1. Suppose you would like to buy a house and you decided you can pay $5,000 per month for 30 years. Your bank has approved you for a 30-year fixed-rate mortgage loan at a quoted APR (or Annual Percentage Rate) 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.Solar Panel Company, a cash-rich energy firm, is choosing between two mutually exclusive investment projects in solar energy. The first project requires an immediate investment of $15 million, and generates cash flows equal to $0 in year 1, $2.4 million in year 2, $3.9 million in year 3, $5.3 million in year 4 and $20 million in year 5. The second project requires an investment of $10 million, and generates cash flows of $2 million in year 1, $5 million in year 2 and 3, and $3 million in year 4 and 5. The cost of capital for both projects equals 14%. Determine the IRR and the NPV of both investment projects. Which project should the firm undertake? Explain your answer.
3. You are investing in a diversified portfolio of U.S. stocks with an expected rate of return of 17% and standard deviation of 15% per year and a portfolio of corporate bonds with an expected rate of return of 9% and standard deviation of 12% per year. The correlation between the returns on the two portfolios is 0.30. In you invest 40% in stocks and 60% 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 your answers. How would your answers change if you can invest in the risk free asset at a rate of return of 3%?
4. 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 .9.
(ii) Portfolio A has an expected return of 20% with a standard deviation of 30%, while portfolio B has an expected return of 12% 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.
5. 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 a recent year:
AQR Citadel S&P500 T-Bills
Realized Return 18% 11% 9% 3%
Standard Deviation 45% 35% 17% 0%
Beta 2.6 1.5 1 0
Using CAPM as a benchmark against which to evaluate these two hedge funds, which hedge fund had the best performance or alpha?
6. Suppose that among the many stocks in the market, there are two securities, A and B, with the following characteristics: security A has a mean return of 4% and a standard deviation of 10%, and security B has a mean return of 3% and a standard deviation of 5%. 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.
7. Suppose you started a new company which is expected to generate a ROE of 15%. The current book value per share equals $30. The capitalization rate for the firm is 12% and you expect to grow at a constant rate of 4% forever. You are considering a strategy to increase your ROE to 18%, but expect that the focus on profitability will reduce your growth rate to 2% indefinitely. Based on this information, 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? Motivate your answer and show all your calculations.
8. 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 million of dollars) at year-end 5, 10 and 15 years in the future:
Year 5 Year 10 Year 15
Pension Obligations 240 390 570
The interest rate (at all maturities) equals 4%. What is the present value of the liabilities, and what is the McCauley duration? Suppose 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 30-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 in practice? Explain your answer.