CHAPTER 3
PROFITABILITY ANALYSIS AND PLANNING
Exercise 3-3
a. Sales
Variable costs
Contribution margin
$800,000
(380,000)
$420,000
Contribution margin ratio = $420,000/$800,000 = 0.525
Annual break-even dollar sales volume = $210,000/0.525 = $400,000
b. Annual margin of safety in dollars:
Sales
$800,000
Break-even sales dollars
(400,000)
Margin of safety
$400,000
c. To determine the variable and total costs lines, it is necessary to compute the
variable cost ratio:
Variable = variable costs = $380,000 = 0.475
cost ratio
sales
$800,000
At a volume of $1,000,000 sales dollars, variable costs are $475,000.
$1,000,000
Profit =
$210,000
Total
Revenues
and
Total
Costs
$750,000
Fixed costs =
$210,000
$500,000
Variable costs =
$380,000
$250,000
$0
$0
$250, $500, $750, $1,00
000
000
000 0,000
Total Revenues
d. Revised annual break-even dollar sales:
($210,000 + $52,500)/0.525 = $500,000
59
60 Chapter 3
Exercise 3-8
a. Contribution margin
Sales
Contribution margin ratio
$380,000
950,000
0.40
Break-even point in sales dollars = $190,000/0.40
= $475,000
b. Current sales
Break-even sales
Margin of safety
$950,000
(475,000)
$475,000
c. Current fixed costs
Impact of increase
New fixed costs
$190,000
50,000
$240,000
Revised break-even point = $240,000/0.40
= $600,000
d. Required before-tax income = $200,000/(1  0.36)
= $312,500
Sales volume required to provide an after-tax income of $200,000:
($190,000 + $312,500)/0.40 = $1,256,250
e. Sales
Variable costs (60% of sales)
Contribution margin (40% of sales)
Fixed costs
Net income before taxes
Income taxes (36%)
Net income after taxes
$1,256,250
(753,750)
$ 502,500
(190,000)
$ 312,500
(112,500)
$ 200,000
Profitability Analysis and Planning 61
Problem 3-16
Once the following, or a similar, format is established, each case is solved by
filling in the given information and working toward the unknowns.
Case 1
1,000
Unit sales
$20,000
Case 2
800
Case 3
4,300?*
Sales revenue
Variable costs:
Unit
Unit sales
Total
Contribution margin
Fixed costs
Net income
$
10
 1,000
( 10,000)
$10,000 ?
(8,000)
$ 2,000 ?
$ 1
$
12
 800
 4,300
(800)
(51,600
$ 800
$ 86,000 ?
(400)? (80,000)
$ 400
$ 6,000?#
$
5?
 3,000?
15,000 ?
$45,000 ?
(30,000) ?
$15,000?#
Unit cont. margin:
Cont. margin
Unit sales
Unit contribution
$10,000 ?
 1,000
$
10 ?
$ 800
 800
$
1?
$86,000 ?
 4,300 ?
$ 20 ?
$45,000 ?
 3,000 ?
$ 15
Break-even point:
Fixed costs
$8,000
Unit cont. margin
 $10 ?
Unit break-even point
800 ?
$ 400
 $1 ?
400 ?
$ 80,000
 $20 ?
4,000
$30,000 ?
 $15
2,000
Margin of safety (unit
sales less unit breakeven point)
200 ?
$ 1,600? $137,600?
Case 4
3,000?*
400 ?
$60,000
300
*Solved as the unit break-even point plus the margin of safety.
#Solved as the unit contribution margin times margin of safety.
1,000
62 Chapter 3
Problem 3-19
a. Prior to solving this problem it is necessary to determine the variable costs per
unit, the fixed costs per year, and the unit selling price.
Using the high-low method:
Variable costs
per unit
= ($90,000  $75,000)/(8,000  5,000) = $5
Fixed costs = $90,000  $5(8,000) = $50,000
or
= $75,000  $5(5,000) = $50,000
Unit selling price = $65,000/5,000 = $104,000/8,000 = $13
Unit contribution margin = $13  $5 = $8
Break-even point = $50,000/$8 = 6,250 units
b. Sales volume required to earn a profit of $10,000:
($50,000 + $10,000)/$8 = 7,500 units
Profitability Analysis and Planning 63
Problem 3-22
a. Contribution margin
ratio of Touring model = ($80.00  $52.80)/$80.00 = 0.34
b. Required before-tax profit = $24,000/(1  0.40)
= $40,000
Required sales
of touring model = ($316,800 + $40,000)/($80.00  $52.80)
= 13,118 pairs
c.
Profit of Mountaineering model = Profit of Touring model
Let X = unit sales
$88.00X  ($369,600 + $52.80X) = $80.00X  ($316,800 + $52.80X)
$35.2X  $369,600 = $27.2X  $316,800
$8X = $52,800
X = $52,800/$8
X = 6,600 pairs
Before-tax profit or (loss): Mountaineering:
($88.00  $52.80)6,600  $369,600 = $(137,280)
Before-tax profit or (loss): Touring:
($80.00  $52.80)6,600  $316,800 = $(137,280)
d.
Contribution margin ratio
of Mountaineering model = ($88.00  $52.80)/$88.00 = 0.40
Contribution margin ratio
of Touring model
= ($80.00  $52.80)/$80.00 = 0.34
Profit of Mountaineering model = Profit of Touring model
0.40X  $369,600 = 0.34X  $316,800
0.06X = $52,800
X = $52,800/0.06
X = $880,000
Before-tax profit or (loss):
Mountaineering: 0.40($880,000)  $369,600 = $(17,600)
Before-tax profit or (loss):
Touring:
0.34($880,000)  $316,800 = $(17,600)
64 Chapter 3
Problem 3-22 (cont.)
e. The Siberian Ski Company should produce the Mountaineering model. This
model is shown, below, to have a higher profit at a sales volume of 12,000 pairs.
Because it has a higher unit contribution margin, this profit advantage will
increase beyond 12,000 pairs.
Minimum profit of
Mountaineering model = ($88.00  $52.80)12,000  $369,600
= $52,800
Minimum profit of
Touring model
= ($80.00  $52.80)12,000  $316,800
= $9,600
f. Break-even point of
Mountaineering model = $369,600/($88.00  $52.80)
= 10,500 pairs
The problem is to find the variable costs for the Touring model that will produce
the same break-even point. Let b represent this cost. Then:
$316,800/($80.00  b) = 10,500
($80.00  b)/$316,800 = 1/10,500
$80  b = $316,800/10,500
$80  b = $30.17
b = $80  $30.17
b = $49.83
Current variable costs
Variable cost to produce desired break-even point
Decrease in variable costs per pair
g.
New variable costs: $52.80  0.90 = $47.52
New fixed costs: $316,800  1.10 =$348,480
New break-even point = $348,480/($80.00  $47.52)
of touring ski
= 10,729 pairs
$52.80
(49.83)
$ 2.97