Question

A corporate bond has 17 years to maturity, a face value of $1,000, a coupon rate of 5.3% and pays interest semiannually. The annual market interest rate for similar bonds is 3.2% and is quoted as a semi-annually compounded simple interest rate, i.e 1.6% per 6-month period.

What is the price of the bond?

Answer 1

The current bond price is computed as shown below:

The coupon payment is computed as follows:

= 5.3% / 2 x $ 1,000 (Since the payments are semi annual, hence divided by 2)

= $ 26.5

YTM is computed as follows:

= 3.2% / 2 (Since the payments are semi annual, hence divided by 2)

= 1.6% or 0.016

N is computed as follows:

= 17 x 2 (Since the payments are semi annual, hence multiplied by 2)

= 34

So, the price of the bond will be computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 26.50 x [ [ (1 - 1 / (1 + 0.016)³⁴ ] / 0.016 ] + $ 1,000 / 1.016³⁴

= $ 26.50 x 26.06708277 + $ 582.9266756

= $ 1,273.70 Approximately