DUKE UNIVERSITY Fuqua School of Business. FINANCE CORPORATE FINANCE Problem Set #8 Prof. Simon Gervais Fall 2011 Term 2

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1 DUKE UNIVERSITY Fuqua School of Business FINANCE CORPORATE FINANCE Problem Set #8 Prof. Simon Gervais Fall 2011 Term 2 Questions 1. Hors d Age Cheeseworks has been paying a regular cash dividend of $4 per share each year for over a decade. The company is paying out all its earnings as dividends and is not expected to grow. There are 100,000 shares outstanding selling for $80 per share. The company has sufficient cash on hand to pay the next annual dividend. Suppose that Hors d Age decides to cut its cash dividend to zero and announces that it will repurchase shares instead. (a) What is the immediate stock price reaction? Ignore taxes, and assume that the repurchase program conveys no information about operating profitability or business risk. (b) How many shares will Hors d Age purchase? (c) Project and compare future stock prices for the old and new policies. Do this for at least years 1, 2, and Formaggio Vecchio has just announced its regular quarterly cash dividend of $1 per share. (a) When will the stock price fall to reflect dividend payment on the record date, the ex-dividend date, or the payment date? (b) Assume that there are no taxes. By how much is the stock price likely to fall? (c) Now assume that all investors pay tax of 30% on dividends and nothing on capital gains. What is the likely fall in the stock price? (d) Suppose, finally, that everything is the same as in part (c), except that security dealers pay tax on both dividends and capital gains. How would you expect your answer to (c) to change? Explain. 3. Refer back to the last question. Assume no taxes and a stock price immediately after the dividend announcement of $100. (a) If you own 100 shares, what is the value or your investment? How does the dividend payment affect your wealth? (b) Now suppose that Formaggio Vecchio cancels the dividend payment and announces that it will repurchase 1% of its stock at $100. Do you rejoice or yawn? Explain. 4. The expected pretax return on three stocks is divided between dividends and capital gains in the following way: Expected Expected Stock Dividend Capital Gain A $0 $10 B $5 $5 C $10 $0 1

2 (a) If each stock is priced at $100, what are the expected net returns on each stock to (i) a (tax-exempt) pension fund; (ii) a corporation paying tax at 35% (recall that corporations are taxed on only 30% of the dividends that they receive; they are fully taxed on the capital gains); (iii) an individual paying tax at 39.6% on investment income and 28% on capital gains; (iv) a security dealer paying tax at 35% on investment income and capital gains? (b) Suppose that before the 1986 Tax Reform Act stocks A, B and C were priced to yield an 8% after-tax return to individual investors paying 50% tax on dividends and 20% tax on capital gains. What would A, B and C each sell for? 5. The net income of Novis Corporation, which has 10,000 outstanding shares and a 100% payout policy, is $32,000 today. The expected value of the firm one year hence is $1,545,600. The appropriate discount rate for Novis is 12%. (a) What is the current value of the firm? (b) What is the ex-dividend price of Novis stock if the board follows its current dividend policy? (c) At the dividend declaration meeting, several board members claimed that the dividend is too meager and is probably depressing Novis stock price. They propose that Novis sell enough new shares to finance a $4.25 dividend. Assume that the new shareholders are not entitled to this dividend (i.e., assume that their shares are issued ex-dividend). (i) Comment on the claim that the low dividend is depressing the stock price. Support your argument with calculations. (ii) If the proposal is adopted, at what price will the new shares sell and how many will be sold? 6. Payall Inc., Payless Inc., and Paynone Inc. have identical operations. They follow a large, medium, and zero (no dividend) payout policy respectively. Paynone Inc. s shares currently tradeat $100, andareexpectedtotradeat$125 inoneyear. Theexpecteddividendspershare (in one year) for Payall and Payless are $25 and $12.50 respectively, and their ex-dividend stock prices are expected to be $100 and $ respectively. The market prices are set so that their after-tax expected returns are equal. What should the current share prices of Payless Inc. and Payall Inc. be? Assume that the marginal personal tax rate on dividends is 25%, and the effective tax rate on capital gains is zero. 7. The SharpeCo. has a period 0 dividend of $1.25. Its target payout ratio is 40%. The period 1 EPS is expected to be $4.5. (a) If the adjustment rate is 0.3 as defined in the Lintner model, what will be the Sharpe Co. dividend in period 1? (b) If the adjustment rate is 0.6 instead, what is the dividend in period 1? (Difficult) 8. The Nilpoj corporation has 1 million shares outstanding with a total market value of $20 million. Nilpoj is expected to pay $1million of dividendsat theendof theyear (i.e. one year from 2

