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I know that when there are multiple changes of sign in the sequence of cash flows of a project, the project may have multiple IRR, which render this criterion impractical. Therefore, in such situations, avoiding IRR and using other criteria, particularly NPV, is often advocated. Now, my question is that if this problem occurs in the context of calculation of Money-weighted Rate of Return of an investment, what should be done? (Regarding that Money-weighted Rate of Return is just IRR and criteria such as NPV cannot be utilized in this situation)

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Therefore, in such situations, avoiding IRR and using other criteria, particularly NPV, is often advocated.

This is true if you have an appropriate discount factor to use. Note that, by definition, if a cash flow stream has multiple IRRs, that means that there are multiple discount rates for which the NPV is zero, so choosing an appropriate discount rate is critical for a meaningful NPV.

So you can either 1) choose the IRR that is more reasonable in your case (e.g. if you get IRRs of 5% and 200%, then the 5% is probably more reasonable), or 2) choose an appropriate discount factor based on projects of similar risk and use the NPV rule.

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