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.
This product (the Samoan Delight) has a CM ratio of only 20%, which
causes the average contribution margin per dollar of sales to shift
downward.
This problem shows the somewhat tenuous nature of break-even analy-
sis when the company has more than one product. The analyst must be
very careful of his or her assumptions regarding sales mix, including the
addition (or deletion) of new products.
It should be pointed out to the president that even though the break-
even point is higher with the addition of the third product, the com-
pany’s margin of safety is also greater. Notice that the margin of safety
increases from $68,000 to $275,000 or from 8.5% to 22%. Thus, the
addition of the new product shifts the company much further from its
break-even point, even though the break-even point is higher.
Problem 6-30 (60 minutes)
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