The sign of cash flows: A source of error in present value approximations

We show that if an asset has both positive and negative cash flows, then the error in present value attributable to the end-of-period timing convention of cash flows might be infinitely large. Under certain conditions requiring knowledge of the respective sums of positive and negative cash flows in the periods, however, the maximum possible error is finite and minimized by the formula we develop. This optimal formula is an adjusted harmonic mean of the end-of-period and beginning-of-period present values. We find that the maximum possible error is increased if the cash flow signs are not identical.