Brown Enterprises’ bonds currently sell for $1,025. They have a 9-year maturity, an annual coupon of $80, and a par value of $1,000. What is their current yield?
So the present value
= 1000(1+i)^-9 + 80(1 - (1+i)^-9 )/i
so 1000(1+i)^-9 + 80(1 - (1+i)^-9 )/i = 1025
A very nasty equation to solve.
I tried a few values:
i = .08, RS = 1000 , looking for 1025
i = .09, RS = 940, so let's lower the i
i = .07, RS = 1065 , too low
i = .075, RS = 1031.894 getting closer
i = .077, RS = 1018.977
ok, so i is between .075 and .077
.075 .... 1031.894
i ...........1025
.077 ......1018.977
use interpolation by setting up a ratio
(i - .075)/(.077-.075) = (1025-1031.894)/(1018.977-1031.894)
I will leave the arithmetic up to you, but I got
i = .07607
To calculate the current yield of a bond, you need to divide the annual coupon payment by the bond's market price.
The annual coupon payment is given as $80, and the market price of the bond is $1,025.
Current Yield = (Annual Coupon Payment) / (Market Price of the Bond)
Current Yield = $80 / $1,025
Now, divide $80 by $1,025 to get the current yield:
Current Yield ≈ 0.078 or 7.8%
Therefore, the current yield of Brown Enterprises' bonds is approximately 7.8%.