Continuous Funds Flow Discounted Cash Flow ROR by Numerical Methods Using the HP-41 Series Calculator
Authors: Newell T. M. 
Published: December 2007

ABSTRACT
A standing challenge for many years, particularly to the petroleum industry, has been the development of means to perform economic evaluations of potential investment opportunities in terms of Net Present Value (NPV) and the Discounted Cash Flow Rate of Return (DCFROR) based on continuous-funds-flow algorithms describing the entire economic life of the investment.
Historically, the complex algorithms required have been tedious to write, for often it is desired to use as components of the algorithms expressions that are least squares fits of models to data, procedures frequently requiring huge amounts of computation. Further, for procedures based on the DCFROR, the measuring stick preferred by most sophisticated companies1, the complex overall algorithm is an implicit function of the DCFROR, and the latter cannot be solved for by formal mathematical procedures. Computers utilizing numerical methods reduce these two constraints to neglible status. This paper will demonstrate that such evaluations can be adequately performed even on an HP-41 Series programmable calculator.
Most companies require in the making of economic evaluations of investment opportunities the use of a number of measuring sticks. Continuous-funds-flow analyses have been highly desired over a period of several decades as one of these. To the best of my knowledge, all published versions are of limited flexibility. The approaches have required severe simplifications in scenarios, making them of little practical use.
A monumental attempt was published by F. Brons & M.S. McCarry, Jr.2 The procedure is tedious, requiring interpolations in specially prepared tables, and is applicable only to specific cases not characteristics of most real world situations. The authors were well aware of this, and clearly stated the limitations in the paper.
The major limitation of the procedure of Brons & McCarry, Jr., is that net cash flow must follow the same decline model as does the production rate (exponential, hyperbolic, harmonic or constant) for the entire lifetime of the project. This limitation arises because Brons & McCarry, Jr., as well as others, have used formal mathematical procedures as the means to arrive at solutions for NPV and DCFROR.
All that is needed to expand these procedures to real world situations is to abandon solutions by formal mathematical procedures and resort to numerical methods. The application of numerical methods to this general problem is the subject of this paper. The approach will be demonstrated by evaluation of a simulated oil field problem, as follows.
In late 1982, a property evaluator for a major oil company was completing a reevaluation of a producing property for the purpose of making a final presentation to a prospective buyer. January 1, 1983, was selected as the date for transfer of ownership. Similar deals had been made with the prospective buyer, an independent, in the past, and the major company knew that the independent's operation remained near a 42% tax bracket and that the independent had no difficulty in raising money in the amount of the $750,000 asking price.