B.A. 130 Fall 1996
Midterm 1, Version
A

Part A (20 minutes): Identifications. Write one sentence on each.

1. What is a corporate bond?
2. What is a required rate of return?
3. What is meant by the phrase: "the present value of the firm's growth opportunities"?
4. What is meant by the term "beta"?
5. What is a dividend?
6. What is a certainty-equivalent value?
7. What is a Treasury bill?



Part B (20 minutes): Net Present Values. Show your work.

1. The net present value today at a discount rate of ten percent per year of a security that will pay you $1,100,000 two years from now, and $1,100,000 a year thereafter.
2. The net present value today, at a discount rate of eight percent per year, of a nine-year annuity of $100,000 a year.
5. The approximate present value, at a discount rate of 6% per year, of $100,000,000 payable seventy-two years from now.
6. The approximate present value, at a discount rate of 6% per year, of $200,000,000 payable seventy-two years from now.
2. The net present value today, at a discount rate of ten percent per year, of a security that will pay you $1,650,000 two years from now, and $1,650,000 a year thereafter.
3. The approximate net present value today, at a discount rate of eight percent per year, of a nine-year annuity of $200,000 a year.
4. The net present value today, at a discount rate of 25% per year, of a security that will pay you $1,250,000 two years from now, and $1,250,000 a year thereafter.
5. The net present value, at a discount rate of 10% per year, of a cash flow that is $1,210,000 in year two, $605,000 in year three, and that grows at a rate of 5% per year thereafter.



Part C (20 minutes): Risk, Return, and the Capital Asset Pricing Model. Show your work.

1. Suppose the covariance of the Betatron Company's annual return with the market is .04, and the standard deviation of the market return is 20% per year. Suppose further that half of the market value of the Betatron Company is held in the form of bonds, and half is held in the form of common stocks. What is the beta of the Betatron Company's common stock?
2. Suppose we have two stocks with uncorrelated returns. Suppose further that the standard deviation of each of their annual returns is 20%. What is the standard deviation of the return on a portfolio that puts half of its value into each of these two stocks?
3. Suppose we have a risk-free rate of 5% per year, and a market rate of 10% per year. What is the value of a stock with an expected dividend next year of $5, an expected dividend growth rate thereafter of 2% per year, and a beta of one?
4. Suppose that the risk-free rate is 5% per year, and the market rate is 10% per year. Suppose that we have two stocks with returns that are perfectly negatively correlated. Suppose further that the standard deviation of each of their annual returns is 20%. What is the expected return on a portfolio that puts half of its value into each of these two stocks?
5. Suppose that the risk-free rate is 5% per year, and that we have two stocks with returns that are perfectly positively correlated. Suppose further that the standard deviation of each of their annual returns is 20%. What is the standard deviation of a portfolio that puts half of its value into each of these two stocks?



Part D (20 minutes): Further Topics.

1. Suppose that we have five portfolios:
A client asks if you can construct a portfolio that has an expected return of 7.5% per year and a standard deviation of no more than 17.5% per year. Can you? Explain your reasoning.

A client asks if you can construct--out of A through D alone--a portfolio with a standard deviation of less than 50% per year and an expected return of 20% per year. Can you? Explain your reasoning. Suppose that you also had access to a risk-free asset that paid an expected return of 5% per year. Would it change your answer?