Question: Wilson Pharmaceuticals’ stock has done very well in the market during the last three years. It has risen from \(55 to \)80 per share. The firm’s current statement of stockholders’ equity is as follows:

a. How many shares would be outstanding after a two-for-one stock split? What would be its par value?

b. How many shares would be outstanding after a three-for-one stock split? What would be its par value?

c. Assume that Wilson earned $11 million. What would its earnings per share be before and after the two-for-one stock split? After the three-for-one stock split?

d. What would be the price per share after the two-for-one stock split? After the three-for-one stock split? (Assume that the price-earnings ratio of 36.36 stays the same.)

e. Should a stock split change the price-earnings ratio for Wilson?

The shares outstanding will be 10 million and its par value will be $5 per share.

$$\begin{gathered} Numberofshares=Existingshares\times Stocksplitratio \\ =5million\times 2 \\ =10million \\ Parvalueofshares=\frac{Existingprices}{stocksplitratio} \\ =\frac{\$10}{2} \\ =\$5 \end{gathered}$$

The shares outstanding will be 15 million and its par value will be $3.33 per share.

$$\begin{gathered} Numberofshares=Existingshares\times Stocksplitratio \\ =5million\times 3 \\ =15million \\ Parvalueofshares=\frac{Existingprice}{Stocksplitratio} \\ =\frac{\$10}{3} \\ =3.33\$ \end{gathered}$$

The EPS will be $ 2.2 before stock split, $1.1 after two – for – one stock split, and $0.73 after three – for -one stock split.

$$\begin{gathered} EPS=\frac{Earnings}{Shareouts\tan ing} \\ =\frac{\$11,000,000}{5,000,000} \\ =\$2.2 \\ EPS=\frac{Earnings}{Shareouts\tan ing} \\ =\frac{\$11,000,000}{10,000,000} \\ =\$1.1 \\ EPS=\frac{Earnings}{Shareouts\tan ing} \\ =\frac{\$11,000,000}{15,000,000} \\ =\$0.73 \end{gathered}$$

The price of stock will be $40 after two – for – one stock split, and $26.54 after three – for -one stock split.

$$\begin{gathered} Stockprice=EPS\times \raisebox{1ex}{$P$}\!\left/ \!\raisebox{-1ex}{$E$}\right.ratio \\ =\$1.1\times 36.36 \\ =\$40 \\ Stockprice=EPS\times \raisebox{1ex}{$P$}\!\left/ \!\raisebox{-1ex}{$E$}\right.ratio \\ =\$0.73\times 36.36 \\ =\$26.54 \end{gathered}$$

The stock split should not impact the price-earnings ratio as the price-earnings ratio will change only when there is any change in the earnings or the stock price. In the stock split, the value of common stock remains the same, so there is no impact on the other factors only the number of shares outstanding and par value of shares change.