I. Multiple choice questions: Circle one answer that is the best. (2.5 points each)

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1 I. Multiple choice questions: Circle one answer that is the best. (2.5 points each) 1. An investor discovers that for a certain group of stocks, large positive price changes are always followed by large negative price changes. This finding is a violation of the: A) moderate form of the efficient market hypothesis. B) semi-strong form of the efficient market hypothesis. C) strong form of the efficient market hypothesis. D) weak form of the efficient market hypothesis. E) none of the above. 2. If the weak form of efficient markets holds, then: A) technical analysis is useless. B) stock prices reflect all information contained in past prices. C) stock prices follow a random walk. D) all of the above. E) none of the above. 3. The shareholders of the Unicorn Company need to elect 3 new directors. There are two million shares outstanding. If I have 250,001 shares I can be guaranteed to elect one director if A) The firm has straight voting. B) The firm has cumulative voting. C) Both A) and B). D) Neither A) nor B). I need at least 500,001 shares under cumulative voting. E) Neither A) nor B). I need one million shares under straight voting. 4. A firm has a debt-to-equity ratio of If it had no debt, its cost of equity would be 15%. Its cost of debt is 10%. What is its cost of equity if there are no taxes or other imperfections? A) 21.5%. B) 19.5%. C) 15%. D) 10%. E) None of the above. Answer: A. r_s = r_0 + B/S (r_0 r_b) = (15 10) = Consider two corporations, G and H, that have exactly the same risk. They both have a current stock price of $60. Corporation G pays no dividend and will have a price of $66 one year from now. Corporation H pays dividends and will have a price of $63 one year from now after payment of a dividend. Corporations pay no income taxes. Investors pay no taxes on capital gains, but they pay a 30% income tax on dividends. What is the value of the dividend that investors expect Corporation H to pay? A) $4.29. B) $3.00. C) $3.15. D) $3.30. E) It is impossible to calculate expected dividend without the discount rate. Answer: A. The expected return on both firms will have to same. For firm G, it is 10%. For H, it is, (63-60)/60 + Div. (1-.3)/60. Set it to 10% and we ll have dividend =

2 6. The straight debt of RBC is yielding 6.50% per annum. You find that a debenture maturing on April 26, 2011 of RBC is offering a yield of 8.20% per annum. What can be a possible reason? (A) The debenture is callable. (B) The debenture is backed by assets. (C) The debenture is retractable. (D) The debenture is convertible. Answer: A. C,D all give rise to lower yield than regular bond. B is not right, debenture by definition is not backed by any asset. 7. The Telescoping Tube Company is planning to put a manufacturing facility in place to build observatory quality but recreational scale telescopes. The initial investment cost is $2,000 and the expected year-end EBIT is $500 in perpetuity starting from year 1. Assume the firm is in distress prior to doing the project it has $3,000 in debt liability but its assets, all in the form of fixed assets, are worth only $2,000 and can not be liquidated. The firm s cost of equity is 20%. An all-equity firm which is otherwise identical to The Telescoping Tube would have a cost of equity of 10%. Debt holders are not willing to finance the project; therefore, the project has to be financed by equity only. Will the equityholders of the firm do the project? (A) Yes. Because the project has a positive NPV of $500. (B) Yes. Because the project has a positive NPV of $3,000. (C) Indifferent. Doing the project or not makes the shareholder equally well off. (D) No. Because the firm is in distress and doing the project creates negative $500 NPV net of the wealth transfer to the bondholders. (E) Yes. Because although the firm is in distress, doing the project creates $2,000 NPV net of the wealth transfer to the bondholders. Answer: E. If the project is done, the correct discount rate should be r_0, since the project will be done in an all-equity manner. NPV = 500/.1 2,000 = 3,000. After the project, the wealth transfer to Bondholders is 1000, resulting a net 2,000 increase in wealth to S/H. 8. Today is June 20, Manulife Financial Group (NYSE:MFC) just announced today that it will pay a $0.82 cash dividend per share to shareholders on record as of Aug. 20, 2007 (which is a Monday). There is no holiday in August. Which of the following best describes the stock market reaction? A) Stock price is most likely to decline more than $0.82 on Aug. 20, B) Stock price is most likely to decline less than $0.82 on Aug. 20, C) Stock price is most likely to decline more than $0.82 on Aug. 18, D) Stock price is most likely to decline less than $0.82 on Aug. 18, E) Stock price is most likely to decline more than $0.82 on Aug. 16, F) Stock price is most likely to decline less than $0.82 on Aug. 16, Answer: F. Realizing Aug. 20 is the record date and is a Monday, then the ex-div. date should be Aug. 16. We observe that price fall is usually less than dividend amount. 9. When graphing firm value against debt levels, the debt level that maximizes the value of the firm is the level where: A) the increase in the present value of distress costs from an additional dollar of debt is greater than the increase in the present value of the debt tax shield. B) the increase in the present value of distress costs from an additional dollar of debt is equal to the increase in the present value of the debt tax shield. 2

