# Question: Robert Campbell and Carol Morris are senior vice presidents of

Robert Campbell and Carol Morris are senior vice presidents of the Mutual of Chicago Insurance Company. They are codirectors of the company’s pension fund management division, with Campbell having responsibility for fixed-income securities (primarily bonds) and Morris 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 any asset whose value is based on expected future cash flows?

c. How do you determine the value of a bond? What is the value of a one-year, $1,000 par value bond with a 10 percent annual coupon if its required rate of return is 10 percent? What is the value of a similar 10-year bond?

d. (1) What would be the value of the 10-year bond described in part (c) if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13 percent return? Is the security now a discount bond or a premium bond?

(2) What would happen to the bond’s value if inflation fell and rd declined to 7 percent? 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) 13 percent or (ii) remained at 7 percent?

e. (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 a bond sells at a discount or at a premium tell you about the relationship between rd and the bond’s coupon rate?

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

f. Suppose that the bond described in part (e) is callable in five years at a call price equal to $1,090. What is the 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?

g. What is interest rate price risk? Which bond in part (c) has more interest rate price risk, the one-year bond or the 10-year bond?

h. What is interest reinvestment rate risk? Which bond in part (c) has more interest rate reinvestment rate risk, assuming a 10-year investment horizon?

i. Redo parts (c) and (d), assuming that the bonds have semiannual rather than annual coupons.

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. Both bonds are equally risky. Which would you prefer? If $1,000 is the proper price for the semiannual bond, what is the proper price for the annual payment bond?

k. What is the value of a perpetual bond with an annual coupon of $100 if its required rate of return is 10 percent? 13 percent? 7 percent? Assess the following statement: “Because perpetual bonds match an infinite investment horizon, they have little interest rate price risk.”

a. What are the key features of a bond?

b. How do you determine the value of any asset whose value is based on expected future cash flows?

c. How do you determine the value of a bond? What is the value of a one-year, $1,000 par value bond with a 10 percent annual coupon if its required rate of return is 10 percent? What is the value of a similar 10-year bond?

d. (1) What would be the value of the 10-year bond described in part (c) if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13 percent return? Is the security now a discount bond or a premium bond?

(2) What would happen to the bond’s value if inflation fell and rd declined to 7 percent? 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) 13 percent or (ii) remained at 7 percent?

e. (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 a bond sells at a discount or at a premium tell you about the relationship between rd and the bond’s coupon rate?

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

f. Suppose that the bond described in part (e) is callable in five years at a call price equal to $1,090. What is the 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?

g. What is interest rate price risk? Which bond in part (c) has more interest rate price risk, the one-year bond or the 10-year bond?

h. What is interest reinvestment rate risk? Which bond in part (c) has more interest rate reinvestment rate risk, assuming a 10-year investment horizon?

i. Redo parts (c) and (d), assuming that the bonds have semiannual rather than annual coupons.

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. Both bonds are equally risky. Which would you prefer? If $1,000 is the proper price for the semiannual bond, what is the proper price for the annual payment bond?

k. What is the value of a perpetual bond with an annual coupon of $100 if its required rate of return is 10 percent? 13 percent? 7 percent? Assess the following statement: “Because perpetual bonds match an infinite investment horizon, they have little interest rate price risk.”

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