DUKE UNIVERSITY Fuqua School of Business FINANCE 351 - CORPORATE FINANCE Problem Set #8 Prof.Simon Gervais 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 3. 2. 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 Fall 2011 – Term 2 (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.600. dividend in period 1? (b) If the adjustment rate is 0. Support your argument with calculations.000 outstanding shares and a 100% payout policy. What should the current share prices of Payless Inc.5. Assume that the new shareholders are not entitled to this dividend (i. (ii) If the proposal is adopted. and Payall Inc. and are expected to trade at $125 in one year.545. The Sharpe Co. assume that their shares are issued ex-dividend). (i) Comment on the claim that the low dividend is depressing the stock price. what will be the Sharpe Co.6 instead.25. The net income of Novis Corporation. at what price will the new shares sell and how many will be sold? 6. They propose that Novis sell enough new shares to ﬁnance a $4. (a) If the adjustment rate is 0. Payless Inc. have identical operations. Nilpoj is expected to pay $1 million of dividends at the end of the year (i.25 dividend. The Nilpoj corporation has 1 million shares outstanding with a total market value of $20 million.000 today. is $32. The period 1 EPS is expected to be $4.6% on investment income and 28% on capital gains.’s shares currently trade at $100. The appropriate discount rate for Novis is 12%. The expected value of the ﬁrm one year hence is $1. (ii) a corporation paying tax at 35% (recall that corporations are taxed on only 30% of the dividends that they receive. and Paynone Inc. and zero (no dividend) payout policy respectively. (iii) an individual paying tax at 39. (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. they are fully taxed on the capital gains). and the eﬀective tax rate on capital gains is zero. What would A. 7. The market prices are set so that their after-tax expected returns are equal. which has 10.3 as deﬁned in the Lintner model..(a) If each stock is priced at $100.e. Paynone Inc. and their ex-dividend stock prices are expected to be $100 and $112.. Payall Inc. be? Assume that the marginal personal tax rate on dividends is 25%. 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. has a period 0 dividend of $1.. They follow a large. B and C each sell for? 5. medium. one year from 2 . Its target payout ratio is 40%.50 respectively. several board members claimed that the dividend is too meager and is probably depressing Novis’ stock price.50 respectively. what are the expected net returns on each stock to (i) a (tax-exempt) pension fund.e. what is the dividend in period 1? (Diﬃcult) 8. The expected dividends per share (in one year) for Payall and Payless are $25 and $12. $1. The tax rate on personal income is 30%. i. 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.05 million at the end of year 2 and increasing at 5% a year in each subsequent year.e.05 million. (a) What is Nilpoj’s cost of capital. the company has heard that the value of a share depends on the ﬂow of dividends. and thereafter the amount paid out is expected to grow by 5% a year in perpetuity. Assume that the (after-tax) interest rate is 10%. The corporate tax rate is 35%. and that the extra cash will be raised at the end of the year by an issue of shares. and is about to go ex-dividend. the total amount paid out in dividends each year will be as previously forecast. show that the present value of the cash ﬂows to the original shareholders remains $20 million). After that. that the dividend is paid immediately and that all taxes are paid one year from now.now). The Government in Dukeraine imposes a ﬂat tax rate of 20% on realized capital gains and losses. 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 . The stock of a ﬁrm in Dukeraine is currently priced at $100 per share. However. (Optional) 9.e. paying $1 as dividend to holders of record. and so on. Therefore it announces that this year’s dividend will be increased to $2 million (from $1 million). (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. Thus the expected dividend at the end of the second year is $1. The remaining 100.4M 100.4M 100.4M 100.535 90.384 92.4M 0.0M 8. we ﬁnd n = 4. (a) There should be no reaction.000 80 4.762 and P = 84.000. (a) On the ex-dividend date. With $400.000.000.000 − n (2) (1) Solving for n and P in (1) and (2). (b) Solution 1: The total dividend is $4(100. Solution 2: Without the dividend payment.61 8. which is $8 100. 