Question

Calculate the value of a non-callable 10-year bond with a face value of $1,000 and a coupon rate of 9% compounded semi-annually if you expect 7% yield on the bond.

$1,142

$1,212

$1,782

$735

$1,042

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 9% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 45

The YTM will be as follows:

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

= 3.5% or 0.035

N will be as follows:

= 10 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 20

So, the bond price is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 45 x [ [ (1 - 1 / (1 + 0.035)²⁰ ] / 0.035 ] + $ 1,000 / 1.035²⁰

= $ 45 x 14.2124033 + $ 502.5658844

= $ 1,142 Approximately

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