Final answer:
The price of a perpetual bond with a 7.6% coupon rate when the market interest rate is 8.2% is calculated using the present value of a perpetuity formula and is approximately $926.83, which is less than its par value due to the higher market interest rate.
Step-by-step explanation:
The question involves calculating the price of a perpetual bond when the market interest rate is different from the bond's coupon rate. In this case, a perpetual bond with a par value of $1,000 that pays a annual coupon of 7.6% is considered while the market interest rate is 8.2%.
To calculate the price of the bond, we use the formula for the present value of a perpetuity: Price = (Coupon Payment) / (Market Interest Rate). In this scenario, the coupon payment is $76 per year (7.6% of $1,000). The expected return, based on the current market interest rate, is 8.2%.
Using the formula, Price = $76 / 0.082, which gives us a price of approximately $926.83. This means that the bond will sell for less than its par value because the coupon rate is lower than the current market interest rate, making it less attractive to investors compared to new bonds with higher interest rates.
In summary, if interest rates rise, the price of existing bonds falls to bring the yield in line with the new rates. Conversely, if market rates fall, the price of the bond would increase, as its higher coupon payments would be more valuable.