Question

The white sands company has $1,000-par-value bonds outstanding with the following characteristics:

currently selling at par; 5 years until final maturity; and a 9 percent coupon rate (with interest paid semiannually). Interestingly, American Express has a very similar bond issue outstanding. In fact, every bond feature is the same as for the white sands bonds, except that American express bonds mature in exactly 10 year. Now, assume that the market’s nominal annual required rate of return for both bond issues suddenly fell from 9 percent to 8 percent.

Required:

a) At the market’s new, lower required rate of return for these bonds, determine the price for each bond. [10]

b) Also, explain which the bond’s price increased the most, and by how much?

Answer 1

Given:

Duration of White Sands Bond = 5years i.e., 10 payments as coupon payment is semiannual

Duration of American Express Bond = 10 yeras i.e., 20 payments as coupon payment is semiannual

YTM (after fall) = 8% p.a. i.e., 4% semi annually

Coupon Rate of both Bonds = 9% As both bonds are trading at par which means YTM equals coupon rate.

A. Calculation of New Price of the Bond :

• New Price of White Sands Bond = $1040.55
• New Price of American Express Bond = $1067.95

B. Price of American Express bond increases the most i.e., by $67.95 (1067.95-1000) on each bond. This is because American Express Bond has longer maturity as compared to White Sands which results in more number of coupon payments at the same coupon rate and features.