Final answer:
A perpetuity can have a finite duration due to the concept of time discounting, which diminishes the value of future cash flows as they are received over time. The duration is the weighted average time to receive the present value of all future cash flows, and as the discount rate increases, the duration shortens.
Step-by-step explanation:
The question of how a perpetuity, which by definition provides constant cash flows infinitely, can have a duration much shorter like 10 or 20 years, is often a point of confusion. The duration of a perpetuity represents the weighted average time it takes to receive the present value of all future cash flows and is a measure of its interest rate sensitivity. This calculated duration can indeed be finite due to the concept of time discounting.
Time discounting is the principle that cash flows in the future are less valuable than cash flows today because of the potential for earning interest over time. As time goes on, the present value of each successive cash flow becomes incrementally smaller due to the higher discount factor applied, which effectively diminishes their contribution to the overall duration of the perpetuity. Therefore, even though the series of cash flows never ends, the value and impact of those cash flows decrease over time, resulting in a finite duration, which also suggests why 'financial innovation' is not the correct answer.
Thus, it is time discounting that allows for a perpetuity to have a finite duration that might seem surprisingly short compared to its infinite nature. A perpetuity with a higher discount rate will have a shorter duration, as future cash flows become less influential in the present value calculation more rapidly.