Equações algébricas e progressões geométricas utilizadas nos métodos de decisão de investimentos baseados no VPL e TIR

Abstract

We present three classical methods of financial decision making: the Net Present Value (NPV), the Equivalent Annual Equivalent Value and the Internal Rate of Return (IRR). The first two are rather simplistic. The third one involves an interesting mathematical problem, since it implies a discussion about the existence and uniqueness of the rates involved. This is a theme often neglected in the writings in Portuguese in this area. Our work aims, at least partially, solving this problem and also refining the very definition of this rate. We used the Descartes Signal Rule to demonstrate the existence and uniqueness of the Internal Rate of Return of a conventional cash flow project. We also present a method of decision making via IRR even with multiple IRRs. Finally, we explored some practical and elementary applications that can be useful in teaching the subject.