3 now), and thereafter the amount paid out is expected to grow by 5% a year in perpetuity. Thus the expected dividend at the end of the second year is $1.05 million, and so on. However, the company has heard that the value of a share depends on the flow of dividends. Therefore it announces that this year s dividend will be increased to $2 million (from $1 million), and that the extra cash will be raised at the end of the year by an issue of shares. After that, the total amount paid out in dividends each year will be as previously forecast, i.e. $1.05 million at the end of year 2 and increasing at 5% a year in each subsequent year. (a) What is Nilpoj s cost of capital. (b) What will the total value of the firm be at the end of the year (after the extra cash is raised and after the $2 million dividend is paid out)? (c) How many shares will the firm need to issue, and what is the price per share at the end of the year (after the extra cash is raised and after the $2 million dividend is paid out)? (d) What fraction of future dividends (starting with the second-year dividends) belongs to the original shareholders? (e) Show that the original shareholders are not made better off by this decision (i.e. show that the present value of the cash flows to the original shareholders remains $20 million). (Optional) 9. The Government in Dukeraine imposes a flat tax rate of 20% on realized capital gains and losses. The tax rate on personal income is 30%. The corporate tax rate is 35%. The stock of a firm in Dukeraine is currently priced at $100 per share, and is about to go ex-dividend, paying $1 as dividend to holders of record. Assume that the (after-tax) interest rate is 10%, that the dividend is paid immediately and that all taxes are paid one year from now. What should be the ex-dividend price for an investor who is planning to hold the stock for one year to be indifferent between buying the stock immediately before or immediately after it goes ex-dividend? How do you explain the difference between the cum-dividend (with dividend) and ex-dividend (without dividend) prices? 3

4 1. (a) There should be no reaction. Solutions (b) Solution 1: The total dividend is $4(100,000) = $400,000. If Hors d Age repurchases n shares at a price of P each, then we need np = 400,000. (1) The remaining 100,000 n shares should be worth P each as well, and so 8,000, ,000 n = P (2) Solving for n and P in (1) and (2), we find n = 4,762 and P = Solution 2: Without the dividend payment, the firm is worth V = $80(100,000) + $4(100,000) = $8,400,000, which is $8,400, ,000 = $84 per share. With $400,000, the firm can therefore repurchase $400,000 $84 = 4,762 shares. (c) Old policy: New policy: Year 1 Year 2 Year 3 Total Assets beginning of year 8.0M 8.0M 8.0M end of year 8.4M 8.4M 8.4M Dividends (= Earnings) 0.4M 0.4M 0.4M Number of shares 100, , ,000 Price per share (ex-dividend) Year 1 Year 2 Year 3 Total Assets beginning of year 8.0M 8.0M 8.0M end of year 8.4M 8.4M 8.4M Earnings 0.4M 0.4M 0.4M Beginning of year number of shares 100,000 95,238 90,703 price per share Number of shares repurchased 4,762 4,535 4,319 End of year number of shares 95,238 90,703 86,384 price per share (ex-dividend) (a) On the ex-dividend date. (b) The stock price will fall by $1. 4

