Talk:Internal rate of return

Alternative method to IRR and NPV
The paper states that "A method called marginal IRR can be used to adapt the IRR methodology to this case." However, the method known as "Return Duration", developed in 2004 is more widely used and appropriate. More information can be found through the article: http://www.findarticles.com/p/articles/mi_qa3621/is_200401/ai_n9364326 or by a simple Google search.

"interest rate" should be replaced with "discount rate"

Perhaps "Return Duration" deserves its own page. Jonathan G. G. Lewis 02:34, 16 November 2013 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)

IRR limitations
As an investment decision tool the IRR can be misleading in the case, that the money bound in an investment is verly little or changing very much. This is the situation if investments are financed with debt. The computation of the IRR from the cash flows may result a highly positive IRR. But on very little capital bound. So you are ending with an investment that bears a high risk because of the loan and a little positive cash flow. In this cases it is better to calculate the NPV, because one may recognizies the the small value compared to the high loan. Another example is stocktrading where the money is not always invested. Therfore the bound capital is changeing very much over the investment duration and the calculated IRR is too high.

An in-deep discussion of strong points and limitations of IRR probably someone writing about this should take into account.


 * Returns in general deserve special attention in the context of leverage or margin trading. There are the returns on net capital, which are the leveraged returns, and the returns on gross capital, the unleveraged return. Comparing leveraged returns with returns on investments without leverage is indeed potentially deceptive. Jonathan G. G. Lewis 04:16, 31 December 2015 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)


 * Furthermore, the issues the contributor mentions do not apply only to the IRR method: the return measured by any method is liable to be volatile, and could be hard to interpret, when the net capital invested is small compared with the cash flows, or changes a lot.
 * Jonathan G. G. Lewis 05:27, 18 March 2019 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)

I expanded the quotations from Ludovic Phalippou's paper, An Inconvenient Fact: Private Equity Returns & The Billionaire Factory to provide fuller context, added more neutral tone to what is a contentious statement, and moved them to their own subsection on private equity. I also rewrote the introductory line to these quotes. --Jonathan G. G. Lewis 23:07, 24 October 2020 (UTC)

dollar-weighted return
I see 193.30.236.72 has removed my statement that this is also known as dollar-weighted return. I wonder why, as this is a common term. See, for example, "Investments" (1999) by Sharpe, Alexander, and Bailey, page 827. If your objection to this is the US centrism of "dollar", then I propose "money-weighted return". This is to be contrasted with time-weighted return, which is just another name for the geometric mean rate of return. What do others think? Btyner 03:22, 23 August 2005 (UTC)

You are in the right - there are two types of RR's that I know of: Dollar-weighted Rate of Return, and Time-weighted Rate of Return. Dollar-weighted is just another way of saying IRR.

Remember also the Simple Dietz and Modified Dietz returns, which are methods also classed as money-weighted returns. Jonathan G. G. Lewis 01:28, 16 November 2013 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)

I disagree slightly with the description of time-weighted return as "just another name for the geometric mean rate of return". The key to the time-weighted return method is to break the period at the point when there are external flows. If you don't do this, you are missing the point. Jonathan G. G. Lewis 04:20, 31 December 2015 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)

external Weblink
"Capital Budgeting, audio lecture with slideshow": slideshow has few information and no audio.

Calculation of IRR
I am curious about the calculation of IRRs. Specifically, in none of the sources I've seen has anyone mentioned that not only can you get multiple answers because you have to solve an n-th degree equation, but you could also end up with a complex number as the solution, and I don't see how this could make sense. How can you tell which r is the correct answer given multiple possible rs, and what does one do in the case that the solution is complex?


 * Both r's are correct. One may be useful. I would argue that when there are multiple answers, prudent financial players would take the lowest. Note that multiple answers only exist, if I remember correctly, when there are more than two negative cash flows (assuming this is an investment project). One can also massage the numbers carefully to check for reality - for example, if the project has a maintenance issue in year 5 that causes negative cash flows in that year, spread the maintenance costs over two years (to avoid the negative) and see roughly where the IRR comes in. Or to put this a different way, if you have up/down cash flows like this, it is an indication that the project needs to be studied more carefully.--Gregalton 16:08, 5 January 2007 (UTC)


