Question

Botox Facial Care had earnings after taxes of \(370,000 in 20X1 with 200,000 shares of stock outstanding. The stock price was \)31.50. In 20X2, earnings after taxes increased to \(436,000 with the same 200,000 shares outstanding. The stock price was \)42.00

a. Compute earnings per share and the P/E ratio for 20X1. The P/E ratio

equals the stock price divided by earnings per share.

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

c. Give a general explanation of why the P/E ratio changed.

Short answer

(a) For the year 20X1,

Earning per share: $1.85

P/E ratio: 17.03

(b) For the year 20X2,

Earning per share: $2.18

P/E ratio: 19.27

(c) The increase in the P/E ratio is due to the increase in the stock price of the share.

Step-by-step solution

Earning per share for 20X1

$\begin{array}{rcl}\mathrm{Earnings}\mathrm{per}\mathrm{share}& =& \frac{\mathrm{Earnings}\mathrm{after}\mathrm{tax}}{\mathrm{No}\mathrm{of}\mathrm{outstanding}\mathrm{shares}}\\ & =& \frac{\$370,000}{200,000}\\ & =& \$1.85\end{array}$

Calculation of P/E ratio

$\begin{array}{rcl}\mathrm{P}/\mathrm{E}\mathrm{Ratio}& =& \frac{\mathrm{Stock}\mathrm{price}}{\mathrm{Earning}\mathrm{per}\mathrm{share}}\\ & =& \frac{\$31.50}{\$1.85}\\ & =& 17.03\end{array}$

Earning 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

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

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 earning per share. Hence, when the market price of the share goes up, the P/E ratio also increases.