Modern Furniture Company had finally arrived at the point where it had a sufficient excess cash flow of \(4.8 million to consider paying a dividend. It had 3 million shares of stock outstanding and was considering paying a cash dividend of \)1.60 per share. The firm’s total earnings were \(12 million, providing \)4.00 in earnings per share. The stock traded in the market at \(88.00 per share.

However, Al Rosen, the chief financial officer, was not sure that paying a cash dividend was the best route to go. He had recently read a number of articles in The Wall Street Journal about the advantages of stock repurchases and before he madea recommendation to the CEO and board of directors, he decided to do a number of calculations.

a. What is the firm’s P/E ratio?

b. If the firm paid the cash dividend, what would be its dividend yield and dividend payout ratio per share?

c. If a stockholder held 100 shares of stock and received the cash dividend, what would be the total value of his portfolio (stock plus dividends)?

d. Assume instead of paying the cash dividend, the firm used the \)4.8 million of excess funds to purchase shares at slightly over the current market value of \(88 at a price of \)89.60. How many shares could be repurchased? (Round to the nearest share.)

e. What would the new earnings per share be under the stock repurchase alternative? (Round to three places to the right of the decimal point.)

f. If the P/E ratio stayed the same under the stock repurchase alternative, what would be the stock value per share? If a stockholder owned 100 shares, what would now be the total value of his portfolio? (This answer should be approximately the same as the answer to part c.)

Step by step solution

01

Calculation of P/E ratio

The P/E ratio will be 22.

$\begin{array}{rcl}P/Eratio& =& \frac{Stockprice}{EPS}\\ & =& \frac{\$88}{\$4}\\ & =& 22\end{array}$

02

Calculation of dividend yield and dividend pay-out ratio

The dividend yield will be 1.82% and the dividend pay-out ratio will be 40%.$\begin{array}{rcl}Dividendyield& =& \frac{Dividendpershare}{Shareprice}\\ & =& \frac{\$1.60}{\$88}\\ & =& 1.82\%\end{array}$

$\begin{array}{rcl}\text{Dividend pay - out ratio}& =& \frac{\text{Dividend per share}}{\text{EPS}}\\ & =& \frac{\$1.60}{\$4}\\ & =& 40\%\end{array}$

03

Calculation of total value of shareholder portfolio

The value of the portfolio will be $8,960.

$\begin{array}{rcl}\text{Portfolio value}& =& \text{Total value of shares}+\text{Total value of dividend}\\ & =& \left(100\times \$88\right)+\left(100\times \$1.6\right)\\ & =& \$8,800+\$160\\ & =& \$8,960\end{array}$

04

Calculation of number of shares that can be repurchased

The company can repurchase 53,571 shares.

$\begin{array}{rcl}\text{Number of shares that can be repurchased}& =& \frac{\text{Funds available}}{\text{Market value of shares}}\\ & =& \frac{\$4,800,000}{\$89.60}\\ & =& 53,571\text{shares}\end{array}$

05

Calculation of new EPS after stock repurchase

The new EPS after stock repurchase will be $4.07.

$\begin{array}{rcl}\text{EPS}& =& \frac{\text{Total earnings}}{\text{Total shares outstanding}}\\ & =& \frac{\$12,000,000}{3,000,000-53,571}\\ & =& \frac{\$12,000,000}{2,946,429}\\ & =& \$4.07\end{array}$

06

Calculation of stock price and portfolio value after stock repurchase

After stock repurchase, the stock price will $89.54 and the portfolio value will be $8,954.

$\begin{array}{rcl}\text{Stock price}& =& \text{EPS}\times \text{P/E ratio}\\ & & \text{= \$ 4.07}\times \text{22}\\ & =& \$89.54\end{array}$

$\begin{array}{rcl}\text{Portfolio value}& =& \text{Total value of shares}\\ & =& \left(100\times \$89.54\right)\\ & =& \$8,954\end{array}$

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