Aggregate Return on Investment under Uncertainty

Abstract

This paper deals with capital budgeting decisions under uncertainty. We present an Aggregate Return On Investment (AROI), obtained as the ratio of total (undiscounted) cash flow to total invested capital and show that it is a genuine rate of return which, compared with the risk-adjusted cost of capital, correctly signals wealth creation. For choosing between two mutually exclusive projects, we derive an incremental AROI and an incremental risk-adjusted cost of capital, by means of which two unequal-risk projects can be correctly compared. Iterating the incremental procedure, we show that the AROI approach correctly ranks any bundle of different-risk competing projects. Relations with other criteria such as Modified Internal Rate of Return, Average Internal Rate of Return, Cash Multiple, and Profitability Index are provided.Theoretically, the AROI approach constitutes a link between arbitrage choice theory and corporate investment theory, and shows that explicit discounting is not necessary for measuring economic profitability.Practically, the AROI is a user-friendly, easy-to-compute rate of return derived from the same set of data required by the net present value (NPV). Also, it does not incur the difficulties met by the internal rate of return: in particular, it is unique and it is based on economically significant capital values (i.e., market-driven values). As such, the AROI significantly expresses the efficiency of the project's invested capital.