Bond Valuation

Robert Campbell and Carol Morris are senior vice-presidents of the Mutual of Chicago Insurance Company. They are co-directors of the companys pension fund management division, with Campbell having responsibility for fixed income securities (primarily bonds) and Morris being responsible for equity investments. A major new client, the California League of Cities, has requested that Mutual of Chicago present an investment seminar to the mayors of the represented cities. Campbell and Morris, who will make the actual presentation, have asked you to help them by answering the following questions.

a. What are the key features of a bond?

b. How do you determine the value of a bond?

c. What is the value of a 1-year, $1,000 par value bond with a 8% annual coupon if its required rate of return is 11%? What is the value of a similar 10-year bond?

d. (1) What would be the value of the bond described in part (c) if, just after it had been issued, the expected inflation rate rose by three percentage points, causing investors to require a 14% return? Is the security now a discount bond or a premium bond?

(2) What would happen to the bonds value if inflation fell, and r_d declined to 7%? Would it now be a premium bond or a discount bond?

(3) What would happen to the value of the 10-year bond over time if the required rate of return remained at (i) 14% or (ii) remained at 7%?

e. (1) What is the yield to maturity on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does the fact that a bond sells at a discount or at a premium tell you about the relationship between r_d and the bonds coupon rate? Describe what the yield to maturity means from the perspective of the bond buyer.

(2) What is the current yield, the capital gains yield, and the total return in each case in the preceding question?

6. Suppose that the bond described in part (e) is callable in 5 years at a call price equal to $1,090. What is the yield to call (YTC) on the bond if its market value is $887? What is the YTC on the same bond if its current market price is $1,134.20?