Chapter 03 – Fundamentals of Cost-Volume-Profit Analysis
3-31
3-52. (30 min.) Extensions of the CVP Model—Multiple Products: Sell Block.
a.
Individuals
+
Partnerships
+
Corporations
60,000 $200
+
4,000 $1,000
+
16,000 $2,000
=
$48,000,000
PX
60,000 $180
+
4,000 $900
+
16,000 $1,800
=
43,200,000
VX
60,000 $20
+
4,000 $100
+
16,000 $200
=
$ 4,800,000
(P – V)X
3,690,000
F
$ 1,110,000
Profit
b. Compute the weighted-average contribution margin.
Weights:
Individuals
=
60,000 ÷ (60,000 + 4,000 + 16,000) = .75
Partnerships
=
4,000 ÷ (60,000 + 4,000 + 16,000) = .05
Corporations
=
16,000 ÷ (60,000 + 4,000 + 16,000) = .20
Weighted-average CM
=
0.75 $20 + 0.05 $100 + 0.20 x $200
=
$15 + $5 + $40
Weighted-average CM
=
$60
Compute break-even:
Profit
=
(P – V)X – F
$0
=
$60X – $3,690,000
$60X
=
$3,690,000
X
=
$3,690,000 ÷ $60
X
=
61,500 total returns
Individuals: prepare 0.75 61,500 = 46,125 returns
Partnerships: prepare 0.05 61,500 = 3,075 returns
Corporations: prepare 0.20 61,500 = 12,300 returns
Chapter 03 – Fundamentals of Cost-Volume-Profit Analysis
3-32
3-52. (continued).
c. New weights:
Weights:
Individuals
=
.60
Partnerships
=
.10
Corporations
=
.30
Weighted-average CM
=
0.6 $20 + 0.1 $100 + 0.3 x $200
=
$12+ $10 + $60
Weighted-average CM
=
$82
Compute breakeven:
Profit
=
(P – V)X – F
$0
=
$82X – $3,690,000
$82X
=
$3,690,000
X
=
$3,690,000 ÷ $82
X
=
45,000 total units
3-53. (20 min.) Extensions of CVP Analysis—Multiple Products: Clovis Supply.
At the break-even point of 500 total units, the total contribution margin will equal the fixed
costs. Let X = the number of basic saddles sold at the break–even point. Then (500 − X)
Chapter 03 – Fundamentals of Cost-Volume-Profit Analysis
3-33
3-54. (30 min.) Extensions of the CVP Basic Model—Multiple Products and Taxes:
Ocean King Products.
a. Compute weighted-average contribution margins for each product.
Weights
Selling
Price per
case
Variable
Cost per
Case
Contribution
Margin per
Case
Variety 1
.40
$ 3
$ 2
$1
Variety 2
.35
5
3
2
Variety 3
.25
10
6
4
Weighted-average Revenue
=
.4 x $3 + .35 x $5 + .25 x $10
=
$5.45
Weighted-average CM
=
.4 x $1 + .35 x $2 + .25 x $4
=
$2.10
Weighted-average CM%
=
$2.10 ÷ $5.45 = 38.5321% (rounded)
Compute break-even revenue:
Break-even revenue
=
F ÷ Weighted-average CM%
=
$46,200 ÷ 38.5321%
=
$119,900 (rounded)
b.
After-tax income:
=
$40,950
Before-tax income
=
[$40,950 ÷ (1 – .35)]
=
($40,950 ÷ .65)
=
$63,000
Compute required revenue:
Revenue
=
(F + Required profit) ÷ Weighted-average CM%
=
($46,200 + $63,000) ÷ 38.5321%
=
$109,200 ÷ 38.5321%
=
$283,400
(rounded)
Chapter 03 – Fundamentals of Cost-Volume-Profit Analysis
3-34
3-55. (30 min.) Extensions of the CVP Model—Multiple Products and Taxes:
Limitless Labs, Inc.
a.
Basic
+
Retest
+
Vital
Total
Revenue
850 $500
+
100 $800
+
50 $4,000
=
$705,000
Variable costs
850 $120
+
100 $400
+
50 $2,800
=
282,000
Contribution margin
850 $380
+
100 $400
+
50 $1,200
=
$ 423,000
Fixed cost
390,000
Profit before taxes
$ 33,000
Income tax (@ 40%)
13,200
Profit
$19,800
b. Compute weighted-average contribution margin percentages for each product.
