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 / 1.0375^{40}

= $ 35 x 20.55098999 + $ 229.3378753

**= $ 948.62 Approximately**

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