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# Estimating Price of a Bond

Consider the two bonds described below:
Bond A Bond B
Maturity Years 15 20
Coupon Rate 10 6
(Paid Semiannually)
Par Value 1,000 1,000

a. If both bonds had a required return of 8%, what would the bonds prices be? Show work

b. Describe what it means if a bond sells at a discount, a premium, and at its face amount (par value). Are these two bonds selling at a discount, premium or par?

c. If the required return on the two bonds rose to 10%, what would the bonds' prices be? Show work

#### Solution Preview

Solution:

a. If both bonds had a required return of 8%, what would the bonds prices be? Show work

Bond A
C=coupon payments=(1000*10%)/2=\$50
n=number of coupon payments=15*2=30
Maturity Value =M=\$1000
Required rate of return (semi annual) =r=8%/2=4%

Price of bond =C/r*(1-1/(1+r)^n)+M/(1+r)^n
Price of bond A=50/4%*(1-1/(1+4%)^30)+1000/(1+4%)^30=\$1172.92

Bond B
C=coupon payments=(1000*6%)/2=\$30
n=number of coupon payments=20*2=40
Maturity ...

#### Solution Summary

Solution explains the formula and methodology to estimate price of coupon paying bond at given discount rates.

\$2.19