Weights
Selling Price
per Test
Variable Cost
per Test
Contribution
Margin per Test
Basic
.85
$ 500
$ 120
$380
Retest
.10
800
400
400
Vital
.05
4,000
2,800
1,200
Weighted-average Revenue
=
.85 x $500 + .10 x $800 + .05 x $4,000
=
$705
Weighted-average CM
=
.85 x $380 + .10 x $400 + .05 x $1,200
=
$423
Weighted-average CM%
=
$423 ÷ $705 = 60%
Compute break-even revenue:
Break-even revenue
=
F ÷ Weighted-average CM%
=
$390,000 ÷ 60%
=
$650,000
Chapter 03 – Fundamentals of Cost-Volume-Profit Analysis
3-55. (continued).
c.
After-tax income:
=
$180,000
Before-tax income
=
[$180,000 ÷ (1 – .40)]
=
($180,000 ÷ .60)
=
$300,000
(F + Required profit) ÷ Weighted-average CM%
($390,000 + $300,000) ÷ 60%
Variable costs
Contribution margin
Fixed cost
Chapter 03 – Fundamentals of Cost-Volume-Profit Analysis
3-36
3-56. (30 min.) Extensions of the CVP Model—Multiple Products and Taxes:
Painless Dental Clinics, Inc.
a.
Cleaning
+
Filling
+
Capping
Total
Revenue
9,000 $120
+
900 $400
+
100 $1,200
=
$1,560,000
Variable costs
9,000 $80
+
900 $300
+
100 $500
=
1,040,000
Contribution margin
9,000 $40
+
900 $100
+
100 $700
=
$ 520,000
Fixed cost
400,000
Profit before taxes
$ 120,000
Income tax (@ 30%)
36,000
Profit
$84,000
b. Compute weighted-average contribution margin percentages for each product.
Weights
Selling Price
per Service
Variable Cost
per Service
Contribution Margin
per Service
Cleaning
.90
$ 120
$ 80
$ 40
Filling
.09
400
300
100
Capping
.01
1,200
500
700
Weighted-average Revenue
=
.90 x $120 + .09 x $400 + .01 x $1,200
=
$156
Weighted-average CM
=
.90 x $40 + .09 x $100 + .01 x $700
=
$52
Weighted-average CM%
=
$52 ÷ $156 = 33.33% (rounded)
Compute break-even revenue:
Break-even revenue
=
F ÷ Weighted-average CM%
=
$400,000 ÷ 33.33%
=
$1,200,000 (rounded)
c.
After tax income:
=
$140,000
Before tax income
=
[$140,000 ÷ (1 – .30)]
=
($140,000 ÷ .70)
=
$200,000
Compute required revenue:
Revenue
=
(F + Required profit) ÷ Weighted-average CM%
=
($400,000 + $200,000) ÷ 33.33%
=
$600,000 ÷ 33.33%
Chapter 03 – Fundamentals of Cost-Volume-Profit Analysis
3-37
=
$1,800,000 (rounded)
3-56. (continued).
d.
Cleaning
+
Filling
+
Capping
Total
Revenue
12,000 $120
+
1,000 $400
+
0 $1,200
=
$1,840,000
Variable costs
12,000 $80
+
1,000 $300
+
0 $500
=
1,260,000
Contribution margin
12,000 $40
+
1,000 $100
+
0 $700
=
$ 580,000
Fixed cost
450,000
Profit before taxes
$ 130,000
Income tax (@ 30%)
39,000
Profit
$91,000
Based on after-tax profit, Painless Dental Clinics should change the product mix.
Solutions to Integrative Case
3-57. (60 min.) Financial Modeling: Roseville Brewing Company.
a. Potential investors and bankers were concerned about the accuracy of the income
statement projections. They wanted to know what would happen if the projections
were overly optimistic. Operating profit was heavily influenced by projected sales
Chapter 03 – Fundamentals of Cost-Volume-Profit Analysis
3-38
included in the cost of a product, particularly when this information is used for pricing
and other forms of decision-making.
3-57 (continued).
(3) RBC is selling many different products that change daily. It is difficult if not
impossible, to measure units of product for a brew pub. This same argument holds
true for most service companies as well. Service companies do not sell “units” of
Chapter 03 – Fundamentals of Cost-Volume-Profit Analysis
3-39
= $1,020,000 ÷ .421