Question

Assume that you are considering the purchase of a 14-year, noncallable bond with an annual coupon rate of 7.70%. The bond has a face value of $1000, and it makes semiannual interest payments. If you require an 11.00% yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

Answer 1

Maximum price that should be willing to pay for the Bond = $767

Face Value of the bond = $1,000

Annual Coupon Amount         = [$1,000 x 7.70%] x ½ = $38.50

Yield to Maturity                    = 11% / 2 = 5.50% [Semiannual compounding]

Maturity Period            = 14 Years x 2 = 28 Years [Semiannual compounding]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the Face Value

= $38.50[PVIFA 5.50%, 24 Years] + $1,000[PVIF 5.50%, 28 Years]

= [$38.50 x 14.121422] + [$1,000 x0.2233218]

= $543.68 + 223.32

= $767 [Rounded]