Question

Thomas Foundation 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 a maturity of 1 year.
a. What will be the value of each of these bonds when the going rate of interest is (1) 5%,
(2) 8%, and (3) 12%? Assume that there is only one more interest payment to be made on
Bond S.
b. Why does the longer-term (15-year) bond fluctuate more when interest rates change than
does the shorter-term bond (1-year)?

Answer 1

a. Coupon =100
Par Value =1000
Number of years of maturity =15 (L bond)
Number of years of maturity =1 (S bond)



1.At Interest rate of 5% Bond Price
Price of Bond L =PV of Coupons+PV of Par Value =100*((1-(1+5%)^-15)/5%)+1000/(1+5%)^15=1518.98
Price of Bond S =PV of Coupons+PV of Par Value =100*((1-(1+5%)^-1)/5%)+1000/(1+5%)^1=1047.62

2. At Interest rate of 8% Bond Price
Price of Bond L =PV of Coupons+PV of Par Value =100*((1-(1+8%)^-15)/8%)+1000/(1+8%)^15=1171.19
Price of Bond S =PV of Coupons+PV of Par Value =100*((1-(1+8%)^-1)/8%)+1000/(1+8%)^1=1018.52

3.  At Interest rate of 12% Bond Price
Price of Bond L =PV of Coupons+PV of Par Value =100*((1-(1+12%)^-15)/12%)+1000/(1+12%)^15=863.78
Price of Bond S =PV of Coupons+PV of Par Value =100*((1-(1+12%)^-1)/12%)+1000/(1+12%)^1=982.14

b. Long term bonds fluctuate more than short term bonds because of following reason:
Percentage change in price is dependent on duration of bond. Higher the duration more is the fluctuation. Duration for higher maturity bond is more than duration for lower maturity bond. Hence price fluctuation is more in lower maturity bond.
This relationship is given by following formula
Percentage change in price =-Duration *Change in YTM