $150,000/$16.67
= 8,999 packages
Floor lamps: 1 × 8,999 = 8,999
Desk lamps: 1 × 8,999 = 8,999
Note: packages have been rounded up to ensure attainment of breakeven.
3.
Operating leverage
= CM/Operating income
= $200,000/$50,000
= 4.0
Percentage change in profits = 4.0 × 40% = 160%
380
11–28
1.
Break-even units = $300,000/$14* = 21,429
*$406,000/29,000 = $14
Break-even in dollars = 21,429 × $42** = $900,018
or
= $300,000/(1/3) = $900,000
The difference is due to rounding error.
**$1,218,000/29,000 = $42
2.
Margin of safety = $1,218,000 – $900,000 = $318,000
3.
Sales
Variable costs (0.45 × $1,218,000)
Contribution margin
Fixed costs
Operating income
$ 1,218,000
548,100
$ 669,900
550,000
$ 119,900
Break-even in units = $550,000/$23.10* = 23,810
Break-even in sales dollars = $550,000/0.55** = $1,000,000
*$669,900/29,000 = $23.10
**$669,900/$1,218,000 = 55%
381
11–29
1.
The annual break-even point in units at the Peoria plant is 73,500 units and at
the Moline plant, 47,200 units, calculated as follows:
Unit contribution calculation:
Selling price
Less variable costs:
Manufacturing
Commission
G&A
Unit contribution
Peoria
$150.00
Moline
$150.00
(72.00)
(7.50)
(6.50)
$ 64.00
(88.00)
(7.50)
(6.50)
$ 48.00
Fixed costs calculation:
Total fixed costs = (Fixed manufacturing cost + Fixed G&A)
× Production rate per day × Normal working days
Peoria = [$30.00 + ($25.50 – $6.50)] × 400 × 240
= $4,704,000
Moline = [$15.00 + ($21.00 – $6.50)] × 320 × 240
= $2,265,600
Break-even calculation:
Break-even units = Fixed costs/Unit contribution
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 divisional 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 per unit ($48 – $8).
Contribution per plant:
Peoria (96,000 × $64)
Moline (76,800 × $48)
Moline (19,200 × $40)
Total contribution
Less: Fixed costs
Operating income
$ 6,144,000
3,686,400
768,000
$ 10,598,400
6,969,600
$ 3,628,800
382
11–29 Concluded
3.
If this plan is followed, 120,000 units will be produced at the Peoria plant and
72,000 units at the Moline plant.
Contribution per plant:
Peoria (96,000 × $64)
Peoria (24,000 × $61)
Moline (72,000 × $48)
Total contribution
Less: Fixed costs
Operating income
$ 6,144,000
1,464,000
3,456,000
$ 11,064,000
6,969,600
$ 4,094,400
383
11–30
1.
Break-even dollars (in thousands)
X = Variable cost of goods sold + Current fixed costs + Fixed cost of hiring +
Commissions
X = 0.45aX + $6,120b + $1,890c + 0.1X + 0.05(X – $16,000)
= 0.60X + $6,120 + $1,890 – $800
= $18,025
a
$11,700/$26,000 = 45%
Current fixed costs (in thousands):
Fixed cost of goods sold
Fixed advertising expenses
Fixed administrative expenses
Fixed interest expenses
Total
c
Fixed cost of hiring (in thousands):
Salespeople (8 × $80)
Travel and entertainment
Manager/secretary
Additional advertising
Total
b
$2,870
750
1,850
650
$6,120
$ 640
600
150
500
$1,890
2.
Break-even formula set equal to net income (in thousands):
0.6(Sales – Var. COGS – Fixed costs – Commissions) = Net income
0.6(X – 0.45X – $6,120 – 0.23X) = $2,100
0.192X – $3,672 = $2,100
0.192X = $5,772
X = $30,063
3.
The general assumptions underlying break-even analysis that limit its usefulness include the following: all costs can be divided into fixed and variable
elements; variable costs vary proportionally to volume; and selling prices remain unchanged.
384
MANAGERIAL DECISION CASES
11–31
1. Break-even point = F/(P – V)
First process:
$100,000/($30 – $10) = 5,000 cases
Second process: $200,000/($30 – $6) = 8,333 cases
2.
I
X($30 – $10) – $100,000
$20X – $100,000
$100,000
X
= X(P – V) – F
= X($30 – $6) – $200,000
= $24X – $200,000
= $4X
= 25,000
The manual process is more profitable if sales are less than 25,000 cases; the
automated process is more profitable at a level greater than 25,000 cases. It is
important for the manager to have a sales forecast to help in deciding which
process should be chosen.
3.
The divisional manager has the right to decide which process is better. Danna is morally obligated to report the correct information to her superior. By altering the sales forecast, she unfairly and unethically influenced the decisionmaking process. Managers do have a moral obligation to assess the impact of
their decisions on employees, and to be fair and honest with employees.
