In Search of the 'Lost Capital': A Theory for Valuation, Investment Decisions, Performance Measurement

Abstract

This paper presents a theoretical framework for valuation, investment decisions, and performance measurement based on a nonstandard theory of residual income. It is derived from the notion of “unrecovered” capital, which is here named “lost” capital because it represents the capital foregone by the investors. Its theoretical strength and meaningfulness is shown by deriving it from four main perspectives: financial, microeconomic, axiomatic, accounting. Implications for asset valuation, capital budgeting and performance measurement are investigated. In particular: an aggregation property is shown, which makes the simple average residual income play a major role in valuation; a dual relation between the standard theory and the lost-capital theory is proved, clarifying the way periodic performance is computed in the two paradigms and the rationale for measuring performance with either paradigm; the average accounting rate of return is shown to be more reliable than the internal rate of return as a capital budgeting criterion, and maximization of the average residual income is shown to be equivalent to maximization of Net Present Value (NPV). Two metrics are also presented: one enjoys the nice property of robust goal congruence irrespective of the sign of the cash flows; the other one enjoys periodic consistency in the sense of Egginton (1995). The results obtained suggest that this theory might prove useful for real-life applications in firm valuation, capital budgeting decisions, ex post performance measurement, incentive compensation.

Keywords: Residual income, valuation, capital budgeting, performance measurement, lost capital, accounting rate, average, Economic Value Added

JEL Classification: M41, G11, G12, G31, M21, M52, D46