Irr, Roe and Npv: Formal and Conceptual Convergences in a Systemic Approach

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]