What are a bond’s key features? What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky? How is the value of any asset whose value is based on expected future cash flows determined?

Bonds and Their Valuation

7-22 Bond valuation

Robert Black and Carol Alvarez are vice presidents of Western Money Management and co-directors of the company’s pension fund management division. A major new client, the California League of Cities, has requested that Western present an investment seminar to the mayors of the represented cities, and Black and Alvarez, who will make the actual presentation, have asked you to help them by answering the following questions.

a. What are a bond’s key features?

b. What are call provisions and sinking fund provisions? Do these provisions make bonds more or less risky?

c. How is the value of any asset whose value is based on expected future cash flows determined?

d. How is a bond’s value determined? What is the value of a 10-year, $1,000 par value bond with a 10 percent annual coupon if its required return is 10 percent?

e. (1) What is the value of a 13 percent coupon bond that is otherwise identical to the bond described in part d? Would we now have a discount or a premium bond?
(2) What is the value of a 7 percent coupon bond with these characteristics? Would we now have a discount or a premium bond?
(3) What would happen to the values of the 7 percent, 10 percent, and 13 percent coupon bonds over time if the required return remained at 10 percent?

[Hint: With a financial calculator, enter PMT, I/YR, FV, and N, and then change (override) N to see what happens to the PV as it approaches maturity.]

f. (1) What is the yield to maturity on a 10-year, 9 percent, annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.20? What does the fact that it sells at a discount or at a premium tell you about the relationship between r d and the coupon rate?
(2) What are the total return, the current yield, and the capital gains yield for the discount bond? (Assume it is held to maturity and the company does not default on it.)

g. What is interest rate (or price) risk? Which has more interest rate risk, an annual payment 1-year bond or a10-year bond? Why?

h. What is reinvestment rate risk? Which has more reinvestment rate risk, a 1-year bond or a 10-year bond?

i. How does the equation for valuing a bond change if semiannual payments are made? Find the value of a 10-year, semiannual payment, 10 percent coupon bond if nominal rd 13 percent.

j. Suppose you could buy, for $1,000, either a 10 percent, 10-year, annual payment bond or a 10 percent, 10-year, semiannual payment bond. They are equally risky. Which would you prefer? If $1,000 is the proper price for the semiannual bond, what is the equilibrium price for the annual payment bond?

k. Suppose a 10-year, 10 percent, semiannual coupon bond with a par value of $1,000 is currently selling for $1,135.90, producing a nominal yield to maturity of 8 percent. However, it can be called after 4 years for $1,050.
(1) What is the bond’s nominal yield to call (YTC)?
(2) If you bought this bond, do you think you would be more likely to earn the YTM or the YTC? Why?

l. Does the yield to maturity represent the promised or expected return on the bond? Explain.

m. These bonds were rated AA by S&P. Would you consider them investment-grade or junk bonds?

n. What factors determine a company’s bond rating?

o. If this firm were to default on the bonds, would the company be immediately liquidated? Would the bondholders be assured of receiving all of their promised payments? Explain.