5 (c) The stock price will fall by the after-tax dividend, i.e., by $1(1 0.3) = $0.70, so that the after-tax return on dividends and capital gains are the same. To see this more clearly, suppose the stock price is 10 before the dividend is paid. If you buy the stock right before the dividend is paid and sell it right after, your net profit should be essentially zero since you ve held the stock for a small amount of time (a second, say). Here are your cash flows: buy now: ; dividend: +1.00; tax on dividend: -0.30; sell after dividend: S (to be found). So the sum of all these cash flows should be zero: S = 0 S = The stock price fell by $10.00 $9.30 = $0.70. (d) In this case, there should be no tax effects, i.e., the stock price will fall by $1. To better see this, suppose you buy the stock (for $10, say) right before the dividend is paid, and sell it right after the dividend is paid. Because you hold the stock for a small amount of time (a second, say), your net profit should be zero. You pay $10 for the stock, you receive $1 as a dividend which is taxed at 30%; then you sell it for S (to be found) and pay taxes of 30% (S 10) on your capital gains (which are going to be negative here). So you net profit is 10+(1 0.30)+S 0.30(S 10) = 0. Solving for S, we find S = 9. So the change in S is $10 $9 = $1. 3. (a) After the dividend announcement, the value of your investment is 100 $100 = $10,000. After the dividend payment, the stock price drops to $99, and you will have received a dividend of $1 for each share you own. Hence, your wealth will remain the same: (100 $99)+(100 $1) = $10,000. (b) You yawn. After Formaggio Vecchio repurchases 1% of your shares (i.e., one share) at $100 each, you will be left with 99 shares worth $100 each. Your total wealth after the repurchase will then be: (99 $100) +(1 $100) = $10,000. 5

6 4. (a) Here are the net expected returns on each stock for each of the four investors: Investor Stock A Stock B Stock C (i) Pension fund (ii) Corporation (iii) Individual (iv) Security dealer 10(1 0.35) = (1 0.28) = (1 0.35) = 6.5 5[1 (0.3)(0.35)] +5(1 0.35) = ( ) +5(1 0.28) = (1 0.35) = [1 (0.3)(0.35)] = ( ) = (1 0.35) = 6.5 (b) The yearly after-tax payoff of stock A is 10(1 0.2) = 8, so that the price of stock A should be P A = = 100. The yearly after-tax payoff of stock B is 5(1 0.5)+5(1 0.2) = 6.5, so that the price of stock B should be P B = = The yearly after-tax payoff of stock C is 10(1 0.5) = 5, so that the price of stock C should be P C = = (a) The value of the firm is the present value of its dividends and future value: V 0 = 32,000+ 1,545, = 1,412,000. (b) Before the dividend is paid, each share is worth P 0 = 1,412,000 10,000 = After the dividend is paid, the shares will be worth P 0 = 1,545,600/ ,000 = 1,412,000 32,000 10,000 = Notice that the difference between P 0 and P 0 is the dividend per share, 32,000/10,000 = (c) (i) According to Modigliani and Miller, it cannot be true that the low dividend is depressing the price. In fact, since the 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 through the stock price (capital gains). These directors merely want to 6

7 change the timing of the dividends (more now, less in the future). As shown below, the current shareholders wealth is unaffected by this dividend increase, i.e., the shareholders are not made better off. To pay the $4.25 dividend per share (for a total dividend of $42,500), new shares must be sold. These new shares must have a value of $10,500 ($42,500 $32,000). This means that some of the $1,545,600 firm value in one year will belong to the new shareholders. How much? Well, these new shareholders will also demand a 12% return on their investment, i.e., their $10,500 should then be worth $11,760 ($10, ). So the current shareholders wealth at time 0 must be W 0 = 42,500+ 1,545,600 11, = 1,412,000, the same as before. (ii) Let n denote the number of new shares that have to be issued, and P 0 the price after the $4.25 dividend has been paid. Solution 1: Since the new shareholders will not be fooled and will require their $10,500 investment to be worth exactly that after the dividend is paid, we must have = 10,500. (3) np 0 Also, after the dividend is paid, the shareholders (both old and new) will be sharing the future value of the firm, that is P 0 = 1,545,600/ ,000+n. (4) Solving (3) and (4) for n and P 0 yields n = and P 0 = Solution 2: After the dividend is paid and the money is raised from the new equity issue, the firm is worth V = 1,545,600 = 1,380, For the new shareholders to be willing to pay $10,500 for their share in the firm, it must be that their claim is worth $10,500. This implies that 1,380,000 10,500 = 1,369,500 belongs to the old shareholders, that is, P 0 = 1,369,500 10,000 = per share. The number of new shares that must be issued is therefore n = 10, =

