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If NPV on a project is negative, is there always the assumption that IRR is going to be less than the cost of capital on the project. 

I hear from the Kaplan text there could be exceptions to this case (where the IRR and NPV  give conflicting messages with regards to a project).

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For a single project, NPV and IRR will always give the same answer: if NPV is positive, IRR will be greater than the cost of capital, and if NPV is negative, IRR will be less than the cost of capital.

However, if you’re trying to rank several projects from best to worst, NPV and IRR may give different rankings.

Simplify the complicated side; don't complify the simplicated side.

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A problem might occur if a project has irregular cash flows (regular would be an initial investment payments and then subsequent recoveries only). Then you might have multiple IRRs, some of which above, some below the cost of capital.