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?
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%.
To find the effective annual yield (EAY) of the bond, we can use the following formula:
EAY = (1 + periodic yield)^(number of periods) - 1
First, let's calculate the periodic yield. Since the bond makes semiannual payments, the periodic yield is equal to the semiannual coupon rate.
Coupon rate = 11.8% = 0.118
Periodic yield = Semiannual coupon rate = 0.118/2 = 0.059
Next, we need to determine the number of periods. Since the bond has a 17-year maturity and makes semiannual payments, there are 17 * 2 = 34 periods.
Now, let's plug these values into the formula to find the effective annual yield (EAY):
EAY = (1 + 0.059)^(34) - 1
Calculating this expression gives us:
EAY = (1.059)^(34) - 1 ≈ 1.4893 - 1 ≈ 0.4893
Therefore, the effective annual yield of the bond is approximately 48.93%.