Unformatted text preview: After‐class practice is important and helpful for the purpose of knowledge learning. However, it by no means replaces activities such as participating classes, understanding the lecture notes, and discussing with your classmates, which could be more important and rewarding. I hope you bear this caveat in mind when enjoying the following practices. ☺ FNCE201 Corporate Finance Suggested Homework for Capital Structure Berk/DeMarzo Textbook 2nd Edition • Chapter 14 Problems 1‐6 • Chapter 15 Problems 1‐9, 16‐25 • Chapter 16 Problems 1‐11, 15‐18, 20‐22, 24‐26 *Solutions are attached in the next pages (To be honest, I have not worked through every problem by myself. So please discuss with your classmates first if you don’t understand the solutions). 1|Page Chapter 14 Capital Structure in a Perfect Market 14-1. Consider a project with free cash flows in one year of $130,000 or $180,000, with each outcome being equally likely. The initial investment required for the project is $100,000, and the project’s cost of capital is 20%. The risk-free interest rate is 10%. a. What is the NPV of this project? b. Suppose that to raise the funds for the initial investment, the project is sold to investors as an allequity firm. The equity holders will receive the cash flows of the project in one year. How much money can be raised in this way—that is, what is the initial market value of the unlevered equity? c. Suppose the initial $100,000 is instead raised by borrowing at the risk-free interest rate. What are the cash flows of the levered equity, and what is its initial value according to MM? a. E ⎡C (1)⎤ = ⎣ ⎦ b. Equity value = PV ( C (1)) = c. Debt payments = 100, 000, equity receives 20,000 or 70,000. 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 Initial value, by MM, is 129,167 − 100, 000 = $29,167 . 14-2. You are an entrepreneur starting a biotechnology firm. If your research is successful, the technology can be sold for $30 million. If your research is unsuccessful, it will be worth nothing. To fund your research, you need to raise $2 million. Investors are willing to provide you with $2 million in initial capital 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. According to MM, what fraction of the firm’s equity will you need to sell to raise the additional $1 million you need? c. a. Total value of equity = 2 × $2m = $4m b. MM says total value of firm is still $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. c. 14-3. What is the value of your share of the firm’s equity in cases (a) and (b)? In (a), 50% × $4m = $2m. In (b), 2/3 × $3m = $2m. Thus, in a perfect market the choice of capital structure does not affect the value to the entrepreneur. 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 Acort’s 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 Acort’s equity in this case? 2|Page c. . What is th expected return of Acort equity with he t’s hout leverage? What is the expected retu of ? urn Acort’s equ with lever uity rage? d. What is the lowest possib realized re . e ble eturn of Acort equity with and without leverage? t’s h 44 4 = $40m. 10 1.1 a. b. . D= c. Without lev verage, r= 44 44 4 − 20 − 1 = 10% , with leverage, r = − 1 = 14 4.55%. h 40 20.952 d. . 14-4. E[Value in one year] = 0.8 ( 50 ) + 0.2 ( 20 ) = 44 . E = 8 0 Without lev verage, r= 20 0 − 1 = −50% , wi leverage, r = − 1 = −100%. ith 20.952 40 20 = 19.048 . Theref fore, E = 40 − 1 19.048 = $20.952m. 1.05 Wolfrum Tech W hnology (WT) has no debt Its assets w be worth $450 million in one year if the t. will ec conomy is stro ong, but only $200 million i one year if the economy is weak. Both events are eq in h qually lik kely. The mar rket value today of its assets is $250 millio s on. a. . What is the expected ret e turn of WT sto without le ock everage? b. Suppose th risk-free int . he terest rate is 5 5%. If WT bo orrows $100 m million today a this rate and uses at d the proceed to pay an i ds immediate cas dividend, w sh what will be th market value of its equit just he ty after the di ividend is paid according to MM? d, c. . a. (.5 × 450+.5 × 200)/250 = 1.30 => 30% 5 b. . E + D = 250 D = 100 => E = 150 0, c. 14-5. What is the expected ret e turn of MM st tock after the dividend is pa in part (b)? aid (.5 × (450-1 105) + .5 × (20 00-105))/150 = 1.4667 => 46. .67% uppose there are no taxes. F a Firm ABC has no debt, and firm XYZ ha debt of $50 on which it pays d as 000 Su in nterest of 10% each year. B % Both compani have ident ies tical projects that generate free cash flo of e ows $8 or $1000 each year. Af 800 fter paying an interest on debt, both companies use all remaining free ny n e ca flows to pa dividends e ash ay each year. a. . Fill in the table below s showing the p payments debt and equity h t holders of eac firm will receive ch given each of the two possible levels of free cash flow f ws. b. Suppose yo hold 10% of the equity of ABC. W . ou y What is anothe portfolio you could hold that er d would prov vide the same cash flows? c. . Suppose yo hold 10% of the equity of XYZ. If yo can borrow at 10%, wh is an altern ou ou w hat native strategy th would prov hat vide the same cash flows? a. FCF $800 $1,000 ABC Debt Payment D ts Equity D Dividends 0 800 0 0 1000 0 XYZ Debt Paymen nts