3 C) the increase in the present value of distress costs from an additional dollar of debt is less than the increase of the present value of the debt tax shield. D) distress costs as well as debt tax shields are zero. E) distress costs as well as debt tax shields are maximized. Answer: B 10. Aspen Ski Resorts, Inc., borrows $50,000 for two years. There is a 90% chance of repayment. There is a 10% chance of bankruptcy, which can happen only at the end of year 1. If bankruptcy occurs, the firm s assets can be sold for $30,000 and the bankruptcy costs are $5,000. Suppose the bank charges interest so to earn an average return of 10% from similar companies. How much interest rate (yield) should the bank charge Aspen Ski Resorts? A) 10%. B) 13.28% C) 16.67%. D) 15.56%. E) Less than 10%. If similar firm: 2 years later, 50000*(1.1)^2 If Aspen: 0.9*[50000*(1+y)^2] + 0.1*[( )*(1.1)] = 45000* (1+y)^2 = 50000*(1.1)^2 0.1* 25000*1.1 y = 13.28% II. Short answer questions 1. You just read this on Reuters news: SAN FRANCISCO - Intel (NSDQ: INTC) posted a 43 percent rise in quarterly profit on strong demand for its microprocessors, and gave a better-than-expected outlook. Its shares rose 5 percent in after-hours trading Tuesday. What does this tell you about market efficiency? (3 points) Any sensible answer will give you 3 points. 3

4 2. Do the following observations appear to indicate market efficiency? Use one sentence to explain why or why not. Your answer should clarify whether the efficiency/inefficiency is weak, semi-strong, or strong. (i) One could make excess returns by buying stocks with high book to market equity ratio and selling stocks with low book to market equity ratio. (2 points) --This is semi-strong form inefficiency since abnormal returns can be made by fundamental analysis. (ii) In any year, approximately 50% of pension funds outperform the market (but the rest does not). (2 points) --This is semi-strong form efficiency. On average, pension fund performances match that of the market; hence 50% outperform the market. 4

5 III. True/False, or uncertain? All marks are based on the quality of your argument. (3 pts) Firms with higher earnings volatility tend to have higher leverage ratio. This is consistent with the pecking order theory. False. First, firms with higher earnings volatility tend to have higher default probability and therefore LOWER leverage ratio. (1.5 pt). Second, this is consistent with the tradeoff theory instead of pecking order theory, because higher default probability is related to the cost of debt (therefore tradeoff b/w benefit and cost). (1.5 pts) IV. Calculations (Show your process to get partial credit). Question 1 (18 points) ABC Inc., is an unlevered firm with expected annual earnings before taxes (EBIT) of $30 million in perpetuity. The required return on the firm s unlevered equity is 15%, and the firm distributes all of its earnings as dividends at the end of each year. ABC has 1 million shares of common stock outstanding and is subject to a corporate tax rate of 30%. The firm is planning a recapitalization under which it will issue $50 million of perpetual debt and use the proceeds to buy back shares. The annual cost of debt is 10%. Assume that there is no issuing cost and that the firm is operating under perfect capital markets but with corporate tax. (a). Calculate the value of ABC before the recapitalization plan is announced. What is the price per share? (3 points) 30(1-.3)/.15 = 140 m(2 pts) 140m/1m = 140 per share (1 pt) (b). Calculate the value of ABC after the recapitalization plan is announced. What is the price per share right after the announcement? (3 points) V_L = V_0 + T_c B = (50) = 155m (2.5 pts) 155m/1m = 155. (.5 pt) (c). How many shares will be repurchased (assume shares are perfectly divisible, i.e. can take fractional shares)? (2 points) 50million/155 = 322, shares Question 1 cont d: 5