 * I don't understand how they both could be. In the case of a second degree one could end up with a positive and a negative r, for example. Say, on the example from p807 of Investments by Bodie, Kane, Marcus, where it is stated that rate of return is 7.117% (the example is $$50 + \frac{53}{1+r} = \frac{2}{1+r} + \frac{112}{(1+r)^2}$$), which makes perfect sense, but the same equation could also yield an answer of -309%, which makes no sense at all. --Johs 17:09, 5 January 2007 (UTC)


 * In a sense it makes sense, and in a sense it doesn't. The mathematical equation itself has no problem with either value, because the equation does actually 'not' represent the true meaning of IRR from a real-world perspective, only the approximated meaning. Any value below -100% would make no sense from a financial point of view (ie you can't get a 105% discount on a product that only has a 100% value unless required by law, in which case it would be a cash outflow instead of an inflow), but from a mathematical point of view, it's very much so possible because math just doesn't care about us puny earthlings130.226.173.119 (talk) 10:11, 13 February 2008 (UTC)


 * I disagree with the previous couple of comments. Just as a negative NPV indicates a loss-making project, or liability rather than an asset, in the same way, a return of less than -100% indicates an asset turning into a liability over the period of measurement, or vice versa. This could happen more than once for a project or portfolio.


 * Jonathan G. G. Lewis 02:48, 16 November 2013 (UTC)


 * To correct myself, a negative NPV does not indicate a loss-making project. A negative NPV indicates that a project destroys value, i.e. engaging in such a project should reduce the theoretical value of the firm, which is not the same as a loss. A negative IRR would indicate a net loss over the lifetime of the project.


 * Jonathan G. G. Lewis 07:51, 6 January 2014 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)


 * To clarify the point I was trying to make above in November last year however, a rate of return of -300% for example would indicate that the value of the investment flips between positive and negative (or between asset and liability) each period, and each period it also doubles in magnitude - rather strange and unusual behaviour for an investment, but not entirely incomprehensible.


 * Jonathan G. G. Lewis 07:58, 6 January 2014 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)


 * I think IRR is trying to define a sort of average of periodic percent returns. That doesn't give you any sort of useful answer if some periods are positive and some negative.  A 50% loss in one period is not offset by a 50% gain in the following period.  e.g. Start with $100, lose 50%, you have $50.  Gain 50% next period and you have $75.  The average return for the two periods is 0%, but the overall loss is $25, which is 25% of the original amount. Percents don't average cleanly. I think economists use natural logs.  SueHay 18:38, 17 January 2007 (UTC)


 * The contributor SueHay I think is referring to continuously-compounded or logarithmic returns. These do not allow the switching between asset and liability I mentioned above. Whether this is seen as an advantage or limitation is a matter of point of view.


 * Jonathan G. G. Lewis 02:48, 16 November 2013 (UTC)

This Talk Page is intended for discussion of the main article rather than general discussion of the subject-matter, but hopefully some of it may be relevant to indicating where confusion should be cleared up in the main article.

Jonathan G. G. Lewis 03:01, 16 November 2013 (UTC)

Cross over point method
I'd suggest adding information regarding the cross over point method. —The preceding unsigned comment was added by 59.167.70.183 (talk) 18:56, 17 April 2007 (UTC).

IRR is not a Compounded Rate
This article states that, "The IRR is the annualized effective compounded return rate which can be earned on the invested capital," but this is not the case. A compounded rate uses the interest accumulated towards the principle each period, but an IRR only accounts for the amount of money still invested (not interested or principle reinvested). If you break down the IRR mathematically, the return "OF" investment fluctuates period to period, depending on the amount of cash coming in, but the return "ON" investment (i.e. interest earned) isn't brought to the next period. I will try to explain using a series of cash flows (CF0 through CF3), where CF0 is the initial investment and CF1-CF3 are EOP figures:

CF0=150, CF1=25, CF2=25, CF3=193.2, IRR=20%

Year 1: 150x.2=30 (The actual cash flow (CF1) is 25 and so 5 is added into (internally) to deal (30 "ON", -5 "OF"))

Year 2: 155x.2=31 (The actual cash flow (CF2) is 25 and so 6 is added into (internally) to deal (31 "ON", -6 "OF"))

Year 3: 161x.2=32.2 (The actual cash flow (CF3) is 193.2, representing the internally invested 161.2, plus 32.2 in interest)

Note that when you take away the 5 added in year 1 and 6 added in year 2 from the 161 in year 3 you get your original investment "OF" 150 back. When you take the 30 in year 1, 31 in year 2, and 32.2 in year 3 you get your return "ON" investment (93.2). Your return "OF" investment (150), plus the return "ON" investment (93.2) is 243.2, totals 243.2. This of course is the sum of all the cash flows (CF1-CF3) after the initial investment (25+25+193.2=243.2). Simply put, the return "ON" investment (the interest) is never added to the principle, and so the IRR cannot be a compounded rate of return.


