Chapter 13, Problem 22PSB

a)

To determine

Calculate the number of times interest earned for the year 2017 and 2018.

Explanation of Solution

Times Interest Earned Ratio:

 It is one of the solvency ratios. It is a measure to evaluate the net income for interest payment on debt of a company.

The calculation of the number of times interest earned in the year 2018 is as follows:

$\begin{array}{c} \text{Interest turnover ratio}=\frac{\text{Income before interest and taxes }}{\text{Interest expenses }}\\ =\frac{\$180,000}{\$20,000}\\ =9\text{ times}\end{array}$

Hence, the number of times interest earned in the year 2018 is 9 times.

The calculation of the number of times interest earned in the year 2017 is as follows:

$\begin{array}{c} \text{Interest turnover ratio}=\frac{\text{Income before interest and taxes }}{\text{Interest expenses }}\\ =\frac{\$150,000}{\$16,000}\\ =9.38\text{ times}\end{array}$

Hence, the number of times interest earned in the year 2017 is 9.38 times.

b)

To determine

Calculate the earnings per share based on the number of outstanding shares for the year 2017 and 2018.

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.

The calculation of earnings per share for the year 2018 is as follows:

$\begin{array}{c}\text{Earning per share}=\frac{\text{Net income }}{\text{ Number of outstanding common shares }}\\ =\frac{\$128,000}{16,000}\\ =\$8\end{array}$

Hence, the earning per share for the year 2018 is $8.

The calculation of earnings per share for the year 2017 is as follows:

$\begin{array}{c}\text{Earning per share}=\frac{\text{Net income }}{\text{ Number of outstanding common shares }}\\ =\frac{\$108,000}{15,000}\\ =\$7.20\end{array}$

Hence, the earning per share for the year 2017 is $7.20.

c)

To determine

Calculate the price-earnings ratio for the year 2017 and 2018.

Explanation of Solution

 Price/Earnings Ratio:

It depicts the relation of market price of a share to earnings per share of that company. The price/earnings ratio presents 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.

The calculation of price-earnings ratio for the year 2018 is as follows:

$\begin{array}{c}\text{Price-earnings ratio}=\frac{\text{Common stock price}}{\text{Earnings per share }}\\ =\frac{\$30}{\$8}\\ =3.75\text{ times}\end{array}$

Hence, the price-earnings ratio for the year 2018 is 3.75 times.

The calculation of price-earnings ratio for the year 2017 is as follows:

$\begin{array}{c}\text{Price-earnings ratio}=\frac{\text{Common stock price}}{\text{Earnings per share }}\\ =\frac{\$24}{\$7.20}\\ =3.33\text{ times}\end{array}$

Hence, the price-earnings ratio for the year 2017 is 3.33 times.

d)

To determine

Calculate the return on equity for the year 2017 and 2018.

Explanation of Solution

Return on equity ratio:

Rate of return on equity ratio is used to determine the relationship between the net income available for the common stockholders’ and the average common equity that is invested in the company.

The calculation of return on equity for the year 2018 is as follows:

$\begin{array}{c} \text{Return on Equity}=\frac{\text{Net}\text{Income}}{\text{Average}\text{Stockholder'}\text{s Equity}}\\ =\frac{\$128,000}{\$330,000(1)}\\ =38.78\%\end{array}$

Hence, the return on equity for the year 2018 is 38.78%.

The calculation of return on equity for the year 2017 is as follows:

$\begin{array}{c} \text{Return on Equity}=\frac{\text{Net}\text{Income}}{\text{Average}\text{Stockholder'}\text{s Equity}}\\ =\frac{\$108,000}{\$270,000(2)}\\ =40\%\end{array}$

Hence, the return on equity for the year 2017 is 40%.

Working note:

The calculation of average stockholders’ equity for the year 2018 is as follows:

$\begin{array}{c}\text{Average stock holders equity}=\frac{\left(\begin{array}{l}\text{Stockholders equity (2018)}+\\ \text{Stockholders equity (2017)}\end{array}\right)}{2}\\ =\frac{\$360,000+\$300,000}{2}\\ =\frac{\$660,000}{2}\\ =\$330,000\end{array}$

Hence, the average stockholders’ equity for the year 2018 is $330,000. (1)

The calculation of average stockholders’ equity for the year 2017 is as follows:

$\begin{array}{c}\text{Average stock holders equity}=\frac{\left(\begin{array}{l}\text{Stock holders equity (2017)}+\\ \text{Stock holders equity (2016)}\end{array}\right)}{2}\\ =\frac{\$300,000+\$240,000}{2}\\ =\frac{\$540,000}{2}\\ =\$270,000\end{array}$

Hence, the average stockholders’ equity for the year 2017 is $270,000. (2)

e)

To determine

Calculate the net margin for the year 2018 and 2017.

Explanation of Solution

Net margin:

This ratio gauges the operating profitability by quantifying the amount of income earned from business operations from the sales generated.

The calculation of net margin in the year 2018 is as follows:

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

Hence, the net margin for the year 2018 is 12.80%.

The calculation of net margin in the year 2017 is as follows:

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

Hence, the net margin for the year 2017 is 13.50%.