Exercise Session #8 Suggested Solutions

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JEM034 Corporate Finance Winter Semester 2017/2018 Instructor: Olga Bychkova Date: 28/11/2017 Exercise Session #8 Suggested Solutions Problem 1. (14.

1 JEM034 Corporate Finance Winter Semester 2017/2018 Instructor: Olga Bychkova Date: 28/11/2017 Exercise Session #8 Suggested Solutions Problem 1. (14.2) The authorized share capital of the Alfred Cake Company is 100,000 shares. The equity is currently shown in the company s books as follows: (a) How many shares are issued? (b) How many are outstanding? (c) Explain the difference between your answers to (a) and (b). (d) How many more shares can be issued without the approval of shareholders? (e) Suppose that Alfred Cake issues 10,000 shares at $2 a share. Which of the above figures would be changed? (f) Suppose instead that the company bought back 5,000 shares at $5 a share. Which of the above figures would be changed? common stock 40, 000 (a) Number of issued shares = = = 80, 000. par value 0.5 (b) N umber of outstanding shares = number of issued shares number of treasury shares = = 80, 000 2, 000 = 78, 000. (c) 2,000 shares are held as Treasury stock. (d) T he authorized share capital number of issued shares = 100, , 000 = = 20, 000 shares. (e) Common stock = 40, , = $45, 000. Additional paid in capital = 10, , , = $25, 000. Common equity = common stock+additional paid in capital+retained earnings = = 45, , , 000 = $100, 000. Net common equity = common equity treasury stock = 100, 000 5, 000 = = $95, 000. (f) T reasury stock = 5, , = $30, 000. Net common equity = common equity treasury stock = 80, , 000 = 1

2 = $50, 000. Problem 2. (14.15) The shareholders of the Pickwick Paper Company need to elect five directors. There are 200,000 shares outstanding. How many shares do you need to own to ensure that you can elect at least one director if (a) the company has majority voting? (b) it has cumulative voting? (a) For majority voting, you must own or otherwise control the votes of a simple majority of the shares outstanding, i.e., one half of the shares outstanding plus one. Here, with 200,000 shares outstanding, you must control the votes of 100,001 shares. (b) With cumulative voting, the directors are elected in order of the total number of votes each receives. With 200,000 shares outstanding and five directors to be elected, there will be a total of 1,000,000 votes cast. To ensure you can elect at least one director, you must ensure that someone else can elect at most four directors. That is, you must have enough votes so that, even if the others split their votes evenly among five other candidates, the number of votes your candidate gets would be higher by one. Let x be the number of votes controlled by you, so that others control 1, 000, 000 x votes. To elect one director: 1, 000, 000 x x = Solving, we find x = 166, votes, or 33,333.4 shares. Because there are no fractional shares, we need 33,334 shares. Problem 3. (15.6) You need to choose between making a public offering and arranging a private placement. In each case the issue involves $10 million face value of 10 year debt. You have the following data for each: A public issue: The interest rate on the debt would be 8.5%, and the debt would be issued at face value. The underwriting spread would be 1.5%, and other expenses would be $80,000. A private placement: The interest rate on the private placement would be 9%, but the total issuing expenses would be only $30,000. (a) What is the difference in the proceeds to the company net of expenses? (b) Other things being equal, which is the better deal? (c) What other factors beyond the interest rate and issue costs would you wish to consider before deciding between the two offers? (a) Net proceeds of public issue = 10, 000, , 000, , 000 = $9, 770, 000. Net proceeds of private placement = 10, 000, , 000 = $9, 970, 000. ( ) , 000, (b) P V of extra interest on private placement = 1 = $328, 000, i.e., extra cost of higher interest on private placement more than outweighs saving in issue costs (= net proceeds of private placement net proceeds of public issue = $200, 000). Thus, a public isuue is a better deal. 2

(c) Private placement debt can be custom tailored and the terms more easily renegotiated. Problem 4. (15.21) Here is recent financial data on Pisa Construction, Inc.