 * Does anyone have references they can cite to support the points made above?


 * Jonathan G. G. Lewis 03:11, 16 November 2013 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)


 * The cash flows CF0, CF1, CF2, CF3 are all positive, so no IRR can be calculated. I would assume instead, by the contributor's reference to "initial investment" and "EOP figures", that it is intended that CF0 should have the opposite sign to the others.


 * Jonathan G. G. Lewis 03:26, 16 November 2013 (UTC)


 * I'm inclined to draw the conclusion that the contributor who made this argument in this section has been blindsided by the use of the word "compounded" in the statement in question from the article. The use of the word "compounded" in this context, it seems to me, does not carry equivalence to "reinvestment" that the contributor seems to take it to carry here.


 * The long example he presents here indeed demonstrates that cash flows are not reinvested. Indeed, if they were reinvested, then they would not appear as cash flows. (At least, they would not appear as cash flows at the points in time that they do appear, and the particular amount of cash flow each time.) So this point which the contributor seeks to make so far is certainly true, that the cash flows at each point in time are exactly that, cash flows at each point in time, and they are not reinvested.


 * But what is the implication of this? Does this mean that the IRR is not the "annualized effective compounded return rate which can be earned on the invested capital"?


 * A subsidiary question is whether the word "compounded" makes any difference to this sentence. I would suspect that it is not entirely necessary, but I do not think it is incorrect either.


 * The reason I believe the original contributor included the word "compounded" is that the IRR applies compounding in its essence. IRR without compounding is not IRR at all. (Without compounding, it would be identical to the modified Dietz method of estimating return, in fact.) The concepts of compounding and discounting are basic to the notion of net present value, which is essential to the method of IRR.


 * So please let's just leave the word "compounding" in.


 * Jonathan G. G. Lewis 08:32, 21 November 2013 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)

IRR is not a profitability metrics.
IRR is not a profitability metrics. Since it is a discount rate at which NPV=0, it is a threshold that separates a good project from a bad project. If WACC is higher than IRR then NPV is negative and vice versa. —Preceding unsigned comment added by 164.114.248.33 (talk) 17:39, 5 October 2010 (UTC)


 * How does it follow from these statements that IRR is not a profitability metric? I see no logic in this argument. Jonathan G. G. Lewis 07:10, 6 January 2014 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)


 * Perhaps the contributor is unaware of any uses of IRR beyond capital budgeting, and might be interested to discover it is also used to compare private equity investments. Jonathan G. G. Lewis 07:41, 6 January 2014 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)

Jonazo, the first sentence in the article reads: "The internal rate of return (IRR) or economic rate of return (ERR) is a rate of return used in capital budgeting to measure and compare the profitability of investments.". We are not talking about PE - if you want to add a section on other uses, I would welcome it.

To elaborate a bit on the original comment, let's say a project IRR is 10%. Does it make it profitable? We do not know unless we compare it to the relevant WACC. If WACC is below this 10%, then NPV will be positive and the project is profitable. How profitable? We do not know on the basis of IRR only and therefore cannot compare profitability of investments. Why not? Because these investments may have different WACC.

Even in case of PE, when you put a cash in/cash out sheet and calculate IRR, it gives you return on your equity investment and not profitability, unless you are using a different definition.

Hope this was useful. — Preceding unsigned comment added by 164.114.206.185 (talk) 23:03, 8 January 2015 (UTC)


 * On their own, by some similar corresponding arguments to the one above, neither would any other alternative measures of return be measures of profit either. So what are they? They are fundamentally profit/capital, especially in the absence of interim cash flows. If that's not a profitability metric, then what is?


 * Just to elaborate, comparing a rate of return with WACC as a hurdle rate is an indicator of added value to the firm (if any). Positive NPV is not the same as profitability. A profitable project adds no value unless it has IRR above WACC, and even destroys value if IRR < WACC. According to my understanding therefore, IRR is a measure of profitability, but only indicates added value in comparison with WACC. Jonathan G. G. Lewis 10:18, 30 December 2015 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)

Error in IRR example
The results of the example IRR calculation given in this article are incorrect! The stated result for the IRR of 14.3% is way off. The correct IRR from the data presented is 153.69%. In fact, it should be obvious from the input data that the IRR will be much greater than 14.3%.

