Question

Blanchard Company manufactures a single product that sells for \(180 per unit and whose total variable costs are \)135 per unit. The company’s annual fixed costs are \(562,500. Management targets an annual pretax income of \)1,012,500. Assume that fixed costs remain at $562,500. Compute the (1) unit sales to earn the target income and (2) dollar sales to earn the target income.

Short answer

1. The business entity has to sell35,000units to earn a targeted income of $1,012,500.
2. The business entity has to make the sale of$6,300,000 to earn a targeted income of $1,012,500.

Step-by-step solution

Definition of Break-Even Units

The number of units that a business entity must sell to achieve the situation of no-profit, no-loss is known as break-even units. It is calculated using the fixed cost and the contribution margin per unit.

Unit sales to earn targeted income

$\begin{array}{rcl}\mathrm{Units}\mathrm{sales}\mathrm{for}\mathrm{targeted}\mathrm{profit}& =& \frac{\mathrm{Fixed}\mathrm{expenses}+\mathrm{Targeted}\mathrm{income}}{\mathrm{Sales}\mathrm{price}\mathrm{per}\mathrm{unit}-\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}}\\ & =& \frac{\$562,500+\$1,012,500}{\$180-\$135}\\ & =& \frac{\$1,575,000}{\$45}\\ & =& 35,000\mathrm{units}\end{array}$

Dollar sales to earn targeted income

$\begin{array}{rcl}\mathrm{Dollar}\mathrm{sales}\mathrm{for}\mathrm{targeted}\mathrm{profit}& =& \frac{\mathrm{Fixed}\mathrm{expenses}+\mathrm{Targeted}\mathrm{income}}{\mathrm{Contribution}\mathrm{margin}\mathrm{ratio}}\\ & =& \frac{\$562,500+\$1,012,500}{0.25}\\ & =& \$6,300,000\end{array}$

Working note:

Calculation of contribution margin ratio:

$\begin{array}{rcl}\mathrm{Contribution}\mathrm{margin}\mathrm{ratio}& =& \frac{\mathrm{Sales}\mathrm{price}\mathrm{per}\mathrm{unit}-\mathrm{Variable}\mathrm{cost}\mathrm{per}\mathrm{unit}}{\mathrm{Sales}\mathrm{price}\mathrm{per}\mathrm{unit}}\\ & =& \frac{\$180-\$135}{\$180}\\ & =& 0.25\end{array}$