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연세대학교 경영학과 재무관리 기말고사 SOLUTIONS Part 1: Short Answer 1. (5 points) If it is the case that the market places the same value on a dollar of dividends as on a dollar of capital gains, then firms with different dividend payout ratios will appeal to different clienteles of investors. However, one clientele is as good as any other: a firm can not increase its value by changing dividend policies. Yet we see strong correlations between payout ratios and other characteristics of firms. For instance, small rapidly growing firms that have just gone public almost always have dividend payout ratios of zero. All earnings are reinvested in the business. How would you explain this if dividend policy was irrelevant? Answer: Investors value a dollar of dividends = a dollar of capital gains, but if a growing firm pays out dividends then it would need to return to the capital markets to obtain additional funds, incurring transaction costs, thus growing firms retain their earnings. 2. (5 points) Last month, Durham Pulp and Paper, which had been having trouble with its cost overruns at its timberfarm in Bahama, announced that it would be temporarily suspending its dividend payments due to cash flow crunch associated with its investment program. The company’s stock price dropped 10% on the news. How would you interpret this change in the stock price? I.e what caused it? Answer: the announcement must have contained some information that was not already in the market. Perhaps the cash flow problems were worse than expected. 3. (5 points) Smith-Corona typewriter, Inc. has common stock, bonds, and bank loans in its capital structure. The bank loans are secured by the company’s industrial plant. Its bonds are currently selling at a discount and offer a rate of return appropriate to a BBB rated bond. They have been incurring losses lately, and they do not have sufficient cash flow to pay for the the new backspace eraser ribbon technology that they have ordered for their new line of typewriters. They may be able to get some bank financing for some of it, but need some long term financing, either by issuing some new common stock or by issuing some additional bonds. They have accumulated so many losses in recent years, and have so many tax loss carryforwards that , even if they start to make a profit they will be in the zero percent tax bracket for years to come. Their investment banker has advised them that given their losses there is no tax advantage to debt. He has also stated that, even though the new ribbon technology may be a positive NPV investment, the current shareholders might be made worse off if they go ahead and finance through an equity offering. How could it be the case that, even though the project has a positive NPV, financing it through an equity offering could make the current equity holders worse off? Answer: The new equity does increase the value of the firm, but much of that increase goes to the bond holders, not the equity holders. Now the equity is diluted with the new shareholders getting a pro rata share of the equity. The new equity holders pay only what their stake is worth, so any transfer to the bondholders comes at the expense of the old shareholders. 4. (5 points) You are considering two movie proposals from two writers. The first movie involves couple who meet on a plane, fall in love, and then the plane explodes and they die. The second movie involves a guy on a plane that is hijacked and the guy kills the terrorist and safely lands the plane. The first movie will cost you $100 m to make today and is expected to have the following payoffs in one years time: Probability 50% blockbuster 25% sleeper 25% dud payoff 250m 50m 10m The second movie also costs $100 is expected to have the following payoffs: 35% 50% 15% a. blockbuster 250m modest success 50m straight to video 10m your discount rate is 15%. Which is the better movie? How much would you be willing to pay for the rights to each script? Assume zero discount rate Answer: Sad movie: E (value) = 0.50*250 + 0.25*50 + 0.25 * 10 = 140 –100 = 40 Dopey movie: E (value) = 0.35*250 * 0.5*50 +0.15*10 = 114-100=14 b. Your assistant, Irving, points out that maybe the second movie is worth more than it appears because it could create a franchise i.e. allow for a sequel. If the movie is a blockbuster, we can invest $50m in a schlockola sequel on a boat at t=1 (one year from now) and get payoffs that will look like this at t=2 (two years from now). Assume zero discount rate. 35% blockbuster 250m 50% modest success 50 m 15% Bad News Bears III 0 The writers for the second movie have said that we can have the sequel rights with the script. Now how much are we willing to pay? Use Expected value calculation. Answer: Dopey movie now worth more now: Value of call = 0.35 [ (0.35*250 + 0.50*50 + 0.15 *0) – 50] = 21.875 Still not worth as much as the doomed love movie. Part 2: Short problems 1. (10 points) A local real estate broker has approached you with a proposal. There is an old lady who currently owns a plot of land near where a bank might be built next year. If the bank is built, her plot will be worth $305, but if it is not built, the plot will be worth only $55 six