On Algebraic Anomalies in Polynomials and Net-Present-Value Decisions

Investment Decision Analysis using NPV has become the primary method of investment evaluation. However, NPV, Modified-IRR (MIRR) and related approaches are deeply flawed and are very sensitive to the time horizon, the signs of the periodic cash flows, and discount rates that exceed 100% or are below -100%. The NPV-MIRR Model does not accommodate the differences between compounded interest rates and simple interest rates and does not account for Real Options, Regret or Rejoice in decision making. This article contributes to the existing literature by: i) simulating and proving new biases and errors inherent in the NPV-MIRR model, ii) developing the necessary and sufficient conditions for Monotonic NPV ("well behaved" NPV); iii) developing the necessary and sufficient conditions for the anomalous behavior of NPV, iv) explaining the conditions under which Discount Rates can be negative (less than zero); v) developing the conditions under which Negative Discount Rates are justified, and vi) proving that the Power Rule and the Inverse Function Rule in differential Calculus, are both wrong