Rate of return analysis: Project balance implications, a new class of iterations, and project selection

Problem Investigated. Engineering projects are commonly selected by comparing a project's anticipated rate of return to an internal corporate hurdle rate. A computed rate of return may or may not be unique and, depending on the magnitude and pattern of the net cash flows, a project can have positive real, negative real, and imaginary rates of return.;Procedure and Methods. We develop a fixed-point iteration scheme that is proved to converge linearly and then utilize a sequence acceleration technique to achieve quadratic convergence. We design and analyze an experiment to investigate which combination(s) of selected parameters and at what levels are best-suited to compute accurate results relative to a standard benchmark. Our fixed-point algorithmic scheme is applied to the computation of the positive real rates of return for 36 projects in a specimen batch containing both conventional and unconventional projects.;Results. Our iteration scheme (powered by sequence acceleration) has a favorable impact on achieving our primary goal of accuracy and a secondary goal of speed of computation. (1) Conventional projects converge with 100% accuracy in a maximum of 50 iterations per root at a tolerance of 10 -5. This is achieved at an average speed disadvantage of less than 0:024 seconds compared to the benchmark. (2) Unconventional projects converge with 100% accuracy in a maximum of 500 iterations per root at a tolerance of 10-8. This is achieved at an average speed disadvantage of less than 0:033 seconds compared to the benchmark. (3) The 51 real positive rates of return for all 36 projects in the specimen batch converge with 100% accuracy in a total of 934 iterations, an average of 18 iterations per root. This is a composite of both conventional and unconventional projects. The average number of iterations for conventional projects is 9 and the average number of iterations for unconventional projects is 23.;Conclusions. The new class of iterative algorithm is of value from both business and theoretical perspectives: (1) Business. If the computed minimum and maximum positive real rates of return are equal, a unique rate of return has been found and the use of an internal rate of return project selection method is appropriate. If not, an alternative project selection approach can be adopted. (2) Theoretical. The approach taken currently to determine all positive real rates of return is to compute the eigenvalues from the companion matrix to the future-worth polynomial. The new algorithm presented here could be considered a simpler alternative to an eigenvalue approach to compute and report all positive real rates of return.