3 (c) Private placement debt can be custom tailored and the terms more easily renegotiated. Problem 4. (15.21) Here is recent financial data on Pisa Construction, Inc. Pisa has not performed spectacularly to date. However, it wishes to issue new shares to obtain $80,000 to finance expansion into a promising market. Pisa s financial advisers think a stock issue is a poor choice because, among other reasons, sale of stock at a price below book value per share can only depress the stock price and decrease shareholders wealth. To prove the point they construct the following example: Suppose 2,000 new shares are issued at $40 and the proceeds are invested. (Neglect issue costs.) Suppose return on investment does not change. Then Book net worth = $580, 000. T otal earnings = , 000 = $46, , 400 Earnings per share = 12, 000 = $3.87. Thus, EPS declines, book value per share declines, and share price will decline proportionately to $38.7. Evaluate this argument with particular attention to the assumptions implicit in the numerical example. Assume a 10% interest rate. Pisa Construction s return on investment is 8%, whereas investors require a 10% rate of return. Pisa proposes a scenario in which 2,000 shares of common stock are issued at $40 per share, and the proceeds ($80,000) are then invested at 8%. Assuming that the 8% return is received in the form of a perpetuity, then the NPV for this scenario is computed as follows: 0.08 $80, 000 NP V = $80, = $16, Share price would decline as a result of this project, not because the company sells shares for less than book value, but rather due to the fact that the NPV is negative. Note that, if investors know price will decline as a consequence of Pisa s undertaking a negative NPV investment, Pisa will not be able to sell shares at $40 per share. Rather, after the announcement of the project, the share price will decline to: Therefore, Pisa will have to issue: $400, 000 $16, , 000 $80, 000 $38.4 = $38.4. = 2, 083 new shares. One can show that, if the proceeds of the stock issue are invested at 10%, then share price remains unchanged. 3

4 Problem 5. (16.3) (a) Wotan owns 1,000 shares of a firm that has just announced an increase in its dividend from $2 to $2.5 a share. The share price is currently $150. If Wotan does not wish to spend the extra cash, what should he do to offset the dividend increase? (b) Brunhilde owns 1,000 shares of a firm that has just announced a dividend cut from $8 a share to $5. The share price is currently $200. If Brunhilde wishes to maintain her consumption, what should she do to offset the dividend cut? (a) Reinvest 1, 000 ($2.5 $2) = $500 in the stock. If the ex dividend price is $150 $2.5 = 500 $147.5, this should involve the purchase of shares. (b) Sell shares worth 1, 000 ($8 $5) = $3, 000. If the ex dividend price is $200 $5 = 3, 000 $195, this should involve the sale of 15 shares. 195 Problem 6. (16.10) Little Oil has outstanding 1 million shares with a total market value of $20 million. The firm is expected to pay $1 million of dividends next year, and thereafter the amount paid out is expected to grow by 5% a year in perpetuity. Thus the expected dividend is $1.05 million in year 2, $1.105 million in year 3, and so on. However, the company has heard that the value of a share depends on the flow of dividends, and therefore it announces that next year s dividend will be increased to $2 million and that the extra cash will be raised immediately by an issue of shares. After that, the total amount paid out each year will be as previously forecasted, that is, $1.05 million in year 2 and increasing by 5% in each subsequent year. (a) At what price will the new shares be issued in year 1? (b) How many shares will the firm need to issue? (c) What will be the expected dividend payments on these new shares, and what therefore will be paid out to the old shareholders after year 1? (d) Show that the present value of the cash flows to current shareholders remains $20 million. (a) At t = 0 each share is worth $20 million /1 million = $20. This value is based on the expected stream of dividends: $1 million /1 million = $1 per share at t = 1, and increasing by 5% in each subsequent year. Thus, we can find the appropriate discount rate for this company as follows: r = DIV 1 + g = $ = 0.1 or 10%. P 0 $20 Beginning at t = 2, each share in the company will enjoy a perpetual stream of growing dividends: $1.05 at t = 2, and increasing by 5% in each subsequent year. Thus, the total value of the shares at t = 1 (after the t = 1 dividend is paid and after N new shares have been issued) is given by: V 1 = $1.05 million = $21 million.

