Question

A bond has a 10 percent coupon rate and a $100 face value. Interest is paid semi-annually and the bond has 20 years to maturity. If investors require a 12 percent pa yield, what is the bond's value?

How can I solve this question. Can you please explain the formula for bond's value

Thank you

Answer 1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =20x2

Bond Price =∑ [(10*100/200)/(1 + 12/200)^k]     +   100/(1 + 12/200)^20x2

k=1

Bond Price = 84.95

doubt 1

semi annual coupon = coupon rate*par value/(number of semi annual periods in a year*100)

=10*100/(2*100) = 10*100/200

doubt 2

bond price = coupon*PVIFA+par value/(1+YTM)^n

for semi annual coupon bond

price = semiannual coupon*[(1-(1+(i/2)/100)^(-2*n))/((i/2)/100)]+par value/(1+YTM/2)^(2*n)

where [(1-(1+(i/2)/100)^(-2*n))/((i/2)/100)] = PVIFA factor

plugging in values

price = 5*[(1-(1+(12/2)/100)^(-2*20))/((12/2)/100)]+100/(1+0.12/2)^(2*20)

=84.95