Final answer:
The present value of a future cash flow is calculated as the Future Value divided by (1 + r)^n. This formula reflects the time value of money concept and changes with varying interest or discount rates.
Step-by-step explanation:
When calculating the present value of a future cash flow, the correct formula is a. Present Value = Future Value / (1 + r)^n. This formula accounts for the time value of money, which is the concept that money available now is worth more than the same amount in the future due to its potential earning capacity. Using the correct formula, if we consider a two-year bond with a future value of $3,000 and an annual interest rate of 8%, the calculations would look like this:
- Year 1 Interest Payment PV: $240 / (1 + 0.08)^1
- Year 2 Interest Payment PV: $240 / (1 + 0.08)^2
- Maturity Payment PV: $3,000 / (1 + 0.08)^2
If the interest rates were to rise to 11%, the discount rate also changes, impacting the present value:
- Year 1 Interest Payment PV: $240 / (1 + 0.11)^1
- Year 2 Interest Payment PV: $240 / (1 + 0.11)^2
- Maturity Payment PV: $3,000 / (1 + 0.11)^2
The present value changes with the fluctuations in the interest rates or discount rates, which highlights the importance of understanding present value calculations in bond valuation.
the correct formula is a. Present Value = Future Value / (1 + r)^n.