Question

Nanotech, Inc., has a bond issue maturing in seven years that is paying a coupon rate of 8.87 percent (semiannual payments). Management wants to retire a portion of the issue by buying the securities in the open market. If it can refinance at 7.63 percent, how much will Nanotech pay to buy back its current outstanding bonds? (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25.)

Nanotech will pay $

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 8.87% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 44.35

The YTM will be as follows:

= 7.63% / 2 (Since the payments are semi annually, hence divided by 2)

= 3.815% or 0.03815

N will be as follows:

= 7 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 14

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

= $ 44.35 x [ [ (1 - 1 / (1 + 0.03815)¹⁴ ] / 0.03815 ] + $ 1,000 / 1.03815¹⁴

= $ 44.35 x 10.6933 + $ 592.0501

= $ 474.2479 + $ $ 592.0501

= $ 1,066.30