Question

Jerry Rice and Grain Stores has \(4,780,000 in yearly sales. The firm earns 4.5 percent on each dollar of sales and turns over its assets 2.7 times per year. It has \)123,000 in current liabilities and $349,000 in long-term liabilities.

b. If the asset base remains the same as computed in part a, but total asset

turnover goes up to 3, what will be the new return on stockholders’ equity?Assume that the profit margin stays the same as do current and long-term

liabilities.

Short answer

Return on stockholder’s equity: 18.41%

Step-by-step solution

Net Sales

$\begin{array}{rcl}\mathrm{Net}\mathrm{sales}& =& \mathrm{Average}\mathrm{total}\mathrm{asset}\times \mathrm{Total}\mathrm{asset}\mathrm{turnover}\mathrm{ratio}\\ & =& \$1,770,370\times 3\\ & =& \$5,311,110\end{array}$

Net income

$\begin{array}{rcl}\mathrm{Net}\mathrm{income}& =& \mathrm{Sales}\times \mathrm{profit}\mathrm{margin}\\ & =& \$5,311,110\times 4.5\%\\ & =& \$239,000\end{array}$

Shareholder’s equity

$\begin{array}{rcl}\mathrm{Shareholder}\text{'}\mathrm{s}\mathrm{equity}& =& \mathrm{Total}\mathrm{assets}-\mathrm{Current}\mathrm{liabilities}-\mathrm{Long}\mathrm{term}\mathrm{liabilities}\\ & =& \$1,770,370-\$123,000-\$349,000\\ & =& \$1,298,370\end{array}$

Return on equity

$\begin{array}{rcl}\mathrm{Return}\mathrm{on}\mathrm{shareholder}\text{'}\mathrm{s}\mathrm{equity}& =& \frac{\mathrm{Net}\mathrm{income}}{\mathrm{Shareholder}\text{'}\mathrm{s}\mathrm{equity}}\\ & =& \frac{\$239,000}{\$1,298,370}\\ & =& 18.41\%\end{array}$