# Conflict Between NPV and IRR (And Problem with IRR)

When you are analyzing a single conventional project, both NPV and IRR will provide you the same indicator about whether to accept the project or not. However, when comparing two projects, the NPV and IRR may provide conflicting results. It may be so that one project has higher NPV while the other has a higher IRR. This difference could occur because of the different cash flow patterns in the two projects.

The following example illustrates this point.

 Project A Project B Year 0 -5000 -5000 Year 1 2000 0 Year 2 2000 0 Year 3 2000 0 Year 4 2000 0 Year 5 2000 15000 NPV $2,581.57$4,313.82 IRR 29% 25%

The above example assumes a discount rate of 10%. As you can see, Project A has higher IRR, while Project B has higher NPV.

If these two projects were independent, it wouldn’t matter much because the firm can accept both the projects. However, in case of mutually exclusive projects, the firm needs to decide one of the two projects to invest in.

When facing such a situation, the project with a higher NPV should be chosen because there is an inherent reinvestment assumption. In our calculation, there is an assumption that the cash flows will be reinvested at the same discount rate at which they are discounted. In the NPV calculation, the implicit assumption for reinvestment rate is 10%. In IRR, the implicit reinvestment rate assumption is of 29% or 25%. The reinvestment rate of 29% or 25% in IRR is quite unrealistic compared to NPV. This makes the NPV results superior to the IRR results. In this example, project B should be chosen.

The above example illustrated the conflicting results of NPV and IRR due to differing cash flow patterns. The conflicting results can also occur because of the size and investment of the projects. A small project may have low NPV but higher IRR.

 Project A Project B Year 0 -5000 -20000 Year 1 2000 7000 Year 2 2000 7000 Year 3 2000 7000 Year 4 2000 7000 Year 5 2000 7000 NPV $2,581.57$6,535.51 IRR 29% 22%

In this case, Project A has lower NPV compared to Project B but a higher IRR. Again, if these were mutually exclusive projects, we should choose the one with higher NPV, that is, project B.

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