Chapter 13, Problem 22BP

a.

To determine

Determine the number of times interest was earned for Company F for Year 3 and Year 2.

Explanation of Solution

Number of times interest is earned: Number of times interest is earned quantifies the number of times the earnings before interest and taxes can pay the interest expense. First, determine the sum of income before income tax and interest expense. Then, divide the sum by interest expense.

$\begin{array}{l}\text{Number of times }\\ \text{interest is earned}\end{array}\}=\frac{\text{Earnings before interest and taxes expense}}{\text{Interest expense}}$

Determine the number of times interest earned of Company F for Year 2.

$\begin{array}{c}\begin{array}{l}\text{Number of times }\\ \text{interest is earned}\end{array}\}=\frac{\text{Earnings before interest and taxes expense}}{\text{Interest expense}}\\ =\frac{\$150,000}{\$16,000}\\ =9.38\text{ times}\end{array}$

Determine the number of times interest earned of Company F for Year 3.

$\begin{array}{c}\begin{array}{l}\text{Number of times }\\ \text{interest is earned}\end{array}\}=\frac{\text{Earnings before interest and taxes expense}}{\text{Interest expense}}\\ =\frac{\$180,000}{\$20,000}\\ =9\text{ times}\end{array}$

Hence, the number of times interest earned of Company F for Year 2 and Year 3 is 9.38 times and 9 times respectively.

b.

To determine

Compute the earnings per share based on the average number of shares outstanding for Company F for Year 3 and Year 2.

Explanation of Solution

Earnings per Share: Earnings per share help to measure the profitability of a company. Earnings per share are the amount of profit that is allocated to each share of outstanding stock.

$\text{Earnings per share}=\frac{\text{Net earnings available for common stock}}{\text{Average number of outstanding common shares}}$

Determine the earnings per share of Company F for Year 2.

$\begin{array}{c}\text{Earnings per share}=\frac{\text{Net earnings available for common stock}}{\text{Average number of outstanding common shares}}\\ =\frac{\$108,000}{15,000\text{}\text{ shares}}\\ =\$7.20\text{ per share}\end{array}$ (1)

Determine the earnings per share of Company F for Year 3.

$\begin{array}{c}\text{Earnings per share}=\frac{\text{Net earnings available for common stock}}{\text{Average number of outstanding common shares}}\\ =\frac{\$128,000}{16,000\text{ shares}}\\ =\$8\text{ per share}\end{array}$ (2)

Hence, the earnings per share of Company F for Year 2 and Year 3 are $7.20 per share and $8 per share respectively.

c.

To determine

Determine the price earnings ratio for Company F for Year 3 and Year 2.

Explanation of Solution

Price/Earnings Ratio: The price/earnings ratio shows the market value of the amount invested to earn $1 by a company. It is major tool to be used by investors before the decisions related to investments in a company.

$\text{Price/Earnings Ratio}\text{=}\frac{\text{Market Price per Share }}{\text{Earnings per Share}}$

Determine the price/earnings ratio of Company F for Year 2.

$\begin{array}{c}\text{Price/Earnings Ratio}\}=\frac{\text{Market price per share}}{\text{Earnings per share}}\\ =\frac{\$24}{\$7.20\left(1\right)}\\ =3.33\text{times}\end{array}$

Determine the price/earnings ratio of Company F for Year 3.

$\begin{array}{c}\text{Price/Earnings Ratio}\}=\frac{\text{Market price per share}}{\text{Earnings per share}}\\ =\frac{\$30}{\$8\left(2\right)}\\ =3.75\text{times}\end{array}$

Hence, the price earnings ratio of Company F for Year 2 and Year 3 is 3.33 times and 3.75 times respectively.

d.

To determine

Determine the return on equity.

Explanation of Solution

Return on average equity: It is one of the profitability ratios. Return on average equity ratio is used to determine the relationship between the net income available for the common stockholders’ and the average total stockholders’ equtiy. Return on equity is calculated as follows:

$\text{Return on average equity }\text{=}\frac{\text{Net}\text{Income}}{\text{Average}\text{Total}\text{Stockholders'}\text{Equity}}$

Determine the return on average equity of Company F for Year 2.

$\begin{array}{c}\text{Return on average equity }\text{=}\frac{\text{Net}\text{Income}}{\text{Average}\text{Total}\text{Stockholders'}\text{Equity}}\\ =\frac{\$108,000}{\$270,000\left(3\right)}\\ =40\text{\%}\end{array}$

Determine the average total stockholders’ equity.

$\begin{array}{c}\begin{array}{l}\text{Average}\text{Total}\\ \text{Stockholders'}\text{Equity}\end{array}\}\text{=}\frac{\left[\begin{array}{l}\text{Ending }\\ \text{stockholders' }\\ \text{equity}\end{array}\right]+\left[\begin{array}{l}\text{Beginnning }\\ \text{stockholders' }\\ \text{equity}\end{array}\right]}{2}\\ =\frac{\$300,000+\$240,000}{2}\\ =\frac{\$540,000}{2}\\ =\$270,000\end{array}$ (3)

Determine the return on average equity of Company F for Year 3.

$\begin{array}{c}\text{Return on average equity }\text{=}\frac{\text{Net}\text{Income}}{\text{Average}\text{Total}\text{Stockholders'}\text{Equity}}\\ =\frac{\$128,000}{\$330,000\left(4\right)}\\ =38.78\%\end{array}$

Determine the average total stockholders’ equity.

$\begin{array}{c}\begin{array}{l}\text{Average}\text{Total}\\ \text{Stockholders'}\text{Equity}\end{array}\}\text{=}\frac{\left[\begin{array}{l}\text{Ending }\\ \text{stockholders' }\\ \text{equity}\end{array}\right]+\left[\begin{array}{l}\text{Beginnning }\\ \text{stockholders' }\\ \text{equity}\end{array}\right]}{2}\\ =\frac{\$360,000+\$300,000}{2}\\ =\frac{\$660,000}{2}\\ =\$330,000\end{array}$ (4)

Hence, the return on average equity of Company F for Year 2 and Year 3 is 40.00% and 38.78% respectively.

e.

To determine

Determine the net margin.

Explanation of Solution

Net profit margin: It is one of the profitability ratios. Profit margin ratio is used to measure the percentage of net income that is being generated per dollar of revenue or sales. It is calculated by using the formula:

$\text{Net margin}=\frac{\text{Net income}}{\text{Net sales}}$

Determine the net margin of Company F for Year 2.

$\begin{array}{c}\text{Net margin}=\frac{\text{Net income}}{\text{Net sales}}\\ =\frac{\$108,000}{\$800,000}\times 100\\ =13.50\%\end{array}$

Determine the net margin of Company F for Year 2.

$\begin{array}{c}\text{Net margin}=\frac{\text{Net income}}{\text{Net sales}}\\ =\frac{\$128,000}{\$1,000,000}\times 100\\ =12.80\%\end{array}$

Hence, the net margin of Company F for Year 2 and Year 3 is 13.50% and 12.80% respectively.