Final answer:
To calculate the coupon rate of a bond, you need to rearrange the present value formula of a bond and input the current bond price, face value, yield to maturity, and number of years until maturity. The coupon rate is the annual paid interest expressed as a percentage of the bond's face value.
Step-by-step explanation:
The student is asking how to find the coupon rate of a corporate bond given its price, yield to maturity, face value, and term to maturity. The bond's coupon rate is the annual paid interest rate that is expressed as a percentage of the bond's face value. With an 8.24% yield to maturity and a current price of $756.10 for a 26-year bond, we can calculate the coupon rate using the formula for the present value of a bond:
P = (C * (1 - (1 + r) ^-n)/r) + (FV / (1 + r) ^n)
Where:
- P = Current bond price ($756.10)
- C = Annual coupon payment (unknown)
- r = Yield to maturity (0.0824)
- n = Number of years until maturity (26)
- FV = Face value of the bond ($1,000)
By rearranging the formula to solve for C and applying the given values, we get:
C = (P - (FV / (1 + r) ^n)) * r / (1 - (1 + r) ^-n)
We then insert the known values:
C = ($756.10 - ($1,000 / (1 + 0.0824) ^26)) * 0.0824 / (1 - (1 + 0.0824) ^-26)
After computing the above equation, you will arrive at the coupon rate as a percentage of the face value. This will tell you the amount of annual interest payment made by the bond.