Question

Calculate your answer to at least 2 decimal places. Gibraltar Industries is issuing a bond with a 5.25% coupon rate that matures in 15 years. At a yield to maturity of 5.90%, the price per $100 is closest to: A. $93.65. B. $93.59. C. $106.69.

Note well: unless stated otherwise, we assume bonds pay coupons semi-annually and would therefore make the appropriate adjustments to our calculations

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 5.25% / 2 x $ 100 (As the payments are semi annually, hence divided by 2)

= $ 2.625

The YTM will be as follows:

= 5.90% / 2 (As the payments are semi annually, hence divided by 2)

= 2.95% or 0.0295

N will be as follows:

= 15 x 2 (As the payments are semi annually, hence multiplied by 2)

= 30

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

= $ 2.625 x [ [ (1 - 1 / (1 + 0.0295)³⁰ ] / 0.0295 ] + $ 100 / 1.0295³⁰

= $ 2.625 x 19.72773066 + $ 41.80319456

= $ 93.59

Do ask in case of any doubts.