4. Calculate the market prices of the following multiple-payment bonds:

A. The bond from Question 1.C of Part 1 of this assignment, which returned a payment of $3000 after one year, a payment of $5000 after three years, and a (final) payment of $2000 after five years. The market interest rate is 8.55 percent.

B. 1. A bond that returns a payment of $20,000 after five years and a payment of $75,000 after ten years. The market interest rate is 2.3 percent.

2. Why isnt the price of this bond equal to the sum of the prices of the bonds from Questions 1.A and 1.B? Is it higher, or lower? Why? Explain carefully.

5. A P&I bond with a term of eight years has a face value of $10,000 and returns annual interest payments of $350.

A. What is the coupon interest rate on this bond?

Note: Answer Part B before doing Part C.

B. Suppose the market interest rate at the time the bond is issued is 4.5 percent.

1. Will this bond be sold at a discount or a premium? How do you know?

2. Suppose the issuer of this bond wants it to sell in the market at par.

Would he have to increase or decrease the annual interest payments? By how much? (Be specific.)

C. Calculate the market price of this bond if the market interest rate is 4.5 percent. What is the value of the discount or premium at which it sells?

6. The Indianapolis Colts turn to the free agent market to try to replace a wide receiver who has refused to report to training camp. They find an attractive free agent and sign him to long-term (12-year) contract. The contract has the following provisions:

The player receives a signing bonus of $1,500,000 immediately.

He receives a salary payment of $3,000,000 at the end of each of the next five years.

He receives deferred payments of $500,000 per year for seven years, beginning at the end of the sixth year after he signs the contract.

During a press conference at which the signing is announced, the players agent describes the agreement as a twenty million dollar contract.

A. In what sense is the agents description correct? Explain.

B. 1. In what sense is the agents description incorrect? Explain.

Hint: It may be helpful to answer the next question before you try to answer this one.

Assume, here and below, that the market interest rate is 6 percent. How much would it cost the Colts, in money paid up front, to arrange for a bank to make the various payments, including the signing bonus, required by the contract?

Hints: What is the market price of a bond that returns these payments? What is the present value of a payment received immediately? How can you adapt the annuity formula to cover the case of equal annual payments that begin several years in the future?

3. How much would each of the five annual salary payments have to be increased, leaving the other payments unchanged, so that the present value of the contract would really be $20 million?