Choice "A" is correct. Product one unit sales of 39,000 will result in an overall breakeven for the company. The call of the question asks for the level of sales for an overall breakeven (not breakeven per product) so the company must generate a contribution margin equal to combined fixed costs of $312,000 ($100,000 for the first product + $212,000 for the second product) assuming the relative sales volumes given in the problem. Contribution margins (CM) are computed as follows:
First product: | $10 selling price - $6 variable cost$4 contribution margin |
Second product: | $25 selling price - $13 variable cost$12 contribution margin |
Since the relative sales volume of product is 75% for the first product and 25% of the second product, total breakeven units can be algebraically expressed as follows:
(First product CM X 75% of total units) + (Second product CM X 25% of total units) |
($4 x 75%x) + ($12 x 25%x) |
$3x +$3x$312,000 |
$6x$312,000 |
x$312,000/$6 |
x |
The call of the question is for the number of units of the first product. The first product represents 75% of the total units.
First product sales at breakeven |
Choice "d" is incorrect. Total units at breakeven is 52,000. The problem requires taking the extra step of computing the first product's percentage of the total.
Choice "c" is incorrect. The first product would achieve break even at 25,000 unit sales, however, based on the assumptions of the problem, the second product would only generate sales of 8,333 units (consistent with the relative volume of 75% and 25%). The second product (and the entire company) would not break even.Choice "b" is incorrect. The solution of 14,625 does not weight the contribution margins by relative percentage of total sales to arrive at the total break even units.
