Question

Consider the following semi-annual coupon bond: $1,000 par value; 5 years until maturity; 7% coupon rate; YTM of 6%. Calculate the bond’s price today. NOTE: This is a coupon bond.

Please show all work

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:

= 6% / 2 (Since the payments are semi annually, hence divided by 2)

= 3% or 0.03

N will be as follows:

= 5 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 10

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 + 0.03)¹⁰ ] / 0.03 ] + $ 1,000 / 1.03¹⁰

= $ 35 x 8.530202837+ $ 744.0939149

= $ 1,042.65 Approximately

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