1. Suppose you would like to buy a house and you decided you can pay 3500 per month for 30 years. Your bank has approved you for a 30-year fixed rate mortgage loan at a quoted APR of 4%, compounded monthly. Based on this information what is the monthly rate that the bank is offering you, and what is the maximum value of the house you can buy if you finance the house entirely with the mortgage?
2. Your are asked to value a small all equity financed startup company that is expected to generate a cash flow of -$50 million next year, and -$20 million in the following year (year 2), before turning profitable in year 3. Its first positive cash flow equals $5 million, and cash flows are expected to grow at a rate of 20% per year for 7 years (until year 10). After this period, the growth rate drops to 5% per year indefinitely. Value the start-up company if the relevant discount rate (or capitalization rate) is 9%.
3. Duane Reade, a pharmacy chain, is evaluating a 5-year pilot project to offer grocery products in some of its locations. The project requires an investment of $50 million, and generates cash flows of $15 million in each of the next 4 years and $30 million in year 5. The cost of capital for the project equals 15%. Should Duane Reade undertake the project? Explain your answer.
4. You are investing in a diversified portfolio of U.S. stocks with an expected rate of return of 12% and standard deviation of 16% per year and a portfolio of corporate bonds with an expected rate of return of 4% and standard deviation of 12% per year. The correlation between the returns on the two portfolios is 0.25. In you invest 20% in stocks and 80% in bonds, what are the expected return and the standard deviation of the combined portfolio? Would any investor prefer an all-bond portfolio over this portfolio in equilibrium? And would any investor prefer an all-stock portfolio? Explain How would your answer change if you can invest in the risk free asset?
5. Consider the following two situations for two investment portfolios, A and B:
(i) Portfolio A and B both have an expected return of 15%, but portfolio A has a beta of 1.2, while portfolio B has a beta of 1.0.
(ii) Portfolio A has an expected return of 20% with a standard deviation of 30%, while portfolio B has an expected return of 15% with a standard deviation of 35%.
In a world in which assets are priced according to the CAPM, could either, both or neither of these situations occur in equilibrium? Explain your answer.
6. The table below presents performance statistics for two famous hedge funds, AQR and Citadel, as well as for the S&P 500 index and T-bills for one of the past years.
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AQR
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Citadel
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S&P 500
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T-bills
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Expected return
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13%
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11%
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8%
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3%
|
|
Standard deviation
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40%
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24%
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13%
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1%
|
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Beta
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2
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1.5
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0
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|
|
|
|
|
|
Using CAPM as a benchmark against which to evaluate these two hedge funds, which hedge fund had the best performance or alpha?
7. Suppose that among the many stock in the market, there are two securities, A and B, with the following characteristics: security A has a mean return of 8% and a standard deviation of 40%, and security B has a mean return of 13% and a standard deviation of 60%. If the correlation between the return on A and B equals -1, how can we create a zero-risk portfolio, and what would be the resulting equilibrium risk free rate in the market? Motivate your approach and show your calculations.
8. A U.K. firm expects to pay a dividend of 3.7 pounds next year (paid annually) and expects the dividend to grow at a constant rate in the future. The firm's beta equals 0.90. The risk free rate is 3%, and the expected return on the market index is 8%. Investors use the CAPM to compute the required return on the firm's stock and the Dividend Discount Model to determine its intrinsic value. If the stock is trading the market at 82 pounds, what are the market's expectations with respect to the firm's growth?
9. Suppose you started a new company which is expected to generate a ROE of 15%. The current book value per share equals $50. The capitalization rate for the firm is 12% and you expect to grow at a constant rate of 9% forever. You are considering a strategy to increase your ROE to 20%, but expect that the focus on profitability will reduce your growth rate to 5% indefinitely. Using the Gordon Growth Model, determine the intrinsic value per share under the new strategy. Are you better off with a focus on growth or with a focus on ROE? Explain your answer.
10. Suppose you are an equity analyst following Google, and want to calculate the intrinsic value of the stock. You have determined that t Google's earnings for 2011 were $16 per share, and expect the earnings to grow at a rate of 30% in the next 5 years. During this period, Google is not expected to pay any dividends. You furthermore project that after 2015, Google will mature and will maintain a constant growth of 5% per year forever. The corresponding retention ratio would be 50%. The capitalization rate for Google is 13%. Based on this information, determine the value of a Google share. Which part of the value of the stock is due to growth? Explain your answer.
11. Suppose you bought a bond with coupon rate of 6% (paid annually), a par value of $1,000 and a remaining maturity of 5 years on January 1, 2011. The yield to maturity at the time of purchase was 55. If you sold the bond immediately after receiving the first coupon payment on January 1, 2012 and the yield to maturity was 3% at that time, what was your holding period return on the bond?
12. Suppose you are the CFO of a large pension fund in charge of interest rate management. The following table shows all payments you expect to make to retirees (in millions of dollars) in the next three years:
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Year 1
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Year 2
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Year 3
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Payments
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16
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13
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25
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The interest rate (at all maturities) equals 6%. What is the present value of the liabilities, and what is the McCauley duration? The fund currently holds an amount of cash equal to the present value of the liabilities. If you can buy a portfolio of 1-year zero coupon bonds and 10-year zero coupon bonds, what could you do to immunize the pension fund against changes in the interest rate and what are the benefits and drawbacks of this approach? Explain your answer.
13. Without performing any calculations, indicate which of the following four bonds will be the most sensitive to interest rate changes. Explain your answer intuitively.
(i) A 15-year bond with a 10% coupon.
(ii) A 20-year bond with a 9% coupon.
(iii) A 20-year bond with a 7% coupon.
(iv) A 10 year zero-coupon bond.
14. Suppose you have a negative view on a certain stock and would like to sell it short. However, since you are an individual investor with a relatively small portfolio, no securities firm is willing to let you engage in short selling. But your broker agrees to let you trade options. How could you construct an investment position involving a put and a call on this stock along with either (risk free) borrowing or lending that would produce the same outcome as if you had sold the stock short? Explain your answer.
15. Suppose you are a portfolio manager considering to execute a covered call strategy on LinkedIn stock by selling 1 year call options with an exercise price of $75. You own 500 shares of LinkedIn stock which currently trades at $70 per share. The risk free rate is 3% and the volatility of the returns on the stock equals 30%. You expect the stock price to either go up or down by $20 in the next year. Using the Binomial option pricing approach, what is the total premium you expect to collect from selling the call options? If you expect that the volatility of the stock will be lower, what could you do to increase the premium from this strategy? Motivate your approach and show your calculations.