71.229.207.177 (talk) 18:55, 22 December 2011 (UTC)


 * Thanks. Someone put some random numbers in there a few days ago.  I've restored the previous example which checks to 14.3.  Kuru   (talk)  23:34, 22 December 2011 (UTC)

The reinvestment misconception
I come at this from a from a non-finance background, so please excuse if I am misunderstanding the content, I am simply reading this at face value from a technical non-specialist perspective. The section on 'The reinvestment misconception' seems invalid and not sufficiently supported by reputable citations. If Equation B yields the results of Equation A by explicity applying the results of Equation A, then it's fair to say that Equation A implicitly satisfies the implications of Equation B. In this case, putting the IRR in the MIRR as the re-investment rate yields equivalent results. The implication is the incorrectly named 'hidden assumption'. Further, the quoted sources for the 'hidden' (it is implicit, not hidden) 'assumption' (it is a mathematical equivalence or property, not an assumption) are indeed reputable. The source for the contrary view is propertymetrics.com, hardly a reputable published source. Is this content WP:OR? Although I don't feel sufficiently familiar with the material to WP:BE BOLD, I suggest this section should be rewritten or removed. Doug (talk) 22:56, 29 July 2014 (UTC)
 * The reinvestment misconception section may not have had a lot of citations but it is correct and is well-done. There are a number of good citations available. See, for example, Jack Lohman's article (Engineering Economist, summer 1988), or Keef and Roush's article (Accounting Education,2001,10(1), pp.105-116). At its simplest, the IRR cannot be based on an implicit assumption that cash inflows will be reinvested at the IRR because the IRR would be the same even if the firm chooses to distribute all cash inflows to shareholders rather than to reinvest them. There is no necessity to reinvest any of the cash flows. Of course if inflows were to be reinvested at the IRR rate then this combined project (the original project combined with the reinvestment project) would also have an IRR the same as the original project. However the combined project would be a very different project from the original project, since it would have a longer duration and likely a different NPV. Somehow, some people have confused the unlikely possibility of reinvesting a project's inflows at the IRR as an implicit assumption of the IRR calculation. However the cash flows of a project are reinvested (if they are) at whatever rate,the IRR of the original project is unchanged. GrayBorn (talk) 12:30, 26 August 2014 (UTC)
 * I side with those who disagree that there is any implicit or hidden assumption in the definition of IRR that reinvestment of outflows is available at the IRR (or alternative investments are available yielding the IRR for inflows, prior to the point of time they flow into the investment). MIRR serves a somewhat different purpose to IRR, because instead of a return on a single investment or instrument, with its own characteristic inflows and outflows, it is actually a return on a portfolio combining the investment in question and an alternative instrument, with a fixed rate of return, to receive and hold the cash outflows, (or possibly delayed inflows as well), so that there are no flows between start and end of the period, only an inflow at the start, and an outflow at the end. Failure to see this distinction seems to me to be the root of the confusion. If someone needs a portfolio return such as MIRR, then it is suitable, and IRR unsuitable for their purposes, but IRR has its own many purposes, and my guess is that it is the vastly more important measure of the two. The validity of MIRR for its purposes in no way invalidates IRR, and vice versa. Reputable sources who refer to hidden assumptions in the definition IRR are no doubt being rhetorical and not strictly rigorous, and are trying to explain the purpose of MIRR. They are not seriously trying to undermine the obvious importance and validity of IRR. Jonathan G. G. Lewis 11:30, 26 October 2014 (UTC)  — Preceding unsigned comment added by Jonazo (talk • contribs)
 * I specialize in the analysis of private equity, a field where IRR is used frequently and I agree with Doug that this section has serious flaws and should be removed or be revised substantially. To keep this section, especially given the lack of substantive references, does a great disservice to the readers. To contend that the reinvestment hypothesis is merely a "misconception" is to ignore how IRR is used (and misused) in practice. Bottom line, while it may technically be the case that it might be the case "there is no hidden reinvestment assumption associated" in the IRR formula/algorithms itself, it is easily demonstrated that IRR is arithmetically identical to MIRR where the interest and finance rates are the same as the resulting rate of return. As a result, using IRR to measure returns of an investment with interim distributions is absolutely equivalent to a rate of return where those distributions are reinvested at the same rate. This reinvestment hypothesis cannot be dismissed as a mere "misconception": It is the root of the reason why one should never use IRR to measure performance of investments with interim distributions.Robertmryan (talk) 18:19, 25 April 2015 (UTC)
 * It would be nice to find some wording which everyone can agree is both truthful and neutral. As a mathematician, I am somewhat taken aback by claims there is some absolute mathematical truth behind one side of the argument or the other. I see merit on both sides, and no knock-down logic, either mathematical or any other kind, to demolish either point of view. There is subtlety to this issue which goes to the heart of the concept of IRR, so for the sake of the layperson Wikipedia readership, I hope contributors aim towards a happy compromise in the main article. Even this discussion page is not meant as a forum to argue over content. Jonathan G. G. Lewis 07:52, 30 December 2015 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)