8 6. The following table shows the after-tax return calculations for the three companies. Paynone Payless Payall Next year s stock price Dividend Total pre-tax payoff Today s stock price P less P all Capital gains P less P all Tax on dividend Tax on capital gains Total after-tax income ( P less ) +( P all ) After-tax rate of return 25% 25% 25% Since we would like the three after-tax expected returns to be the same, we must have These imply P less = and P all = % = ( P less), and P less 25% = ( P all). P all 7. We know that the Lintner dividend model is given by D 1 = a(p E 1 )+(1 a)d 0, where, in this case, p = 0.4, E 1 = 4.50, and D 0 = (a) If a = 0.3, we have (b) If a = 0.6, we have D 1 = 0.3( )+(1 0.3)1.25 = D 1 = 0.6( ) +(1 0.6)1.25 = Notice that the increase in the dividend is more conservative in part (a) since the adjustment rate is lower (i.e., more weight is put on last year s dividend). 8. (a) We know that the current value of Nilpoj is $20 million, and that this number represents the present value of discounted dividends, i.e., 20,000,000 = 1,000,000 1+r + 1,000,000(1.05) (1+r) 2 + 1,000,000(1.05)2 (1+r) 3 + = 1,000,000 r This implies that the cost of capital for Nilpoj is r = 10%. 8

9 (b) At the end of the year, the value of the firm will be [ 1.05 V 1 = 1,000,000 [ 1.05 = 1,000, (1.05) = 21,000,000. ] (1.1) 2 + ] (c) Let n denote the number of new shares that will need to be issued, and P 1 the price of each share (old and new) at the end of the first year. Since the total number of shares after the new issue will be 1,000,000 +n, we have P 1 = V 1 1,000,000+n = 21,000,000 1,000,000 +n. (5) It also has to be the case that the extra dividend of $1 million paid at the end of the first year is financed by the new issue of shares (i.e., the new investors get what they pay for): np 1 = 1,000,000. (6) Using this last equation in (5) yields: (1,000,000 +n)p 1 = 21,000,000 (6) 1,000,000P 1 +1,000,000 = 21,000,000 P 1 = 20. We can now use this value in (6) to obtain n = 1,000, = 50,000 shares. (d) The new shareholders will be getting a fraction 50,000 1,000, ,000 = 1 21 offuturedividends,whereastheoriginalshareholderswillbegettingafraction1 1 of these dividends. (e) The present value of the cash flows to the original shareholders is { 2 PV = 1,000, { 2 = 1,000, = 20,000,000. [ 1.05 (1.1) 2 + (1.05)2 (1.1) 3 + (1.05)3 [ ]} ]} (1.1) =

10 9. Let S ed denote the ex-dividend stock price. We then have the following cash flows associated with buying cum-dividend or ex-dividend: Cash Flow Today Cash Flow in 1 Year Buy cum-dividend S (S 1 100) 0.30(1) Buy ex-dividend S ed S (S 1 S ed ) Difference in CF s 99+S ed S ed Investors would be indifferent between buying cum-dividend or ex-dividend if and only if the present value of the differential cash flow is zero, i.e., if 99+S ed S ed 1.10 = 0. Solving, gives S ed = Therefore, after the dividend payment, the stock price drops by less than $1. This reflects the fact that capital gains are taxed at a lower rate than dividends. 10

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