1. Suppose you are the agent for a baseball pitcher. Suppose he is offered the following contract by the New York Yankees: a signing bonus of $5,000,000 (to be received immediately), a first year’s salary of $4,000,000 (to be received one year from today), a second year’s salary of $5,000,000 (to be received two years from today), and a third year’s salary of $8,000,000 (to be received three years from today). Suppose he is also offered the following contract by the San Francisco Giants: a signing bonus of $5,000,000, a first year’s salary of $6,500,000, and a third year’s salary of $6,000,000. If you believe the relevant discount rate is 10%, which offer would you advice the pitcher to accept? Would your advice change if you believed the relevant discount rate were 5%?

2. What is the present value of a bond that pays $340 one year from now and $5340 two years from now at a constant interest rate of 6.8%?

3. If the interest rate is 8%, what is the present value of $5000 payable five years from now?

4. Suppose that you have just bought a four-year, $10,000 coupon bond with a coupon rate of 5% when the market interest rate is 5%. Immediately after you buy the bond, the market interest rate falls to 4%. What happens to the value of the bond?

5. Suppose that in exchange for allowing a road to pass through his farmland, George Pequod has been promised that he and future owners of his land would receive this payment in perpetuity. Now, however, the township has offered, and he has accepted, a one-time payment of $1125, in exchange for his giving up the right to receive the annual $135 payment. What implicit interest rate have George and the township used in arriving at this settlement?

6. Suppose that you are considering the purchase of a coupon bond that has the following future payments: $600 in one year, $600 in two years, $600 in three years, and $600 + $10,000 in four years.

a. What is the bond worth today if the market interest rate is 6%? What is the bond’s current yield?

b. Suppose that you have just purchased the bond, and suddenly the market interest rate falls to 5% for the foreseeable future. What is the bond worth now? What is its current yield now?

c. Suppose that one year has elapsed, you have received the first coupon payment of $600, and the market interest rate is still 5%. How much would another investor be willing to pay for the bond? What was your total return on the bond? If another investor has bought the bond a year ago for the amount you calculated in (b), what would the investor’s total return have been?

d. Suppose that two years have elapsed since you bought the bond, and you have received the first two coupon payments for $600 each. Now suppose that the market interest rate suddenly jumps to 10%. How much would another investor be willing to pay for your bond? What will the bond’s current yield be over the next year? Suppose another investor has bought the bond at the price you calculated in (c). What would that investor’s total return have been over the past year?

7.  If the risk-free rate of return is 3% and if a risky asset is available with a return of 5% and a standard deviation of 4%, what is the maximum rate of return you can achieve if you are willing to accept a standard deviation of 2%?  What percent of your wealth would have to be invested in the risky asset?

8.  What is the price of risk in problem 1?

9.  If an individual stock has a beta of 1.6, the return on the market is 7%, and the risk-free rate of return is 3%, what expected rate of return should this stock offer according to the Capital Asset Pricing Model?