The Allen Company had the following income statement for the month of July: $\begin{array}{c}
\text { Allen Company}\
\text { Income Statement}\
\text { For the Month of July}\\
\begin{array}{lrr}
\text { Sales }(\$ 60 \times 10,000) & & \$ 600,000 \
\text { Cost of goods sold: } & & \
\text { Direct materials }(\$ 12 \times 10,000) & \$ 120,000 \
\text { Direct labour }(\$ 9 \times 10,000)& 90,000 & \
\text { Variable factory overhead }(\$ 7.50 \times 10,000)& 75,000 \
\text { Fixed factory overhead } & \underline{120,000} & \underline{405,000} \
\text { Gross profit } & & \$ 195,000 \
\text { Selling and administrative expenses: } \
\text { Variable }(\$ 1.50 \times 10,000) & \$ 15,000 & \
\text { Fixed }& \underline{90,000} & \underline{105,000} \
\text { Operating income }& & \$ 90,000
\end{array}\end{array}$
-What is the sales volume required to earn a profit of $9,000?

Question

The Allen Company had the following income statement for the month of July: $\begin{array}{c}
\text { Allen Company}\
\text {  Income Statement}\
\text {  For the Month of July}\\
\begin{array}{lrr}
\text { Sales }(\$ 60 \times 10,000) & & \$ 600,000 \
\text { Cost of goods sold: } & & \
\text { Direct materials }(\$ 12 \times 10,000) & \$ 120,000 \
\text { Direct labour }(\$ 9 \times 10,000)& 90,000  & \
\text { Variable factory overhead }(\$ 7.50 \times 10,000)& 75,000 \
\text { Fixed factory overhead } & \underline{120,000} & \underline{405,000}  \
\text { Gross profit } & & \$ 195,000 \
\text { Selling and administrative expenses: } \
\text { Variable }(\$ 1.50 \times 10,000)  & \$ 15,000 & \
\text { Fixed }& \underline{90,000} & \underline{105,000} \
\text { Operating income }& & \$ 90,000
\end{array}\end{array}$ 
-What is the sales volume required to earn a profit of $9,000?

Quizplus · Accepted Answer

To find the sales volume required to earn a profit of $9,000, we first calculate the contribution margin per unit and then the break-even point, including the desired profit. The contribution margin per unit is calculated by subtracting variable costs per unit from the selling price per unit. The selling price per unit is $600,000 / 10,000 units = $60. The variable costs per unit include direct materials ($12), direct labor ($9), variable factory overhead ($7.50), and variable selling and administrative expenses ($1.50), totaling $30. Thus, the contribution margin per unit is $60 - $30 = $30. Fixed costs include fixed factory overhead ($120,000) and fixed selling and administrative expenses ($90,000), totaling $210,000. To earn a profit of $9,000, the total required contribution margin is fixed costs plus desired profit, which is $210,000 + $9,000 = $219,000. The number of units required to achieve this is $219,000 / $30 (contribution margin per unit) = 7,300 units.

The Allen Company Had the Following Income Statement for the Month