 * I have read content on several websites claiming there are assumptions underlying the IRR. I do not find any of them helpful. The IRR method has no such assumptions, as far as I can tell, any more than the Modified Dietz method or time-weighted method has any such hidden assumptions. It is quite possible to jump to erroneous conclusions, if one does not understand properly what IRR really means, but that does not mean the method has any implicit assumptions. Jonathan G. G. Lewis 04:45, 31 December 2015 (UTC)


 * Commentators arguing that IRR has some hidden assumption which will throw the unwary, have emphasised the fact that fixing the reinvestment rate to the IRR makes the MIRR equal to the IRR, but what does this really tell us about any purported assumptions underlying the IRR method? It tells me that, since people tend to run the risk of naïvely assuming that all the capital is invested at the beginning, and expect all the return to be realised at the very end, people should think more carefully about the nature of returns. IRR caters for much more complex cash flow scenarios, and the naïve assumptions are nothing to do with the IRR method itself, it seems to me, but in the users' interpretation of return instead.


 * Timing of cash flows is important. If you are confused about the nature of rates of return, check out the time-weighted return article, which explains how the timing of cash flows and returns in the sub-periods between cash flows can be combined over the overall period in such a way to remove the effect of good or bad timing of cash flows. This is conspicuously not the case with IRR, or other money-weighted methods. The timing of cash flows is taken into account calculating IRR, in such a way that every dollar returns the same rate, for as long as it is included in the project or investment. Before it is paid in, or after it is paid out, is another story.


 * Consider the absurdity of arguing that the dividend yield on a stock, or the current yield on bond, has to depend on a reinvestment rate. The fact that dividend or coupon income might be paid at shorter intervals than a year means that the income return is not the same as the dividend yield or the current yield, but the rate you can reinvest the income should not change the simple formulae for dividend yield or current yield into some kind of MIRR. It is a confusion of purposes of these different metrics, nothing more.--Jonathan G. G. Lewis 03:45, 2 January 2016 (UTC)


 * There is an important reason for including the section on the reinvestment misconception. Advocates of the MIRR approach motivate the MIRR in two steps by arguing: (i) that the IRR implicitly assumes reinvestment at the IRR, and (ii) that assuming reinvestment at the IRR is unreasonable. There is no issue with step (ii), but if step (i) is false then the main case for using the MIRR collapses. I reference five academic articles on the main page [starting with Dudley (1972)] that refute step (i). Since Dudley’s paper was published, to the best of my knowledge not one academic finance journal article has contradicted any of these five articles.


 * RobertMryan in a comment above states: “using IRR to measure returns of an investment with interim distributions is absolutely equivalent to a rate of return where those distributions are reinvested at the same rate”. Although this statement is correct in the very weak sense that the rate of return is the same in each case, the economic realities in the two cases can be vastly different. Suppose a small investment of $50 returns $100 in one year. That is a return of 100% p.a. Its IRR and its NPV both would be increased very slightly (IRR = 100.000004%) if the investment had returned an additional dollar in year 20. In other words, the additional dollar in 20 years time has no economic significance. However, if you believe that the IRR has an implicit assumption that inflows are reinvested at the IRR rate, then you believe that the IRR calculation implies that the $50 investment will turn into more than $52,000,000 by year 20! That certainly would be a strong implicit assumption, were it correct. [Of course, the MIRR is strongly affected by the additional dollar in year 20. With an assumed reinvestment rate of 10%, the investment’s MIRR would drop to just 13.3%.]GrayBorn (talk) 22:51, 3 January 2016 (UTC)


