Question

Stilley Corporation had earnings after taxes of \(436,000 in 20X2 with 200,000 shares outstanding. The stock price was \)42.00. In 20X3, earnings after taxes declined to \(206,000 with the same 200,000 shares outstanding. The stock price declined to \)27.80.

a. Compute earnings per share and the P/E ratio for 20X2.

b. Compute earnings per share and the P/E ratio for 20X3.

c. Give a general explanation of why the P/E changed. You might want to

consult the text to explain this surprising result.

Short answer

(a) For the year 20X2,

Earnings per share: $2.18

P/E ratio: 19.27

(b) For the year 20X3,

Earnings per share: $1.03

P/E ratio: 27

(c) The increase in the P/E ratio is due to a decrease in the stock price per share and earnings per share of the company.

Step-by-step solution

Earnings per share for 20X2

$\begin{array}{rcl}\mathrm{Earnings}\mathrm{per}\mathrm{share}& =& \frac{\mathrm{Earnings}\mathrm{after}\mathrm{tax}}{\mathrm{No}\mathrm{of}\mathrm{outstanding}\mathrm{shares}}\\ & =& \frac{\$436,000}{200,000}\\ & =& \$2.18\end{array}$

Calculation of P/E ratio

$\begin{array}{rcl}\mathrm{P}/\mathrm{E}\mathrm{Ratio}& =& \frac{\mathrm{Stock}\mathrm{price}}{\mathrm{Earning}\mathrm{per}\mathrm{share}}\\ & =& \frac{\$42}{\$2.18}\\ & =& 19.27\end{array}$

Earnings per share for 20X3

$\begin{array}{rcl}\mathrm{Earnings}\mathrm{per}\mathrm{share}& =& \frac{\mathrm{Earnings}\mathrm{after}\mathrm{tax}}{\mathrm{No}\mathrm{of}\mathrm{outstanding}\mathrm{shares}}\\ & =& \frac{\$206,000}{200,000}\\ & =& \$1.03\end{array}$

Calculation of P/E ratio

$\begin{array}{rcl}\mathrm{P}/\mathrm{E}\mathrm{Ratio}& =& \frac{\mathrm{Stock}\mathrm{price}}{\mathrm{Earning}\mathrm{per}\mathrm{share}}\\ & =& \frac{\$27.80}{\$1.03}\\ & =& 27\end{array}$

Explanation for the increase in the P/E ratio

The P/E ratio is computed by dividing the market price of the share by the earnings per share. Hence, the changes in the P/E ratio are caused by the changes in the market price per share from $42 to $27.80 and the earnings per share from $2.18 to $1.03 of the company.