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Abstract:
In an interesting recent paper, DeAngelo and DeAngelo (2006) highlight that Miller and Modigliani’s (1961) proof of dividend irrelevance is based on the assumption that the amount of dividends distributed to shareholders is equal or greater than the free cash flow generated by the fixed investment policy. They claim that, if retention is allowed, dividend policy is not irrelevant. This paper shows that the dividend irrelevance proposition holds even in case of retention. The key assumption has not to do with retention but with the NPV of the extra funds (either retained or raised): if NPV is zero, dividend irrelevance applies. Yet, the dichotomy retention/no-retention is useful, because if agency problems are present, managers tend to retain funds and invest them in negative-NPV projects, and therefore the zero-NPV assumption must be removed, so that dividend irrelevance does not apply any more.

Dividend policy, irrelevance, retention, zero-NPV, epistemology, agency theory

Abstract:
The Net Present Value maximizing model has a respectable ancestry and is considered by most scholars a theoretically sound decision model. In real-life applications, decision makers use the NPV rule, but apply a subjectively determined hurdle rate, as opposed to the allegedly correct opportunity cost of capital. According to a heuristics-and-biases-program approach, this implies that the hurdle-rate rule is a biased heuristic. This papers shows that the hurdle-rate rule may be interpreted as a fruitful strategy of bounded rationality, where several important element are integrated and condensed into an aspiration level. This paper also addresses the issue of a fruitful cooperation between bounded and unbounded rationality, of which the heuristic NPV is one significant example.

Finance, investment decisions, Net Present Value, bounded rationality, hurdle rate, heuristic, methodology

Abstract:
This paper deals with the CAPM-derived capital budgeting criterion, and in particular with Rubinstein's (1973) criterion, according to which a project is profitable if the project rate of return is greater than the risk-adjusted cost of capital, where the latter depends on the project's disequilibrium systematic risk. It is shown that the disequilibrium net present value implied by this criterion, widely used in corporate finance, is nonadditive. Four proofs are provided: (i) a counterexample taken from Copeland and Weston (1988), (ii) a modus-tollens argument showing that this notion of NPV is incompatible with additivity, (iii) a formalization showing that this NPV does not fulfil the principle of description invariance (iv) an example showing that CAPM-minded evaluators may incur arbitrage losses. The disequilibrium NPV should therefore be dismissed in investment decisions and valuations.

Investment, decision, valuation, NPV, disequilibrium, CAPM, capital budgeting, nonadditivity, framing effects

Abstract:
The use of CAPM‐based disequilibrium betas and Net Present Value (NPV) for investment decisionsand valuations is widespread in finance. Actually, its use is logically deducted from the CAPM assumptions. This paper deals with decisions about purchase of a firm and the related issue of firm valuation. In particular, it contrasts disequilibrium betas and NPVs with Modigliani and Miller’s Proposition I, and shows that disequilibrium betas and NPVs should not be used because they lead to irrational valuations and unreliable decisions; in particular, they lead decision makers to infringe Modigliani and Miller’s Proposition I. To prove the thesis, a counterexample is shown where two firms with same expected free cash flows are valued, one of which is levered, the other one is unlevered. A formal generalization is also provided. The results indicate that the use of disequilibrium NPV should be avoided, because valuations are incorrect and decisions are unsafe, leaving decision makers open to framing effects and arbitrage losses.

Firm value, Free Cash Flow, CAPM, Modigliani and Miller's Proposition I, Net Present Value, disequilibrium, arbitrage, decision making

Abstract:
This paper focuses on inconsistencies arising from the use of NPV and CAPM for capital budgeting. It shows that (i) CAPM capital budgeting decision-making based on disequilibrium NPV is deductively inferred by the Capital Asset Pricing Model, (ii) the use of the disequilibrium NPV is widespread in finance both as a decision rule and as a valuation tool, (iii) the disequilibrium NPV does not guarantee additivity nor consistency with arbitrage pricing, so that it is unreliable for valuation, (iv) Magni's (2002, 2007a, forthcoming) criticism of the NPV criterion refers to the disequilibrium NPV, and De Reyck's (2005) project valuation method, on the basis of which Magni's criticism to NPV is objected, leaves decision makers open to arbitrage losses and incorrect decisions.

Finance, investment analysis, Net Present Value, Capital Asset Pricing Model, disequilibrium, decision, valuation, nonadditivity, arbitrage

Abstract:
For one-period projects under certainty, the notion of Net Present Value (NPV) formally translates the notion of economic profit, where the discount rate is the cost of capital. Under uncertainty, the cost of capital is the expected rate of return of an equivalent-risk alternative that the investor might undertake and is often found by making recourse to the Capital Asset Pricing Model. This paper shows that the notions of disequilibrium NPV and economic profit for risky one-period projects are not equivalent: NPV-minded agents are open to framing effects and to arbitrage losses, which imply violations of Modigliani and Miller's Proposition I. The notion of disequilibrium (present) value, deductively derived from the CAPM by several authors and widely used in applied corporate finance, should therefore be dismissed.

