Final answer:
Only the first statement is true because the present value of a future cash flow is discounted, it decreases with a higher discount rate, and it diminishes as it moves further into the future. The correct statement is: The higher the discount rate, the higher the present value of a given future cash flow.
Step-by-step explanation:
The question pertains to the concept of present value in finance. The correct answer is that only statement I is true. According to financial principles, the present value of a future cash flow is discounted to reflect the time value of money, thereby never exceeding the actual future amount. Also, a higher discount rate decreases the present value because the future cash flow is discounted more heavily. Lastly, as a cash flow moves further into the future, its present value decreases due to the increased time period over which it is discounted.
Looking at the provided information, it's clear that when the interest rate increases, like going from 8% to 11%, the present value of the same future cash flows falls. This is because the cash flows are discounted at a higher rate. On the other hand, the first calculation reinforces the principle that the present value of a cash flow at the time of borrowing or lending (when the interest rate equals the discount rate) is equal to the actual money exchanged.
Statement I is false because the present value of a cash flow can be greater than the future dollar amount if a discount rate greater than 100% is applied. For example, if you have a future cash flow of $100 and discount it at a rate of 120%, the present value will be $83.33.
Statement III is false because the present value of a cash flow actually decreases as it moves further into the future due to the effect of discounting. This means that the present value is lower the further out the cash flow is.