Abstract

The average internal rate of return (AIRR) fixes many deficiencies associated with the traditional internal rate of return (IRR), including apparent inconsistency with net present value (NPV). The AIRR approach breaks down project NPV into scale (the capital invested) and economic efficiency (the AIRR), and maintains NPV consistency for accept/reject decisions. Here we examine extensions of the AIRR to risky capital asset projects, a domain where the IRR appears intractable. We show that one can uniquely break down a risky NPV into a risk-sensitive project scale and a risk-sensitive extended AIRR, representing risky project efficiency, so that consistency with NPV for accept/reject decisions is maintained in the certainty-equivalent sense, in direct analogy to the deterministic case. This novel breakdown gives managerial insight by helping determine a risky project’s locus of uncertainty, be it the project scale, or economic efficiency, or both. In this way, risky features of competing projects can be explored in more detail, leading to insights substantiating the NPV ranking. We also show that under risk neutrality, the expected AIRR is equal to the AIRR of the expected cash flow, a property that notoriously fails for the stochastic IRR.

摘要

该返回的平均内部率（AIRR）修复带返回（IRR）的传统的内部速率相关联许多不足，其中包括与净现值（NPV）明显不一致。AIRR方法将项目净现值分解为规模（投资资本）和经济效率（AIRR），并保持NPV一致性以接受/拒绝决策。在这里，我们研究了将AIRR扩展到风险资本资产项目（IRR似乎难以解决的领域）的情况。我们证明一个人可以独特将有风险的NPV分解为风险敏感的项目规模和代表风险项目效率的风险敏感的扩展AIRR，以便在确定性等价的意义上保持与NPV一致以接受/拒绝决策，这与确定性直接相似案件。通过帮助确定风险项目的不确定性源（项目规模或经济效率，或两者兼而有之），这种新颖的分类为管理人员提供了洞察力。通过这种方式，可以更详细地探讨竞争项目的风险特征，从而获得可以证明NPV排名的见解。我们还表明，在风险中性的情况下，预期的内部收益率等于预期现金流量的内部收益率，该属性因随机性内部收益率而臭名昭著。