A company issues a 10-year bond at par with a coupon rate of 6% paid semi-annually. The YTM at the beginning of the third year of the bond (8 years left to maturity)is 7.8%. What is the new price of the bond?

Question

Quizplus · Accepted Answer

To calculate the new price of the bond, we need to calculate the present value of all future cash flows (coupons and principal) discounted at the YTM of 7.8%. Here are the steps to calculate the new price of the bond:

1. Calculate the present value of the coupon payments remaining over the next 8 years (16 coupon payments in total):
PV of coupon payments = (C / 2) * [(1 - (1 / (1 + r)^n)) / (r / 2)]
where C = coupon payment, r = semi-annual YTM, and n = number of semi-annual periods
PV of coupon payments = (30 / 2) * [(1 - (1 / (1 + 0.039))^16) / (0.039 / 2)]
PV of coupon payments = $525.10

2. Calculate the present value of the principal payment at maturity:
PV of principal = F / (1 + r)^n
where F = face value of the bond, r = semi-annual YTM, and n = number of semi-annual periods
PV of principal = 1,000 / (1 + 0.078)^16
PV of principal = $353.25

3. Add the present value of the coupon payments and principal payment to get the new price of the bond:
New price = PV of coupon payments + PV of principal
New price = $525.10 + $353.25
New price = $878.35

The closest option is B: $894.35, which is the correct answer.

A Company Issues a 10-Year Bond at Par with a Coupon