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Stock repurchase versus cash dividend

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Hello, i am trying to figure this problem out. However, one of my classmates presented a vague anwser, please add to it or fix it for us.

Question
10. Is repurchasing stock a good alternative to cash dividends (a) on a regular basis and (b) under special conditions? (Note: No large, publicly owned company has ever been challenged by tax authorities on its repurchase program, and no challenge is likely to occur.)

Vague anwser:

a stock repurchase means the shareholder gets one FINAL distribution of cash versus dividends which is an INCOME STREAM into the future. After a stock repurchase, the company owns the stock and the shareholder is not entitled to any more. Also, the question whether repurchasing stock on a regular basis is not answered. I would say NO because regular repurchasing uses up cash that should go into operations and investing activities (the reasons the company exists), and this also would keep shrinking the pool of shareholders available who are the source of equity financing.

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Whether the firm repurchases stock or gives dividends, in both cases it is using up cash.

If firm repurchases on a regular basis, the benefit that the shareholder gets is that repurchase is usually at a price higher than the curent market price and hence benefits the shareholders who exit, it also benefits the shareholders who continue since the EPS may go up in the future and lesser liquidity may drive up the market price. Once it is on a regular basis, then the shareholders already know about it and hence ...

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The solution explains the difference between stock repurchase and cash dividends

$2.19
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Cash Dividends vs Stock Repurchase

Lyle Communications had finally arrived at the point where it had sufficient excess cash flow of $2.4 million to consider paying a dividend. It had 2 million shares outstanding and was considering paying a cash dividend of $1.20 per share. The firm's total earnings were $8 million providing $4.00 in earnings per share. Lyle Communications stock traded in the market at $64.00 per share.
 
However, Liz Crocker, the chief financial officer, was not sure paying the cash dividend was the best route to go. She had recently read a number of articles in The Wall Street Journal about the advantages of stock repurchases and before she made a recommendation to the CEO and board of directors, she 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 the firm's 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?

d.   Assume instead of paying the cash dividend, the firm used the $2.4 million of excess funds to purchase shares at slightly over the current market value of $64 at a price of $65.20. How many shares could be repurchased?

e.   What would the new earnings per share be under the stock repurchase alternative?

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?

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