months from now. Everyone agrees that the land is worth $100 now. But your buddy has created a corporation which has obtained an exclusive option to purchase the land from the lady six months from now for $205. This corporation was financed by debt which has a face value of 50 due six months from now. The option is the corporations only asset. He wants to sell you half of the corporation’s equity. How much would you be willing to pay? Risk free rate is 10%. Answer: value of land: 305 Value of call option: 100 100 55 0 To get value of call find hybrid position w/ comparable payoff: Borrow 50 and buy the land and you get: 250 50 so the option must be worth 20 0 The payoff to the bond holders is identical to the payoff to the equity holders, namely: 50 so they must both be worth 10. Half the equity is worth 5. 0 2. (10 points) There are two stocks in the market, Cemex and Pemex. The following data is given: P0 (cemex) today = $50 The P1 (cemex) tomorrow will be $40 if the economy is in a recession next year $55 if the economy is normal next year $60 if the economy is booming next year The probablities of recesssion, normalcy, and boom are 0.1, 0.8, and 0.1 respectively. (rm) = std. Deviation of the market portfolio = 0.10 E ( r p) = expected return on Pemex = 9% (r p ) = std. Dev. Of Pemex returns= 12% The correlation of Cemex and the market, cm = 0.8 The correlation of Pemex and the market, pm = 0.2 The correlation of Cemex and Pemex, cp = 0.6 a. If you are a typical risk averse investor, which stock would you prefer, if any? Why ? Answer: Hard to tell. Cemex gives you rc = 8% with a = 9.8%, while Pemex gives you rp = 9% with a = 12%. b. What is the expected return and standard deviation of a portfolio consisting of 70% Cemex and 30% Pemex? Answer: E ( r ) = 8.3% = 9.47% from 2 = wc2*2 + wp2*p2 + 2*wc*wp*c*p*cp = (0.7)2 * (0.098)2 + 0.09*(0.12)2 + 2*(0.7)*(0.3)*(0.898)*(0.12)*(0.6) = 0.008962 c. What is the Beta of the portfolio in b above? Answer: Bc = cm/2m = cm*c*m/m2 = (0.8)(9.8)(0.10)/(0.10)2 = 0.784 Bp = pm/2m = pm*p*m/m2 = (0.2)(9.8)(0.10)/(0.10)2 = 0.240 B (portfolio) = 0.7*(0.784) + 0.3 * (0.240) = 0.6208 3. (10 points) There are 4 groups of investors with the following wealth and tax rates on interest income in Sport-land. Group Tax rate Basketball players Football players Figure skaters Curlers 50 40 20 0 Total wealth 450 1200 200 800 Amount in stock Amount in bonds 200 1200 0 0 0 0 200 800 Amount in foreign real estate 250 0 0 0 Corporate bonds and common stock are the only financial assets in the economy. Income from stock is taxfree for all investors. The corporate income tax rate is 40 percent. Corporations as a group have annual cash flow of $200 m. before interest and taxes. There are no investment tax credits, tax loss carryforwards or institutional arrangements allowing investors to shelter income in Sportland. All investors can earn a tax free return of 5% by investing in Caribbean real estate. (assume that neither bonds nor stock nor foreign real estate has any systematic risk, and that investors simply prefer the investment with the highest after tax return and prefer domestic to foreign all else equal and will prefer stocks to bonds all else equal. The interest rate on corporate bonds is_____8.33_________ percent The total value of corporate securities is ___2400_________ million The total corporate tax bill is ___46 2/3_____________million per year. Given your answer to the above questions, could an individual firm change its value by making a small change to its d/e ratio, assuming that it can make use of its incremental interest deductions? No Answer: first you realize that rd (1-Tc) = re re = 0.05 tc=0.40 This implies that r=8.33 = 0.05/0.6 X = interest payments x/0.08333 = D since D = 83.33/0.0833 = 1000 x = 83 1/3 (200 –x)(1-TC)/ 0.05 = E = 116.67 (0.6)/0.05 = 1400 D + E = 2400 4. (10 points) You have identified three potential investments with the following characteristics: Investment Expected return Beta Unique risk Bill Gates IOUs IBM stock Microsoft stock 10% 14% 20% None None None 0.0 1.0 1.6 Is there an arbitrage opportunity? yes How could you earn profits on a zero investment, zero risk portfolio? In other words, if Xa, Xb, and Xc represent asset weights on your portfolio, with Xa +Xb+Xc =0, in what security or securities would you hold a short position? Answer: go short ibm Assuming that you invest $1 in microsoft how much money would you put in the other investments? Answer: Bill Gates 0.60 IBM -1.60 MSFT 1.00 How is equilibrium restored in the market if the above investments were available? Answer: Arbitrage drives down the price of IBM and bids up the others until their expected returns are on the SML 5. (10 points) You are Special.com is considering a $2m investment in a web page that generates messages of self affirmation. This project is expected to generate cash flows of $600,000 a year at the end of the each of the next six years, with the first positive cash flow received exactly one year after the investment is made. Rates of return on investments of similar risk are 12%. The NPV of this project is: Answer: -2m + A (t=6, r=.12 C=600,000) = 466,844 YAS will finance this project entirely by the sale of stock. The