Question

J&J Manufacturing just issued a bond with a $1,000 face value and a coupon rate of 7%. If the bond has

a life of 20 years, pays semi-annual coupons, and the yield to maturity is 7.5%, what is the value

of the bond? (948.62)

Answer provided. Please explain and how to do it.

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 7% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 35

The YTM will be as follows:

= 7.5% / 2 (Since the payments are semi annually, hence divided by 2)

= 3.75% or 0.0375

N will be as follows:

= 20 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 40

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

= $ 35 x [ [ (1 - 1 / (1 + 0.0375)⁴⁰ ] / 0.0375 ] + $ 1,000 / 1.0375⁴⁰

= $ 35 x 20.55098999 + $ 229.3378753

= $ 948.62 Approximately