Question

Bond C has a $1,000 face value and provides an 8% coupon rate for 15 years. The coupons are paid semi-annually. The discount rate is 10% (annual rate). What is the value of the coupon bond?

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

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

= $ 40

The YTM will be as follows:

= 10% / 2 (Because the coupons are semi annually, hence divided by 2)

= 5% or 0.05

N will be as follows:

= 15 x 2 (Because the coupons are semi annually, hence multiplied by 2)

= 30

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

= $ 40 x [ [ (1 - 1 / (1 + 0.05)³⁰ ] / 0.05 ] + $ 1,000 / 1.05³⁰

= $ 40 x 15.37245103 + $ 231.3774487

= $ 614.8980412 + $ 231.3774487

= $ 846.28 Approximately