Question

Crane, Inc., has a bond issue maturing in seven years that is paying a coupon rate of 9.5 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 8.0 percent, how much will Crane pay to buy back its current outstanding bonds?

Answer 1

The amount is computed as shown below:

The coupon payment is computed as follows:

= 9.5% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 47.50

The YTM will be as follows:

= 8% / 2 (Since the payments are semi annually, hence divided by 2)

= 4% or 0.04

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

= $ 47.50 x [ [ (1 - 1 / (1 + 0.04)¹⁴ ] / 0.04 ] + $ 1,000 / 1.04¹⁴

= $ 47.50 x 10.56312293 + $ 577.4750828

= $ 1,079.22 Approximately

Feel free to ask in case of any query relating to this question