6 (d). How will your answer to (c) change if the debt issuing cost is 1% of the $50 million of the amount issued? Note that the tax code says that the debt issuing costs are amortized over the life the debt or 5 years, whichever is less. (6 points) PV(Issuing costs) = -.01 (50) + Tc [.01(50)/5] A.10 5 = *(0.1) *(3.7908) = m (2 points) V_L = V_0 + T_c B + PV(issuing costs) = = (2 pts) Price per share: m/ 1m = $ (.5pt) Net amount borrowed: 50 (.99) (1 pt) Shares repurchased: 50m*(.99)/ = 320, (.5 pt) (e) Continuing with (b), now assume that debt is risky. The yield of the risky debt equals the Treasury bond yield plus a yield spread. The yield spread depends on the firm s credit rating, which in turn is determined by the interest coverage ratio. Also, there is a cost of 25% of firm value in the case the bankruptcy the probability of which also depends on a firm s credit rating. The current Treasury-bond yield is 4%. The bonds are issued at par with annual interest payment. The following is the rating table: If the interest Credit rating Yield Spread Default Probability coverage ratio is + to A 1% 1% 5 to - B 3% 10% What will the new share price be? (4 points) A: The bonds are issued at par with annual interest payment interest rate = yield. (1pt) Suppose the spread is X, Interest coverage ratio (ICR) = 30/ [50(4% + X)] Try X = 1%, we have ICR = 12 > 5 rating of A, spread of 1%, match. (Try X = 3%, we have ICR = 30/[50(7%)] > 5, does not match.) There X = 1%, rating A, and default prob. is 1%. (2 pts) [Note: you might start with different starting point for trial, e.g., start with credit rating.] The new firm value is: (.25)(0.01) = The share price is: /1 = (1pt) 6

7 Question 2 (16 points) BlueJays Inc. has 200,000 shares outstanding. Earnings will be $500,000 at the end of year 1 and $800,000 at the end of year 2. An investment outlay of $200,000 at the end of year 1 (using the earnings of year 1) has already been decided upon. BlueJays is all-equity financed with a required rate of return of 16%. The firm will be liquidated after 2 years. Assume that the firm operates in a world with perfect capital markets without taxes. The firm s policy is to pay out any surplus cash as dividends. (a) What is the current share price of BlueJays stock? (3 points) y1 I1 y2 500, , ,000 V 0 = + = + = $853, (2) r (1 + r) , The share price is then: P 0 = = $ (1) 200,000 (4 decimal places for question d. you can take two decimal place and point out rounding error for question d.) (b) Margaret owns 10% of BlueJays Inc. and wants an income from the firm of $20,000 at the end of year 1. Show how she can achieve this (without a change in the firm s dividend policy). What percentage of the firm will she own after the end of year 1 if she follows this strategy? (5 points) The total dividend paid at the end of year 1 is $300,000. Since Margaret owns 10% of the firm, she receives $30,000. To reduce this to $20,000 she should purchase $10,000 worth of additional shares at the end of year 1. (1) The firm value at the end of year 1 is: y2 800, 000 V 1 = = = $ 689, (1.5) 1 + r This implies a share price of: 689, P 1 = = $3.45 (1.5) 200,000 This means that Margaret should purchase 10,000/3.45= 2,899 more shares. She would then own 22,899 shares or 11.45% of the firm. (1) (c) What does part (b) imply about the relevance of dividend policy? Support your answer with the value of Margaret s holdings before and after her decision. (4 points) It implies that in an MM world with perfect markets and a constant investment policy, dividend policy is irrelevant since investors can use homemade dividends to create any dividend policy that they want. (1.5 pt) Hence they will not attribute any additional value to the firm for changing its dividend policy. Value Before: 0.10 * (200,000) * = $85,316 (0.5 pt) Value after: $20,000/ *(800,000)/(1.16^2) = $85,315.1 (1.5 pt. You may use shares to count the value as well.) 7

