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|A project's rates of return (RORs)1, be it the internal rates return (IRRs) or one of the many IRR surrogates, frequently needs to be approximated. The success and efficiency an ROR- approximation procedure depend on the quality the approximation-initiating parameters, such as bounds or seed values (guesses). The existing approximation procedures commonly use bounds and guesses suggested by intuition rather than supported by mathematical considerations. This paper presents three mathematically founded ROR-bounding and eleven ROR-guessing approaches and examines their suitability by using examples of typical project cash-flowpatterns (CFPs). The calculated bounds and guesses not only improve the approximation efficiency, but also allow the process of the ROR discovery to be automated, thereby making it more convenient and reliable.|