Question

Your broker faxed to you the following information about two annual coupon bonds that you are considering as a potential investment.​ Unfortunately, your fax machine is blurring some of the​ items, and all you can read from the fax on the two different bonds is the​ following:   

Features IBM Coupon Bond AOL Coupon Bond   

Face value $1,000 ​$5,000   

Coupon rate 10.5​% ​?   

Yield to maturity 11.5​% 5.5​%   

Years to maturity 30 25   

Price ​ ? ​ $5,335.35

Answer 1

Let Number of periods = n
Yield I/Y= r
Annual Payment = P
Face Value = FV
Hence, PV = P/(1+r) + P/(1+r)² + .... + P/(1+r)ⁿ + FV/(1+r)ⁿ = P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ

For IBM Bond,
n = 30
r = 11.5%
P = 10.5% of 1000 = $105
FV = 1000
=> PV = P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ = 105[1 - (1+0.115)^-30]/0.115 + 1000/(1+0.115)³⁰ =$916.36

For AOL Bond
n = 25
r = 5.5%
P = ?
FV = 5000
=> PV = 5335.35
PV = P[1 - (1+r)^-n]/r + FV/(1+r)ⁿ
=> 5335.35 = P[1 - (1+0.055)^-25]/0.055 + 5000/(1+0.055)²⁵
=> P = 300
Hence, Coupon Rate = 300/5000 *100% = 6%