Answer to the Corporate Finance

Chapter 14 Capital Structure in a Perfect Market 14-1. take up a project with throw in the towel cash flows in one year of $130,000 or $180,000, with in all(prenominal) outcome being equally likely. The sign investment undeniable for the project is $ one C,000, and the projects live of working cap is 20%. The insecurity-free touch calculate is 10%. a. What is the NPV of this project? b. call back that to mounting the funds for the initial investment, the project is sold to investors as an all- right substantial. The justice holders depart receive the cash flows of the project in one year. How much money can be elevated in this waythat is, what is the initial market appreciate of the unlevered equity? . a. Suppose the initial $100,000 is instead raised by get at the risk-free interest rate. What atomic number 18 the cash flows of the levered equity, and what is its initial value according to MM? E ? C (1)? = ? ? 1 (130, 000 + 180, 000) = 155, 000, 2 155, 000 NPV = ? 100, 000 = 129,167 ? 100, 000 = $29,167 1. 20 155, 000 = 129,167 1. 20 b. c. impartiality value = PV ( C (1)) = Debt payments = 100, 000, equity receives 20,000 or 70,000. Initial value, by MM, is 129,167 ? 100, 000 = $29,167 . 14-2. You are an entrepreneur starting a biotechnology rigid. If your research is successful, the technology can be sold for $30 meg.If your research is unsuccessful, it will be worth nothing. To fund your research, you need to raise $2 one million million million. Investors are willing to provide you with $2 million in initial keen in exchange for 50% of the unlevered equity in the firm. a. What is the total market value of the firm without leverage? b. Suppose you borrow $1 million. match to MM, what fraction of the firms equity will you need to sell to raise the additional $1 million you need? c. What is the value of your get by of the firms equity in cases (a) and (b)? a. b. c. Total value of equity = 2 ? 2m = $4m MM says total value of firm is s till $4 million. $1 million of debt implies total value of equity is $3 million. Therefore, 33% of equity must be sold to raise $1 million. In (a), 50% ? $4m = $2m. In (b), 2/3 ? $3m = $2m. Thus, in a perfect market the choice of chapiter expression does not affect the value to the entrepreneur. 2011 Pearson Education, Inc. Publishing as scholar residency Berk/DeMarzo integrated Finance, Second variance 14-3. 185 Acort Industries owns assets that will have an 80% probability of having a market value of $50 million in one year.There is a 20% chance that the assets will be worth only $20 million. The current risk-free rate is 5%, and Acorts assets have a cost of capital of 10%. a. If Acort is unlevered, what is the current market value of its equity? b. Suppose instead that Acort has debt with a face value of $20 million due in one year. According to MM, what is the value of Acorts equity in this case? c. What is the evaluate upshot of Acorts equity without leverage? What is the pass judgment return of Acorts equity with leverage? d. What is the lowest possible realized return of Acorts equity with and without leverage? . b. c. d. 14-4. EValue in one year = 0. 8 ( 50 ) + 0. 2 ( 20 ) = 44 . E = D= 44 = $40m. 1. 10 20 = 19. 048 . Therefore, E = 40 ? 19. 048 = $20. 952m. 1. 05 44 44 ? 20 ? 1 = 10% , with leverage, r = ? 1 = 14. 55%. 40 20. 952 20 0 ? 1 = ? 50% , with leverage, r = ? 1 = ? 100%. 40 20. 952 Without leverage, r= Without leverage, r= Wolfrum Technology (WT) has no debt. Its assets will be worth $450 million in one year if the providence is strong, but only $200 million in one year if the economy is weak. Both events are equally likely. The market value today of its assets is $250 million. . What is the expected return of WT seam without leverage? b. Suppose the risk-free interest rate is 5%. If WT borrows $100 million today at this rate and uses the proceeds to pay an immediate cash dividend, what will be the market value of its equity hon ourable after the dividend is paid, according to MM? c. What is the expected return of MM stock after the dividend is paid in part (b)? a. b. c. 14-5. (. 5 ? 450+. 5 ? 200)/250 = 1. 30 = 30% E + D = 250, D = 100 = E = 150 (. 