 * I sympathize with the gist of the comments immediately above, but I would not go so far as to argue that the weakness of the imputed argument against IRR (in favour of replacing it with MIRR 'in all circumstances') trashes the usefulness the MIRR method altogether. They can happily coexist, as far as I see it - although if no such reinvestment rate is available, you cannot calculate MIRR, which seems a bit of a dead end. In practical terms, you calculate what you can, don't you? I think this whole debate hinges on a different misconception, which is that there is some "true" method of calculating "the" rate of return, which trumps any others. In reality, all returns methods are tools for analysis of the data available. --Jonathan G. G. Lewis 01:40, 4 January 2016 (UTC)


 * First, I want to say that this section has gotten much better than earlier iterations. Second, on the question of whether there is a real reinvestment assumption implicit in IRR or whether it's a "naive" misuse of IRR, I'd suggest that this section adopt a more neutral position. What I think that we can conclude is IRR, alone, has limitations when attempting capture certain characteristics of an investment, especially when comparing it to another series of cash flows. And, by the way, this section discusses the issue as being the duration of the investment, but it's also the handling of interim investments or distributions. Also, I wouldn't characterize this as IRR vs MIRR, because there are other measurements (e.g. Public Market Equivalent, amongst many others) of capturing the opportunity costs and/or returns of interim cash flows. Finally, I would hesitate to characterize NPV as a "superior" measure for capital budgeting. Again, I think a more neutral discussion is warranted. Perhaps we should include references to other models, such as Capital asset pricing model or others. Robertmryan —Preceding undated comment added 20:41, 28 January 2017 (UTC)


 * I agree with Robertmryan that a neutral tone is desirable. I find the misconception debate actually a bit "old hat" now. What matters is users understanding of the facts. I have just now done some further tidying up, and added new content to the article contrasting investment objectives, i.e. maximizing returns versus maximizing NPV. --Jonathan G. G. Lewis 05:19, 23 March 2017 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)

New section: Unannualized Internal Rate of Return
Studying the Global Investment Performance Standards, I notice that Since Inception Internal Rate of Return (SI-IRR) for a period of less than a year is not annualized, but is a holding period return.

Do we need a fuller explanation of SI-IRR? Jonathan G. G. Lewis 11:07, 26 October 2014 (UTC) — Preceding unsigned comment added by Jonazo (talk • contribs)

The internal rate of return in personal finance
This section would appear to be the promotion of the author's FREQ methodology, with links to a commercial site. I would suggest this section be removed. (As an aside, the problem that this technique appears to try to be solving is better addressed with MIRR where interest and reinvestment rates can be specified.)Robertmryan (talk) 18:33, 25 April 2015 (UTC)

IRR does not account for risk, therefore it is of little value
in order to select a discount rate for an NPV calculation, you need to choose a discount rate that applies to projects of comparable risk. The NPV calculation confronts you with this question directly, and to compensate for lack of knowledge you might look at a few discount rates spanning a range to see what effect they have on your calculation. IRR does not confront you with this problem and therefore may lead you to confuse a higher IRR with higher quality when in fact it may simply indicate substantially higher risk with a lower NPV. IRR only works as a tool in a straightforward way when comparing similar projects with similar known risks; many businesses are like this, say oil drilling or home building; but never use IRR to compare two different businesses, it simply can't do that; or, if you understand enough about risk (and don't read the wikipedia page about it, that will get you nowhere) to make the right compensation, you will already understand that NPV is the only way to go. 68.175.11.48 (talk) 19:46, 7 April 2016 (UTC)


 * It's true, IRR says nothing about risk, but without tweaking the NPV method to apply a risk-adjusted discount rate, neither does NPV. Explaining the discount rate adjustment for risk, using CAPM or whatever, does not belong in the IRR article, it belongs in the NPV or CAPM articles. --Jonathan G. G. Lewis 06:07, 23 March 2017 (UTC)  — Preceding unsigned comment added by Jonazo (talk • contribs)

article need explain also XIRR
standard label XIRR used to define "internal rate of return for irregular cash flows", so IRR with non-regular dates. See Basic-XIRR database-XIRR --Krauss (talk) 22:45, 4 March 2017 (UTC)


 * I don't agree that the term IRR is in any way limited to regular cash flows. --Jonathan G. G. Lewis 05:12, 23 March 2017 (UTC)


