Question

Zero-coupon bond. Addison Company will issue a zero-coupon bond this coming month. The bond's projected yield is 8%. If the par value is $5,000, what is the bond's price using a semiannual convention if a. the maturity is 10 years? b. the maturity is 35 years? c. the maturity is 70 years? d. the maturity is 100 years?

Answer 1

The annual rate of interest is 8%, after dividing the annual rate with 2 the semi-annual interest rate comes out to be 4%.

(a)

Compute the PVIF at 4% and 20 half-years, using the equation as shown below:

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

              = 1/ (1 + 0.04)²⁰

         = 1/ 2.19112314293

         = 0.45638694612

Hence, the PVIF at 4% and 20 half-years is 0.45638694612.

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

Bond price = Face value*PVIF_{4%, 20}

                   = $5,000*0.45638694612

                   = $2,281.9347306

Hence, the price of the bond is $2,281.9347306.

(b)

Compute the PVIF at 4% and 70 half-years, using the equation as shown below:

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

              = 1/ (1 + 0.04)⁷⁰

         = 1/ 15.5716183484

         = 0.06421940069

Hence, the PVIF at 4% and 70 half-years is 0.06421940069.

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

Bond price = Face value*PVIF_{4%, 70}

                   = $5,000*0.06421940069

                 = $321.09700345

Hence, the price of the bond is $321.09700345.

(c)

Compute the PVIF at 4% and 140 half-years, using the equation as shown below:

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

              = 1/ (1 + 0.04)¹⁴⁰

         = 1/ 242.475298046

         = 0.00412413144

Hence, the PVIF at 4% and 140 half-years is 0.00412413144.

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

Bond price = Face value*PVIF_{4%, 140}

                   = $5,000*0.00412413144

                 = $20.6206572

Hence, the price of the bond is $20.6206572.

(d)

Compute the PVIF at 4% and 200 half-years, using the equation as shown below:

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

              = 1/ (1 + 0.04)²⁰⁰

         = 1/ 2550.749791096

         = 0.00412413144

Hence, the PVIF at 4% and 200 half-years is 0.00039204159.

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

Bond price = Face value*PVIF_{4%, 200}

                   = $5,000*0.00039204159

                 = $1.96020795

Hence, the price of the bond is $1.96020795.