5 ? (450-105) + . 5 ? (200-105))/150 = 1. 4667 = 46. 67% Suppose there are no taxes.Firm first rudiment has no debt, and firm XYZ has debt of $ d0 on which it pays interest of 10% severally year. Both companies have identical projects that generate free cash flows of $800 or $ guanine each year. After paying any interest on debt, both companies use all rest free cash flows to pay dividends each year. a. Fill in the table below showing the payments debt and equity holders of each firm will receive given each of the two possible levels of free cash flows. b. Suppose you hold 10% of the equity of ABC. What is another portfolio you could hold that would provide the resembling cash flows? 2011 Pearson Education, Inc. Publishing as Prentice Hall 186 Berk/DeMarzo Corporate Finance, Second Edition c. Suppose you hold 10% of the equity of XYZ. If you can borrow at 10%, what is an alternative strategy that would provide the same cash flows? ABC Debt Payments legality Dividends 0 800 0 1000 XYZ Debt Payments Equity Dividends 500 300 500 500 a. FCF $800 $1,000 b. c. 14-6. Unlevered Equity = Debt + Levered Equity. Buy 10% of XYZ debt and 10% of XYZ Equity, get 50 + (30,50) = (80,100) Levered Equity = Unlevered Equity + Borrowing. Borrow $500, buy 10% of ABC, receive (80,100) 50 = (30, 50)Suppose important Industries and izzard Technology have identical assets that generate identical cash flows. Alpha Industries is an all-equity firm, with 10 million shares outstanding that workmanship for a price of $22 per share. Omega Technology has 20 million shares outstanding as well as debt of $60 million. a. According to MM marriage proposal I, what is the stock price for Omega Technology? b. Suppose Omega Technology stock soon trades for $11 per sha re. What trade opportunity is available? What assumptions are necessary to exploit this opportunity? a. b. V(alpha) = 10 ? 22 = 220m = V(omega) = D + E ?E = 220 60 = 160m ? p = $8 per share. Omega is overpriced. Sell 20 Omega, buy 10 alpha, and borrow 60. Initial = 220 220 + 60 = 60. plays we can trade shares at current prices and that we can borrow at the same terms as Omega (or own Omega debt and can sell at same price). 14-7. Cisoft is a highly profitable technology firm that soon has $5 billion in cash. The firm has decided to use this cash to buy shares from investors, and it has already announced these plans to investors. Currently, Cisoft is an all-equity firm with 5 billion shares outstanding. These shares currently trade for $12 per share.Cisoft has issued no other securities except for stock options given to its employees. The current market value of these options is $8 billion. a. What is the market value of Cisofts non-cash assets? b. With perfect capital markets, what is the market value of Cisofts equity after the share repurchase? What is the value per share? a. Assets = cash + non-cash, Liabilities = equity + options, Non-cash assets = equity + options cash = 12 ? 5 + 8 5 = 63 billion. Equity = 60 5 =55. Repurchase Per share value = 55 = $12 . 4. 583 5b = 0. 417b shares ? 4. 583 b shares remain. 12 b. 14-8.Schwartz Industry is an industrial company with 100 million shares outstanding and a market capitalization (equity value) of $4 billion. It has $2 billion of debt outstanding. Management have decided to delever the firm by issuing sassy equity to repay all outstanding debt. a. How many stark naked shares must the firm issue? b. Suppose you are a shareowner holding 100 shares, and you disagree with this decision. Assuming a perfect capital market, describe what you can do to undo the effect of this decision. a. Share price = 4b/100m = $40, erupt 2b/40 = 50 million shares 2011 Pearson Education, Inc. Publishing as Prentice HallBerk /DeMarzo Corporate Finance, Second Edition 187 b. You can undo the effect of the decision by borrowing to buy additional shares, in the same proportion as the firms actions, thus relevering your own portfolio. In this case you should buy 50 unsanded shares and borrow $2000. 14-9. Zetatron is an all-equity firm with 100 million shares outstanding, which are currently trading for $7. 