Capital Asset Pricing Model, Net Present Value, economic profit, disequilibrium, framing effects, arbitrage, Modigliani and Miller's Proposition I

Abstract:
This paper deals with the use of the CAPM for investment decisions and evaluations. Four different measures are deductively drawn from this model: the disequilibrium Net Present Value, the equilibrium Net Present Value, the disequilibrium Net Future Value, the equilibrium Net Future Value. It is shown that all of them may be used for accept-reject decisions, but only the equilibrium Net Present Value and the disequilibrium Net Future Value may be used for valuation, given that they enjoy the additivity property. The two nonadditive indexes cannot be deducted from the CAPM assumptions if the decision problem “invest/no invest” is reframed as “invest in Z/invest in Y”. Despite their additivity, the equilibrium Net Present Value and the disequilibrium Net Future Value are unreliable for both valuation and decision, because they do not signal arbitrage opportunities whenever there is some state of nature for which they are decreasing functions with respect to the end-of-period cash flow. In this case, the equilibrium value of a project is not the price it would have if it were traded in the security market. This result is the capital-budgeting counterpart of Dybvig and Ingersoll’s (1982) result.

capital budgeting, project, risk-adjusted rate of return, CAPM, equilibrium, disequilibrium, present value, future value, decision, valuation. investment appraisal, cost, risk, decision making

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. 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; Fernandez'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.

Management accounting, corporate finance, residual income, value creation, incentive compensation, outstanding

Abstract:
Practitioners and a few academics use potential dividends rather than actual payments to shareholders for valuing a firm’s equity. The paper underlines the differences between the two methods and presents some arguments supporting the thesis that firm valuation with potential dividends overstates the actual value of the firm’s equity. In particular, consistent with DeAngelo and DeAngelo (2006 and 2007), the paper underlines that cash flows create value for shareholders only if they are withdrawn from the firm, and that the use of potential dividends may lead to contradictions.

Abstract:
Practitioners and some academics use potential dividends rather than actual payments to shareholders for valuing a firm's equity. We underline the differences between the two methods and present some arguments supporting the thesis that firm valuation with potential dividends overstate the actual value of the firm's equity. In particular, consistently with DeAngelo and DeAngelo (2006, 2007), we underline that cash flows create value for shareholders only if they are withdrawn from the firm, and that the use of potential dividends may lead to contradictions. This paper is a modified version of the theoretical part (sections 1-3) of Velez-Pareja, I., and Magni, C.A. (2008). Potential Dividends and Actual Cash Flows. Theoretical and Empirical Reasons for Using 'Actual' and Dismissing 'Potential', Or: How not to Pull Potential Rabbits Out of Actual Hats. Available at SSRN.

Cash flows, cash flow to equity, liquid assets, potential dividends, firm valuation, equity value, Modigliani and Miller

Abstract:
Practitioners and academics in valuation include changes in liquid assets (potential dividends) in the cash flows. This widespread and wrong practice is inconsistent with basic finance theory. We present economic, theoretical, and empirical arguments to support the thesis. Economic arguments underline that only flows of cash should be considered for valuation; theoretical arguments show how potential dividends lead to contradiction and to arbitrage losses. Empirical arguments, from recent studies, suggest that investors discount potential dividends with high discount rates, which means that changes in liquid assets are not value drivers. Hence, when valuing cash flows, we should consider only actual payments.

Cash flows, cash flow to equity, free cash flow, liquid assets, potential dividends, firm value, equity value, Modigliani and Miller, levered value, error in valuation

Abstract:
Discounted Cash Flow techniques are the generally accepted methods for valuing firms. Such methods do not provide explicit acknowledgment of the value determinants and overlook their interrelations. This paper proposes a different method of firm valuation based on fuzzy logic and expert systems. It does represent a conceptual transposition of Discounted Cash Flow techniques but, unlike the latter, it takes explicit account of quantitative and qualitative variables and their mutual integration. Financial, strategic and business aspects are considered by focusing on twenty-nine value drivers that are combined together via if-then rules. The output of the system is a real number in the interval [0,1], which represents the value-creation power of the firm. To corroborate the model a sensitivity analysis is conducted. The system may be used for rating and ranking firms as well as for assessing the impact of managers' decisions on value creation and as a tool of corporate governance.

firms' evaluation, fuzzy logic, expert system, rating, acquisition, sensitivity analysis, pricing

Abstract:
This work presents a notion of residual income called Systemic Value Added (SVA). It is antithetic to Stewart's (1991) EVA, though it is consistent with it in overall terms: a project's Net Final Value (NFV) can be computed as the sum of capitalized EVAs or as the sum of uncapitalized SVAs. As a result, SVA and EVA decompose the NFV in different ways. Two numerical examples show the application of the model proposed. The two notions are the result of a different cognitive approach. The existence of possible formal translations of the residual income concept induces to regard residual income as a mere conventional notion.

systemic approach, residual income, net final (present) value, EVA, SVA, decomposition

Abstract:
This paper uses counterexamples and simple formalization to show that the standard CAPM-based Net Present Value may not be used for investment valuations. The reason is that the standard CAPM-based capital budgeting criterion implies a notion of value which does not comply with the principle of additivity. Framing effects arise in decisions so that different descriptions of the same problem lead to different choices. As a result, the CAPM-based NPV as a tool for valuing projects and making investment decisions is theoretically unsound, even if the CAPM assumptions are met.

