Question

Suppose you are considering to purchase a 30-year, semiannual bond with a coupon rate of 10% and a par value of $1,000. If you require a 12 percent nominal yield to maturity on the bond, how much would you be willing to pay for the bond?

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 10% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 50

The YTM will be as follows:

= 12% / 2 (Since the payments are semi annually, hence divided by 2)

= 6% or 0.06

N will be as follows:

= 30 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 60

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

= $ 50 x [ [ (1 - 1 / (1 + 0.06)⁶⁰ ] / 0.06 ] + $ 1,000 / 1.06⁶⁰

= $ 50 x 16.16142771 + $ 30.31433769

= $ 838.39

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