Question

PLEASE ANSWER CORRECTLY AND FAST

From the perspective of someone holding a ten-year bond, which would have a higher net present value: a level coupon bond with a face value of $1,000 with a 2% annual coupon rate, or a zero-coupon bond with the same face value? Be sure to explain your answer, and assume coupon payments for the level coupon bond start in Year 1 (the bond is purchased in Year O).

Answer 1

Let’s assume the yield to maturity is 6% for both the bonds.

Compute the annual coupon using the equation as shown below:

Annual coupon = Face Value * Coupon rate

                         = $1,000 * 2%

                          = $20

Hence, the annual coupon is $20.

Compute the PVIFA at 6% and 10 years, using the equation as shown below:

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

                   = {1 – (1 + 6%)^-10}/ 6%

            = 7.360087051

Hence, the PVIFA at 6% and 10 years is7.360087051.

Compute the present value of coupon bond using the equation as shown below:

Present Value = ( Coupon * PVIFA _{Rate, Period}) + Face Value / ( 1 + YTM) ^Period

                       = ( Coupon * PVIFA _{6%, 10}) + Face Value / ( 1 + YTM) ^Period

                       = ($20 * 7.360087051) + $1,000 / ( 1 + 6%) ¹⁰

                       = $705.5965179

Hence, the present value of the coupon bond is $705.5965179.

Compute the present value of the zero-coupon bond using the equation as shown below:

Present Value = Face Value / ( 1 + YTM) ^Period

                       = $1,000 / ( 1 + 6%) ¹⁰

                  = $558.3947769

Hence, the present value of the zero-coupon bond is $558.3947769.

Thus, the net present value of the coupon bond would be higher.