We’ve seen that it’s possible to get more than one IRR. If you wanted to make sure that you had found all of the possible IRRs, how could you do it?

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The answer comes from the great mathematician, philosopher, and financial analyst Descartes (of “I think; therefore I am” fame). Descartes’s Rule of Sign says that the maximum number of IRRs that there can be is equal to the number of times that the cash flows change sign from positive to negative and/or negative to positive[latex].^{7}[/latex]
In our example with the 25 percent and 33 1⁄3 percent IRRs, could there be yet another IRR? The cash flows flip from negative to positive, then back to negative, for a total of two sign changes. Therefore, according to Descartes’s rule, the maximum number of IRRs is two and we don’t need to look for any more. Note that the actual number of IRRs can be less than the maximum (see Example 9.5).

Question 9.6: We’ve seen that it’s possible to get more than one IRR. If y...

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