8 Question 2 cont d: (d) Now assume that the firm can continue for another 5 years at the end of year 2 but has no more positive NPV projects. There are two types of taxes corporate tax rate at 35% and a universal personal tax rate of 28%. The firm is contemplating about whether to retain the $800,000 year 2 earnings within the firm or to distribute part or all of it to investors at the end of year 2. If the firm keeps the money, it can invest in a puttable preferred stock with an annual yield of 3% and can sell the preferred back at the purchase price any time. The investors can invest the money in the T-bill with an annual yield of 4%. Would investors prefer the firm to retain the earnings or distribute dividend at the end of year 2? What does this imply about the relevance of dividend policy? (4 marks) If firm retains earnings, it earns 3% after-tax (since dividends from corporate investment in preferred stocks are tax-exempt) (1 pt) After tax return of firm: 3% After tax return by investors: 4%(1-.28) = 2.88%, smaller than after-tax return by firm. retain earnings. (2 points) (You can go with a more complicated version, i.e., calculate the future value in 5 years, either with or without reinvestment and arrive at the same conclusion. E.g., future value to investors (with reinvestment) if firm retains earnings is: 800,000*(1+3%) 5 *(1-.28) versus if investors get dividend today, future value of 800,000*(1-.28) [1+ (1-.28)*4%] 5. ) This illustrates that with taxes, dividend policy is relevant ---if firm has greater investment return it should retain the earnings. (1 pt) 8

9 Question 3 (11 points) GrabbaaJava Corp. has established a joint venture with GrabbaCurry to set up cafeterias in Canadian universities. The set-up costs are estimated to be $5 million and will incur at the beginning of the first year. Net revenue collection from the cafeterias is projected to be $1 million per annum for 10 years starting from the end of the first year. The applicable corporate tax rate is 20 percent. The required rate of return for an all-equity firm is 12 percent and the annual cost of debt is 8 percent. The federal government will subsidize the project with a $3 million, 5-year loan at an interest rate of 5 percent a year, applied to the set-up costs. (a) What is the NPV of the project? (6 points) APV = NPV_u + NPV(subsidized loan) NPV_u = -5,000, ,000,000 (1-.20) A = -5,000, ,000* = -479, (2 points) NPV subsidized loan = 3,000,000 3,000,000*0.05*(1-.20) A ,000,000/(1.08) 5 =3,000,000 3,000,000*0.05*(1-.20) ,000,000/(1.08) 5 =479, (3 points fail to use appropriate discount rate, -1 in one occurrence.) APV = = = $ (1 point) (b) There are three approaches to evaluating the NPV of a levered project: APV, FTE or the WACC. You just used one in (a). Could you have used the other two in answering this question? Why or why not? (2 points) You (have to) use APV. You cannot use the FTE or WACC approach because you don t know the debt-equity ratio. Also, these methods require a constant debt-to-equity ratio throughout the life of the project which is not the case here. 9

10 Question 4 (15 points) Timberland Corporation, a furniture manufacturer, is considering installing a milling machine for $40,000 to be used for 2 years. The machine has a CCA rate of 20% and will have an economic residual of 50% after two years. Assume that the asset pool is terminated after two years. Timberland has been financially distressed and thus the company does not expect to get tax shields over the next five years. Canadian Leasing Company, a highly profitable firm, has offered to lease the machine over the next 2 years with a residual guarantee by Timberland of 50%. The corporate tax rate is 35%. The appropriate before-tax interest rate is 6% for both firms. Lease payments occur at the beginning of the year. Also assume that the asset pool is terminated after two years for Canadian Leasing. Bean Counter Inc. is hired to evaluate this leasing. They have determined that the leasing is an operating leasing. They suggest a lease payment of $11,000 a year. Is this lease payment acceptable to Timberland and Canadian Leasing? Please base your analysis using the incremental cashflow approach. Depreciation Schedule: (4 pts) AT cashflow Depreciation.5(40,000)*.2=4,000 (1 pt) (40,000-4,000)*.2 = 7,200 (1pt) UCC 36,000 28,800 Disposal gain/loss =.5(40,000) 28,800 = -8,800 (2 pt) Approach 1: Calculate reservation prices For Canadian Leasing: Lease (1) X(1-.35) X(1-.35) (2) Drepreciation tax 4,000*.35 = 1,400 7,200*.35 = 2520 shield (3) Residual 20,000 (20,000-28,800)*.35 = 23,080 Sell (1) Proceeds 40,000 Incremental cashflow 0.65X-40, X + 1, = 25,600 Discount rate: 6%(1-.35) = Reservation lease payment: 0.65X-40, x/ / ,600/1.039^2 = X =0 -> X = 11, (6 pts) For Timberland: 10