4 .762 95.20 Year 3 8.0M 8.0M 8.4M 0.000. If Hors d’Age repurchases n shares at a price of P each.238 84.000.0M 8.4M 0.000 =P 100.0M 8.000) + .238 84.Solutions 1.703 88.000 80 Year 3 8. the ﬁrm is worth V = $80(100.000 $84 = 4.319 86.000 80 $400.0M 8.00 Year 2 8.000) = $400.000 $4(100.703 88.400.20 4. then we need nP = 400. (b) The stock price will fall by $1.4M 100. the ﬁrm can therefore repurchase (c) Old policy: Year 1 Total Assets beginning of year end of year Dividends (= Earnings) Number of shares Price per share (ex-dividend) New policy: Year 1 Total Assets beginning of year end of year Earnings Beginning of year number of shares price per share Number of shares repurchased End of year number of shares price per share (ex-dividend) 2.762 shares.4M 95.4M 0.4M 0.400.4M 90.00 4. 8.000 − n shares should be worth P each as well.00.000) = $8.000 = $84 per share. and so 8.4M 0.000 80 Year 2 8. 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). To better see this.30(S − 10) = 0. To see this more clearly.(c) The stock price will fall by the after-tax dividend.70. say). you receive $1 as a dividend which is taxed at 30%. your wealth will remain the same: (100 × $99) + (100 × $1) = $10. suppose you buy the stock (for $10.3) = $0. so that the after-tax return on dividends and capital gains are the same. So the change in S is $10 − $9 = $1. tax on dividend: -0. and you will have received a dividend of $1 for each share you own.000. Here are your cash ﬂows: • • • • buy now: -10.30..e. sell after dividend: S (to be found). After Formaggio Vecchio repurchases 1% of your shares (i. Solving for S . say). by $1(1 − 0. (d) In this case. there should be no tax eﬀects. (b) You yawn.e. the value of your investment is 100 × $100 = $10. the stock price will fall by $1. 3.00.30 + S = 0 The stock price fell by $10.. you will be left with 99 shares worth $100 each. one share) at $100 each. i. we ﬁnd S = 9. Your total wealth after the repurchase will then be: (99 × $100) + (1 × $100) = $10.30) + S − 0. You pay $10 for the stock. the stock price drops to $99. After the dividend payment.000. So the sum of all these cash ﬂows should be zero: −10 + 1 − 0.30 = $0. i.00. your net proﬁt should be zero. (a) After the dividend announcement.e. say) right before the dividend is paid. Because you hold the stock for a small amount of time (a second. So you net proﬁt is −10 + (1 − 0. ⇒ S = 9. If you buy the stock right before the dividend is paid and sell it right after. Hence.70. suppose the stock price is 10 before the dividend is paid. and sell it right after the dividend is paid. 5 . your net proﬁt should be essentially zero since you’ve held the stock for a small amount of time (a second..000.00 − $9. dividend: +1.30. 000 = 3.545.25. 1.412.04 10(1 − 0.62 10(1 − 0.412.5 10(1 − 0.35) = 6.545.08 The yearly after-tax payoﬀ of stock B is 5(1 − 0. 10. 32. each share is worth P0 = 1.5 Stock C 10 10[1 − (0. 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 .35) = 6.00.3)(0. (a) The value of the ﬁrm is the present value of its dividends and future value: V0 = 32.000 10.000 After the dividend is paid.35) = 6.2) = 6.12 1.5) = 5.725 5(1 − 0.95 10(1 − 0.35) = 7.000/10.3)(0.000 = = 138.28) = 6. In fact. PA = 0.396) = 6. it cannot be true that the low dividend is depressing the price.000 − 32. so that the price of stock B should be 6.000. so that the price of stock C should be 5 = 62.412. (c) (i) According to Modigliani and Miller. so that the price of stock A should be 8 = 100. PB = 0.50.000 + 1.2 10(1 − 0.5 (iii) Individual (iv) Security dealer (b) The yearly after-tax payoﬀ of stock A is 10(1 − 0.4. (a) Here are the net expected returns on each stock for each of the four investors: Investor (i) Pension fund (ii) Corporation Stock A 10 10(1 − 0.12 (b) Before the dividend is paid.5 = 81.000 = 141.08 The yearly after-tax payoﬀ of stock C is 10(1 − 0.20.5.2) = 8. the shares will be worth P0 = 1.600 = 1.20.600/1.35)] +5(1 − 0.000 Notice that the diﬀerence between P0 and P0 is the dividend per share.28) = 7.35) = 6.396) +5(1 − 0. PC = 0.35)] = 8.5) + 5(1 − 0. since the dividend policy is irrelevant. 10.5 Stock B 10 5[1 − (0.08 5. 760 = 1.000.000 − 10.412. How much? Well..000 The number of new shares that must be issued is therefore n= 10.380.600 V = = 1.000 + n (4) Solving (3) and (4) for n and P0 yields n = 76. and P0 the price after the $4.500).e..500 should then be worth $11. So the current shareholders’ wealth at time 0 must be W0 = 42. we must have nP0 = 10. it must be that their claim is worth $10. that is P0 = 1.545. As shown below.500 = 76. P0 = 1. after the dividend is paid.600 − 11. 