However, Danna’s behavior is not justified by the fact that it helped a number
of employees retain their employment. First, she had no right to make the decision. She does have the right to voice her concerns about the impact of automation on employee well-being. In so doing, perhaps the divisional manager would come to the same conclusion even though the automated system
appears to be more profitable. Second, the choice to select the manual system may not be the best for the employees anyway. The divisional manager
may have more information, making the selection of the automated system
the best alternative for all concerned, provided the sales volume justifies its
selection. For example, the divisional manager may have plans to retrain and
relocate the displaced workers in better jobs within the company. Third, her
motivation for altering the forecast seems more driven by her friendship for
Jerry Johnson than any legitimate concerns for the layoff of other employees.
Danna should examine her reasoning carefully to assess the real reasons for
her behavior. Perhaps in so doing, the conflict of interest that underlies her
decision will become apparent.
385
11–31 Concluded
4. Some standards that seem applicable are III-1 (conflict of interest), III-2 (refrain from engaging in any conduct that would prejudice carrying out duties
ethically), and IV-1 (communicate information fairly and objectively).
11–32
1.
Number of seats sold (expected):
Seats sold = Number of performances × Capacity × Percent sold
Dream
Petrushka
Nutcracker
Sleeping Beauty
Bugaku
Type of Seat
B
3,024
3,024
15,120
6,048
3,024
30,240
A
570
570
2,280
1,140
570
5,130
C
3,690
3,690
19,680
7,380
3,690
38,130
Total revenues = ($35 × 5,130) + ($25 × 30,240) + ($15 × 38,130)
= $179,550 + $756,000 + $571,950
= $1,507,500
Segmented revenues (Seat price × Total seats):
Dream
Petrushka
Nutcracker
Sleeping Beauty
Bugaku
A
$19,950
19,950
79,800
39,900
19,950
B
$ 75,600
75,600
378,000
151,200
75,600
386
C
$ 55,350
55,350
295,200
110,700
55,350
Total
$150,900
150,900
753,000
301,800
150,900
11–32 Continued
Segmented variable-costing income statement:
Sales
Variable costs
Contribution margin
Direct fixed costs
Segment margin
Sales
Variable costs
Contribution margin
Direct fixed costs
Segment margin
Common fixed costs
Operating (loss)
2.
Dream
$ 150,900
42,500
$ 108,400
275,500
$(167,100)
Petrushka
$150,900
42,500
$108,400
145,500
$ (37,100)
Nutcracker
$753,000
170,000
$583,000
70,500
$512,500
Sleeping Beauty
$ 301,800
85,000
$ 216,800
345,000
$(128,200)
Bugaku
$ 150,900
42,500
$ 108,400
155,500
$ (47,100)
Total
$ 1,507,500
382,500
$ 1,125,000
992,000
$ 133,000
401,000
$ (268,000)
Contribution margin per ballet performance:
Dream
Petrushka
Nutcracker
Sleeping Beauty
Bugaku
$108,400/5 = $21,680
$108,400/5 = $21,680
$583,000/20 = $29,150
$216,800/10 = $21,680
$108,400/5 = $21,680
Segment break-even point:
X = F/(P – V)
Dream
Petrushka
Nutcracker
Sleeping Beauty
Bugaku
$275,500/$21,680 =
$145,500/$21,680 =
$70,500/$29,150 =
$345,000/$21,680 =
$155,500/$21,680 =
387
13
7
3
16
8
11–32 Continued
3.
Weighted contribution margin (package): Mix: 1:1:4:2:1
$21,680 + $21,680 + 4($29,150) + 2($21,680) + $21,680 = $225,000
X = F/(P – V)
X = ($992,000 + $401,000)/$225,000 = 6.19 or 7 (rounded up)
7 Dream, Petrushka, and Bugaku; 14 Sleeping Beauty; 28 Nutcracker
Provided the community will support the number of performances indicated
in the break-even solution, I would alter the schedule to reflect the break-even
mix.
4.
Additional revenue per performance:
114 × $30 × 80% = $ 2,736
756 × $20 × 80% =
12,096
984 × $10 × 80% =
7,872
$ 22,704
Increase in revenues ($22,704 × 5)
Less: Variable costs ($8,300 × 5)
Increase in contribution margin
$113,520
41,500
$ 72,020
New mix 1:1:4:2:1:1
Contribution margin per matinee: $72,020/5 = $14,404
Adding the matinees will increase profits by $72,020.
New break-even point:
X = F/(P – V)
= ($992,000 + $401,000)/($225,000 + $14,404)
= $1,393,000/$239,404 = 5.82 packages, or 6 (rounded up)
6 Dream, Petrushka, Bugaku, and Nutcracker matinees
12 Sleeping Beauty
24 Nutcracker
388
11–32 Concluded
5.
Current total segment margin
Add: Additional contribution margin
Add: Grant
Projected segment margin
Less: Common fixed costs
Operating (loss)
$ 133,000
72,020
60,000
$ 265,020
401,000
$ (135,980)
No, the company will not break even. This is a very thorny problem faced by
ballet companies around the world. The standard response is to offer as
many performances of The Nutcracker as possible. That action has already
been taken here. Other actions that may help include possible increases in
prices of the seats (particularly the A seats), offering additional performances
of some of the other ballets, cutting administrative costs (they seem somewhat high), and offering a less expensive ballet (direct costs of Sleeping
Beauty are quite high).
RESEARCH ASSIGNMENT
11–33
Answers will vary.
389
390