# 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

© BrainMass Inc. brainmass.com June 3, 2020, 10:56 pm ad1c9bdddfhttps://brainmass.com/business/bond-valuation/estimating-price-of-a-bond-256727

#### 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.