Capital budgeting, CAPM, investment decisions, nonadditivity, framing effects

Abstract:
This paper deals with the notion of residual income, which may be defined as the surplus profit that residues after a capital charge (opportunity cost) has been covered. While the origins of the notion trace back to the 19th century, in-depth theoretical investigations and widespread real-life applications are relatively recent and concern an interdisciplinary field connecting management accounting, corporate finance and financial mathematics (Peasnell, 1981, 1982; Peccati, 1987, 1989, 1991; Stewart, 1991; Ohlson, 1995; Arnold and Davies, 2000; Young and O'Byrne, 2001; Martin, Petty and Rich, 2003). This paper presents both a historical outline of its birth and development and an overview of the main recent contributions regarding capital budgeting decisions, production and sales decisions, implementation of optimal portfolios, forecasts of asset prices and calculation of intrinsic values. A most recent theory, the systemic-value-added approach (also named lost-capital paradigm), provides a different definition of residual income, consistent with arbitrage theory. Enfolded in Keynes's (1936) notion of user cost and fore run by Pressacco and Stucchi (1997), the theory has been formally introduced in Magni (2000a,b,c; 2001a,b; 2003), where its properties are thoroughly investigated as well as its relations with the standard theory; two different lost-capital metrics have been considered, for value-based management purposes, by Drukarczyk and Schueler (2000) and Young and O'Byrne (2001). This work illustrates the main properties of the two theories and their relations, and provides a minimal guide to construction of performance metrics in the two approaches.

Accounting, finance, residual income, excess profit, firm valuation, net present value, opportunity cost, performance measurement

Abstract:
The problem of decomposing a cash flow has been treated in recent years by Gronchi (1986, 1987), Peccati (1987, 1991, 1992), Stewart (1991), Pressacco and Stucchi(1997). After showing that the Economic Value Added introduced by Stewart bears a strong resemblance to (and in some conditions coincides with) the periodic Net Present (or Final) Value in Peccati's model and that Pressacco-Stucchi's model can be seen as a formal generalization of Stewart's model, this paper proposes a different decomposition model introducing the Systemic Value Added, which lends itself to a disaggregation in periodic shares whose uncompounded sum coincides with Peccati's and Pressacco-Stucchi's Net Final Value. The model proposed offers the opportunity to dwell on the notion of residual income, showing that the interpretation given by the three previous models fails to explain the correct evolution of the investor's financial system. The evaluation process is then reshaped by introducing the concept of shadow project, by means of which Peccati's and Stewart's model can be retrieved. Pressacco-Stucchi's model can also be retrieved and generalized and some of its assumptions are relaxed. The formal results in the last section provide sufficient and necessary conditions for integrating all models in the systemic framework here adopted. Finally, some hints shows that the results Pressacco and Stucchi obtain can be proved by using the systemic approach here suggested.

Residual incomes, decomposition, cash flow, Net Final Value, Systemic Value Added

Abstract:
This paper presents a real-life application of a fuzzy expert system aimed at rating and ranking firms. Unlike standard Discounted Cash Flow (DCF) models, it integrates financial, strategic and business determinants and processes both quantitative and qualitative variables.Twenty-one value drivers are defined concerning the target firm (strategic assets in place and prospective financial performance), the acquisition (synergies, quality of management) and the sector (intensity of competition, entry barriers). Their combination via ‘if-then’ rules leads to the definition of an output represented by a real number in the interval (0, 1). Such a number expresses the value-generating power of the target firm inclusive of synergies with the bidder (here named Strategic Enterprise Value). The system may be used for rating and ranking firms operating in the same sector. A regression analysis, using hostile takeover multiples, may be employed to translate the score into price. The real-life case refers to Camuzzi, a natural gas distributor, acquired by Enel, the Italian ex-monopolist of electric energy.

Abstract:
In this paper we present a real-life application of a fuzzy expert system aimed at rating and ranking firms. Unlike standard DCF models, it integrates financial, strategic and business determinants and processes both quantitative and qualitative variables. Twenty-one value drivers are defined, concerning the target firm (strategic assets in place and expected financial performance), the acquisition (synergies, quality of management) and the sector (intensity of competition, entry barriers). Their combination via if-then rules leads to the definition of an output represented by a real number in the interval [0,1]. Such a number expresses the valuegenerating power of the target firm inclusive of synergies with the bidder (Strategic Enterprise Value). The system may be used for rating and ranking firms operating in the same sector. A regression analysis using hostile takeovers multiples may be employed to translate the score into price. The real-life case refers to Camuzzi (a natural gas distributor), acquired by Enel, the Italian ex monopolist of electric energy.

