Question

Assume that you wish to buy a bond with 19 years to maturity, with a par value of $1,000, and a coupon rate of 20.02%. Assume semi-annual payments. If the yield to maturity (YTM) is 20.69%, what is today's price of this bond?

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 20.02% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 100.10

The YTM will be as follows:

= 20.69% / 2 (Since the payments are semi annually, hence divided by 2)

= 10.345% or 0.10345

N will be as follows:

= 19 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 38

So, the price of the bond is computed as follows:

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

= $ 100.10 x [ [ (1 - 1 / (1 + 0.10345)³⁸ ] / 0.10345 ] + $ 1,000 / 1.10345³⁸

= $ 100.10 x 9.437065913 + $ 23.73553132

= $ 968.39 Approximately