Question

What is the value of a 5-year, 8.0% coupon rate, $1,000 face value bond with semi-annual coupon payments, if similar bonds (same maturity, same risk profile) are trading at a yield to maturity of 6.25%?

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 8% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 40

The YTM will be as follows:

= 6.25% / 2 (Since the payments are semi annually, hence divided by 2)

= 3.125% or 0.03125

N will be as follows:

= 5 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 10

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

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

= $ 40 x [ [ (1 - 1 / (1 + 0.03125)¹⁰ ] / 0.03125 ] + $ 1,000 / 1.03125¹⁰

= $ 40 x 8.476043766 + $ 735.1236323

= $ 1,074.17 Approximately

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