Abstract
This paper presents a new way of measuring residual income, originally introduced by Magni (2000a,b,c, 2001a,b, 2003). Contrary to the standard residual income, the capital charge is equal to the capital lost by investors multiplied by the cost of capital. The lost capital may be viewed as (a) the foregone capital, (b) the capital implicitly infused into the business, (c) the outstanding capital of a shadow project , (d) the claimholders’ credit. Relations of the lost capital with book values and market values are studied, as well as relations of the lost capital residual income with the classical standard paradigm; many appealing properties are derived, among which an aggregation property. Different concepts and results, provided by different authors in such different fields as economic theory, management accounting and corporate finance, are considered: O’Hanlon and Peasnell’s (2002) unrecovered capital and Excess Value Created; Ohlson’s (2005) Abnormal Earnings Growth; O’Byrne’s (1997) EVA improvement; Miller and Modigliani’s (1961) investment opportunities approach to valuation; Young and O’Byrne’s (2001) Adjusted EVA; Keynes’s (1936) user cost; Drukarczyk and Schueler’s (2000) Net Economic Income; Fernández’s (2002) Created Shareholder Value; Anthony’s (1975) profit. They are all conveniently reinterpreted within the theoretical domain of the lost-capital paradigm and conjoined in a unified view. The results found make this new theoretical approach a good candidate for firm valuation, capital budgeting decision-making, managerial incentives and control.
Highlights
Residual income is income in excess of an income that could be obtained if investors invested their funds at the opportunity cost of capital
While the notion of lost capital has been previously introduced as a foregone capital, Proposition 3 allows us to reinterpret it as the capital infused by investors into the firm at the beginning of each period: The time-t Net Present Value Nt just measures by how much the value of the firm exceeds the capital infused into the business
The above Proposition compellingly proposes a subclass of RI models that always signal a positive residual income if and only if Net Present Value is positive, i.e if and only if value exceeds capital infused into the business
Summary
Residual income is income in excess of an income that could be obtained if investors invested their funds at the opportunity cost of capital. The purpose is to show that this new paradigm may be useful for both valuation and management compensation, and that it is capable of encompassing seemingly disparate perspectives conjoining them in one single theoretical domain To this end, the lost-capital paradigm is thoroughly investigated in two senses: (i) Formal results are provided aimed at clarifying both the link between performance and value creation and the link between residual income and compensation plan; in addition, the formal and conceptual relations that the two paradigms bear one another are studied; (ii) several notions, models and results in the literature are considered, spanning from the 1930s up to most recent years, ranging from microeconomics to management accounting and corporate finance. With no loss of generality, we will assume that the final cash flow dn is inclusive of the project’s terminal value (a finite-time horizon is assumed); (d) for the sake of notational convenience, cost of capital is constant (generalization to variable costs of capital is just a matter of symbology); (e) main notational conventions are collected in Table 0 at the end of the paper
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