Final answer:
The price of the SmartAs Company bond next year, assuming a constant interest rate of 7.5%, is calculated by discounting the sum of the next coupon payment and today's bond price by the yield, which results in a price of $764.65 after the next coupon is paid.
Step-by-step explanation:
The price of a bond one year from now, if interest rates remain unchanged, can be calculated by discounting the expected future cash flows at the current yield to maturity. Since the SmartAs Company has a bond with an annual coupon of $2.6 and the bond price today is $820 with a yield of 7.5%, we can assume that this yield stays the same for the next year. After the next coupon is paid, the expected cash flow from the bond will be the coupon payment plus the price of the bond one year from now.
Given that interest rates do not change, the expected payment next year will be the next coupon of $2.6 plus the current bond price without the coupon just paid, which is $820. So, we discount this amount at the current yield to find the price one year from now: future price = ($2.6 + $820) / (1 + 0.075) = $764.65. Therefore, the expected bond price next year, after the next coupon is paid and rounding to two decimal places, will be $764.65.
Note that in the real world, bond prices fluctuate with market conditions and changes in credit risk, but this calculation assumes a constant interest rate environment and no change in the risk profile of the issuer.