136.500 + 1. 1. 10. To pay the $4. (ii) Let n denote the number of new shares that have to be issued.25 dividend per share (for a total dividend of $42. Solution 2: After the dividend is paid and the money is raised from the new equity issue.545. their $10.369.500 belongs to the old shareholders.500 − $32.545. i.change the timing of the dividends (more now. This means that some of the $1.67 and P0 = 136. new shares must be sold.95 per share. less in the future).95.500 investment to be worth exactly that after the dividend is paid.760 ($10.25 dividend has been paid.67.500.545. 10.500 = 1.12 For the new shareholders to be willing to pay $10.369. these new shareholders will also demand a 12% return on their investment. 1.12).95 7 .500.000).12 the same as before. (3) Also.500 ($42. the current shareholders’ wealth is unaﬀected by this dividend increase.380.600/1. the shareholders (both old and new) will be sharing the future value of the ﬁrm. the ﬁrm is worth 1. Solution 1: Since the new shareholders will not be fooled and will require their $10. This implies that 1. that is. i. the shareholders are not made better oﬀ.12 . These new shares must have a value of $10.e.500 for their share in the ﬁrm.600 ﬁrm value in one year will belong to the new shareholders.500 × 1.000.500 = 136. 00 Pall 100.25.50) + (1 − 0.00 Pless 112.000 = 1.50 − Pless ) .00 0.000.3(0.00 100. (b) If a = 0.e.00 12.00 25. and that this number represents the present value of discounted dividends.3)1. i.50 and Pall = 95. Pless 25.13 0.000 + + + ··· = . Notice that the increase in the dividend is more conservative in part (a) since the adjustment rate is lower (i.00.000 1.00 − 6.6(0.00 25.000(1...000. where.000.25 = 1. E1 = 4.00 − Pall 6.00 125. and D0 = 1.05) 1.50 − 3.4 × 4.00 125.00 0. in this case. more weight is put on last year’s dividend). 20. p∗ = 0.000.50.00 25% Payless 112.6.05)2 1.50 − Pless ) 25% Payall 100.4.25 + (100. Paynone 125.13 + (112.415. 8 .50 125. (a) We know that the current value of Nilpoj is $20 million. 8. (a) If a = 0.000(1.00 25.00 − Pall ) .25 +(100.6)1.25 = 1.50 12.05 This implies that the cost of capital for Nilpoj is r = 10%.25 0. we have D1 = 0.50 − Pless 3.6.00 0.000. 2 3 1+r (1 + r ) (1 + r ) r − 0.50 − 3.50) + (1 − 0. The following table shows the after-tax return calculations for the three companies.e.00 − 6. we must have 25% = 25% = 12.00 25.4 × 4.58.13 +(112.00 − Pall ) 25% Next year’s stock price Dividend Total pre-tax payoﬀ Today’s stock price Capital gains Tax on dividend (@25%) Tax on capital gains (@0%) Total after-tax income After-tax rate of return Since we would like the three after-tax expected returns to be the same. We know that the Lintner dividend model is given by D1 = a(p∗ E1 ) + (1 − a)D0 .3. we have D1 = 0. 7. Pall and These imply Pless = 97. the new investors get what they pay for): nP1 = 1.000.000 = 21.000 + 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.000..000 = 1.000. 20 (d) The new shareholders will be getting a fraction 50.1)2 (1. we have P1 = 21. Since the total number of shares after the new issue will be 1.000. We can now use this value in (6) to obtain n= 1.000.05)2 (1.000.1 (1.1 21 0.000 V1 = .1)2 1.05 1.000.000 + n 1.000 = 50.000.1)4 2 1 20 1.000.000 = 20.05 = 1.000.000 + n)P1 = 21.000.000 shares.000 + n.1 − 0.000.(b) At the end of the year. (6) Using this last equation in (5) yields: (1.05 (1.05 (1. (c) Let n denote the number of new shares that will need to be issued. whereas the original shareholders will be getting a fraction 1− 21 of these dividends.000 1 = 1.000 (6) ⇔ 1.1 − 0.05)3 + + + + ··· 1.1 21 (1. 1.000P1 + 1.000.000.000.000 21 1 = of future dividends.1)3 (1.000. the value of the ﬁrm will be V1 = 1.000. and P1 the price of each share (old and new) at the end of the ﬁrst year.e.000 + 50. 20 21 (e) The present value of the cash ﬂows to the original shareholders is PV = 1.000.000.05)2 + + ··· 1.000 1.000.000 0. 2 20 1.1 9 .000.05 = 21.05 + 1.000 ⇔ P1 = 20. 20(S1 − 100) − 0.10 Solving. We then have the following cash ﬂows associated with buying cum-dividend or ex-dividend: Cash Flow Today Buy cum-dividend Buy ex-dividend Diﬀerence in CF’s −100 + 1 −Sed −99 + Sed Cash Flow in 1 Year S1 − 0.30(1) S1 − 0. 1. the stock price drops by less than $1. 10 .20(S1 − Sed ) 19.111. This reﬂects the fact that capital gains are taxed at a lower rate than dividends. Let Sed denote the ex-dividend stock price. i. after the dividend payment.e.7 − 0.9.7 − 0. Therefore.20Sed 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.20Sed = 0. gives Sed = 99. if −99 + Sed + 19..