Question

Iron Maiden became the first​ heavy-metal band to sell bonds when it arranged a​ $30 million deal in February 1999. The collateral on the bonds​ (and source of cash flow for interest and principal​ payments) consisted of future royalties from the​ band's albums like​ "The Number of the​ Beast." Each bond in the issue had a face value of

​$1,000​,

a term of

22

years and paid semiannual coupons at the rate of

5.5​%.

The yield to maturity on the bond was

9​%.

At what price did each of the bonds​ sell?

Answer 1

The value of the bond is computed as shown below:

The coupon payment is computed as follows:

= 5.5% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 27.5

The YTM will be as follows:

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

= 4.5% or 0.045

N will be as follows:

= 22 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 44

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

= $ 27.5 x [ [ (1 - 1 / (1 + 0.045)⁴⁴ ] / 0.045 ] + $ 1,000 / 1.045⁴⁴

= $ 27.5 x 19.01838305 + $ 144.1727626

= $ 667.18