50 per share. A month ago, Zetatron announced it will change its capital structure by borrowing $100 million in short-term debt, borrowing $100 million in long-term debt, and issuing $100 million of best-loved stock.The $300 million raised by these issues, plus another $50 million in cash that Zetatron already has, will be used to repurchase existing shares of stock. The exercise is scheduled to occur today. Assume perfect capital markets. a. What is the market value balance sheet for Zetatron i. Before this transaction? ii. After the new(a) securities are issued but before the share repurchase? iii. After the share repurchase? b. At the conclusion of this transaction, how many shares outstanding will Zetatron have, and what will the value of those shares be? . i. ii. A = 50 cash + 700 non-cash L = 750 equity A = 350 cash + 700 non-cash L = 750 equity + 100 short-term debt + 100 long-term debt + 100 preferred stock iii. A = 700 non-cash L = cd equity + 100 short-term debt + 100 long-term debt + 100 preferred stock b. 14-10. Repurchase 350 400 = 46. 67 shares ? 53. 33 remain. Value is = 7. 50. 7. 50 53. 33 Explain what is wrong with the following argument If a firm issues debt that is risk free, because there is no casualty of default, the risk of the firms equity does not change.Therefore, risk-free debt allows the firm to get the proceeds of a low cost of capital of debt without raising its cost of capital of equity. Any leverage raises the equity cost of capital. In fact, risk-free leverage raises it the most (because it does not share any of the risk). 14-11. Consider the entrepreneur expound in Section 14. 1 (and referenced in Tables 14. 114. 3). Suppose she funds the project by borrowing $750 rather than $500. a. According to MM Proposition I, what is the value of the equity? What are its cash flows if the economy is strong? What are its cash flows if the economy is weak?What is the risk premium of equity in each case? What is the sensitivity of the levered equity return to systematic risk? How does its sensitivity compare to that of unlevered equity? How does its risk premium compare to that of unlevered equity? What is the firms WACC in this case? b. What is the return of the equity in each case? What is its expected return? c. d. What is the debt-equity proportionality of the firm in this case? e. a. b. E = 1000 750 = 250. CF = (1400,900) 500 (1. 05) = (612. 5,112. 5) Re = (145%, 55%), ERe = 45%, Risk premium = 45% 5% = 40% 2011 Pearson Education, Inc. Publishing as Prentice Hall 88 Berk/DeMarzo Corporate Finance, Second Edition c. d. e. 14-12. Return sensitivity = 145% (-55%) = 200%. This sensitivity is 4x the sensitivity of unlevered equity (50%). Its risk premium is also 4x that of unlevered equity (40% vs. 10%). 750 = 3x 250 25%(45%)+75%(5%) = 15% Hardmon Enterprises is currently an all-equity firm with an expected return of 12%. It is considering a leveraged recapitalization in which it would borrow and repurchase existing shares. a. Suppose Hardmon borrows to the top that its debt-equity proportionality is 0. 50. With this amount of debt, the debt cost of capital is 6%.What will the expected return of equity be after this transaction? b. Suppose instead Hardmon borrows to the pinnacle that its debt-equity ratio is 1. 50. With this amount of debt, Hardmons debt will be much riskier. As a result, the debt cost of capital will be 8%. What will the expected return of equity be in this case? c. A senior manager argues that it is in the best interest of the shareholders to choose the capital structure that lead s to the highest expected return for the stock. How would you respond to this argument? a. b. c. 14-13. re = ru + d/e(ru rd) = 12% + 0. 50(12% 6%) = 15% re = 12% + 1. 0(12% 8%) = 18% Returns are high because risk is higherthe return fairly compensates for the risk. There is no free lunch. Suppose Microsoft has no debt and an equity cost of capital of 9. 2%. The average debt-to-value ratio for the software industry is 13%. What would its cost of equity be if it took on the average amount of debt for its industry at a cost of debt of 6%? At a cost of debt of 6% D (rU ? rD ) E 0. 13 rE = 0. 092 + (0. 092 ? 0. 06) 0. 87 = 0. 0968 rE = rU + = 9. 