Equity Dividends y 500 300 500 500 3|Page 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 Alpha Industries and Omega Technology have identical assets that generate identical cash flows. Alpha Industries is an all-equity firm, with 10 million shares outstanding that trade 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 Proposition I, what is the stock price for Omega Technology? b. Suppose Omega Technology stock currently trades for $11 per share. What arbitrage opportunity is available? What assumptions are necessary to exploit this opportunity? a. V(alpha) = 10 × 22 = 220m = V(omega) = D + E ⇒ E = 220 – 60 = 160m ⇒ p = $8 per share. b. Omega is overpriced. Sell 20 Omega, buy 10 alpha, and borrow 60. Initial = 220 – 220 + 60 = 60. Assumes 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). 4|Page Chapter 15 Debt and Taxes 15-1. Pelamed Pharmaceuticals has EBIT of $325 million in 2006. In addition, Pelamed has interest expenses of $125 million and a corporate tax rate of 40%. a. What is Pelamed’s 2006 net income? b. What is the total of Pelamed’s 2006 net income and interest payments? c. If Pelamed had no interest expenses, what would its 2006 net income be? How does it compare to your answer in part (b)? d. What is the amount of Pelamed’s interest tax shield in 2006? a. Net Income = EBIT − Interest − Taxes = ( 325 − 125) × (1 − 0.40 ) = $120 million. b. Net income + Interest = 120 + 125 = $245 million c. Net income = EBIT − Taxes = 325 × (1 − 0.40 ) = $195 million. This is 245 − 195 = $50 million lower than part (b). d. 15-2. Interest tax shield = 125 × 40% = $50 million Grommit Engineering expects to have net income next year of $20.75 million and free cash flow of $22.15 million. Grommit’s marginal corporate tax rate is 35%. a. If Grommit increases leverage so that its interest expense rises by $1 million, how will its net income change? b. For the same increase in interest expense, how will free cash flow change? a. b. 15-3. Net income will fall by the after-tax interest expense to $20.750 − 1× (1 − 0.35) = $20.10 million. Free cash flow is not affected by interest expenses. Suppose the corporate tax rate is 40%. Consider a firm that earns $1000 before interest and taxes each year with no risk. The firm’s capital expenditures equal its depreciation expenses each year, and it will have no changes to its net working capital. The risk-free interest rate is 5%. a. Suppose the firm has no debt and pays out its net income as a dividend each year. What is the value of the firm’s equity? b. Suppose instead the firm makes interest payments of $500 per year. What is the value of equity? What is the value of debt? c. What is the difference between the total value of the firm with leverage and without leverage? d. The difference in part (c) is equal to what percentage of the value of the debt? a. Net income = 1000 × (1 − 40% ) = $600 . Thus, equity holders receive dividends of $600 per year with no risk. E = b. 600 = $12, 000 5% Net income = (1000 − 500 ) × (1 − 0.40 ) = $300 ⇒ E = 300 = $6000 . Debt holders receive interest of 5% $500 per year ⇒ D = $10,000 5|Page c. With levera = 6,000 + 1 age 10,000 = $16,0 000 Without lev verage = $12,00 00 Difference = 16,000 – 12, ,000 = $4000 . d. 15-4. 4, 000 4 ate = 40% = corpora tax rate 10, 000 Braxton Enter B rprises curren ntly has debt outstanding of $35 millio and an in on nterest rate of 8%. Braxton plans to reduce its debt by repay B ying $7 millio in principa at the end o each year fo the on al of for ne five years. If Braxton’s marginal cor ext . rporate tax ra is 40%, wh is the inter tax shield from ate hat rest d Braxton’s debt in each of the next five yea B e ars? Year 0 35 Debt Interest Tax Shield d 15-5. 2 21 2.2 24 0.8 896 3 14 1.68 0.672 2 4 7 1.12 0.448 5 0 0.56 0.224 Your firm curr Y rently has $10 million in d 00 debt outstandi with a 10% interest rat The terms of the ing % te. lo oan require th firm to re he epay $25 mill lion of the ba alance each y year. Suppose that the marginal co orporate tax rate is 40%, an that the int r nd terest tax shie have the s elds same risk as th loan. What is the he t pr resent value of the interest tax shields fro this debt? o om Year 0 100 Debt Interest Tax Shield d PV $8.30 15-6. 1 28 2 2.8 2 1.12 1 1 75 7 10 1 4 2 50 7.5 5 3 3 25 5 2 4 0 2.5 1 5 0 0 0 Arnell Industri has just issued $10 million in debt (a par). The fi A ies at irm will pay in nterest only o this on de Arnell’s marginal tax r ebt. m rate is expecte to be 35% f the foresee ed for eable future. a. . Suppose Arnell pays inte erest of 6% pe year on its debt. What is its annual int er terest tax shiel ld? b. What is the present valu of the intere tax shield, assuming its r is the sam as the loan? . e ue est risk me ? c. . a. Interest tax shield = $10 × 6% × 35% = $ $0.21 million b. . PV(Interest tax shield) = t c. 15-7. Suppose in nstead that the interest rate on the debt is 5%. What is the present v e s s value of the in nterest tax shield in this case? i Interest tax shield = $10 × 5% × 35% = $0.175 million PV = n. $0.21 = $3.5 m million 0.06 $0.175 5 = $3.5 millio on. 0.05 Ten T years have passed sinc Arnell issue $10 million in perpetua interest on debt with a 6% ce ed al nly an nnual coupon as in Proble 6. Tax rates have remained the same at 35% but interest rates have n, em e s dr ropped so Arn nell’s current cost of debt capital is 4%. a. . What is Ar rnell’s annual interest tax sh hield? b. What is the present valu of the intere tax shield t . e ue est today? 