The Desreumaux Company has two bond issues outstanding. Both bonds pay$100 annual interest plus $1,000 at maturity. Bond L has a maturity of 15 years and Bond S has a maturity of one year.

1. What will be the values of these bonds when the going rate of interest is (a) 5 percent, (b) 7 percent, and (c) 11 percent? Assume that there is only one more interest payment to be made on Bond S. (this question is asking for the value of each bond at each of the difference levels of interest rates.i.e. Bond S at 5%, 7%, & 11% and Bond L at 5%, 7%, & 11%).
2. Why does the longer term (15-year) bond fluctuate more when interest rates change than does the shorter term bond (one-year)?

1.

Formula Solutions:

\( Vd = PMT [ \frac{1- \frac{1}{(1+r)^N}}{r}] + \frac{M}{(1+r)^N} \)

5%: Bond L:V_d= $100(10.37966) + $1,000(0.48102) = $1,518.99

Bond S:V_d= ($100 + $1,000)(0.95238) = $1,047.62

7%:Bond L:V_d= $100(9.107914) + $1,000(0.362446) = $1,273.24

Bond S:V_d= ($100 + $1,000)(0.934579) = $1,028.04

11%:Bond L:V_d= $100(7.19087) + $1,000(0.209004) = $928.09

Bond S:V_d= ($100 + $1,000)(0.900901) = $990.99

Calculator solutions:

5%:Bond L:Input N = 15, I/Y= 5, PMT = 100, and FV = 1000; compute PV =-1,518.98

Bond S:Change N = 1; compute PV = -1,047.62

7%:Bond L:Input N = 15, I/Y= 7, PMT = 100, and FV = 1000; compute PV = -1,273.24

Bond S: Change N = 1; compute PV = -1,028.04

11%:Bond L:Input N = 15, I/Y= 11, PMT = 100, and FV = 1000; compute PV = -928.09

Bond S: Change N = 1; compute PV = -990.99

2.Think about a bond that matures in one month. Its present value is influenced primarily by the maturity value, which will be received in only one month. Even if interest rates double, the price of the bond still will be close to $1,000. The value of a one-year bond would fluctuate more than the value of a one-month bond's value because of the difference in the timing of receipts. However, its value would still be fairly close to $1,000 even if interest rates doubled. A longterm bond paying semiannual coupons, on the other hand, will be dominated by distant receipts, receipts that are multiplied by 1/(1 + r_d)^N, and if r_dincreases, these multipliers will decrease significantly. Another way to view this problem is from an opportunity point of view. A one-month bond can be reinvested at the new rate very quickly, and hence the opportunity to invest at this new rate is not lost; however, the long-term bond locks in returns, which could be subnormal, for a long period of time.