标题： 定义非常规现金流的回收期：一种公理化方法 显示英文标题

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

摘要： 对于传统投资项目，即一系列现金流出之后跟随一系列现金流入的项目，回收期有明确的定义。对于非传统项目，其定义更具挑战性，因为它们的余额（累计现金流）可能有多个盈亏平衡点。学者和从业者提出了几种相互矛盾的方法来处理这个问题，建议使用余额的第一个盈亏平衡点、余额的最后一个盈亏平衡点或修改后的累计现金流的盈亏平衡点，表示累计现金流入超过总现金流出的时间点。在本说明中，我们表明项目余额的最后一个盈亏平衡点是与一组经济上有意义的公理一致的回收期的唯一定义。对于贴现回收期也建立了类似的结果。 显示英文摘要

摘要： 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.