A Method And Computer Algorithm For Isolation And Calculation Of The Real Internal Rates Of Return

The identification of the real internal rates of return (IRR's) of a project is essential for its economic evaluation. The existing methods for the calculation of IRR's are both cumbersome and unreliable, mainly because of their inability to effectively isolate the real IRR's and incapability of discovering multiple IRR's of even multiplicity. In this paper, a concept of the 'cash flow pattern tree used for isolation of the real IRR's of a project is presented. This concept, combined with the Sturm procedure for counting the real distinct zeros of a polynomial within a specified interval, leads to the development of a method and computer program for isolation and calculation of the real IRR's of a project. The method examines whether or not real IRR's exist, and if they do, isolates them within bounded and narrow intervals in a mathematically founded way. The isolated IRR's, whether simple or multiple, are subsequently calculated either directly or by means of an appropriate approximation procedure. Numerical examples assist the development of the method and the corresponding computer algorithm. Because any Net Present Value treated as a function of interest rate can easily be transformed into a polynomial, the method presented also constitutes a method for finding the real zeros of a polynomial.