# IRR Is Flawed; Use NPV Or MIRR Instead

by: Michal Šperka

## Summary

IRR is not equal to annual rate of return.

Assumptions of IRR are not always reasonable and rational. IRR itself may produce misleading results.

What should investors use instead of IRR?

Internal Rate of Return (IRR) is a widely-used financial metric. However, the truth is that concept of IRR is flawed and stock investors usually should not use it for investment appraisal.

An informal survey revealed that 6 out of 30 executive managers could not explain all critical drawbacks of IRR, even though they had used it on a daily basis.

If IRR of Investment A is 20% and cost of capital 10%, it is appropriate to accept the investment, right? If we can invest in Investment B with IRR 25%, it is better to invest in Investment B. Unfortunately, things are not so simple and investors should be extremely careful when interpreting IRR.

Almost every investor needs to decide, whether to use primarily Net Present Value (NPV) or IRR. In terms of absolute valuation, there is almost no other way. However, a large number of investors choose IRR, because it is… so simple to use and calculate. When one evaluates the company, one needs to predict future cash flows (CFs). This step is same for both NPV and IRR. However, NPV method requires discount rate, which is the subject of passionate discussions. Why not skip this step by using IRR? In the end, it is just one very simple Excel function. Still, there are a lot of reasons why not to use IRR.

Multiple IRRs

IRR is a discount rate, for which NPV is equal to 0. However, since IRR function is not linear, it is possible to calculate more IRRs for one stream of CFs, so called unconventional cash flows. There are as many IRRs as changes of CFs from positive to negative and vice versa.

Let's demonstrate it on example. The simplest one is with only three CFs.

 CF 1 -100 CF 2 248 CF 3 -150

Chart describing relationship between NPV and IRR can be found below. As you can see, there are two outputs of IRR. Which one is correct? Both. Excel function, however, usually calculates the first one, since it starts at 0 (that is why there is also input "Guess").

Incorrect Results for Mutually Exclusive Investments

Mutually exclusive investments arise when investor is not able to invest in all investment opportunities. How many investors are able to invest in all stocks? I dare to say that zero. Every investor has financial constraint in terms of his or her capital. However, IRR is not rational financial metric for mutually exclusive investments, since it gives misleading results.

Again, let's demonstrate this on example. Investor John is able and willing to invest \$10. He is deciding whether to invest in Tanzanian Royalty Exploration Corp. (NYSEMKT:TRX) or Rediff.com India Limited (NASDAQ:REDF). He believes that both companies will go bankrupt in two years. For the sake of simplicity, they will pay out their BV. Table stated below should clearly explain, why depending only on IRR is not always very wise.

Stock Stock Price P/B No. of Stocks IRR Payout
TRX \$0.23 0.73 43 17% \$13.55
REDF \$0.77 0.70 12 20% \$13.20

Evidently, if John chooses investment with higher IRR, he will be worse off (will receive lower payout).

Similar misleading results occur, when we assume different investment horizons regarding mutually exclusive investments.

IRR implicitly assumes reinvestment at IRR rate

Assumption of reinvestment at IRR rate is probably the most crucial and most often violated. Internal rate of return is usually understood as an annual yield. That is true only when

• there are no interim CFs or
• interim CFs are reinvested at IRR rate.

Usually neither one of previously stated applies for stock investing.

If investor finds an investment with IRR equal to 20%, is it his annual yield? Probably not, since investor is not going to be able to reinvest interim CFs at 20% p. a. It is crucial to remember this, since only then, we are able to refrain from making too optimistic predictions, which are so typical for some managers and investors.

How to deal with it?

The simplest advice is stop using IRR. Its concept is trivial and apparently easy to interpret. However, its drawbacks can be crucial. In most cases, the most consistent benchmark should be net present value.

If you have read this far and you still want to use IRR, there is a way. There is very similar concept, derived from IRR, called Modified Internal Rate of Return (MIRR). Calculation of MIRR needs three inputs - stream of CFs, financing rate (applied to negative CFs) and reinvestment rate (applied to positive CFs). With this method, we are able to eliminate some of the flaws of IRR.

• MIRR assumes reinvestment at specified reinvestment rate
• MIRR eliminates problem with multiple outputs

For the last time, let's demonstrate everything on example. Stock price of Dynagas LNG Partners LP (NYSE:DLNG) is \$9.21. The company paid dividend equal to \$1.69. If we assumed dividend growth rate at 2% forever, IRR would be 20.35%.

It is highly unlikely that investor will be able to reinvest received dividends at more than 20%. For that reason, he cannot take IRR as his annual yield. If we use MIRR and reinvest dividends at (still pretty high) 10% p. a., value of MIRR will be 12%. The value of MIRR more precisely approximate annual rate of return for investor.

MIRR function is available in Excel, so its application is as simple as application of IRR. If you are still not persuaded to stop using IRR, I recommend to think thoroughly about the result.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.