Question

Problem Walk-Through

An investor has two bonds in his portfolio that have a face value of $1,000 and pay a 9% annual coupon. Bond L matures in 19 years, while Bond S matures in 1 year.

What will the value of the Bond L be if the going interest rate is 5%, 6%, and 10%? Assume that only one more interest payment is to be made on Bond S at its maturity and that 19 more payments are to be made on Bond L. Round your answers to the nearest cent.

5%.    6%   10%

Bond L $ __ $ __ $ __

Bond S $ __ $ __    $ __

Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?

A)The change in price due to a change in the required rate of return increases as a bond's maturity decreases.

B)Long-term bonds have greater interest rate risk than do short-term bonds.

C)The change in price due to a change in the required rate of return decreases as a bond's maturity increases.

D)Long-term bonds have lower interest rate risk than do short-term bonds.

E)Long-term bonds have lower reinvestment rate risk than do short-term bonds.

Answer 1

Value of bond = (C * ((1-(1+r)^^-n) / r)) + F / (1+r)^ⁿ where

C * ((1-(1+r)^^-n) / r) = value of coupons and

F / (1+r)^ⁿ = present value of face value

C = coupon = 1000 * 9% = 90

R = interest rate = 5%, 6% and 10%

n = number of years = 19 years and 1 year

F = face value = 1000

Value of bond L

at 5% = (90 * ((1-(1+5%)^-19) / 5%)) + 1000 / (1+5%)^19 = 1483.41
at 6% = (90 * ((1-(1+6%)^-19) / 6%)) + 1000 / (1+6%)^19 = 1334.74
at 10% = (90 * ((1-(1+10%)^-19) / 10%)) + 1000 / (1+10%)^19 = 916.35

Value of bond S (since only 1 payment of fave value + coupon is due at the end if 1 year it can be easily discounted with the formula of 1 year)

at 5% = 1090 / (1+5%) = 1038.10
at 6% = 1090 / (1+6%) = 1028.3
at 10% =1090 / (1+10%) = 990.91

Why does the longer-term bond’s price vary more than the price of the shorter-term bond when interest rates change?

Answer : B)Long-term bonds have greater interest rate risk than do short-term bonds

Reason : there are more chance that interest rate rises in future and adversely affect the price of bond.

If interest rate changes in future it will affect long term bond for more years resulting in more variance in prices of long term bonds