The market price of the bond, given a yield-to-maturity of 7.97%, is $1,423.07.
The Breakdown
We have a bond with a par value of $1,000, a coupon rate of 6%, and a yield-to-maturity (YTM) of 7.97%. The bond has a 12-year maturity.
Calculate the present value of the coupon payments:
PV of coupon payments = (Coupon payment) x (Present value factor)
Coupon payment = Par value x Coupon rate = $1,000 x 6% = $60
Present value factor = 1 - (1 + YTM)^(-n) / YTM
n = number of periods = 12
Using the given YTM of 7.97%, we can calculate the present value factor:
Present value factor = 1 - (1 + 0.0797)(-¹²) / 0.0797 ≈ 7.0512
PV of coupon payments = $60 x 7.0512 ≈ $423.07
Step 2: Calculate the present value of the principal payment at maturity:
The principal payment at maturity is the par value of the bond, which is $1,000.
PV of principal payment = $1,000
Step 3: Calculate the market price of the bond:
Market price = PV of coupon payments + PV of principal payment
Market price = $423.07 + $1,000 = $1,423.07
Therefore, the market price of the bond, given a yield-to-maturity of 7.97%, is $1,423.07.
NB: Complete Question
$1,000 par value, 12-year annual bond carries a coupon rate of 6%. Calculate the market price if the yield-to-maturity of this bond is 7.97%.