Chapter 15, Problem 15.4CP

1.

To determine

Financial Ratios: Financial ratios are the metrics used to evaluate the liquidity, capabilities, profitability, and overall performance of a company.

The following ratios for three years:

Rate earned on total assets

Rate earned on stockholders’ equity

Earnings per share

Dividend yield

Price – earnings ratio

Explanation of Solution

Given info: Items of financial statement

a. Rate earned on total assets for three years

$\begin{array}{c}\text{Rate earned on the total assets }\left(\text{Year 3}\right)=\frac{\text{Net}\text{income + Interest expense}}{\text{Average total assets}}\\ =\frac{\$3,064.7+\$782.8}{\$52,237}\\ =7.4\%\end{array}$

$\begin{array}{c}\text{Rate earned on total assets }\left(\text{Year 2}\right)=\frac{\text{Net}\text{income + Interest expense}}{\text{Average total assets}}\\ =\frac{\$2,799.9+\$759.4}{\$45,737}\\ =7.8\%\end{array}$ $\begin{array}{c}\text{Rate earned on total assets }\left(\text{Year 1}\right)=\frac{\text{Net}\text{income + Interest expense}}{\text{Average total assets}}\\ =\frac{\$1,865.0+\$811.4}{\$42,200}\\ =6.4\%\end{array}$

Rate earned on total assets determines the particular company’s overall earning power. It is determined by dividing sum of net income and interest expense and average total assets.

Formula:

$\text{Rate earned on total assets}=\frac{\text{Net}\text{income + Interest expense}}{\text{Average total assets}}$

Hence, rate earned on total assets for year 3, year 2, and year 1 are 7.4%, 7.8%, and 6.4% respectively.

b.

Rate earned on stockholders’ equity for three years

$\begin{array}{c}\begin{array}{l}\text{Rate earned on}\\ \text{ stockholders' equity}\left(\text{Year 3}\right)\end{array}\}=\frac{\text{Net income }}{\text{Average stockholder’s equity}}\\ =\frac{\$3,064.7}{\$6,821}\\ =44.9\%\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Rate earned on }\\ \text{stockholders' equity}\left(\text{Year 2}\right)\end{array}\}=\frac{\text{Net income }}{\text{Average stockholder’s equity}}\\ =\frac{\$2,799.9}{\$6,545}\\ =42.8\%\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Rate earned on }\\ \text{stockholders' equity}\left(\text{Year 1}\right)\end{array}\}=\frac{\text{Net income }}{\text{Average stockholder’s equity}}\\ =\frac{\$1,865.0}{\$5,555}\\ =33.6\%\end{array}$

Rate earned on stockholders’ equity is used to determine the relationship between the net income and the average common equity that are invested in the company.

Formula:

$\text{Rate earned on stockholders' equtiy }=\frac{\text{Net income}}{\text{Average stockholder’s equity}}$

Hence, rate of return on stockholders’ equity for year 3, year 2, and year 1 is 44.9%, 42.8%, and 33.6%.

c.

Earnings per share on the common stock for three years

$\begin{array}{c}\text{Earnings per share }\left(\text{Year 3}\right)=\left[\frac{\text{Net income}-\text{Preferred dividends}}{\left(\text{Weighted average shares of common stock outstanding}\right)}\right]\\ =\frac{\$3,064.7-\$0}{397\text{shares}}\\ =\$7.72\end{array}$ $\begin{array}{c}\text{Earnings per share }\left(\text{Year 2}\right)=\left[\frac{\text{Net income}-\text{Preferred dividends}}{\left(\text{Weighted average shares of common stock outstanding}\right)}\right]\\ =\frac{\$2,799.9-\$0}{417\text{shares}}\\ =\$6.71\end{array}$ $\begin{array}{c}\text{Earnings per share }\left(\text{Year 1}\right)=\left[\frac{\text{Net income}-\text{Preferred dividends}}{\left(\text{Weighted average shares of common stock outstanding}\right)}\right]\\ =\frac{\$1,865-\$0}{424\text{shares}}\\ =\$4.40\end{array}$

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.

Formula

$\text{Earnings}\text{per}\text{share = }\frac{\text{Net}\text{income – Preferred}\text{dividends}}{\text{Weighted average number of common shares outstanding}}$

Hence, earnings per share for year 3, year 2, and year 1 is $7.72, $6.71, and $4.40.

d.