68%. 14-14. Global Pistons (GP) has common stock with a market value of $200 million and debt with a value of $100 million.Investors expect a 15% return on the stock and a 6% return on the debt. Assume perfect capital markets. a. Suppose GP issues $100 million of new stock to buy back the debt. What is the expected return of the stock after t his transaction? i. If the risk of the debt does not change, what is the expected return of the stock after this transaction? b. Suppose instead GP issues $50 million of new debt to repurchase stock. ii. If the risk of the debt increases, would the expected return of the stock be higher or lower than in part (i)? 2011 Pearson Education, Inc. Publishing as Prentice HallBerk/DeMarzo Corporate Finance, Second Edition 2 (15% ) 6% + = 12% = ru . 3 3 189 a. b. wacc = i. re = ru + d / e ( ru ? rd ) = 12 + 150 (12 ? 6) = 18% 150 ii. if rd is higher, re is lower. The debt will share some of the risk. 14-15. Hubbard Industries is an all-equity firm whose shares have an expected return of 10%. Hubbard does a leveraged recapitalization, issuing debt and repurchasing stock, until its debt-equity ratio is 0. 60. Due to the increased risk, shareholders now expect a return of 13%. Assuming there are no taxes and Hubbards debt is risk free, what is the interest rate on the debt? acc = ru = 10% = 1 0. 6 x ? 1. 6 (10) ? 13 = 3 = 0. 6 x ? x = 5% 13% + 1. 6 1. 6 14-16. Hartford Mining has 50 million shares that are currently trading for $4 per share and $200 million worth of debt. The debt is risk free and has an interest rate of 5%, and the expected return of Hartford stock is 11%. Suppose a mining strike causes the price of Hartford stock to fall 25% to $3 per share. The value of the risk-free debt is unchanged. Assuming there are no taxes and the risk (unlevered beta) of Hartfords assets is unchanged, what happens to Hartfords equity cost of capital? u = wacc = 1 1 200 (11) + (5) = 8% . re = 8% + (8% ? 5%) = 12% 2 2 150 14-17. Mercer Corp. is an all equity firm with 10 million shares outstanding and $100 million worth of debt outstanding. Its current share price is $75. Mercers equity cost of capital is 8. 5%. Mercer has just announced that it will issue $350 million worth of debt. It will use the proceeds from this debt to pay off its existing debt, and use the remaining $250 million to pay an immediate dividend. Assume perfect capital markets. a. Estimate Mercers share price just after the recapitalization is announced, but before the transaction occurs. . Estimate Mercers share price at the conclusion of the transaction. (Hint use the market value balance sheet. ) c. Suppose Mercers existing debt was risk-free with a 4. 25% expected return, and its new debt is risky with a 5% expected return. Estimate Mercers equity cost of capital after the transaction. a. b. MM = no change, $75 Initial enterprise value = 75 ? 10 + 100 = 850 million New debt = 350 million E = 850 350 = 500 Share price = 500/10 = $50 c. Ru = (750/850) ? 8. 5% + (100/850) ? 4. 25% = 8% Re = 8% + 350/500(8% 5%) = 10. 1% 2011 Pearson Education, Inc.Publishing as Prentice Hall 190 14-18. Berk/DeMarzo Corporate Finance, Second Edition In June 2009, Apple Computer had no debt, total equity capitalization of $128 billion, and a (equity) beta of 1. 7 (as reported on Google Finance). includ e in Apples assets was $25 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 5% and the market risk premium is 4%. a. c. What is Apples enterprise value? What is Apples WACC? b. What is the beta of Apples business assets? a. b. 128-25=103 million Because the debt is risk free, ?U = E ? E E+D 128 = (1. 7) 103 = 2. 11 c. rWACC = rf + ? ( E RMkt ? rf ) = 5 + 2. 11? 4 = 13. 4% alternatively rE = rf + ? E ( E RMkt ? rf ) = 5 + 1. 7 ? 4 = 11. 8% E D $128 $25 rE + rD = (11. 8%) ? (5%) = 13. 4% E+D E+D $103 $103 rwacc = 14-19. Indell stock has a current market value of $120 million and a beta of 1. 