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 how this problem can be solved without a financial calculator.

Answer 1

price of the bond = (present value of annuity factor * interest payment) + (present value factor * face value)

here,

present value of annuity factor = [1-(1+r)^(-n)]/r

here,

r= 10.7% per annum =>5.35% for 6 months ..........(since we have semi annual payments).

n = 20 years. * 2 semi annual periods

=>40.

now,

present value of annuity factor = [1-(1.0535)^(-40)]/0.0535

=>16.367436.

interest payment = $1,000*9.5%*6/12

=>$47.50.

present value factor = 1/ (1+r)^n

=>1/ (1.0535)^40

=>0.12434216.

face value =$1,000.

now

value of the bond = [16.367436*$47.50] + [0.12434216*$1,000]

=>$901.80.