Systemic Value Added, Residual Income and Decomposition of a Cash Flow Stream

Abstract

Abstract. The problem of decomposing a cash flow has been treated in recent years by Gronchi (1986Gronchi ( , 1987, Peccati (1987Peccati ( , 1991Peccati ( , 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 income and value creation: An investigation into the lost-capital paradigm

“…In Magni (2000aMagni ( ,b, 2001aMagni ( ,b, 2003 attention is drawn on shareholders' wealth. It is assumed that, in case of acceptance of the project, shareholders reinvest the equity cash flows at the cost of capital i (this is the standard assumption of the NPV rule).…”

“…(9) is just eq. (6) disguised in a different shape, given that C t − C t = y t (i) for every t (see Magni, 2000aMagni, , 2003Magni, , 2005: The lost capital may therefore be decomposed into an actual capital C t and a foregone capital C t . In his papers Magni shows that the lost capital is just the outstanding capital of a shadow project whose standard residual income coincides with the lost-capital residual income of project d. 1…”

“…His argument is the only one that is consistent with both paradigms. As for claim [a], it gives us a fourth interpretation of the lost capital, besides the three previously found: The lost capital is the capital which is lost by investors (section 2), is the outstanding capital of a shadow project whose standard RI coincides with the lost-capital RI (Magni, 2000a(Magni, , 2005(Magni, , 2006, is the capital infused into the business (section 5), and is the capital "borrowed" from shareholders, whose interest rate is the equity cost of capital. These four interpretations, while seemingly discordant, are coherently harmonized under the formal lens of the LC paradigm.Claim [b] is evident from Table 3, which uses the definition of CSV and ARI given in the previous and current section respectively: In Anthony's view, value is recorded only in the last period, whereas the previous RIs are zero.…”

“…The traditional accepted formalization of opportunity cost rests on the assumption of investment of the actual capital at the cost of capital. In recent years, a new definition of residual income, called Systemic Value Added, has been proposed in Magni (2000aMagni ( ,b,c, 2001aMagni ( ,b, 2003, derived from the comparison between two alternative dynamic systems: The first one describes the net worth's evolution in case of project acceptance, the second one refers to project rejection. Rather than a particular metric, the Systemic Value Added is a paradigm, on the basis of which one can construct infinite possible metrics.…”

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AbstractThis paper presents a new way of measuring residual income, originally introduced by Magni (2000aMagni ( ,b,c, 2001aMagni ( ,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.

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