5. a. The new CM ratio would be:
Per Unit Percent of Sales
Sales ... $30.00 100%
Less variable expenses .... 18.00 60
Contribution margin ... $12.00 40%
Problem 6-19 (continued)
The new break-even point would be:
Fixed expenses
Break-even point= in unit sales Unit contribution margin
$180,000 + $72,000
= =21,000 units
$12.00 per unit
Break-even point= in sales dollars CM ratio
= =$630,0
0.40 00
b. Comparative income statements follow:
Not Automated Automated
Total Per
Unit % Total Per
Unit %
Sales (26,000
units) ...$780,000 $30.00 100% $780,000 $30.00 100%
Less variable
expenses ... 546,000 21.00 70 468,000 18.00 60
Contribution
margin... 234,000 $ 9.00 30% 312,000 $12.00 40%
Less fixed ex-
penses... 180,000 252,000
Net operating
income ... $ 54,000 $ 60,000
c. Whether or not the company should automate its operations depends
on how much risk the company is willing to take and on prospects for
future sales. The proposed changes would increase the company’s
fixed costs and its break-even point. However, the changes would
also increase the company’s CM ratio (from 0.30 to 0.40). The higher
CM ratio means that once the break-even point is reached, profits will
increase more rapidly than at present. If 26,000 units are sold next
The greatest risk of automating is that future sales may drop back
down to present levels (only 19,500 units per month), and as a re-
sult, 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 help the
company if sales continue to trend upward in future months; the
changes will hurt the company if sales drop back down to or near
present levels.
Note to the Instructor: Although it is not asked for in the problem,
if time permits you may want to compute the point of indifference be-
tween 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
$21.00Q + $180,000 = $18.00Q + $252,000
$3.00Q = $72,000
Q = $72,000 ÷ $3.00 per unit
Q = 24,000 units
If more than 24,000 units are sold in a month, the proposed plan will
yield the greater profits; if less than 24,000 units are sold in a month,
the present plan will yield the greater profits (or the least loss).
Problem 6-20 (60 minutes)
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