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Unformatted text preview: dividend payment, we can calculate the wealth of a shareholder as: Dividend per share = $3,000/600 shares = $5.00 The stock price after the dividend payment will be: PX = $58 – 5 = $53 per share The shareholder will have a stock worth $53 and a $5 dividend for a total wealth of $58. If the company makes a repurchase, the company will repurchase: Shares repurchased = $3,000/$58 = 51.72 shares If the shareholder lets their shares be repurchased, they will have $58 in cash. If the shareholder keeps their shares, they’re still worth $58. b. If the company pays dividends, the current EPS is $1.50, and the P/E ratio is: P/E = $53/$1.50 = 35.33 If the company repurchases stock, the number of shares will decrease. The total net income is the EPS times the current number of shares outstanding. Dividing net income by the new number of shares outstanding, we find the EPS under the repurchase is: EPS = $1.50(600)/(600 − 51.72) = $1.64 The stock price will remain at $58 per share, so the P/E ratio is: P/E = $58/$1.64 = 35.33 402 c. A share repurchase would seem to be the preferred course of action. Only those shareholders who wish to sell will do so, giving the shareholder a tax timing option that he or she doesn’t get with a dividend payment. 14. a. Since the firm has a 100 percent payout policy, the entire net income, $45,000 will be paid as a dividend. The current value of the firm is the discounted value one year from now, plus the current income, which is: Value = $45,000 + $1,635,000/1.12 Value = $1,504,821 b. The current stock price is the value of the firm, divided by the shares outstanding, which is: Stock price = $1,504,821/20,000 Stock price = $75.24 Since the company has a 100 percent payout policy, the current dividend per share will be the company’s net income, divided by the shares outstanding, or: Current dividend = $45,000/20,000 Current dividend = $2.25 The stock price will fall by the value of the dividend to: Ex-dividend stock price = $75.24 – 2.25 Ex-dividend stock price = $72.99 c. i. According to MM, it cannot be true that the low dividend is depressing the price. Since dividend policy is irrelevant, the level of the dividend should not matter. Any funds not distributed as dividends add to the value of the firm, hence the stock price. These directors merely want to change the timing of the dividends (more now, less in the future). As the calculations below indicate, the value of the firm is unchanged by their proposal. Therefore, the share price will be unchanged. To show this, consider what would happen if the dividend were increased to $4.60. Since only the existing shareholders will get the dividend, the required dollar amount to pay the dividends is: Total dividends = $4.60(20,000) Total dividends = $92,000 To fund this dividend payment, the company must raise: Dollars raised = Required funds – Net income Dollars raised = $92,000 – 45,000 Dollars raised = $47,000 403 This money can only be raised with the sale of new equity to maintain the all-equity financing. Since those new shareholders must also earn 12 percent, their share of the firm one year from now is: New shareholder value in one year = $47,000(1.12) New shareholder value in one year = $52,640 This means that the old shareholders' interest falls to: Old shareholder value in one year = $1,635,000 – 52,640 Old shareholder value in one year = $1,582,360 Under this scenario, the current value of the firm is: Value = $92,000 + $1,582,360/1.12 Value = $1,504,821 Since the firm value is the same as in part a, the change in dividend policy had no effect. ii. The new shareholders are not entitled to receive the current dividend. They will receive only the value of the equity one year hence. The present value of those flows is: Present value = $1,582,360/1.12 Present value = $1,412,821.43 And the current share price will be: Current share price = $1,412,821.43/20,000 Current share price = $70.64 So, the number of new shares the company must sell will be: Shares sold = $47,000/$70.64 Shares sold = 665.34 shares 15. a. The current price is the current cash flow of the company plus the present value of the expected cash flows, divided by the number of shares outstanding. So, the current stock price is: Stock price = ($1,400,000 + 20,000,000) / 750,000 Stock price = $28.53 b. To achieve a zero dividend payout policy, he can invest the dividends back into the company’s stock. The dividends per share will be: Dividends per share = [($1,400,000)(.50)]/750,000 Dividends per share = $0.93 And the stockholder in question will receive: Dividends paid to shareholder = $0.93(1,000) 404 Dividends paid to shareholder = $933.33 The new stock price after the dividends are paid will be: Ex-dividend stock price = $28.53 – 0.93 Ex-dividend stock price = $27.60 So, the number of shares the investor will buy is: Number of shares to buy = $933.33 / $27.60 Number of shares to buy = 33.82 16. a. Using the formula from the text proposed by Lintner: Div1 = Div0 +...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of Texas-Tyler.

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