Question

Par Value : $1,000

Coupon Rate : 8%

Maturity period : 5 Years

Market Price : 1,110

Instructions: Please using Trial and Error to find the expected rate of return with PVIFA and PVIF Table and the Duration with the following information:

Duration of a zero-coupon bond equals its maturity. It is only for zero-coupon bonds that duration and maturity are equal. Indeed, for any bond that pays some cash flows prior to maturity, its duration will always be less than its maturity.

Duration of a 5 years bond with 8% coupon paid semiannually and 6% yield.

Last Step find the Bond Valuation:

You are considering the purchase of $1,000 face value bond that pay 6% coupon interest per year, with the coupon paid semiannually. The bond matures in 8 years. If the required rate of return on this bond is 4%. what is the market value of the bond.

Answer 1

Duration of a 5 years bond with 8% coupon paid semiannually and 6% yield:

Duration = Summation (n x PVn)/Summation(PVn) = (0.5 x 4/1.03 + 1 x 4/1.03^2 + 1.5 x 4/1.03^3 + 2 x 4/1.03^4 + 2.5 x 4/1.03^5 + 3 x 4/1.03^6 + 3.5 x 4/1.03^7 + 4 x 4/1.03^8 + 4.5 x 4/1.03^9 + 5 x 104/1.03^10)/(4/1.03 + 4/1.03^2 + 4/1.03^3 + 4/1.03^4 + 4/1.03^5 + 4/1.03^6 + 4/1.03^7 + 4/1.03^8 + 4/1.03^9 + 104/1.03^10) = 4.254 years.

Market Value of Bond = 30/1.02 + 30/1.02^2 + ...........+ 1030/1.02^16 = $1135.77.