Exo-parametric (“inside-out”) model of discounted cash flow calculations using NPV%: Macro calculation of coefficients for an exact, collapsed financial model

Abstract

In a 2013 paper (Mellichamp, 2013), the author developed an internally-consistent discounted cash flow (DCF) model that represents the key financial outputs of a conceptual chemical process design using just four variables:•Total investment, TI (capital required to construct and operate a project for NTotal years),•ROIBT and NPVproj (the traditional annual and long-term (NPV) profitabilities), and•NPV% [a new metric whose reciprocal, (NPV%)−1, directly expresses short-term project risk].A traditional spreadsheet relating these four dependent long- and short-term financial metrics to a project's two independent design variables, PBT and FC, is functionally dependent on the many process design parameters (tax rate, discount factor, etc.) and highly complicated, involving non-linear (mostly geometric) relationships. Surprisingly, an exact linear-in-the-parameters “inner model” including the usual nonlinear relation for ROIBT is obtained by collapsing the original large-scale financial model (the complicated spreadsheet) using these four dependent variables, if the coefficients are functions of fixed design parameters, as when held constant in design. The power/utility to understand several key features of a project's design financial characteristics are revealed via the “inner model” through this reversal of the usual modeling hierarchy. The “outer model” coefficients incorporate the highly non-linear DCF functionalities. The new form is referred to as “exo-parametric” or an “inside-out” model.