Numerical Solution of Multiple Internal Rate of Return with Non-conventional Cash Flows
Keywords:Budan’s theorem, cash flow, Descartes’s rule, IRR, MIRR, net present value, Newton-Raphson method, polynomial, Sturm’s theorem
This paper focuses on solving methods of multiple internal rates of return (MIRR) of the series of non-conventional cash flow when the net present value is equal to zero. The internal rate of return is a popular rule for project acceptance/rejection. When a projects cash flow has three or more sign variations, the internal rate of return (IRR) rule is not easy to obtain multiple internal rates of returns. In his paper, we introduce Descartes’ rule for the maximum positive roots, Bolzano Theorem for the maximum roots in the interval, Budan’s Theorem (sequence), and Sturm’s Theorem (sequence) for the exact numbers of positive real roots and their locations (intervals) where they lie and finally we solve a real problem using Newton-Raphson method for the approximate solution of the polynomial equation.
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