A firm with fixed costs of $161,500 per month sells three products with the following characteristics: $\begin{array}{ccc}
&\text { Sales Mix}&\text { Contribution }\
\underline{\text { Product }} & \underline{\text { Percentage }} & \underline{\text { Margin } }\
\text { P }& 25 \% & \$ 48 \
\text { Q} & 50 \% & 50 \
\text { R }& 25 \% & 52
\end{array}$
How many total units must be sold to breakeven?
A) 3,230
B) 1,230
C) 2,153
D) 1,077

Question

A firm with fixed costs of $161,500 per month sells three products with the following characteristics: $\begin{array}{ccc}
&\text { Sales Mix}&\text { Contribution }\ 
\underline{\text { Product }} & \underline{\text { Percentage }} & \underline{\text { Margin } }\
\text {  P }& 25 \% & \$ 48 \
\text { Q} & 50 \% & 50 \
\text { R }& 25 \% & 52
\end{array}$
 How many total units must be sold to breakeven?
A) 3,230
B) 1,230
C) 2,153
D) 1,077

Quizplus · Accepted Answer

The contribution margin is the difference between the selling price and the variable cost per unit. The contribution margin ratio is the contribution margin divided by the selling price. The breakeven point is the level of sales at which the total contribution margin equals the fixed costs.The total contribution margin is the sum of the contribution margins for each product. The contribution margin for each product is the contribution margin ratio multiplied by the sales volume.The sales volume for each product is the sales mix percentage multiplied by the total sales volume.The total sales volume is the breakeven point divided by the contribution margin ratio.The contribution margin ratio is the sum of the contribution margin ratios for each product, weighted by the sales mix percentages.The contribution margin ratio for product P is $48 / $100 = 0.48.The contribution margin ratio for product Q is $50 / $100 = 0.50.The contribution margin ratio for product R is $52 / $100 = 0.52.The sales mix percentage for product P is 25%.The sales mix percentage for product Q is 50%.The sales mix percentage for product R is 25%.The total contribution margin ratio is (0.48 * 0.25) + (0.50 * 0.50) + (0.52 * 0.25) = 0.495.The breakeven point is $161,500 / 0.495 = $326,263.The total sales volume is $326,263 / 0.495 = $659,139.The sales volume for product P is 0.25 * $659,139 = $164,785.The sales volume for product Q is 0.50 * $659,139 = $329,570.The sales volume for product R is 0.25 * $659,139 = $164,785.The total number of units sold is $164,785 / $48 + $329,570 / $50 + $164,785 / $52 = 3,230 units.

A Firm with Fixed Costs of $161,500 Per Month Sells