6|Page a. Solution Interest tax shield = $10 × 6% × 35% = $0.21 million b. Solution PV(Interest tax shield) = $0.21 = $5.25 million. 0.04 Alternatively, new market value of debt is D = (10 ×.06)/.04 = $15 million. Tc × D = 35% × 15 = $5.25 million. 15-8. Bay Transport Systems (BTS) currently has $30 million in debt outstanding. In addition to 6.5% interest, it plans to repay 5% of the remaining balance each year. If BTS has a marginal corporate tax rate of 40%, and if the interest tax shields have the same risk as the loan, what is the present value of the interest tax shield from the debt? Interest tax shield in year 1 = $30 × 6.5% × 40% = $0.78 million. As the outstanding balance declines, so will the interest tax shield. Therefore, we can value the interest tax shield as a growing perpetuity with a growth rate of g = -5% and r = 6.5%: PV = 15-9. $0.78 = $6.78 million 6.5% + 5% Safeco Inc. has no debt, and maintains a policy of holding $10 million in excess cash reserves, invested in risk-free Treasury securities. If Safeco pays a corporate tax rate of 35%, what is the cost of permanently maintaining this $10 million reserve? (Hint: what is the present value of the additional taxes that Safeco will pay?) D = -$10 million (negative debt) So PV(Interest tax shield) = Tc × D = -$3.5 million. This is the present value of the future taxes Safeco will pay on the interest earned on its reserves. 15-16. Milton Industries expects free cash flow of $5 million each year. Milton’s corporate tax rate is 35%, and its unlevered cost of capital is 15%. The firm also has outstanding debt of $19.05 million, and it expects to maintain this level of debt permanently. a. What is the value of Milton Industries without leverage? b. What is the value of Milton Industries with leverage? 5 = $33.33 million 0.15 a. b. 15-17. VU = V L = V U + τ C D = 33.33 + 0.35 × 19.05 = $40 million Suppose Microsoft has 8.75 billion shares outstanding and pays a marginal corporate tax rate of 35%. If Microsoft announces that it will payout $50 billion in cash to investors through a combination of a special dividend and a share repurchase, and if investors had previously assumed Microsoft would retain this excess cash permanently, by how much will Microsoft’s share price change upon the announcement? Reducing cash is equivalent to increasing leverage by $50 billion. PV of tax savings = 35% × 50 = $17.5 billion, or 17.5/ 8.75 = $2.00 per share price increase. 15-18. Kurz Manufacturing is currently an all-equity firm with 20 million shares outstanding and a stock price of $7.50 per share. Although investors currently expect Kurz to remain an all-equity firm, Kurz plans to announce that it will borrow $50 million and use the funds to repurchase shares. Kurz will pay interest only on this debt, and it has no further plans to increase or decrease the amount of debt. Kurz is subject to a 40% corporate tax rate. 7|Page a. What is the market value of Kurz’s existing assets before the announcement? b. What is the market value of Kurz’s assets (including any tax shields) just after the debt is issued, but before the shares are repurchased? c. What is Kurz’s share price just before the share repurchase? How many shares will Kurz repurchase? d. What are Kurz’s market value balance sheet and share price after the share repurchase? a. Assets = Equity = $7.50 × 20 = $150 million b. Assets = 150 (existing) + 50 (cash) + 40% × 50 (tax shield) = $220 million c. E = Assets – Debt = 220 – 50 = $170 million. Share price = Kurz will repurchase d. $170 million = $8.50 . 20 50 = 5.882 million shares. 8.50 Assets = 150 (existing) + 40% × 50 (tax shield) = $170 million Debt = $50 million E = A – D = 170 – 50 = $120 million Share price = 15-19. $120 = $8.50 / share . 20 − 5.882 Rally, Inc., is an all-equity firm with assets worth $25 billion and 10 billion shares outstanding. Rally plans to borrow $10 billion and use these funds to repurchase shares. The firm’s corporate tax rate is 35%, and Rally plans to keep its outstanding debt equal to $10 billion permanently. a. Without the increase in leverage, what would Rally’s share price be? b. Suppose Rally offers $2.75 per share to repurchase its shares. Would shareholders sell for this price? c. Suppose Rally offers $3.00 per share, and shareholders tender their shares at this price. What will Rally’s share price be after the repurchase? d. What is the lowest price Rally can offer and have shareholders tender their shares? What will its stock price be after the share repurchase in that case? 25 a. Share price b. Just before the share repurchase: = 10 = $2.50 per share Assets = 25 ( existing ) + 10 ( cash ) + 35% × 10 ( tax shield ) = $38.5 billion E = 38.5 − 10 = 28.5 Þshare price = 28.5 = $2.85 / share. 10 Therefore, shareholders will not sell for $2.75 per share. c. Assets = 25 (existing) + 35% × 10 (tax shield) = $28.5 billion E = 28.5 – 10 = 18.5 billion Shares = 10 − 10 18.5 = 6.667 billion. Share price = = $2.775 share. 