Defining the payback period for nonconventional cash flows: an axiomatic approach

TL;DR

This paper establishes a rigorous, axiomatic foundation for defining the payback period in nonconventional projects, resolving contradictions in existing methods by identifying the last break-even point as the consistent measure.

Contribution

It introduces an axiomatic approach that uniquely justifies using the last break-even point for nonconventional cash flow projects, clarifying the concept's theoretical basis.

Findings

The last break-even point is the only consistent payback measure.

The approach extends to discounted payback periods.

Provides a clear, axiomatic justification for payback period definition.

Abstract

The payback period is unambiguously defined for conventional investment projects, projects in which a series of cash outflows is followed by a series of cash inflows. Its definition for nonconventional projects is more challenging, since their balances (cumulative cash flow streams) may have multiple break-even points. Academics and practitioners offer a few contradictory recipes to manage this issue, suggesting to use the first break-even point of the balance, the last break-even point of the balance, or the moment in time at which the cumulative sum of net cash inflows first exceeds the total sum of net cash outflows. In this paper, we show that the last break-even point of the project balance is the only definition of the payback period consistent with a set of economically meaningful axioms. An analogous result is established for the discounted payback period.