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How NPV and IRR Can Rank Projects Differently

Article Quant Q&A · Author: Harsh Sharma
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Summary

The document clarifies that describing net present value as biased toward long-lived projects is not a claim about statistical bias. Rather, NPV and internal rate of return can rank the same projects differently because they measure value in different ways. NPV expresses value in currency at a chosen discount rate, while IRR is the rate that makes a project’s NPV zero.

The examples explain two ranking effects. As a project’s initial investment becomes very small relative to its later positive cash flows, its IRR can become extremely high, while its NPV does not behave in the same way. For distant positive cash flows, the IRR associated with a positive NPV at the chosen discount rate is higher than that discount rate; discounting those distant flows at the higher rate reduces their value more. These are conceptual explanations, not a general ranking rule or empirical test. The document gives no guidance on resolving conflicts between the measures or handling complex cash flows with multiple IRRs.

Key ideas

  • NPV’s supposed bias toward longer projects refers to possible ranking differences, not statistical bias.
  • NPV reports discounted value in currency, while IRR is the rate that makes NPV equal zero.
  • A very small initial investment can make a project’s IRR unusually high without a comparable change in NPV.
  • A higher discount rate reduces the present value of distant cash flows more strongly.
  • The examples illustrate possible differences and do not establish a universal project-ranking rule.

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# Why is NPV a biased measure?


# Why is NPV a biased measure?












I was studying return measures such as NPV and IRR from Damodaran's "Applied Corporate Finance" and one thing that he continuously mentioned was that NPV is biased towards projects with longer lives while IRR is biased towards projects with small initial investment. While the second point seems valid given that IRR is a percentage based scaled measure and should prefer projects with small investments, I haven't been able to wrap my head around the NPV's bias.

Is the author talking about some inherent statistical bias that comes from discounting the cash flows? If yes, then how does this bias comes up?

Any help would be appreciated.

Regards

## Answer by fes (score 3, accepted)

https://quant.stackexchange.com/a/70902

There is no statistical "bias". It is just that NPV and IRR can provide different rankings to projects. For example consider a project with a small initial investment and positive cash flows after that. When the initial investment approaches zero the IRR approaches infinity but NPV does not. Here you can see how the IRR criterion is more favorable to projects with small initial investments.

Assume you have a project with positive cash flows far ahead. Assume the NPV is positive under some discount rate. IRR is defined as the discount rate under which the NPV of the project would be zero so this must be higher than the discount rate you used to obtain a positive NPV. The effects of this higher discount rate compound when discounting cash flows in the distant future so this penalizes such projects more heavily.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.