An infinite series of cash flows can have a finite present value due to the concept of the time value of money. This principle states that a dollar received today is worth more than a dollar received in the future because money can earn interest over time. Therefore, future cash flows are discounted to reflect their present value.

As we project cash flows further into the future, their present value diminishes because each payment is discounted by the rate of return over time. Mathematically, this is represented by:

Where PV is the present value, CF is the cash flow, and r is the discount rate. The further into the future the cash flow occurs, the less it contributes to the present value, eventually making the sum of infinite cash flows finite. This allows investors to evaluate investments that generate cash flows perpetually.