Question

Assume that you are considering the purchase of a 20-year, noncallable bond with an annual coupon rate of 9.5%. The bond has a face value of $1,000, and it makes semiannual interest payments. If you require a 10.7% nominal yield to maturity (YTM) on this investment, what is the maximum price you should be willing to pay for the bond?

(Please show work and explain formula of how you got this answer NOT on excel)

Answer 1

what is the maximum price you should be willing to pay for the bond

=(face value of the bond*periodic coupon rate)*((1-(1+(YTM/m))^(-n*m))/(YTM/m))+FV/(1+(YTM/m))^(n*m)

in above we are trying to find the present value of coupon payments in the first part and then the present value of the face value

n is the number of years while m is the number of compounding periods in a year

what is the maximum price you should be willing to pay for the bond

=(face value of the bond*periodic coupon rate)*((1-(1+(YTM/m))^(-n*m))/(YTM/m))+FV/(1+(YTM/m))^(n*m)

=(1000*9.5%/2)*((1-(1+(10.7%/2))^(-20*2))/(10.7%/2))+1000/(1+(10.7%/2))^(20*2)

=901.80

the above is answer..