Corporate finance, firm, rating, ranking, expert system, fuzzy, evaluation

Abstract:
In capital budgeting, the internal rate of return (IRR) criterion and the net present value (NPV) criterion are considered incompatible in several cases. A longstanding debate developed in past years about the reliability of either method is still an issue of investigation (see, for example, Promislow and Spring, 1996). This paper shows that, employing a systemic perspective, the two models are actually always consistent. Methodologically, the idea is, so to say, accounting-flavoured: it consists of focusing on stocks as well as on flows. In particular the investor's wealth is represented as a financial dynamic system (graphically described by double-entry sheets) and attention is drawn to initial and terminal positions of the system. The equivalence of the IRR and the NPV methods extends to the use of the ROE. An illustrative example is presented where the two alternatives "accept" and "reject" differently reverberate on the system and its terminal position. The comparison between the two alternative terminal positions may equivalently be expressed in terms of the system's IRR or the system's NPV. The systemic approach naturally originates a new definition of residual income, the Systemic Value Added, which is radically different from the standard models (e.g. EVA). The Systemic Value Added (SVA) paradigm is drawn from two different evolutions of the investor's financial system: one relates to the net income in case the project is accepted at time 0, the other one relates to the counterfactual net income that would be obtained from the system if, at time 0, funds were invested in the alternative course of action. It is shown that the sum of the SVAs leads to the Net Final Value with no need of compounding, contrary to the standard residual income.

[An English translation of the section introducing the SVA is provided at the end of the original paper]

capital budgeting, valuation, IRR, NPV, systemic approach, residual income

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 decision-making, ex ante and ex post performance measurement, incentive compensation. A numerical example illustrates the implementation of the paradigm to the EVA model and the Edwards-Bell-Ohlson model.

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

Abstract:
The Economic Value Added formally translates the theoretical notion of excess profit (also known as residual income). Its use is so firmly entrenched in applied corporate finance and management accounting that its name is often used as a noun for denoting the concept of excess profit itself. This paper investigates the conceptual properties of such a notion and, in particular, it studies the relations between the excess profit generated in a period and the excess profit generated in the following period, showing that the classical approach forgets the past story of the project and the evolution of the capital invested. On the basis of this analysis, a new approach to residual income is offered, called Systemic Value Added (SVA). The latter takes account of the dynamic system governing the evolution of the capital invested, and is coherently additive in that the uncompounded sum of the SVAs leads to the Net Final Value. Interesting relations between the classical approach and the new approach are provided, and a final conventionalist position is endorsed: the excess profit is not an unambiguous concept and the choice between either approaches depends on the pieces of information one is willing to retrieve.
[An English translation of sections 3 and 4 is provided at the end of the original paper]

Excess profit, residual income, net present (final) value, decomposition, Economic Value Added, Systemic Value Added

Abstract:
In Magni [Eur. J. Operat. Res. 137 (2002) 206] I present some inconsistencies implicit in the net-present-value criterion, as currently used in finance. This paper shows that the standard use of CAPM for capital budgeting, based on disequilibrium values, is at odds with arbitrage theory, and that the corresponding CAPM-based NPV rule is meaningless even in the simplest case, because net present value is any number one wants it to be. Cognitively, this amounts to saying that the NPV procedure leaves decision makers subject to a framing bias; financially, this amounts to saying that additivity does not hold. De Reyck's [Eur. J. Operat. Res. 161 (2005) 499] objection to my thesis is invalid because he mistakes a project's expected rate of return for a project's cost of capital. De Reyck's Proposition, on the basis of which my thesis is criticized, leaves decision makers open to arbitrage losses, because it is an (admittedly interesting) reframing of the security market line and (as surprising as it might be) the use of the SML for project valuation is incompatible with the no-arbitrage principle. To use NPV and CAPM for capital budgeting is not a good idea.

Finance, Investment Analysis, Net Present Value, Capital Asset Pricing Model, arbitrage

Abstract:
This paper shows that (i) project valuation via disequilibrium NPV CAPM contradicts valuation via arbitrage pricing, (ii) standard CAPM-minded decision makers may fail to profit from arbitrage opportunities, (iii) standard CAPM-based valuation violates value additivity. As a consequence, the standard use of CAPM for project valuation and decision making should be reconsidered.

