Question

Consider the following bond issued by Halliburton:

coupon rate: 7.129%

with semi-annual coupon payments Face value: $1,000

Bond matures in 21 years

Suppose, for the sake of argument, that the annual discount rate is 7.958%, with semi-annual compounding. What is the value of the bond?

Answer 1

The value of the bond is computed as shown below:

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

The coupon payment is computed as follows:

= 7.129% / 2 x $ 1,000 (Since the payments are semi annual, hence divided by 2)

= $ 35.645

The discount rate is computed as follows:

= 7.958% / 2 (Since semi annual compounding, hence divided by 2)

= 3.979% or 0.03979

N is computed as follows:

= 21 x 2 (Since the payments are semi annual, hence multiplied by 2)

= 42

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

= $ 35.645 x [ [ (1 - 1 / (1 + 0.03979)⁴² ] / 0.03979 ] + $ 1,000 / 1.03979⁴²

= $ 35.645 x 20.25093679 + $ 194.2152252

= $ 916.06 Approximately

Feel free to ask in case of any query relating to this question