Question

The Carlton Corporation has \(5 million in earnings after taxes and 2 million shares outstanding. The stock trades at a P/E of 20. The firm has \)4 million in excess cash.

a. Compute the current price of the stock.

b. If the \(4 million is used to pay dividends, how much will dividends per share be?

c. If the \)4 million is used to repurchase shares in the market at a price of $54 per share, how many shares will be acquired? (Round to the nearest share.)

d. What will the new earnings per share be? (Round to two places to the right of the decimal.)

e. If the P/E ratio remains constant, what will the price of the securities be? By how much, in terms of dollars, did the repurchase increase the stock price?

f. Has the stockholders’ total wealth changed as a result of the stock repurchase as opposed to receiving the cash dividend?

g. What are some reasons a corporation may wish to repurchase its own shares in the market?

Short answer

1. The current price of stock will be $50.
2. The dividend per share will be $2.
3. The company will acquire 74,074 shares.
4. The new EPS will be $2.6.The new stock price will be $52 and the stock price has increased by $2 ($52 - $50).
5. The stockholder’s wealth has not changed as the value of the share remains the same.
6. The corporation reacquires shares to increase the value of the shares, prevent merger, and provide additional shares as rewards to shareholders or employees.

Step-by-step solution

Calculation of current price of stock

The current price of stock will be $50.

$\begin{array}{rcl}\text{EPS}& =& \frac{\text{Earnings}}{\text{Shares outstanding}}\\ & =& \frac{\$5,000,000}{2,000,000}\\ & =& \$2.5\end{array}$

$\begin{array}{rcl}\text{Stock price}& =& \text{EPS}\times \text{P/E ratio}\\ & =& \$2.5\times 20\\ & =& \$50\end{array}$

Calculation of dividend per share

The dividend per share will be $2.

$\begin{array}{rcl}\text{Dividend per share}& =& \frac{\text{Total dividend paid}}{\text{Shares outstanding}}\\ & =& \frac{\$4,000,000}{2,000,000}\\ & =& \$2\end{array}$

Calculation of shares acquired in case of repurchase

The company will acquire 74,074 shares.

$\begin{array}{rcl}\text{Number of shares}& =& \frac{\text{Funds available}}{\text{Market price of one share}}\\ & =& \frac{\$4,000,000}{\$54}\\ & =& 74,074\text{shares}\end{array}$

Calculation of new earnings per share

The new EPS will be $2.6.

$\begin{array}{rcl}\text{Shares outstanding after repurchase}& =& \text{Existing shares}-\text{Shares repurchased}\\ & =& 2,000,000-74,074\\ & =& 1,925,926\text{shares}\end{array}$

$\begin{array}{rcl}\text{EPS}& =& \frac{\text{Earnings}}{\text{Shares outstanding}}\\ & =& \frac{\$5,000,000}{1,925,926}\\ & =& \$2.6\end{array}$

Calculation of new stock price

The new stock price will be $52 and the stock price has increased by $2 ($52 - $50).

$\begin{array}{rcl}\text{Stock price}& =& \text{EPS}\times \text{P/E ratio}\\ & =& \$2.6\times 20\\ & =& \$52\end{array}$

Change in stockholder’s wealth

The stockholder’s wealth has not changed. The total value of share in case of cash dividend is $52 and in case of share repurchase it is $52.

$\begin{array}{rcl}\text{Total value per share}& =& \text{Market value per share}+\text{Cash dividend per share}\\ & =& \$50+\$2\\ & =& \$52\end{array}$

Reasons why a corporation repurchases shares

The corporation repurchases shares as:

1. The corporation believes that its shares are undervalued in the market.
2. The shares are reacquired to protect the company against any shareholder that would buy the shares for the merger.
3. The shares are reacquired to provide those shares as reward to the existing shareholders or employees.