11 AT cashflow Lease -X -X Buy (1) Cost -40,000 (2) Drepreciation tax 0 0 shield (3) Residual 20,000 Incremental cashflow -x+40,000 -X -20,000 Discount rate: 6% Reservation lease payment: -x+40,000 x/ ,000/1.06^2 = 22, X x = 11, (4 pts) Conclusion: 11,000 is acceptable to Timerland (lessee) but not Canadian Leasing (Lessor). (1 pt) Approach 2: Direct NPV analysis: For Canadian Leasing: Lease (1) 11000*(1-.35) 11000*(1-.35) (2) Drepreciation tax 4,000*.35 = 1,400 7,200*.35 = 2520 shield (3) Residual 20,000 (20,000-28,800)*.35 = 23,080 Sell (1) Proceeds 40,000 Incremental cashflow -32, = 25,600 Discount rate: 6%(1-.35) = NPV(lease-sell) = -32, / /(1.039^2) = (6pt) Sell (.5 pt) For Timberland: AT cashflow Lease Buy (1) Cost -40,000 (2) Drepreciation tax 0 0 shield (3) Residual 20,000 Incremental cashflow ,000 Discount rate: 6% NPV(lease-buy) = / /1.06^2 = >0 (4 pt) Lease. (.5 pt) 11

12 Question 5 (8 points) The Appalachian Company expects earnings before interest and taxes (EBIT) of $4 million per year in economic good times and EBIT of $2 million in economic bad times forever. Economic good times and bad times are equally likely. Assume there are no taxes and no financial distress costs. The firm s all-equity discount rate (r 0 ) is 15%. The firm has $10 million debt in its capital structure with an interest rate of 10% per annum. It has 1 million shares outstanding. (a) What is Appalachian s firm value? (3 points) E(EBIT) =.5(2) +.5(4) = $3m, (1pt) V_L = V_0 = $3/.15 = $20m. (2pt) (b) You observe that The Rocky Mountain Company generates exactly the same cashflow as The Appalachian Company. However, Rocky Mountain is an all equity firm. Both firms have 100% dividend payout policy. You notice that Rocky Mountain s firm value is $40 million with 2 million shares outstanding. Assume that you can borrow and lend at the same rate as Appalachian, which is 10%. Is there an arbitrage opportunity? If yes, please design one and show it works. (5 points) V_U > V_L, Buy V_L and sell V_U. ( 1 pt) One arbitrage strategy can be: Buy 50% equity in V_L and Sell 50% of equity in V_U. Payoffs (all units in $millions): (1) Buy 50% equity in V_L. The equity value is $10. costs $5 (2) lend $15 to bank, interest income (3) Sell 50% equity in V_U, proceeds $20 Dividend income, Economic Dividend income, Economic good times bad times.5 (4-1).5 (2-1) ($4) -.5($2) Total 1 1 Initial investment = = 0. End of one year, reverse position in (1) (2) (3) and have 0 liability. Making +$ (1 million) in each state of the world with 0 investment and 0 liability. (No matter what you do, a good answer needs to show: (1) zero initial investment (and hence zero future liability) (2 points), and (2) make + profit in every state of the world. (2 points) A loose statement, gives you 0-3 points, depending on how loose it is.) 12

AFM 371 Practice Problem Set #2 Winter Suggested Solutions

AFM 371 Practice Problem Set #2 Winter 2008 Suggested Solutions 1. Text Problems: 16.2 (a) The debt-equity ratio is the market value of debt divided by the market value of equity. In this case we have