Question

What is the price of a bond (to the nearest cent) with 22 years to maturity, 5.8% coupon rate, semiannual payments, par of $1000, and the yield to maturity of 4.83%?
   

5 years ago, you paid $1135 for a 8-year, $1,000 par bond with a 5.6% coupon rate and semiannual payments. You are selling the bond today when its yield to maturity is 2%. What is the selling price today, to the nearest $0.01?

Answer 1

Question - 1

Price of the Bond = $1,130.55

Par Value             = $1,000

Coupon Amount = [ $1,000 x 5.80% ] / 2 = $29

Discounting Rate = 4.83% / 2 = 2.415%

Period                   = 22 Years x 2 = 44 Years

Price of the Bond = Present Value of the Coupon Payments + Present Value of the Par Value

= $29 x (PVIF 2.415%, 44 Years) + $1,000 x (PVF 2.415%, 44 Years)

= [ $29 x 26.91729 ] + [ $1,000 x 0.349948 ]

= $780.60 + 349.95

= $1,130.55

Question – 2

Price of the Bond = $1,264.92

Par Value             = $1,000

Coupon Amount = [ $1,000 x 5.60% ] / 2 = $28

Discounting Rate = 2% / 2 = 1%

Period                   = 8 Years x 2 = 16 Years

Price of the Bond = Present Value of the Coupon Payments + Present Value of the Par Value

= $28 x (PVIF 1%, 16 Years) + $1,000 x (PVF 1%, 16 Years)

= [ $28 x 14.71787 ] + [ $1,000 x 0.852821 ]

= $ 412.10 + 852.82

= $1,264.92