Decomposition of Net Final Values: Systemic Value Added and Residual Income

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.