Bell, Peter N (2015): Effects of Long Cycles in Cash Flows on Present Value.

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Abstract
This paper explores how present value varies over time when the underlying cash flow has a deterministic period. I assume that cash flows are known with certainty and follow a cycle with a long or short period. When the cash flow has a short period, the present value is relatively stable over time because the present value calculation smooths out several cycles. However, when the cash flow has a long period the present value itself develops a long and large cycle. These results are driven by the mathematical definition of the present value and are relevant to the use of present value as a pricing tool in situations where the cash flows of an investment have a long cycle.