Question

1. Two $1,000 par value bonds both with 6% coupon rate payable annually are selling at $1,000. Bond A matures in 4 years while bond B matures in 12 years. Find the price of the two bonds if the market interest rate goes up or down by 1 percentage point. Which bond is more sensitive to the change in the prevailing interest rate?

Answer 1

P = C*{1-[(1+r)^(-n)] / r}. +. { F/ [(1+r)^n]}

Where,

P = Price of Bond

C = Coupon payment

r = interest rate

n = No of years

F = Face value

Bond A

Price of Bond A ( P_A ):

C_A = 6% * 1000 = $60

n_A = 4 years

r_A = 6%

P_A = 60* {1-[(1+0.06)^(-4)] / 0.06} + { 1000 / [(1+0.06)^ 4 ]}

P_A = $1000

Bond B

Price of Bond B ( P_B ):

C_B = 6% * 1000 = $60

n_B = 12 years

r_B = 6%

P_B = 60* {1-[(1+0.06)^(-12)] / 0.06} + { 1000 / [(1+0.06)^ 12 ]}

P_B = $1000

If interest rate goes up by 1%

r_A = r_B = 7%

P_A = 70* {1-[(1+0.07)^(-4)] / 0.07} + { 1000 / [(1+0.07)^ 4]}

P_A = $1000

P_B = 70* {1-[(1+0.07)^(-12)] / 0.07} + { 1000 / [(1+0.07)^ 12]}

P_B = $1000

If interest rate goes down by 1%

r_A = r_B = 5%

P_A = 50* {1-[(1+0.05)^(-4)] / 0.05} + { 1000 / [(1+0.05)^ 4]}

P_A = $1000

P_B = 50* {1-[(1+0.05)^(-12)] / 0.05} + { 1000 / [(1+0.05)^ 12]}

P_B = $1000

Long term bond is likely to be affected more due to interest rate changes because of the following reasons:

a. Interest rate are more likely to change in long term than short period of time

b. Investors are more likely to hold the short term bonds till maturity despite of interest rate changes as less coupon payments are remaining. On the other hand investors in long term bond maturity will be more likely to discount the bond for lesser price due to interest rate changes.