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Problem 3-19 (60 minutes)
1.
Profit
=
Unit CM × Q − Fixed expenses
$0
=
($40 − $25) × Q − $300,000
$0
=
($15) × Q − $300,000
$15Q
=
$300,000
Q
=
$300,000 ÷ $15 per shirt
Q
=
20,000 shirts
20,000 shirts × $40 per shirt = $800,000
Alternative solution:
Fixed expenses
Unit sales =
to break even Unit contribution margin
$300,000
= = 20,000 shirts
$15 per shirt
Fixed expenses
Dollar sales =
to break even CM ratio
$300,000
= = $800,000 in sales
0.375
Break-even sales .................
20,000 shirts
Actual sales .........................
19,000 shirts
Sales short of break-even ....
1,000 shirts
1,000 shirts × $15 contribution margin per shirt = $15,000 loss
Alternative solution:
Variable expenses (19,000 shirts × $25 per shirt) .......
475,000
Contribution margin ..................................................
285,000
Fixed expenses .........................................................
300,000
Net operating loss ....................................................
$(15,000)
Problem 3-19 (continued)
2. Cost-volume-profit graph:
$0
$100
$200
$300
$400
$500
$600
$700
$800
$900
$1,000
$1,100
$1,200
$1,300
0 10,000 20,000 30,000
Dollars (000)
Number of Shirts
Break-even point: 20,000 shirts,
or $800,000 in sales
Fixed Expenses
Total Expenses
Total Sales
Problem 3-19 (continued)
4. The variable expenses will now be $28 ($25 + $3) per shirt, and the
contribution margin will be $12 ($40 – $28) per shirt.
Profit
=
Unit CM × Q − Fixed expenses
$0
=
($40 − $28) × Q − $300,000
$0
=
($12) × Q − $300,000
$12Q
=
$300,000
Q
=
$300,000 ÷ $12 per shirt
Q
=
25,000 shirts
25,000 shirts × $40 per shirt = $1,000,000 in sales
Alternative solution:
Fixed expenses
Unit sales =
to break even Unit contribution margin
$300,000
= = 25,000 shirts
$12 per shirt
Fixed expenses
Dollar sales =
to break even CM ratio
$300,000
= = $1,000,000 in sales
0.30
5. The simplest approach is:
Actual sales ..................................
23,500 shirts
Break-even sales ..........................
20,000 shirts
Excess over break-even sales ........
3,500 shirts
3,500 shirts × $12 per shirt* = $42,000 profit
*$15 present contribution margin – $3 commission = $12 per shirt
Problem 3-20 (60 minutes)
1. The CM ratio is 30%.
Total
Per Unit
Percentage
Sales (13,500 units) .........
$270,000
$20
100%
Variable expenses ............
189,000
14
70%
Contribution margin .........
$ 81,000
$ 6
30%
The break-even point is:
Profit
=
Unit CM × Q − Fixed expenses
$0
=
($20 − $14) × Q − $90,000
$0
=
($6) × Q − $90,000
$6Q
=
$90,000
Q
=
$90,000 ÷ $6 per unit
Q
=
15,000 units
15,000 units × $20 per unit = $300,000 in sales
Alternative solution:
Fixed expenses
Unit sales =
to break even Unit contribution margin
$90,000
= = 15,000 units
$6 per unit
Fixed expenses
Dollar sales =
to break even CM ratio
$90,000
= = $300,000 in sales
0.30
2.
Incremental contribution margin:
$70,000 increased sales × 30% CM ratio ...........
$21,000
Less increased fixed costs:
month.
Problem 3-20 (continued)
The new break-even point would be:
Fixed expenses
Unit sales =
to break even Unit contribution margin
$208,000
= = 16,000 units
$13 per unit
Fixed expenses
Dollar sales =
to break even CM ratio
$208,000
= = $320,000 in sales
0.65
b. Comparative income statements follow:
Not Automated
Automated
Total
Per Unit
%
Total
Per Unit
%
Sales (20,000 units) ....
$400,000
$20
100
$400,000
$20
100
Variable expenses .......
280,000
14
70
140,000
7
35
Contribution margin ....
120,000
$ 6
30
260,000
$13
65
Fixed expenses ...........
90,000
208,000
Net operating income ..
$ 30,000
$ 52,000
Problem 3-20 (continued)
c. Whether or not one would recommend that the company automate
its operations depends on how much risk he or she is willing to take,
and depends heavily on prospects for future sales. The proposed
changes would increase the company’s fixed costs and its break-even
made.
The greatest risk of automating is that future sales may drop back
down to present levels (only 13,500 units per month), and as a
result, losses will be even larger than at present due to the
company’s greater fixed costs. (Note the problem states that sales
are erratic from month to month.) In sum, the proposed changes will
between the two alternatives in terms of units sold; i.e., the point
where profits will be the same under either alternative. At this point,
total revenue will be the same; hence, we include only costs in our
equation:
Let Q
=
Point of indifference in units sold
$14Q + $90,000
=
$7Q + $208,000
$7Q
=
$118,000
Q
=
$118,000 ÷ $7 per unit
Q
=
16,857 units (rounded)
If more than 16,857 units are sold, the proposed plan will
yield the greatest profit; if less than 16,857 units are sold, the present plan
will yield the greatest profit (or the least loss).
Problem 3-21 (60 minutes)
1. The CM ratio is 60%:
Selling price ......................
$15
100%
Variable expenses ..............
6
40%
Contribution margin ...........
$ 9
60%
2.
Fixed expenses
Break-even point in=
total sales dollars CM ratio
$180,000
= =$300,000 sales
0.60
3. $45,000 increased sales × 60% CM ratio = $27,000 increase in
contribution margin. Since fixed costs will not change, net operating
income should also increase by $27,000.
4. a.
Contribution margin
Degree of operating leverage = Net operating income
$216,000
= = 6
$36,000
b. 6 × 15% = 90% increase in net operating income. In dollars, this
increase would be 90% × $36,000 = $32,400.