3 6.667 8|Page d. 15-20. From (b), fair value of the shares prior to repurchase is $2.85. At this price, Rally will have 10 18.5 10 − = 6.49 million shares outstanding, which will be worth = $2.85 after the repurchase. 2.85 6.49 Therefore, shares will be willing to sell at this price. Suppose the corporate tax rate is 40%, and investors pay a tax rate of 15% on income from dividends or capital gains and a tax rate of 33.3% on interest income. Your firm decides to add debt so it will pay an additional $15 million in interest each year. It will pay this interest expense by cutting its dividend. a. How much will debt holders receive after paying taxes on the interest they earn? b. By how much will the firm need to cut its dividend each year to pay this interest expense? c. By how much will this cut in the dividend reduce equity holders’ annual after-tax income? d. How much less will the government receive in total tax revenues each year? e. What is the effective tax advantage of debt τ*? a. $15 × (1 – .333) = $10 million each year b. Given a corporate tax rate of 40%, an interest expense of $15 million per year reduces net income by 15(1 – .4) = $9 million after corporate taxes. c. $9 million dividend cut ⇒ $9 × (1 – .15) = $7.65 million per year. d. Interest taxes = .333 × 15 = $5 million Less corporate taxes = .40 × 15 = $6 million Less dividend taxes = .15 × 9 = $1.35 million ⇒ Govt tax revenues change by 5 – 6 – 1.35 = $2.35 million (Note this equals (a) – (c)). e. 15-21. τ * = 1− (1 − 0.40 )(1 − 0.15) 1 − 0.333 = 23.5% Apple Corporation had no debt on its balance sheet in 2008, but paid $2 billion in taxes. Suppose Apple were to issue sufficient debt to reduce its taxes by $1 billion per year permanently. Assume Apple’s marginal corporate tax rate is 35% and its borrowing cost is 7.5%. a. If Apple’s investors do not pay personal taxes (because they hold their Apple stock in tax-free retirement accounts), how much value would be created (what is the value of the tax shield)? b. How does your answer change if instead you assume that Apple’s investors pay a 15% tax rate on income from equity and a 35% tax rate on interest income? a. $1 billion / 7.5% = $13.33 billion. b. To reduce taxes by $1 billion, Apple will need to make interest payments of 1/.35 = $2.857 billion, or issue 2.857/.075 = $38.1 billion in debt. T × = 1 – (1 – tc)(1 – te)/(1 – ti) = 1 – (.65)(.85)/.65 = 15% T × D = 15% × $38.1 = $5.71 billion 15-22. Markum Enterprises is considering permanently adding $100 million of debt to its capital structure. Markum’s corporate tax rate is 35%. a. Absent personal taxes, what is the value of the interest tax shield from the new debt? 9|Page b. If investors pay a tax rate of 40% on interest income, and a tax rate of 20% on income from dividends and capital gains, what is the value of the interest tax shield from the new debt? a. PV = τ C D = 35% × 100 = $35 million. b. τ * = 1− (1 − 0.35)(1 − 0.20 ) 1 − 0.40 = 13.33% PV = τ C D = 13.33% × 100 = $13.33 million 15-23. Garnet Corporation is considering issuing risk-free debt or risk-free preferred stock. The tax rate on interest income is 35%, and the tax rate on dividends or capital gains from preferred stock is 15%. However, the dividends on preferred stock are not deductible for corporate tax purposes, and the corporate tax rate is 40%. a. If the risk-free interest rate for debt is 6%, what is cost of capital for risk-free preferred stock? b. What is the after-tax debt cost of capital for the firm? Which security is cheaper for the firm? c. Show that the after-tax debt cost of capital is equal to the preferred stock cost of capital multiplied by (1 − τ*). a. Investors receive 6% × (1 – .35) = 3.9% after-tax from risk-free debt. They must earn the same aftertax return from risk-free preferred stock. Therefore, the cost of capital for preferred stock is 3.9% = 4.59% . 1 − 0.15% b. After-tax debt cost of capital = 6% × (1 – .40) = 3.60% is cheaper than the 4.59% cost of capital for preferred stock. c. τ * = 1− (1 − 0.40 )(1 − 0.15 ) 1 − 0.35 = 21.54% 4.59% × (1 – .2154) = 3.60% 15-24. Suppose the tax rate on interest income is 35%, and the average tax rate on capital gains and dividend income is 10%. How high must the marginal corporate tax rate be for debt to offer a tax advantage? τ * = 1− τC > 1− (1 − τ C )(1 − τ e ) 1−τi > 0 if and only if 1 − τ C < 1−τi or equivalently: 1−τ e 1 −τ i 0.65 = 1− = 27.8% . 1 −τ e 0.90 Thus, there is a tax advantage of debt as long as the marginal corporate tax rate is above 27.8%. 15-25. With its current leverage, Impi Corporation will have net income next year of $4.5 million. If Impi’s corporate tax rate is 35% and it pays 8% interest on its debt, how much additional debt can Impi issue this year and still receive the benefit of the interest tax shield next year? Net income of $4.5 million ⇒ 4.5 = $6.923 million in taxable income. 1 − 0.35 Therefore, Arundel can increase its interest expenses by $6.923 million, which corresponds to debt of: 6.923 = $86.5 million. 