Question

Zhao Co. has fixed costs of \(354,000. Its single product sells for \)175 per unit, and variable costs are $116 per unit. If the company expects sales of 10,000 units, compute its margin of safety (a) in dollars and (b) as a percent of expected sales.

Short answer

(a) The margin of safety in dollars is $677,273.

(b) The margin of safety as a percentage of sales is 38.70%.

Step-by-step solution

Definition of Margin of Safety

The margin of safety is when the sales made by the business entity are more than the breakeven point. It is better if the actual sales are higher than the breakeven sales.

(a) Margin of safety in dollars

Particular	Amount $
Expected sales 10,000 units @ $175 per unit	$1,750,000
Less: Break-even sales	(1,072,727)
Margin of safety	$677,273

Working note:

$\begin{array}{rcl}\mathrm{Contribution}\mathrm{margin}\mathrm{ratio}& =& \frac{\mathrm{Sales}\mathrm{price}-\mathrm{Variable}\mathrm{cost}}{\mathrm{Sales}\mathrm{price}}\\ & =& \frac{\$175-\$116}{\$175}\\ & =& 0.33\end{array}$

$\begin{array}{rcl}\mathrm{Break}-\mathrm{even}\mathrm{in}\mathrm{dollars}& =& \frac{\mathrm{Fixed}\mathrm{Cost}}{\mathrm{Contribution}\mathrm{margin}\mathrm{ratio}}\\ & =& \frac{\$354,000}{0.33}\\ & =& \$1,072,727\end{array}$

(b) Margin of safety in percentage

$\begin{array}{rcl}\mathrm{Margin}\mathrm{of}\mathrm{safety}\mathrm{in}\mathrm{percentage}& =& \frac{\mathrm{Margin}\mathrm{of}\mathrm{safety}}{\mathrm{Sales}}\times 100\\ & =& \frac{\$677,273}{\$1,750,000}\times 100\\ & =& 38.70\%\end{array}$