Question

A company has been paying a regular cash dividend of $4.00 per share each year. It pays out all of its earnings as dividends and is not expected to grow. There are 100,000 shares outstanding trading for $80.00 per share after the payment of the $4.00 per share dividend (i.e., after the ex-dividend date; prior to the ex-dividend date, the price included the value of the dividend payment). The company has enough cash on hand to pay dividends. Suppose that the company announces that it will cut its dividend to zero and use the cash to repurchase shares.

(a) What is the immediate stock price reaction to the announcement. Ignore taxes and any signaling effect.

(b) How many shares will the company repurchase at the end of the first year?

(c) Project future stock prices under the dividend policy and the repurchase policy for years 1, 2 and 3.

(d) What is the required return on the common stock?

(e) What is the expected annual rate of increase in the stock price?

Answer 1

Solution:

a) If we ignore taxes and there is no information conveyed by the repurchase when there purchase program is announced, then share price will remains at $80.00.

b) The regular dividend has been $4 per share, and so the company has $400,000 cash on hand. Since the share price is $80, the company will repurchase 5,000 shares.

c) Total asset value (before each dividend payment or stock repurchase) remains at$8,000,000.These assets earn $400,000 per year under either policy.

Old Policy: The annual dividend is $4, which does not changes, so the stock price (immediately prior to the dividend payment) will be $80 in all years.

New Policy: Every year, $400,000 is available for share repurchase. As noted above,5,000 shares will be repurchased at t= 0. At t= 1, immediately prior to the repurchase, there will be 95,000 shares outstanding. These shares will be worth $8,000,000, or $84.21 per share. With $400,000 available to repurchase shares, the total number of shares repurchased will be 4,750.

Time	Shares Outstanding	Share Price ($8m/Number of shares outstanding)	Shares Repurchased
t = 0	100,000	$80.00	5,000 =($400,000 / $80.00)
t = 1	95,000	$84.21	4,750 =($400,000 / $84.21)
t = 2	90,250	$88.64	4,513 =($400,000 / $88.64)
t = 3	85,737	$93.31	4,287 =($400,000 / $93.31)