0.08 10 | P a g e Chapt 16 ter Fina ancial Distre M ess, Manage erial I Incentives, and Inform mation 16-1. Gladstone Cor G rporation is a about to launch a new pro oduct. Depending on the s success of the new e pr roduct, Glads stone may hav one of four values next year: $150 m ve r million, $135 m million, $95 m million, an $80 million These outc nd n. comes are all equally likely and this risk is diversifia y, k able. Gladston will ne no make any payouts to in ot nvestors durin the year. S ng Suppose the r risk-free inter rest rate is 5% and % as ssume perfect capital mark kets. a. . What is the initial value of Gladstone’ equity witho leverage? e ’s out Now N suppose Gladstone has zero-coupon d G debt with a $1 million fac value due n 100 ce next year. b. What is the initial value of Gladstone’ debt? . e ’s c. . What is the yield-to-mat e turity of the de ebt? What is i expected re its eturn? d. What is the initial value of Gladstone’ equity? Wh is Gladston total value with leverag . e ’s hat ne’s ge? a. 0.25 × 150 + 135 + 95 + 80 = $109.52 million 1.05 b. . 0.25 × 100 + 100 + 95 + 80 = $89.28 mill lion 1.05 c. YTM = 10 00 – 1= 12% 89.29 expected re eturn = 5% . d. 16-2. 25 equity = 0.2 × 50 + 35 + 0 + 0 = $20.24 million total v value = 89.28 + +20.24 = $109. million .52 1.05 Baruk Industri has no cash and a debt o B ies h obligation of $ million th is now due The market value $36 hat e. of Baruk’s asse is $81 million, and the fir has no oth liabilities. A f ets rm her Assume perfect capital mar rkets. a. . Suppose Ba aruk has 10 m million shares o outstanding. W What is Baruk current sh k’s hare price? b. How many new shares m . y must Baruk iss to raise th capital need to pay its d sue he ded debt obligation? c. . a. 81 − 36 = $4.5 / share 10 b. . 36 = 8 mil llion shares 4.5 c. 16-3. After repay ying the debt, what will Bar ruk’s share pr be? rice 81 = $4.5 / share 18 When a firm defaults on its debt, debt holders often r W d s receive less th 50% of th amount the are han he ey ow wed. Is the dif fference betwe the amoun debt holder are owed an the amount they receive a cost een nt rs nd t of bankruptcy? f ? 11 | P a g e No. Some of these losses are due to declines in the value of the assets that would have occurred whether or not the firm defaulted. Only the incremental losses that arise from the bankruptcy process are bankruptcy costs. 16-4. Which type of firm is more likely to experience a loss of customers in the event of financial distress: a. Campbell Soup Company or Intuit, Inc. (a maker of accounting software)? b. Allstate Corporation (an insurance company) or Reebok International (a footwear and clothing firm)? a. b. 16-5. Intuit Inc.—its customers will care about their ability to receive upgrades to their software. Allstate Corporation—its customers rely on the firm being able to pay future claims. Which type of asset is more likely to be liquidated for close to its full market value in the event of financial distress: a. An office building or a brand name? b. Product inventory or raw materials? c. a. Office building—there are many alternate users who would be likely to value the property similarly. b. Raw materials—they are easier to reuse. c. 16-6. Patent rights or engineering “know-how”? Patent rights—they would be easier to sell to another firm. Suppose Tefco Corp. has a value of $100 million if it continues to operate, but has outstanding debt of $120 million that is now due. If the firm declares bankruptcy, bankruptcy costs will equal $20 million, and the remaining $80 million will go to creditors. Instead of declaring bankruptcy, management proposes to exchange the firm’s debt for a fraction of its equity in a workout. What is the minimum fraction of the firm’s equity that management would need to offer to creditors for the workout to be successful? Creditors receive 80 million in bankruptcy, so they need to receive at least this much. Therefore, Tefco could offer its creditors 80% of the firm in a workout. 16-7. You have received two job offers. Firm A offers to pay you $85,000 per year for two years. Firm B offers to pay you $90,000 for two years. Both jobs are equivalent. Suppose that firm A’s contract is certain, but that firm B has a 50% chance of going bankrupt at the end of the year. In that event, it will cancel your contract and pay you the lowest amount possible for you to not quit. If you did quit, you expect you could find a new job paying $85,000 per year, but you would be unemployed for 3 months while you search for it. a. Say you took the job at firm B, what is the least firm B can pay you next year in order to match what you would earn if you quit? b. Given your answer to part (b), and assuming your cost of capital is 5%, which offer pays you a higher present value of your expected wage? c. Based on this example, discuss one reason why firms with a higher risk of bankruptcy may need to offer higher wages to attract employees. a. If you quit, you would earn $85k for ¾ of a year, or $63.75k. b. A = 85 + 85/1.05 = $165.95k B = 90 + ½ (90 + 63.75)/1.05 = $163.21 k c. The risk of bankruptcy decreases the expected wage an employee is set to receive, therefore the firm must pay a higher wage to incentivize the employee not to quit 12 | P a g e 16-8. As A in Problem 1, Gladstone Corporation i about to lau is unch a new pr roduct. Depen nding on the su uccess of the new prod f duct, Gladston may have o of four va ne one alues next year $150 million $135 million $95 r: n, n, million, and $8 million. The outcomes are all equally likely, and t m 80 ese y this