Decomposition of a Certain Cash Flow Stream: Systemic Value Added and Net Final Value

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.