Investment, valuation, CAPM, arbitrage, disequilibrium NPV

Abstract:
This paper proposes a new way of decomposing net present values and net final values in periodic shares. Such a decomposition generates a new notion of residual income, radically different from the classical one available in the financial and accounting literature. While the standard residual income is formally computed as profit minus cost of capital times actual capital invested, the new paradigm introduces a fourth element: the capital invested in the so-called shadow project. Such a capital is the counterfactual capital that the investor would own if, at time 0, he invested his funds at the cost of capital, rather than in the project. Two important features are found: in primis, the new residual income is obtained as the sum of the standard residual incomes and the interest earned on past standard residual incomes; in secundis, the new paradigm is shown to be additive: the net final value of the project is computed as the sum of all periodic shares (residual incomes) with no capitalization process (abnormal earnings aggregation). A generalization is provided for a levered portfolio of projects, and a fourthfold decomposition is reached: (i) periodic decomposition, (ii) opportunity account decomposition, (iii) project decomposition, (iv) financing decomposition.

net present value, net final value, decomposition, residual incomes, systemic value, shadow project, acounting, finance, quantitative methods

Abstract:
This paper presents an expert system aimed at evaluating firms and business units. It makes us of fuzzy logic and integrates financial, strategic, managerial aspects, processing both quantitative and qualitative information. Twenty-nine value drivers are explicitly taken into account and combined together via if-then rules to produce an output. The output is a real number in the interval [0,1], representing the value-creation power of the firm. The system may be used for rating, ranking and pricing firms as well as for assessing the impact of managers' decisions on value creation and as a tool of corporate governance.

Firm valuation, fuzzy logic, expert system, acquisition, rating, pricing

Abstract:
This paper deals with the problem of modelling in a formal way the concept of excess profit, also known as residual income. A common idea is that excess profit is an unequivocal concept, being the difference between profit and costs, where all types of costs are taken into account, included the opportunity cost, i.e. the profit the entrepreneur would obtain if she invested in another business. This paper aims at showing that this difference is not univocal and that different approaches may be followed to give voice to such a notion. It turns out that two different interpretations are possible. The one existing in the literature is well described by Preinrich (1938), Edwards and Bell (1961) and, more recently, by Peasnell (1981, 1982) in the accounting literature and by Stewart (1991) in the value-based management literature. The interpretation here provided gives rise to a different way of modelling the notion of excess profit. While the existing models are tied to the financial literature, the model here presented is more akin to a microeconomic perspective. The paper focuses on the formal relations among the various models and necessary and sufficient conditions are provided for the integration of all models in the systemic framework here adopted. Furthermore, it shows that the systemic paradigm enjoys an aggregation property which makes residual incomes aggregate in a value sense and enables one to reduce forecasting errors in valuation.

This paper is a (pre-print) updated version of Magni, C.A. (2004). Modelling excess profit. Economic Modelling, 21(3) (May), 595--617.

excess profit, residual income, model, economic value added, systemic value added, shadow business

Abstract:
Accounting measures are traditionally considered not significant from an economic point of view. In particular, accounting rates of return are often regarded economically meaningless or, at the very best, poor surrogates for the IRR, which is held to be “the” economic yield. Likewise, residual income does not enjoy, in general, periodic consistency with the project NPV, so residual income maximization is not equivalent to NPV maximization. This paper shows that the opposition accounting/economic is artificial and, taking a capital budgeting perspective, illustrates the strong (formal and conceptual) connections existing between economic measures and accounting measures. In particular, the average accounting rate of return is the correct economic yield of a project; the traditional IRR is (whenever it exists) only a particular case of it. The average accounting rate generates a decision rule which is logically equivalent to the NPV rule for both accept/reject decisions and project ranking. The paper also shows that maximization of the simple arithmetic mean of residual incomes is equivalent to NPV maximization, owing to its periodic consistency in the sense of Egginton (1995). Such an index may then be used for incentive compensation as well. Moreover, asset pricing may be interpreted in accounting terms as the process whereby the market determines the income impact on the assets’ value. As a result, the paper harmonizes the notions of accounting rate of return, internal rate of return, residual income, net present value: they are just different ways of cognizing the same notion. This conciliation stems in a rather natural way from three sources: (i) a fundamental accounting identity, which links income and cash flow in a comprehensive way, (ii) the definition of Chisini mean, (iii) a notion of residual income which takes account of the “real” (comprehensive) cost of capital.

capital budgeting, accounting rate of return, economic yield, internal rate of return, residual income, net present value, average, Chisini mean, cost of capital

Abstract:
Two measures of excess profit (residual income) are currently available in the literature: the standard one, of which Economic Value Added (EVA) (Stewart, 1991) is a major instantiation, and Systemic Value Added (SVA) (Magni, 2003, 2004, 2005), also named lost-capital residual income (Magni, 2009a,b). This paper shows that, unlike EVA, SVA is symmetric and additively coherent. Also, EVA and SVA are not simply different in value but also convey different information about good or bad performances.