5 If P 1 is the price per share at t = 1, then: and: V 1 = P 1 (1 million + N) = $21 millon P 1 N = $1 million. Substituting the second equation into the firts one, we obtain P 1 = $20. (b) With P 1 equal to $20 the firm will need to sell 50,000 new shares to raise $1 millon. (c) The expected dividends paid at t = 2 are $1.05 million, increasing by 5% in each subsequent year. With 1.05 millon shares outstanding, dividends per share are: $1.05 million /1.05 million = $1 at t = 2, increasing by 5% in each subsequent year. Thus, total dividends paid to old shareholders are: $1 1 million = $1 million at t = 2, increasing by 5% in each subsequent year. (d) For the current shareholders: P V (t = 0) = $2 million $1 million 1.1 ( ) = $20 million. Problem 7. (16.15) 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. (a) If we ignore taxes and there is no information conveyed by the repurchase when the repurchase program is announced, then share price will remain at $80. (b) The regular dividend has been $4 per share, and so the company has $4 100, 000 = $400, 000 cash on hand. Since the share price is $80, the company will repurchase 400,000/80 = 5, 000 shares. (c) Total asset value (before each dividend payment or stock repurchase) remains at $80 100, 000 = $8 million. These assets earn $400,000 per year, under either policy. Old Policy: The annual dividend is $4, which never 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 100, 000 5, 000 = 95, 000 shares outstanding. These shares will be worth $8 million, or $8 million /95,000 = $84.21 per share. With $400,000 available to repurchase shares, the total number of shares repurchased will be 400,000 /84.21 = 4, 750. Using this reasoning, we can generate the following table: 5

6 Shares Share Shares Time Outstanding Price Repurchased t = 0 100,000 $80 5,000 t = 1 95,000 $ ,750 t = 2 90,250 $ ,513 t = 3 85,737 $ ,287 Note that the stock price is increasing by /80 1 = 5.26% each year. This is consistent with the rate of return to the shareholders under the old policy, whereby every year assets worth $7.6 million (the asset value immediately after the dividend) earn $400,000, or a return of 400,000 /7.6 million = 5.26%. Problem 8. (16.20) The shares of A and B both sell for $100 and offer a pretax return of 10%. However, in the case of company A the return is entirely in the form of dividend yield (the company pays a regular annual dividend of $10 a share), while in the case of B the return comes entirely as capital gain (the shares appreciate by 10% a year). Suppose that dividends and capital gains are both taxed at 30%. What is the after tax return on share A? What is the after tax return on share B to an investor who sells after two years? What about an investor who sells after 10 years? After tax Return on Share A: At t = 1, a shareholder in company A will receive a dividend of $10, which is subject to taxes of 30%. Therefore, the after tax gain is (1 0.3) $10 = $7. Since the initial investment is $100, the after tax rate of return is 107/100 1 = 7%. After tax Return on Share B: If an investor sells share B after 2 years, the price will be: = $121. The capital gain of $21 is taxed at the 30% rate, and so the after tax gain is (1 0.3) $21 = $14.7. On an initial investment of $100, over a 2 year time period, this is an after tax annual rate of return of 114.7/100 1 = 7.1%. If an investor sells share B after 10 years, the price will be: = $ The capital gain of $ is taxed at the 30% rate, and so the after tax gain is (1 0.3) $ = $ On an initial investment of $100, over a 10 year time period, this is an after tax annual rate of return of /100 1 = 7.78%. 6

CHAPTER 17. Payout Policy

CHAPTER 17. Payout Policy CHAPTER 17 1 Payout Policy 1. a. Distributes a relatively low proportion of current earnings to offset fluctuations in operational cash flow; lower P/E ratio. b. Distributes a relatively high proportion