Question

U.S. Steal has the following income statement data:

Units sold	Total variable costs	Fixed costs	Total costs	Total revenue	Operating income (Loss)
60,000	\(120,000	\)50,000	\(170,000	\)360,000	$190,000
80,000	160,000	50,000	210,000	480,000	270,000

b. Confirm that your answer to part a is correct by recomputing DOL using Formula 5-3. There may be a slight difference due to rounding.

$\mathbf{DOL}\mathbf{=}\frac{\mathbf{Q}\mathbf{(}\mathbf{P}\mathbf{-}\mathbf{VC}\mathbf{)}}{\mathbf{Q}\mathbf{(}\mathbf{P}\mathbf{-}\mathbf{VC}\mathbf{)}\mathbf{-}\mathbf{FC}}$

Q represents beginning units sold (all calculations should be done at this level). P can be found by dividing total revenue by units sold. VC can be found by dividing total variable costs by units sold.

Short answer

The degree of operating leverage of the company is 1.26. It is confirmed that the DOL computed in part a is correct.

Step-by-step solution

Calculating the amount of P at 60,000 units sold

$\begin{array}{rcl}\mathrm{P}& =& \frac{\mathrm{Total}\mathrm{revenue}\mathrm{at}60,000\mathrm{units}}{\mathrm{Number}\mathrm{of}\mathrm{units}}\\ & =& \frac{\$360,000}{60,000}\\ & =& \$6\end{array}$

Calculate VC

$\begin{array}{rcl}\mathrm{VC}& =& \frac{\mathrm{Total}\mathrm{variable}\mathrm{cost}}{\mathrm{Number}\mathrm{of}\mathrm{units}\mathrm{sold}}\\ & =& \frac{\$120,000}{60,000}\\ & =& 2\end{array}$

Degree of operating leverage

$\begin{array}{rcl}\mathrm{DOL}& =& \frac{\mathrm{Q}\left(\mathrm{P}-\mathrm{VC}\right)}{\left(\mathrm{P}-\mathrm{VC}\right)-\mathrm{FC}}\\ & =& \frac{60,000\left(\$6-\$2\right)}{60,000\left(\$6-\$2\right)-\$50,000}\\ & =& 1.26\end{array}$

The degree of operating leverage by applying the given formula in question is 1.26.