excess profit (residual income), EVA, SVA, performance measurement

Abstract:
This paper presents a new approach to real options. The current options-based models have provided new insights into capital-budgeting decisions. Unfortunately they are not widely used by corporate managers and practitioners as they are formally complex, rather difficult to understand and rest on strong implicit assumptions that considerably limit their scope of application. We propose a possible alternative by using a fuzzy expert system, on the basis of Mastroleo, Facchinetti and Magni (2001). We draw up a decision tree with multiple uncertain variables affecting the value of an investment opportunity, consisting of a defer option, a growth option, an abandonment option. Some simulations are conducted to test the economic soundness of the model as well as its consistency with the current models in the literature. A rather refined study can be accomplished by showing how inputs and outputs of the model interrelate one another.

fuzzy logic, expert systems, real option

Abstract:
This paper proposes a method for evaluating a project under certainty by means of a systemic outlook, which borrows from accounting the way of representing economic facts while replacing accounting values with cash values. The investor's net worth is regarded as a system whose structure changes over time. On this basis, a profitability index is presented, here named Systemic Value Added (SVA), which lends itself to a periodic decomposition. While as an overall index the Systemic Value Added coincides with the Net Final Value (NFV) of an investment, the systemic partition of a SVA is shown to differ from the Net Present Value (NPV) decomposition model proposed by Peccati (1987, 1992), which in turn bears a strong resemblance to Stewart's (1991) EVA model. The different assumptions the three models rely on are analysed: Some inconsistencies arise in the NFV-based approach, which give rise to Peccati's and Stewart's model, but they can be healed (only in a certain sense) by re-shaping the model and taking account of the systemic approach. To this end, the introduction of a shadow project is needed which enables us to avoid compounding. An interesting result is that we can decompose the SVA of a project by applying Peccati's argument to its shadow, or which is the same, by computing the shadow project's Economic Value Added. The paper then generalizes the approach allowing for a portfolio of projects, multiple debts and multiple synchronic opportunity costs of capital, for which a tetra-dimensional decomposition is easily obtained.

residual income, systemic value added, decomposition

Abstract:
This paper presents a new way of measuring residual income and valuing firms. The method, originally introduced in Magni (2000a, 2000b, 2000c, 2001), is here renamed lost-capital paradigm. In order to enhance comprehension the presentation relies on a very simple numerical example which shows that the new paradigm of residual income enjoys a property of abnormal earnings aggregation, according to which the NPV (and therefore the market value) of the firm does not change if each residual income changes, as long as the (uncapitalized) sum of all residual incomes do not change. While radically different from the standard residual income, the difference between the two notions is equal to the interest accrued on the past cumulated standard residual incomes, which has interesting implications for incentive compensation.

firm valuation, residual income, lost capital, Discount&Sum, Sum&Discount, incentive compensation

Abstract:
This paper tells the story of a student of economics and finance who meets a couple of alleged psychopaths, suffering from the 'syndrome of Zelig', so that they think of themselves to be experts of economic and financial issues. While speaking, they come across the concept of excess profit. The student tells them that the formal way to translate excess profit is to apply Stewart's (1991) EVA model and shows that this model is equivalent to Peccati's (1987, 1991, 1992) decomposition model of a project's Net Present (Final) Value. The 'Zeligs' listen to him carefully, then try to apply themselves the EVA model: Unfortunately, both She-Zelig and He-Zelig seem to feel uneasy with basic mathematics, so they make some mistakes. Consequently, each of them miscalculates the excess profit. Strangely enough, they make different mistakes but both get to the (correct) Net Final Value of the project and, in addition, their excess profits do coincide. Further, the (biased) models presented by the Zeligs, though different from the EVA model, seem to bear strong relations to the latter. The student is rather surprised.

I give my version of this event, arguing that the Zeligs are offering us a rational way of measuring excess profit, alternative to the standard way (EVA) but equally valuable. As I see it, they are only adopting a different cognitive interpretation of the concept of excess profit, which is based on a counterfactual conditional that differs from Stewart's and Peccati's.

Excess profit, residual income, Economic Value Added, Net Final Value, Systemic Value Added, counterfactual

Abstract:
Counterfactual conditionals are cognitive tools that we incessantly use during our lives for judgments, evaluations, decisions. Counterfactuals are used for defining concepts as well; an instance of this is attested by the notions of opportunity cost and excess profit, two all-pervasive notions of economics: They are defined by undoing a given scenario and constructing a suitable counterfactual milieu. Focussing on the standard paradigm [Peasnell, 1981, 1982; Peccati, 1987, 1990, 1991; Ohlson, 1995] and Magni's [2000, 2001, 2003, 2004, 2005, 2006] alternative paradigm this paper shows that the formal translation of the counterfactual state is not univocal and that Magni's approach retains formal properties of symmetry, additive coherence, homeomorphism, which correspond to properties of frame-independence, time invariance, completeness. Two introductory studies are also presented to illustrate how people cope with these counterfactuals and ascertain whether either model is seen as more "natural". A brief discussion of the results obtained is also provided.

