Cycles optimization: The equivalent annuity and the net present value approaches

The paper discusses the use of a generalized version of the equivalent annuity principle, which takes into account interest rate fluctuations over time. When dealing with applications over a sequence of cycles, e.g. plant replacement ones, the equivalent annuity is usually defined with reference to each single cycle or to the whole sequence. First, we study the correspondence between net present values and equivalent annuities as defined above in optimization problems. We show that only the second definition is appropriate for optimization, whenever the length of the cycle is a choice variable. However, also the second is not necessarily correct, when the horizon is finite. Then, we discuss the corresponding problems of optimality, both with an infinite and a finite sequence of cycles. Applications to a simple plant replacement problem are illustrated: they show how different the optimal decisions can be from the equivalent annuity ones.