 * I have just added a section headed "exact dates of cash flows" to the mathematics section. --Jonathan G. G. Lewis 05:42, 23 March 2017 (UTC)


 * Correction - I added it to the calculation section. --Jonathan G. G. Lewis 05:43, 23 March 2017 (UTC)


 * Initial value seems off - it gives numbers that are very large, leading to a high probability of not converging; I'm currently using simple annualized ROI over tN-t0 without accounting for timing of investments as a start value, which works better, but also better ideas would be interesting. — Preceding unsigned comment added by 2003:D2:3F24:0:465C:8F70:73C7:290 (talk) 20:07, 23 July 2022 (UTC)

Rewrite
I found a lot of the article rambling and unstructured, so I have rewritten quite a bit. --Jonathan G. G. Lewis 05:12, 23 March 2017 (UTC)

There is an error under calculation and example. It is not consistent with the formulas given to calculate the irr.

1`==Citations for Verification== I see plenty of references, but are they good enough for some editor to consider removing the template message? I invite other editors to decide. --Jonathan G. G. Lewis 00:23, 7 May 2017 (UTC)

It's some months on now, and no editors have responded to my suggestion above to remove the banner, so I am going to be bold, and just remove it now. --Jonathan G. G. Lewis 05:37, 19 February 2018 (UTC)


 * I put the RefImprove template back in place. The Definition and Uses sections contain lots of text but no citations - none at all. Other sections are not quite so bad, but still could be greatly improved with further references. This seems to be a common problem with articles on financial mathematics. Readers who come to this article seeking knowledge need some way to verify that what they are reading is accurate and accepted by experts in the field. Cordially, BuzzWeiser196 (talk) 10:04, 7 April 2021 (UTC)

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I took out the word naive because it seemed very personal or biasedJamesj320 (talk) 03:13, 30 January 2019 (UTC)

Violates policy on verifiability
Greetings Wikipedians! I commend all the contributors for their efforts. But this article lacks inline citations to reliable, verifiable sources. This violates Wikipedia's policy on verifiability, which states: "Even if you are sure something is true, it must be verifiable before you can add it....The burden to demonstrate verifiability lies with the editor who adds or restores material, and it is satisfied by providing an inline citation to a reliable source that directly supports the contribution." The policy is set forth here: Wikipedia policy on verifiability.

I hope someone will step forward to remedy this problem. There are no citations in the following sections, so we might start there:
 * Definition
 * Uses (until the private equity subsection_
 * Calculation - the heart of the article, yet no authority is given for any of the equations, formulas, etc

Unsourced material is subject to being removed. My qualifications for this subject are set forth in my user profile. Cordially, BuzzWeiser196 (talk) 20:44, 7 April 2021 (UTC)
 * Following up on my 7 April 2021 comment (above), I am removing the Calculation and Mathematics sections because after more than two years, they still lack inline citations to reliable sources. I'm not saying those sections are incorrect. But they violate the Wikipedia policy on verifiability. It is my hope that someone will rebuild those sections with text and citations that comply with that policy. If that doesn't happen soon, I'll work on it myself as I have time. Cordially, BuzzWeiser196 (talk) 10:59, 2 June 2023 (UTC)
 * I have attempted to improve the article, adding multiple citations to reliable sources. My work here is finished, for the time being at least.BuzzWeiser196 (talk) 10:51, 7 June 2023 (UTC)

NPV Calculator: Reliable Source?
I have a concern about using the so-called NPV Calculator as an inline citation in the Calculation section. NPV Calculator is an app that you download from the Apple Store. It does display a formula like the one in the article. The only info as to the author is a link to a website: www.finlightened.com. Before we cite NPV Calculator in this article, I'd like to get some comfort that www.finlightened.com satisfies at least some of the Wikipedia guidelines, such as "a reputation for fact-checking and accuracy" and "editorial oversight." Let's keep in mind the guideline: "articles should be based mainly on reliable secondary sources." I'm going to be bold and delete the citation. But I'm willing to consider other points of view. Cordially, BuzzWeiser196 (talk) 13:40, 14 June 2023 (UTC)


 * This was pretty obviously just somebody trying to spam their external link, there's no reason to be so concerned about reliability. Removing it was obviously correct. MrOllie (talk) 13:43, 14 June 2023 (UTC)
 * Thanks for the response. BuzzWeiser196 (talk) 01:29, 15 June 2023 (UTC)