opportunity cost, excess profit, residual income, counterfactual, modelling, frame-independence, time invariance, completeness

Abstract:
A residual-income model, named Systemic Value Added (SVA), is proposed for decision-making purposes, based on a systemic approach introduced in Magni (2000, 2003, 2004). The model translates the notion of residual income (excess profit) giving formal expression to a counterfactual alternative available to the decision maker. Relations with other residual income models are studied, among which Stewart's Economic Value Added (EVA). The index here introduced differs from EVA in that it rests on a different interpretation of the notion of excess profit and is formally connected with the EVA model by means of a shadow project. The SVA is formally and conceptually threefold, in that it is economic, financial, accounting-flavoured. Some results are offered, providing sufficient and necessary conditions for decomposing Net Final Values. Relations between a project's SVA and its shadow project's EVA are shown, all results of Pressacco and Stucchi (1997) are proved by making use of the systemic approach and the shadow counterparts of those results are also shown.

residual income, excess profit, net final value, decomposition, EVA, SVA, shadow project

Abstract:
This paper analyzes the relations among different concepts such as earnings, profit, interest, rate, consumption, dividend, installment, cash flow, capital. It aims at embracing these notions in a unique conceptual 'umbrella,' consisting of five perspectives: (1) accounting, (2) economic theory, (3) theory of finance, (4) loan theory, (5) financial mathematics. These notions and these domains constitute a seeming mishmash: in fact the hub of the umbrella is given by a unique fundamental relation, shared by all five perspectives and whose ingredients are capital, profit, and cash flow. On the basis of the fundamental relation, market value and book value of a firm are easily obtained.

firm, capital, profit, interest, loan

Abstract:
This paper shows that the CAPM-based capital budgeting criteria proposed by Tuttle and Litzenberger (1968), Mossin (1969), Hamada (1969), Stapleton (1971), Rubinstein (1973), Bierman and Hass (1973), Bogue and Roll (1974) are equivalent: They all state that a project is profitable if its internal rate of return is greater than the risk-adjusted cost of capital, where the latter is given by the sum of the risk-free rate and a risk-premium which is a function of the systematic risk of the project, itself a function of the project cost.

Capital budgeting, investment decisions, capital asset pricing model, equivalence.

Abstract:
This paper presents an axiomatization of residual income, aka excess profit, and illustrates how it may univocally engenders fixed-income or variable-income assets. In the first part it is shown that, depending on the relations between excess profit and the investor's excess wealth, a well-specified theory of residual income is generated: one is the standard theory, which historically traces back to Hamilton (1777) and Marshall (1890) and is a deep-rooted notion in economic theory, finance, and accounting. Another one is the systemic value added or lost-capital paradigm: introduced in Magni (2000, 2003), the theory is enfolded in Keynes's (1936) notion of user cost and is naturally generated by an arbitrage-theory perspective. In the second part, the paper reverts the usual analysis: instead of computing residual incomes profits from a pattern of cash flows, residual incomes are fixed first to derive vectors of cash flows. It is shown that variable- or fixed-income assets may be constructed on the basis of either theory starting from pre-determined growth rates for excess profit. In particular, zero-coupon bonds and coupon bonds traded in a capital market are shown to be deducted as equilibrium vectors of residual-income-based assets.

Residual income, excess profit, capital, arbitrage, bond

Abstract:
This work deals with the classical capital-budgeting criterion derived from the CAPM, according to which a project is profitable if and only if its expected return rate is greater than the cost of capital. This criterion, presented by several authors (e.g. Rubinstein, 1973) is regarded as theoretically impeccable. In fact, it brings about (seeming) theoretical ambiguities, because it induces the existence of four profitable indexes, two of which are nonadditive.The decision process is reshaped by replacing the “invest/no invest" dychotomy with the problem "invest in one of two alternative investments"(one of which is possibly represented by the null alternative). As a result, the two non additive indexes disappear, and the remaining ones are equivalent.

net present value, CAPM, equilibrium, disequilibrium, ambiguities

Abstract:
This paper presents a proposal for evaluating real options. The existing models are not widely used by corporate managers as they are formally complex, rather difficult to understand and rest on strong implicit assumptions. We propose a possible alternative by using a fuzzy expert system that takes into consideration both quantitative variables and qualitative variables, aggregating them through a simple modular approach.

