Final answer:
A higher interest rate results in a lower present value for a lump sum because it increases the opportunity cost of holding money in the future. Out of the scenarios provided, the one with the higher interest rate will result in the lowest present value due to a greater rate of discounting future cash flows back to the present time.
Step-by-step explanation:
The question at hand involves understanding how the present value of money changes with varying conditions. To determine which scenario results in the lowest present value of a lump sum, we must consider the factors that affect present value calculations: interest rate, period, future value, and discount rate.
As depicted in the reference information, we see that raising the interest rate from 8% to 11% lowers the present value of cash flows. This is because a higher interest rate signifies a greater opportunity cost of having money in the future rather than in the present. Thus, a dollar received in the future is worth less today if interest rates are higher. This process of adjusting the value of future cash flows to obtain the present value is called discounting.
Therefore, of the options listed, the scenario resulting in the lowest present value of a lump sum is the one with a higher interest rate. A longer period also reduces present value because it extends the duration until receipt, thus increasing the discount effect. A higher future value does not directly lead to a lower present value, and a lower discount rate would increase present value since it would reduce the rate at which future cash flows are discounted back to the present.