risk is div versifiable. Su uppose th risk-free in he nterest rate is 5% and that in the event of default, 2 t, 25% of the va alue of Gladstone’s as ssets will be lo to bankrup ost ptcy costs. (Ign nore all other market imper rfections, such as taxes.) h a. . What is the initial value of Gladstone’ equity witho leverage? e ’s out Now N suppose Gladstone has zero-coupon d G debt with a $1 million fac value due n 100 ce next year. b. What is the initial value of Gladstone’ debt? . e ’s c. . What is the yield-to-mat e turity of the de ebt? What is i expected re its eturn? d. What is the initial value of Gladstone’ equity? Wh is Gladston total value with leverag . e ’s hat ne’s ge? Su uppose Gladst tone has 10 m million shares o outstanding an no debt at the start of th year. nd he e. . If Gladston does not iss debt, what is its share price? ne sue t f. If Gladston issues deb of $100 mi ne bt illion due nex year and u xt uses the proce eeds to repur rchase shares, wha will its shar price be? W does your answer differ from that in part (e)? at re Why r r n a. 0.25 × 150 + 135 + 95 + 80 = $109.52 million 1.05 b. . 0.25 × 100 + 100 + 95 × 0.7 + 80 × 0.75 75 = $78.87 millio on 1.05 c. YTM = 10 00 − 1 = 26.79 9% 78.87 expected re eturn = 5% . d. 50 + 35 + 0 + 0 = $20.24 million total v value 1.05 150 + 135 + 95 × 0 + 80 × 0.75 0 0.75 = 0.25 × = $99.11 mill lion 1.05 5 equity = 0.2 × 25 (or 78.87 + 20.24 = $99.11 million) e. 109.52 = $10.95 / share 10 f. 99.11 = $9.91 / share Ban nkruptcy cost lo owers share pr rice. 10 Note that Gladstone will raise $78.87 m t million from the debt, and repur rchase 78.87 96 res = 7.9 million shar . Its equi will be w ity worth $20.24 million, for a share pri r ice of 9.91 20.24 = $9.91 after th transaction is completed. he s 10 − 7.96 16-9. Kohwe Corpor K ration plans t issue equity to raise $50 million to f to y 0 finance a new investment. After w making the inv m vestment, Kohwe expects to earn free cash flows of $10 million each year. K f Kohwe cu urrently has 5 million shar outstandin and it has no other asse or opportu res ng, ets unities. Suppo the ose ap ppropriate discount rate fo Kohwe’s f for future free ca flows is 8% and the o ash %, only capital m market im mperfections are corporate taxes and fina a ancial distress costs. s a. . What is the NPV of Koh e hwe’s investme ent? 13 | P a g e b. What is Kohwe’s share price today? Suppose Kohwe borrows the $50 million instead. The firm will pay interest only on this loan each year, and it will maintain an outstanding balance of $50 million on the loan. Suppose that Kohwe’s corporate tax rate is 40%, and expected free cash flows are still $10 million each year. c. What is Kohwe’s share price today if the investment is financed with debt? Now suppose that with leverage, Kohwe’s expected free cash flows will decline to $9 million per year due to reduced sales and other financial distress costs. Assume that the appropriate discount rate for Kohwe’s future free cash flows is still 8%. d. What is Kohwe’s share price today given the financial distress costs of leverage? a. 10 − 50 = $75 million 0.08 b. 75 = $15 / share 5 c. 75 + 0.4 × 50 = $19 / share 5 d. 16-10. 9 − 50 + 0.4 × 50 0.08 = $16 / share 5 You work for a large car manufacturer that is currently financially healthy. Your manager feels that the firm should take on more debt because it can thereby reduce the expense of car warranties. To quote your manager, “If we go bankrupt, we don’t have to service the warranties. We therefore have lower bankruptcy costs than most corporations, so we should use more debt.” Is he right? No, not necessarily. He has neglected the effect on customers. Customers will be less willing to buy the company’s cars because the warranty is not as solid as the company’s competitors. Since the warranty is presumably offered to entice customers to buy more cars, the overall effect could easily be to reduce value. 16-11. Apple Computer has no debt. As Problem 21 in Chapter 15 makes clear, by issuing debt Apple can generate a very large tax shield potentially worth over $10 billion. Given Apple’s success, one would be hard pressed to argue that Apple’s management are naïve and unaware of this huge potential to create value. A more likely explanation is that issuing debt would entail other costs. What might these costs be? Apple has volatile cash flows, a high beta (around 2), and is a human-capital intensive firm. All of these things imply that Apple has relatively high distress costs. 16-15. Real estate purchases are often financed with at least 80% debt. Most corporations, however, have less than 50% debt financing. Provide an explanation for this difference using the tradeoff theory. According to trade-off theory, tax shield adds value while financial distress costs reduce a firm’s value. The financial distress costs for a real estate investment are likely to be low, because the property can generally be easily resold for its full market value. In contrast, corporations generally face much higher costs of financial distress. As a result, corporations choose to have lower leverage. 