costs of floating stock include a fixed cost of $50,000 plus 5% of the gross proceeds. What value of stock must YAS sell in order to net $2,000,000? Answer: 2m = 0.95 x – 50,000 X = 2,157,895 What is the APV of the project? (there are no taxes) Answer: 466,844 – 157,895 = 308,949 6. (10 points) Instalid is a corporation with profitable ongoing operations. They have asked you to evaluate their proposed project for the production of injection molded plastic turbans. Calculate the NPV of this project at a 5% real discount rate. Show your cash flow computations. Physical production Plastic input, in pounds Energy input, in Mw Year 1 100 cases Year 2 200 cases Year 3 200 cases Year 4 150 cases 2000 2000 2000 2000 200 200 200 200 The required investment on January 1, 2000 is $40,000. The firm faces a 40% tax rate, and uses straight line depreciation. The salvage value of the investment will be zero. Plastic costs will be $12/pound at the start of year 2000 and will increase at 2% a year in real terms. The price of the Instalids will be $300/case and will stay constant in real terms. Energy costs will be $5/Mw in January of 2000 and will increase at 5% /year in real terms. The inflation rate is 10%. Reveneue is received and costs are paid at years end. After tax cash flows: 1.1.2000 Answer: (real terms) -40,000 1.1.2001 1.1.2002 1.1.2003 1.1.2004 + 6318 + 23,662 +23,029 +13,416 The NPV is 18,409 Answer: in real terms 1.1.00 Investment Revenue Real Depn Plastic Energy Taxable income Taxes Ncf Pv real 1.1.01 1.1.02 1.1.03 1.1.04 0 30,000 9091 24,480 1050 -4621 60,000 8264 24,970 1102 25,664 60,000 7513 25,469 1158 25,860 45,000 6830 25,978 1216 10,976 -40,000 -40,000 -1848 6318 6017 10,266 23,662 21,462 10,344 23,029 19,893 4390 13,416 11,037 -40,000 7. (10 points) Triangle Trinkets manufactures styrofoam beer can coolers with the insignia of two local ACC schools: Tar Heels and Blue Devils. The Tar Heel division’s customers are primarily casual fans and erratic drinkers and are somewhat sensitive to the business cycle; the tar heel division’s beta is 1.0. The Blue Devil division’s customers are more loyal and so this division’s beta is only 0.5. The Tar Heel Division’s expected net cash flow is currently $200,000 per year, and is expected to grow at 3% per year in real terms. The Blue Devil division’s expected net cash flow is $90,000 per year, and its real growth rate is 4% per year in real terms. TT has no other growth opportunities, it is an all equity firm, there is no inflation, the real risk free rate of interest is 3%, and the risk premium on the market is 8%. TT has annual overhead expenses, which are not allocated to either division, of $45,000 per year, and these are expected to remain constant in real terms. Furthermore, the overhead expenses have no systematic risk. Assume that all cash flows occur at year end. Analyze TT as a combination of “pure plays” i.e the firm is a combination of its divisions. All of the above expenses and net cash flows are net of taxes. What is the Beta of the company? Answer: PV (tar heels) = 200,000/ 0.11 – 0.03 = 2,500,000 Pv (blue devils) = 90,000/0.07-0.04 = 3,000,000 PV (overhead) = -45,000/0.03 = -1.5m PV (entire co.) = 4,000,000 B (company) = B (tar heels) * PV(tar heels)/PV (co.) + B(blue devils) * PV (Blue devils)/PV (co.) = 1.0 * (2.5/4.0) + 0.5 (3.0/4.0) = 1.0 What is the market value of the company? Answer: PV (co) = 4m. 8. (10 points) Because of the large cash inflows from sales of Brealey and Myers Principles of Corporate Finance, the McGRaw Hill corporation has decided to retire all of its outstanding debt and become an allequity corporation. The debt is “permanent” debt, i.e. the maturity date is indefinitiely far away, and it is considered risk free. The debt has a book value of $3,000,000 and it has a 10% coupon rate. However since market interest rates on long term bonds increased to 15%, the market value of the bonds is only $2,000,000. All of the debt is held by a single institution, which would be willing to sell it back to McGraw Hill for $2m. in cash, with no transaction costs. (assume no tax consequences as well). If McGraw Hill did not retire it, it would use the $2,000,000 in cash to buy back some of its stock on the open market, also with no transaction costs. Investors expect McGraw Hill to buy back some of their stock and thus will be completely surprised when the debt retirement plan is announced. Furthermore, when McGraw Hill becomes all equity, it plans to remain unlevered forever. The required rate of return of the equity holders after M-H becomes all equity is 20% in real terms. The expected annual income before interest and taxes for the firm is $1,100,000 and is expected to remain constant. The NPV of growth opportunities is zero, and the company is subject to a 50% tax rate. Assume that the M&M propositions with taxes hold, and that there is no inflation. a. What was the market value of the company before the debt repurchase was announced? Answer: $3,750,000 2,000,000 in debt 1,750,000 in equity b. Value = all equity firm + Tc*D By how much does the required rate of return of equity holders change? Answer: 2.67% Re = $400,000/1,750,000 = 22 6/7% $400,000 = ($1,100,000 - $300,000) (1-Tc)