Question

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.(a) 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?
(b) 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?
(c) 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?

Answer 1

Bonds are investment instruments with a face value, coupon rate, and maturity date, and their present value is calculated by discounting future cash flows. Changing market interest rates and inflation can make a bond trade at a premium or discount. The bond's future value will fluctuate based on the consistent required rate of return over time.

Step-by-step explanation:

Key Features of a Bond

The key features of a bond include its face value (or principal), which is the amount to be paid back at maturity, the coupon rate (or interest rate) which determines periodic interest payments, and the maturity date when the bond will be redeemed. The present value of a bond is calculated considering these features, plus market interest rates, and represents the most an investor would be willing to pay for the bond.

Determining the Value of an Asset

To determine the value of any asset based on expected future cash flows, one would discount these cash flows back to their present value using a discount rate that reflects the riskiness of the investment and other factors such as inflation.

Calculating Bond Value

The value of a bond can be determined by discounting its future cash flows, which include periodic interest payments and the principal amount at maturity, to their present value at the required rate of return. A one-year, $1,000 face value bond with a 10% annual coupon and a required return of 10% would be worth $1,000. The same applies to a similar 10-year bond, but if inflation or required returns change, the present value of this bond will fluctuate as well.

Impact of Changing Inflation and Required Returns

If the expected inflation rate goes up by 3 percentage points and investors require a 13% return, the value of a 10-year bond will decrease. This would make it a discount bond as it will trade below its face value. Conversely, if inflation falls and the required return drops to 7%, the bond's value would increase, making it a premium bond since it will trade above face value. If the required rate of return remains at 13%, the bond's value is likely to stay lower over time, whereas if it remains at 7%, the bond's value would be higher.