Problem 5-25 (45 minutes)
1. The contribution margin per unit on the first 16,000 units is:
Per Unit
Sales price ……………………..
$3.00
Variable expenses …………….
1.25
Contribution margin ………….
$1.75
Per Unit
Sales price ……………………..
$3.00
Variable expenses …………….
1.40
Contribution margin ………….
$1.60
Thus, for the first 16,000 units sold, the total amount of contribution
margin generated would be:
16,000 units × $1.75 per unit = $28,000
Since the fixed costs on the first 16,000 units total $35,000, the $28,000
contribution margin above is not enough to permit the company to
break even. Therefore, in order to break even, more than 16,000 units
would have to be sold. The fixed costs that will have to be covered by
the additional sales are:
Fixed costs on the first 16,000 units …………………..
$35,000
Less contribution margin from the first 16,000 units
28,000
Remaining unrecovered fixed costs …………………….
7,000
Add monthly rental cost of the additional space
needed to produce more than 16,000 units ……….
1,000
Total fixed costs to be covered by remaining sales …
$ 8,000
Problem 5-26 (60 minutes)
1.
Profit
= Unit CM × Q − Fixed expenses
$0
= ($30 − $18) × Q − $150,000
$0
= ($12) × Q − $150,000
$12Q
= $150,000
Q
= $150,000 ÷ $12
Q
= 12,500 pairs
12,500 pairs × $30 per pair = $375,000 in sales
Alternative solution:
Fixed expenses
Unit sales to =
break even Unit CM
$150,000
= = 12,500 pairs
$12.00
Fixed expenses
Dollar sales to =
break even CM ratio
$150,000
= = $375,000 in sales
0.40
2. See the graph on the following page.
3. The simplest approach is:
Break-even sales ……………………
12,500 pairs
Actual sales ………………………….
12,000 pairs
Sales short of break-even ………..
500 pairs
500 pairs × $12 contribution margin per pair = $6,000 loss
Alternative solution:
Sales (12,000 pairs × $30.00 per pair) ….
$360,000
Variable expenses
(12,000 pairs × $18.00 per pair) ……….
216,000
Contribution margin ………………………….
144,000
Fixed expenses ………………………………..
150,000
Net operating loss …………………………….
$ (6,000)
Problem 5-26 (continued)
4. The variable expenses will now be $18.75 ($18.00 + $0.75) per pair,
and the contribution margin will be $11.25 ($30.00 – $18.75) per pair.
Profit
= Unit CM × Q − Fixed expenses
$0
= ($30.00 − $18.75) × Q − $150,000
$0
= ($11.25) × Q − $150,000
$11.25Q
= $150,000
Q
= $150,000 ÷ $11.25
Q
= 13,333 pairs (rounded)
Actual sales …………………………..
15,000 pairs
Break-even sales …………………….
12,500 pairs
Excess over break-even sales ……
2,500 pairs × $11.50 per pair* = $28,750 profit
*$12.00 present contribution margin – $0.50 commission = $11.50
Sales (15,000 pairs × $30.00 per pair) …………..
Contribution margin …………………………………..
Problem 5-27 (45 minutes)
1.
a.
Hawaiian
Fantasy
Tahitian
Joy
Total
Amount
%
Amount
%
Amount
%
Sales ……………………..
$300,000
100%
$500,000
100%
$800,000
100%
Variable expenses …….
180,000
60%
100,000
20%
280,000
35%
Contribution margin ….
$120,000
40%
$400,000
80%
520,000
65%
Fixed expenses ………..
475,800
Net operating income ..
$ 44,200
b.
Fixed expenses $475,800
Dollar sales to = = = $732,000
break even CM ratio 0.65
Margin of safety = Actual sales – Break-even sales
= $800,000 – $732,000 = $68,000
Margin of safety Margin of safety in dollars
=
percentage Actual sales
$68,000
= = 8.5%
$800,000
Problem 5-27 (continued)
b.
Fixed expenses $475,800
Dollar sales to = = = $975,000
break even CM ratio 0.488
Margin of safety = Actual sales – Break-even sales
= $1,250,000 – $975,000 = $275,000
Margin of safety Margin of safety in dollars
=
percentage Actual sales
$275,000
= = 22%
$1,250,000
3. The reason for the increase in the break-even point can be traced to the
decrease in the company’s overall contribution margin ratio when the
third product is added. Note from the income statements above that this
ratio drops from 65% to 48.8% with the addition of the third product.
