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

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.