Investments, real options, fuzzy logic, expert systems, qualitative and quantitative variables

Abstract:
This paper proposes a model aiming at decomposing the Net Final Value of a project under certainty. It makes use of a systemic outlook: the investor's net worth is regarded as a dynamic system whose structure changes over time. On this basis, a profitability index is presented, here named Systemic Value Added (SVA), which lends itself to a periodic decomposition: the periodic shares formally translate the economic concept of residual income (or excess profit). While as an overall index the Systemic Value Added coincides with the Net Final Value (NFV) of an investment, the systemic partition of a SVA is shown to differ from the NFV decomposition model proposed by Peccati (1987, 1991, 1992), which in turn bears a strong resemblance to Stewart's (1991) EVA model. The SVA model and the NFV-based model bear interesting relations: by introducing the concept of a shadow project the SVA model can be re-shaped so that the decomposition of the SVA can be accomplished by applying Peccati's argument to the shadow project, or, which is the same, by computing the shadow project's Economic Value Added. The paper then generalizes the approach allowing for a portfolio of projects, multiple debts and multiple synchronic opportunity costs of capital, for which a tetra-dimensional decomposition is easily obtained.

Abstract:
This paper deals with an investment option depending on two variables, one of which is quantitative and the other one is qualitative. To every value of the quantitative variable, the value of the qualitative variable is determined such that exercise of the option is preferrable. Furthermore, the value of the option is split into quantitative value and qualitative value.

real option, quantitative, qualitative, vague logic

Abstract:
This papers reports some scattered notes on the prisoner's dilemma and on decision theory originated by the reading of Nozick (1993). It aims at highlighting some obscure aspects of decision theory and, in particular, of game theory: excessive abstraction, non-consideration of contexts and cultural and social environments, and focussing on what each player thinks of the other one, neglect of what each player thinks of himself: This induces to propose the principle of probability and aversion, particular cases of which are Nozick's causal and evidential arguments. Decision theory's rationality-with-no emotions may perhaps be integrated by Damasio's (1996) hypothesis of somatic marker, and Magni and Ricci's (1991) indirect utility may be a further step toward a more realistic treatment of decision processes.

Sono riportate nel seguente articolo alcune note sparse sul dilemma del prigioniero e sulla Teoria delle decisioni scaturite dalla lettura di Nozick (1993). Esso mira a cogliere (in modo tutt'altro che sistematico) alcuni aspetti oscuri della Teoria delle decisioni e in particolare della Teoria dei giochi. L'eccessiva astrazione, la non considerazione del contesto e dell'ambiente culturale e sociale in cui il gioco ha luogo e l'attitudine a focalizzare l'attenzione su ciò che ogni giocatore pensa dell'altro, trascurando ciò che ogni giocatore pensa di se stesso, induce a proporre il principio di probabilità e avversione, di cui gli argomenti evidenziale e causale citati da Nozick sono casi particolari. La razionalità senza emozioni tipica della Teoria delle decisioni può forse essere integrata dall'ipotesi del marcatore somatico di Damasio (1996) e l'utilità indiretta di Magni e Ricci (1991) può costituire un ulteriore passo verso una trattazione più realistica dei processi decisionali.

rationality, decision theory, game theory, Nozick, prisoner's dilemma, indirect utility, somatic marker

Abstract:
Business economics does not provide any methodology for appraising strategic investments, relying on informal approaches. Conversely, financial economics offers us plenty of sophisticated mathematical models unsuitable for applications and based on unrealistic assumptions. This paper presents an example of how strategic investments may be handled with a formal but easy-to-undersand tool. While this paper shows a specific application, a real-life case, we think the model here proposed may be generalized, so contributing to developing a new approach to business decisions. In particular, we think of a fuzzy expert system approach as a convenient tool overwhelming many of the shortcomings inherent in the “crisp” approaches of the financial literature (DCF methods, options pricing, dynamic programming), while avoiding at the same time the refusal of any methodology (typical of business economics). The idea here presented develops some results by Magni et al. (2001) and Facchinetti et al. (2001). An evaluation function is drawn up via “if-then” rules; the latter are made to work automatically by means of an expert system, which adequately replicates the evaluation of human experts. A sensitivity analysis is presented to test the soundness of the model.

strategic, real options, fuzzy expert system, sensitivity analysis

Abstract:
This paper makes use of a fuzzy expert system to evaluate a strategic investment. In particular, the model proposed aims at replicating the actual decision process accomplished by Florim S.p.a., an Italian ceramic tile firm which recently had the opportunity of buying a firm in the USA. The model is perfectly consistent with the evaluation process conducted by Florim’s experts and on the basis of the same data available to the expert’s panel, our expert system provides the same investment value and therefore the same solution to the decision process.

strategic investments, fuzzy expert system, investment value

Abstract:
For one-period projects under certainty, the notion of Net Present Value (NPV) formally translates the notion of economic profit, where the discount rate is the cost of capital. Under uncertainty, the cost of capital is the expected rate of return of an equivalent-risk alternative that the investor might undertake and is often found by taking recourse to the Capital Asset Pricing Model (CAPM). This paper shows that the notions of disequilibrium NPV and economic profit for risky one-period projects are not equivalent: NPV-minded agents are open to framing effects and arbitrage losses, which imply violations of Modigliani and Miller's Proposition I. The notion of disequilibrium (present) value, deductively derived from the CAPM by several researchers and widely used in applied corporate finance, should therefore be dismissed.