Question

Bourdon Software has 11.8 percent coupon bonds on the market with 17 years to maturity. The bonds make semiannual payments and currently sell for 107 percent of par. What is the effective annual yield?

Answer 1

To calculate the effective annual yield (EAY), we need to use the following formula:

EAY = (1 + yield rate/n)^n - 1

Where:
yield rate = the bond's coupon rate = 11.8% = 0.118
n = number of compounding periods per year = 2 (semiannual payments)

Using the given information, we can find the yield rate as follows:

Coupon payment = 0.118 * par value of bond
Coupon payment = 0.118 * $100 = $11.8

The bond is currently selling for 107% of par, which means it is selling for 107% * $100 = $107.

The bond has a maturity of 17 years, so it will make 17 * 2 = 34 semiannual payments.

Next, we can calculate the yield rate:

yield rate = ($11.8 / $107) * 2 = 0.2187

Finally, we can calculate the effective annual yield using the formula:

EAY = (1 + 0.2187/2)^2 - 1
EAY = (1 + 0.10935)^2 - 1
EAY = (1.10935)^2 - 1
EAY = 1.2311 - 1
EAY = 0.2311

Therefore, the effective annual yield of the bond is 23.11%.