Dividend yield for three years

$\begin{array}{c}\text{Dividend yield }\left(\text{Year 3}\right)=\frac{\text{Annual dividend per Share}}{\text{Market price per Share}}\times 100\\ =\frac{\$1.79}{\$79.27}\\ =2.3\%\end{array}$

$\begin{array}{c}\text{Dividend yield }\left(\text{Year 2}\right)=\frac{\text{Annual dividend per Share}}{\text{Market price per Share}}\times 100\\ =\frac{\$1.52}{\$80.48}\\ =1.9\%\end{array}$

$\begin{array}{c}\text{Dividend yield }\left(\text{Year 1}\right)=\frac{\text{Annual dividend per Share}}{\text{Market price per Share}}\times 100\\ =\frac{\$1.16}{\$61.18}\\ =1.9\%\end{array}$

Dividend yield ratio is determined to evaluate the relationship between the annual dividend per share and the market price per share.

Formula

$\text{Dividend yield }=\frac{\text{Annual dividend per Share}}{\text{Market price per Share}}\times 100$

Therefore, dividend yield ratio for Company year 3, year 2, and year 1 are 2.3%, 1.9%, and 1.9% respectively.

e.

Price earnings ratio for three years

$\begin{array}{c}\text{Price/Earnings ratio }\left(\text{Year 3}\right)=\frac{\text{Market price per share}}{\text{Earnings per share}}\\ =\frac{\$79.27\text{per share}}{\$7.72\text{per share}}\\ =10.3\end{array}$

$\begin{array}{c}\text{Price/Earnings ratio }\left(\text{Year 2}\right)=\frac{\text{Market price per share}}{\text{Earnings per share}}\\ =\frac{\$80.48\text{per share}}{\$6.71\text{per share}}\\ =12.0\end{array}$

$\begin{array}{c}\text{Price/Earnings ratio }\left(\text{Year 1}\right)=\frac{\text{Market price per share}}{\text{Earnings per share}}\\ =\frac{\$61.18\text{per share}}{\$4.40\text{per share}}\\ =13.9\end{array}$

Dividend yield ratio is determined as the relationship between market price per share and earnings per share.

Formula

$\text{Price/Earnings ratio}=\frac{\text{Market price per share}}{\text{Earnings per share}}$

Therefore, price/earnings ratio for Company year 3, year 2, and year 1 are 10.3, 12.0, and 13.9.

2.

To determine

Ratio of average liabilities to average stockholders' equity for Year 3.

Explanation of Solution

$\begin{array}{c}\begin{array}{l}\text{Ratio of average liabilities }\\ \text{to average stockholder's }\\ \text{equity}\left(\text{Year 3}\right)\end{array}\}=\frac{\text{Average liabilities }}{\text{Average stockholders' equity}}\\ =\frac{\$45,416}{\$6,821}\\ =6.7\%\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Ratio of average liabilities }\\ \text{to average stockholder's }\\ \text{equity}\left(\text{Year 2}\right)\end{array}\}=\frac{\text{Average liabilities }}{\text{Average stockholders' equity}}\\ =\frac{\$39,192}{\$6,545}\\ =6.0\%\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Ratio of average liabilities }\\ \text{to average stockholder's }\\ \text{equity}\left(\text{Year 1}\right)\end{array}\}=\frac{\text{Average liabilities }}{\text{Average stockholders' equity}}\\ =\frac{\$36,645}{\$5,555}\\ =6.6\%\end{array}$

Ratio of average liabilities to average stockholders’ equity is determined by dividing average liabilities and average stockholders’ equity.

Formula:

$\begin{array}{l}\text{Ratio of average liabilities }\\ \text{to average stockholder's }\\ \text{equity}\end{array}\}=\frac{\text{Average liabilities }}{\text{Average stockholders' equity}}$

Average liabilities for three years are determined as the difference between average assets and average stockholder’s equity. They are as below:

$\begin{array}{c}\begin{array}{l}\text{Average liabilities}\\ \text{ for year 3}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Average assets }\\ \text{— Average stockholders'}\\ \text{ equity}\end{array}\right)\\ =\$52,237-\$6,821\\ =\$45,416\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Average liabilities}\\ \text{ for year 2}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Average assets }\\ \text{— Average stockholders'}\\ \text{ equity}\end{array}\right)\\ =\$45,737-\$6,545\\ =\$39,192\end{array}$

$\begin{array}{c}\begin{array}{l}\text{Average liabilities}\\ \text{ for year 1}\end{array}\}\text{ = }\left(\begin{array}{l}\text{Average assets }\\ \text{— Average stockholders'}\\ \text{ equity}\end{array}\right)\\ =\$42,200-\$5,555\\ =\$36,645\end{array}$

3.

To determine

To evaluate: D’s profitability

Explanation of Solution

D’s profitability is measured by earnings per share. It has been improved significantly during the 3-year period. The return on total assets and total stockholders’ equity has improved in a significant manner.

There is a significant improvement in the economy and thus, improved in the construction industry too for the year 2.  The capital equipment has improved and thus, dividend yield has increased in the year 3. This increase is due to large increase in the cash dividend.

The price-earnings ratio has deteriorated during three-year period. The share price is increased in the slower rate when compared to earnings.