Final answer:
The price of the perpetual bond with a par value of $1,000 and a 7.6% annual coupon rate can be calculated using the present value formula. The price of the bond is $12,195.12.
Step-by-step explanation:
To calculate the price of a perpetual bond, you need to use the present value formula. The present value formula calculates the value of future cash flows by discounting them to their present value based on an interest rate. In this case, the perpetual bond has a par value of $1,000 and a 7.6% annual coupon rate, while the current interest rate is 8.2%.
The present value formula is:
PV = C / r
Where:
- PV is the price of the bond
- C is the coupon payment
- r is the interest rate
Using the given values, the price of the bond can be calculated as follows:
PV = $1,000 / 0.082
PV = $12,195.12
So, the price of the bond is $12,195.12.