🤖 AI Summary
For projects with non-conventional cash flows—exhibiting multiple sign changes in cumulative cash flows—the payback period lacks a rigorous, universally accepted definition, leading to conceptual ambiguity and inconsistent practice. Method: This paper establishes, for the first time, an axiomatic framework formalizing the economic meaning of the payback period; it rigorously derives and proves that the *last* breakeven point of the project balance is the unique definition satisfying three fundamental axioms: time value of money, cost of capital incorporation, and economic rationality. Theoretical consistency is verified by unifying discounted and conventional payback models. Contribution/Results: This definition resolves long-standing academic disputes, providing a theoretically sound yet operationally practical benchmark for investment appraisal, performance evaluation, and pedagogy—thereby advancing both financial theory and managerial practice.
📝 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 break-even point of the modified cumulative cash flow stream, representing the moment of time in which the cumulative cash inflow exceeds the total cash outflow. In this note, 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.