50. Indell currently has risk-free debt as well. The firm decides to change its capital structure by issuing $30 million in additional risk-free debt, and then using this $30 million plus another $10 million in cash to repurchase stock.With perfect capital markets, what will be the beta of Indell stock after this transaction? Indell increases its clams deb t by $40 million ($30 million in new debt + $10 million in cash paid out). Therefore, the value of its equity decreases to 120 40 = $80 million. If the debt is risk-free D ? ?u ( E + D ) EV = ? u ? , ? = E? E E ? e = ? u ? 1 + ? ? where D is net debt, and EV is enterprise value . The only change in the equation is the value of equity. Therefore ? = ? e e E 120 = 1. 50 = 2. 25. E 80 14-20. Yerba Industries is an all-equity firm whose stock has a beta of 1. and an expected return of 12. 5%. Suppose it issues new risk-free debt with a 5% yield and repurchases 40% of its stock. Assume perfect capital markets. a. What is the beta of Yerba stock after this transaction? b. What is the expected return of Yerba stock after this transaction? Suppose that prior to this transaction, Yerba expected hire per share this approaching year of $1. 50, with a forward P/E ratio (that is, the share price divided by the expected earnings for the coming year) of 14. 2011 Pearson Education, Inc. Publish ing as Prentice Hall Berk/DeMarzo Corporate Finance, Second Edition . 191 What is Yerbas expected earnings per share after this transaction? Does this change benefit shareholders? Explain. d. What is Yerbas forward P/E ratio after this transaction? Is this change in the P/E ratio reasonable? Explain. a. b. ?e = ? u (1 + d / e ) = 1. 2 ? 1 + ? ? 40 ? ?=2 60 ? 12. 5 ? 5 = 6. 25 ? re = 5 + 2 ( 6. 25) = 17. 5% from the CAPM, or 1. 2 re = r f + b rm ? r f ? rm ? r f = ( ) re = ru + d / e ( ru ? rd ) = 12. 5 + c. 40 (12. 5 ? 5) = 17. 5 60 p = 14 (1. 50 ) = $21 . Borrow 40%(21) = 8. 4, interest = 5%(8. 4) = 0. 42. Earnings = 1. 50 0. 42 = 1. 08, per share = . 08 = 1. 80. 0. 60 No benefit risk is higher. The stock price does not change. d. 14-21. PE = 21 = 11. 67 . It falls due to higher risk. 1. 80 You are CEO of a high- bringth technology firm. You plan to raise $180 million to fund an expansion by issuing any new shares or new debt. With the expansion, you expect earnings next year of $24 million. The firm currently has 10 million shares outstanding, with a price of $90 per share. Assume perfect capital markets. a. If you raise the $180 million by selling new shares, what will the forecast for next years earnings per share be? b.If you raise the $180 million by issuing new debt with an interest rate of 5%, what will the forecast for next years earnings per share be? c. What is the firms forward P/E ratio (that is, the share price divided by the expected earnings for the coming year) if it issues equity? What is the firms forward P/E ratio if it issues debt? How can you explain the difference? a. Issue 180 = 2 million new shares ? 12 million shares outstanding. 90 24 = $2. 00 per share. 12 New EPS = b. Interest on new debt = 180 ? 5% = $9 million. The interest expense will quash earnings to 24 9 15 = $1. 50 per share. $15 million. With 10 million shares outstanding, EPS = 10 By MM, share price is $90 in either case. PE ratio with equity issue is PE ratio with d ebt is $90 = 60 . 1. 50 90 = 45 . 2 c. The higher PE ratio is justified because with leverage, EPS will grow at a faster rate. 2011 Pearson Education, Inc. Publishing as Prentice Hall 192 14-22. Berk/DeMarzo Corporate Finance, Second Edition Zelnor, Inc. , is an all-equity firm with 100 million shares outstanding currently trading for $8. 50 per share. Suppose Zelnor decides to grant a total of 10 million new shares to employees as part of a new compensation plan.The firm argues that this new compensation plan will motivate employees and is a better strategy than giving salary bonuses because it will not cost the firm anything. a. If the new compensation plan has no effect on the value of Zelnors assets, what will be the share price of the stock once this plan is enforced? b. What is the cost of this plan for Zelnors investors? Why is issuing equity costly in this case? a. b. Assets = 850m. New shares = 110. ? price = 850 = $7. 73 110 Cost = 100(8. 50 7. 73) = 77 m = 10(7. 73). I ssuing equity at below market price is costly. 2011 Pearson Education, Inc. Publishing as Prentice Hall