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

a. Compute DOL based on the following formula (see page 131 for an example):

$\begin{array}{rcl}\mathrm{DOL}& =& \frac{\mathrm{Percentage}\mathrm{change}\mathrm{in}\mathrm{operating}\mathrm{income}}{\mathrm{Percentage}\mathrm{change}\mathrm{in}\mathrm{units}\mathrm{sold}}\\ & & \end{array}$

Short answer

The degree of operating leverage of the company is 1.26.

Step-by-step solution

Percent change in operating income

$\begin{array}{rcl}\%\mathrm{change}\mathrm{in}\mathrm{operating}\mathrm{income}& =& \frac{\mathrm{Operating}\mathrm{income}\mathrm{at}80,000\mathrm{units}-\mathrm{Operating}\mathrm{income}\mathrm{at}60,000\mathrm{units}}{\mathrm{Operating}\mathrm{income}\mathrm{at}60,000\mathrm{units}}\\ & =& \frac{\$270,000-\$190,000}{\$190,000}\\ & =& 42.10\%\end{array}$

Percent change in units sold

$\begin{array}{rcl}\%\mathrm{change}\mathrm{in}\mathrm{units}\mathrm{sold}& =& \frac{\mathrm{High}\mathrm{units}-\mathrm{Low}\mathrm{units}}{\mathrm{Low}\mathrm{units}}\\ & =& \frac{80,000-60,000}{60,000}\\ & =& 33.33\%\end{array}$

Degree of operating leverage

$\begin{array}{rcl}\mathrm{DOL}& =& \frac{\mathrm{Percentage}\mathrm{change}\mathrm{in}\mathrm{operating}\mathrm{income}}{\mathrm{Percent}\mathrm{change}\mathrm{in}\mathrm{units}\mathrm{sold}}\\ & =& \frac{42.10\%}{33.33\%}\\ & =& 1.26\end{array}$