The paper discusses the use of a generalized version of the equivalent annuity principle, which takes into account interest rate #uctuations over time. When dealing with applications over a sequence of cycles, e.g. plant replacement ones, the equivalent annuity is usually de"ned with reference to each single cycle or to the whole sequence. First, we study the correspondence between net present values and equivalent annuities as de"ned above in optimization problems. We show that only the second de"nition 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 "nite. Then, we discuss the corresponding problems of optimality, both with an in"nite and a "nite sequence of cycles. Applications to a simple plant replacement problem are illustrated: they show how di!erent the optimal decisions can be from the equivalent annuity ones.