Question

A)

As with most bonds, consider a bond with a face value of $1,000. The bond's maturity is 22 years, the coupon rate is 12% paid annually, and the discount rate is 12%.

What is this bond's coupon payment?

B)

A bond offers a coupon rate of 14%, paid semiannually, and has a maturity of 6 years. Face value is $1,000. If the current market yield is 5%, what should be the price of this bond?

Answer 1

A. The bond's coupon payment is computed as shown below:

= Coupon rate x Face value

= 12% x $ 1,000

= $ 120

B. The price of the bond is computed as shown below:

The coupon payment is computed as follows:

= 14% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 70

The YTM will be as follows:

= 5% / 2 (Since the payments are semi annually, hence divided by 2)

= 2.50% or 0.025

N will be as follows:

= 6 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 12

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

= $ 70 x [ [ (1 - 1 / (1 + 0.025)¹² ] / 0.025 ] + $ 1,000 / 1.025¹²

= $ 70 x 10.2577646 + $ 743.555885

= $ 1,461.60 Approximately

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