91Ó°ÊÓ

The current price of stock will be $50.

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

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

The dividend per share will be $2.

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

The company will acquire 74,074 shares.

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

The new EPS will be $2.6.

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

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

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

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

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.

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

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.