Question

# Your broker faxed to you the following information about two annual coupon bonds that you are...

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

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%