Question

On May 30, 2009, Janice Kerr is considering the newly issued 10-year AAA corporate bonds shown in the following exhibit:

Description	Coupon	Price	Callable	Call Price
Sentinal due, May 30, 2019	6.00%	100	Non-callable	NA
Collina due, May 30, 2019	6.20%	100	Currently callabale	102

a. Suppose that market interest rates decline by 100 basis points (i.e., 1%). Contrast the effect of this decline on the price of each bond.

b. Should Kerr prefer the Colina over the Sentinal bond when rates are expected to rise or to fall?

c. What would be the effect, if any, of an increase in the volatility of interest rates on the prices of each bond?

Short answer

a. The Sentinal bond will increase in value to 107.79 while The price of the Colina bond will increase, but only to the call price of 102

b. If rates are expected to fall, the Sentinal bond is more attractive while If rates are expected to rise, Colina is a better investment.

c. An increase in the volatility of rates increases the value of the firm’s option to call back the Colina bond.

Step-by-step solution

Evaluation of the effect of decline

a. The maturity of each bond is 10 years.

Let’s assume that coupons are paid semiannually.

Since both bonds are selling at par value, the current yield to maturity for each bond is equal to its coupon rate.

If the yield declines by 1%, to 5% (2.5% semiannual yield), the Sentinal bond will increase in value to 107.79 [n=20; i = 2.5%; FV = 100; PMT = 3]

The price of the Colina bond will increase, but only to the call price of 102. The present value of scheduled payments is greater than 102, but the call price puts a ceiling on the actual bond price.

Evaluation of preference between Colina and Sentinal bond

b. If rates are expected to fall, the Sentinal bond is more attractive: because

(i) it is not subject to being called,

(ii) its potential capital gains are higher.

On the other hand, If rates are expected to rise, Colina is a better investment because:

(i) Its higher coupon will provide a higher rate of return than the Sentinal bond.

Calculation of effect due to increase in volatility of interest rates

An increase in the volatility of rates increases the value of the firm’s option to call back the Colina bond. This makes the Colina bond less attractive to the investor.