Question

Tracer Manufacturers issued a 10-year bond six years ago. The bond’s maturity value is $1,000, and its coupon interest rate is 6 percent. Interest is paid semiannually. The bond matures in four years. If investors require a return equal to 5 percent to invest in similar bonds, what is the current market value of Tracer’s bond? *SET TO 4 DECIMAL PLACES*

Answer 1

Compute the semi-annual yield, using the equation as shown below:

Semi-annual yield = Annual yield/ 2

                              = 5%/ 2

                              = 2.5%

Hence, the semi-annual yield is 2.5%.

The time left in maturity is 4 years and the compounding are done on a semi-annual basis and thus the number of periods remaining is 8.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)^Number of periods}/ Rate

                   = {1 – (1 + 0.025)^-8 }/ 2.5%

             = 7.17013716733

Hence, the present value annuity factor is 7.17013716733.

Compute the present value factor (PVF), using the equation as shown below:

PVIF = 1/ (1 + Rate)^Number of periods

              = 1/ (1 + 0.025)^8

         = 1/ 1.21840289749

         = 0.82074657082

Hence, the present value factor is 0.82074657082.

Compute the semi-annual interest, using the equation as shown below:

Semi-annual interest = Face value*Coupon rate/2

                                 = $1,000*6%/2

                                = $30

Hence, the semi-annual interest is $30.

Compute the current bond price, using the equation as shown below:

Bond price = (Interest*PVIFA) + (Face value*PVF)

                   = ($30*7.17013716733) + ($1,000*0.82074657082)

                   = $215.104115019 + $820.74657082

                   = $1,035.85068583

Hence, the price of bond is $1,035.85068583.