Question

Calculate the fair present values of the following bonds, all of which pay interest semiannually, have a face value of $1,000, have 10 years remaining to maturity, and have a required rate of return of 10 percent. The coupon rates are 5%, 7%, and 10%.

Answer 1

Fair present value of bond is equal to the present value of all future interest payments and the principal amount discounted at the required rate of return

Bond with Coupon Rate of 5%

Present Value = 25*PVAF(5%, 20 periods) + 1,000*PVF(5%, 20 periods)

= 25*12.462 + 1,000*0.377

= $688.55

Bond with Coupon Rate of 7%

Present Value = 35*PVAF(5%, 20 periods) + 1,000*PVF(5%, 20 periods)

= 35*12.462 + 1,000*0.377

= $813.17

Bond with Coupon Rate of 10%

Present Value = 50*PVAF(5%, 20 periods) + 1,000*PVF(5%, 20 periods)

= 50*12.462 + 1,000*0.377

= $1,000

Note: Since interest is paid semi-annually, interest rates have been halved and periods have been doubled.