16-16. On May 14, 2008, General Motors paid a dividend of $0.25 per share. During the same quarter GM lost a staggering $15.5 billion or $27.33 per share. Seven months later the company asked for billions of dollars of government aid and ultimately declared bankruptcy just over a year later, on June 1, 2009. At that point a share of GM was worth only a little more than a dollar. 14 | P a g e a. If you ignore the possibility of a government bailout, the decision to pay a dividend given how close the company was to financial distress is an example of what kind of cost? b. What would your answer be if GM executives anticipated that there was a possibility of a government bailout should the firm be forced to declare bankruptcy? a. b. 16-17. Agency cost—cashing out By paying a dividend, executives increased the probability of bankruptcy and therefore the probability of receiving government funds. Since these government funds are funds that investors would not otherwise be entitled to, the payment of a dividend could actually raise firm value in this case. Dynron Corporation’s primary business is natural gas transportation using its vast gas pipeline network. Dynron’s assets currently have a market value of $150 million. The firm is exploring the possibility of raising $50 million by selling part of its pipeline network and investing the $50 million in a fiber-optic network to generate revenues by selling high-speed network bandwidth. While this new investment is expected to increase profits, it will also substantially increase Dynron’s risk. If Dynron is levered, would this investment be more or less attractive to equity holders than if Dynron had no debt? If Dynron has no debt or if in all scenarios Dynron can pay the debt in full, equity holders will only consider the project’s NPV in making the decision. If Dynron is heavily leveraged, equity holders will also gain from the increased risk of the new investment. 16-18. Consider a firm whose only asset is a plot of vacant land, and whose only liability is debt of $15 million due in one year. If left vacant, the land will be worth $10 million in one year. Alternatively, the firm can develop the land at an upfront cost of $20 million. The developed land will be worth $35 million in one year. Suppose the risk-free interest rate is 10%, assume all cash flows are risk-free, and assume there are no taxes. a. If the firm chooses not to develop the land, what is the value of the firm’s equity today? What is the value of the debt today? b. What is the NPV of developing the land? c. Suppose the firm raises $20 million from equity holders to develop the land. If the firm develops the land, what is the value of the firm’s equity today? What is the value of the firm’s debt today? d. Given your answer to part (c), would equity holders be willing to provide the $20 million needed to develop the land? a. equity = 0 debt = 10 = $9.09 million 1.1 b. NPV = 25 – 20 = $2.73 million 1.1 c. debt = 15 = $13.64 million 1.1 equity = d. 35 − 15 = $18.18 million 1.1 Equity holders will not be willing to accept the deal, because for them it is a negative NPV investment (18.18 – 20 <0). 15 | P a g e 16-20. Zymase is a biotechnology start-up firm. Researchers at Zymase must choose one of three different research strategies. The payoffs (after-tax) and their likelihood for each strategy are shown below. The risk of each project is diversifiable. a. Which project has the highest expected payoff? b. Suppose Zymase has debt of $40 million due at the time of the project’s payoff. Which project has the highest expected payoff for equity holders? c. Suppose Zymase has debt of $110 million due at the time of the project’s payoff. Which project has the highest expected payoff for equity holders? d. If management chooses the strategy that maximizes the payoff to equity holders, what is the expected agency cost to the firm from having $40 million in debt due? What is the expected agency cost to the firm from having $110 million in debt due? a. E(A) = $75 million E(B) = 0.5 × 140 = $70 million E(C) = 0.1 × 300 + 0.9 × 40 = $66 million Project A has the highest expected payoff. b. E(A) = 75 – 40 = $35 million E(B) = 0.5 × (140 – 40) = $50 million E(C) = 0.1 × (300 –40) + 0.9 × (40 – 40) = $26 million Project B has the highest expected payoff for equity holders. c. E(A) =$0 million E(B) = 0.5 × (140 – 110) = $15 million E(C) = 0.1 × (300 –110) = $19 million Project C has the highest expected payoff for equity holders. d. With $40 million in debt, management will choose project B, which has an expected payoff for the firm that is 75 – 70 = $5 million less than project A. Thus, the expected agency cost is $5 million. With $110 million in debt, management will choose project C, resulting in an expected agency cost of 75 – 66 = $9 million. 16-21. You own your own firm, and you want to raise $30 million to fund an expansion. Currently, you own 100% of the firm’s equity, and the firm has no debt. To raise the $30 million solely through equity, you will need to sell two-thirds of the firm. However, you would prefer to maintain at least a 50% equity stake in the firm to retain control. a. If you borrow $20 million, what fraction of the equity will you need to sell to raise the remaining $10 million? (Assume perfect capital markets.) b. What is the smallest amount you can borrow to raise the $30 million without giving up control? (Assume perfect capital markets.) 