Hurst Co. manufactures and sells a single product. Price and cost data regarding this product are as follows:$\begin{array}{|l|r|}
\hline \text { Selling price } & \$ 40 \text { per unit } \
\hline \text { Variable manufacturing cost } & \$ 20 \text { per unit } \
\hline \text { Variable selling \& administrative expenses } & \$ 6 \text { per unit } \
\hline \text { Fixed manufacturing overhead } & \$ 208,000 \text { per year } \
\hline \text { Fixed selling \& administrative expenses } & \$ 324,000 \text { per year } \
\hline
\end{array}$

-How many units need to be sold to earn an annual operating income equal to 10% of sales?

Question

Hurst Co. manufactures and sells a single product. Price and cost data regarding this product are as follows:$\begin{array}{|l|r|}
\hline \text { Selling price } & \$ 40 \text { per unit } \
\hline \text { Variable manufacturing cost } & \$ 20 \text { per unit } \
\hline \text { Variable selling \& administrative expenses } & \$ 6 \text { per unit } \
\hline \text { Fixed manufacturing overhead } & \$ 208,000 \text { per year } \
\hline \text { Fixed selling \& administrative expenses } & \$ 324,000 \text { per year } \
\hline
\end{array}$

-How many units need to be sold to earn an annual operating income equal to 10% of sales?

Quizplus · Accepted Answer

To find the number of units needed to earn an annual operating income equal to 10% of sales, we first calculate the contribution margin per unit, which is the selling price per unit minus the variable costs per unit. The variable costs per unit include both the variable manufacturing cost and the variable selling & administrative expenses, so the contribution margin per unit is $40 - ($20 + $6) = $14.Next, we determine the total fixed costs, which are the sum of fixed manufacturing overhead and fixed selling & administrative expenses, totaling $208,000 + $324,000 = $532,000.To achieve an operating income equal to 10% of sales, we set up the equation where the desired profit is 10% of total sales (price per unit times the number of units), and solve for the number of units (X):$$0.10 \times 40X = 532,000 + 14X$$Solving for X gives us the number of units needed to achieve the target operating income. Rearranging the equation:$$4X = 532,000 + 14X$$Subtract 14X from both sides:$$-10X = 532,000$$Divide by -10:$$X = 53,200$$Therefore, 53,200 units need to be sold to earn an annual operating income equal to 10% of sales.

Hurst Co Manufactures and Sells a Single Product -How Many Units Need to Be Sold to Earn an Cost