16 | P a g e a. Market valu of firm Asse = 30 / (2 / 3 = $45 millio With debt o $20 million, equity is wort 45 – ue ets 3) on. of th 20 = 25, so you will need to sell b. . 16-22. 10 = 40 of the equity. 0% 25 Given debt D, equity is w worth 45 – D. Se elling 50% of e equity, togethe with debt mu raise $30 m er ust million: 5 × ( 45 − D ) + D = 30 . Sol for D = $15 million. lve 5 Empire Industr forecasts net income th coming yea as shown be ries his ar elow (in thousa ands of dollar rs): Approximately $200,000 o Empire’s earnings wil be needed to make n A y of ll d new, positive e-NPV in nvestments. Unfortunately, Empire’s ma U anagers are e expected to w waste 10% of its net incom on f me ne eedless perks, pet projects, and other exp , penditures tha do not cont at tribute to the f firm. All rema aining in ncome will be returned to sh hareholders th hrough divide ends and share repurchases. e . a. . What are the two benefi of debt fina t its ancing for Em mpire? b. By how much would each $1 of interest expense reduce Empire’s di . m ividend and share repurchase es? c. . What is th increase in the total funds Empire w pay to in he n will nvestors for e each $1 of in nterest expense? a. In addition to tax benef of leverag debt financ n fits ge, cing can bene Empire by reducing wa efit y asteful investment. . b. . Net income will fall by $1 × 0.65 = $0.6 e 1 65. Because 10 of net incom will be wasted, dividends and share rep 0% me s purchases will fall by $0.65 × (1 – .10) = $0.58 85. c. 16-24. Pay $1 in in nterest, give up $0.585 in div p vidends and sha repurchases ⇒ Increase o 1 – 0.585 = $ are s of $0.415 per $1 of in nterest. Although the major benefit o debt financ A m of cing is easy to observe—the tax shield—m many of the in ndirect co of debt fin osts nancing can be quite subtle and difficult to observe. De escribe some o these costs. of Overinvestment Investing in negative NPV projects: un O t: n V nderinvestment Not investin in positive NPV t: ng e pr rojects; cashin out: paying out dividends instead of inv ng s vesting in pos sitive NPV pro ojects; employee job se ecurity: highly leveraged fir y rms run the ris of bankrupt and so can sk tcy nnot write lon ng-term employment co ontracts and of job security ffer y. 16-25. If it is manage efficiently, Remel Inc. w have asse with a ma f ed will ets arket value of $50 million, $100 f , million, or $150 million next year, with ea outcome b m t ach being equally likely. Howev managers may y ver, en ngage in wast teful empire b building, whic will reduce the firm’s m ch e market value b $5 million in all by ca ases. Manager may also in rs ncrease the ris of the firm changing the probability of each outco sk m, ome to 50 10%, and 40%, respectively. 0%, d a. . What is the expected val of Remel’s assets if it is run efficiently e lue s y? Su uppose managers will enga in empire building unless that beha age e avior increase the likeliho of es ood ba ankruptcy. Th will choos the risk of th firm to ma hey se he aximize the exp pected payoff to equity hold ders. 17 | P a g e b. Suppose Remel has debt due in one year as shown below. For each case, indicate whether managers will engage in empire building, and whether they will increase risk. What is the expected value of Remel’s assets in each case? i. ii. $49 million iii. $90 million iv. c. $44 million $99 million Suppose the tax savings from the debt, after including investor taxes, is equal to 10% of the expected payoff of the debt. The proceeds from the debt, as well as the value of any tax savings, will be paid out to shareholders immediately as a dividend when the debt is issued. Which debt level in part (b) is optimal for Remel? a. 50 + 100 + 150 = $100 million 3 b. i. Empire building: value = 100 – 5 = $95 million ii. Value = $100 million iii. Empire building and increased risk: value = .5(50) + .1(100) + .4(150) – 5 = $90 million iv. Increased risk: value = $95 million c. Because the tax benefits are paid as a dividend, the manager will empire build or increase risk as determined in part (b). We can therefore determine the expected value with leverage by adding the expected tax benefit to the value calculated in part (b). i. $95 + 10%(44) = $99.4 million ii. $100 + 10%(49) = $104.9 million iii. $90 + 10% ( 0.5 × 45 + 0.5 × 90 ) = $96.75 million iv. $95 + 10%(.5 × 50 + .5 × 99) = $102.45 million Therefore, $49 million in debt is optimal; even though there is a tax benefit, the firm’s optimal leverage is limited due to agency costs. 16-26. Which of the following industries have low optimal debt levels according to the trade-off theory? Which have high optimal levels of debt? a. Tobacco firms b. Accounting firms c. Mature restaurant chains d. Lumber companies e. Cell phone manufacturers a. Tobacco firms high optimal debt level—high free cash flow, low growth opportunities b. Accounting firms low optimal debt level—high distress costs c. Mature restaurant chains high optimal debt level—stable cash flows, low growth, low distress costs d. Lumber companies high optimal debt level—stable cash flows, low growth, low distress costs e. Cell phone manufacturers low optimal debt level—high growth opportunities, high distress costs 18 | P a g e ...
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