Calculating and Estimating Internal Rate of Return

Whats the best way to do an IRR calc in your head? is there a simple calculation and relationship when you think about initial investment, sale price and time period? just for back of envelope calcs when youre sitting in a meeting or an interview.

thank you

How To Calculate Internal Rate of Return

The following is a brief refresher on IRR.
From the Wall Street Oasis Finance Dictionary

Internal Rate of Return or IRR is a financial metric used to discount capital budgeting and to make the net present value of all future cash flows equal to zero. For this reason, it is used alongside a Discounted Cash Flow analysis.

Calculating IRR cannot be calculated by hand unless you use a trial and error method to until you reach a solution in which net present value equals zero. Otherwise, you will need a special calculator or a program like Microsoft Excel. However, you can estimate IRR by memorizing simplified outputs of an IRR table.

How to Estimate IRR

The following is an introduction to estimating IRR by certified user @Marcus_Halberstram", an industry CEO. Once you understand the concept you can memorize the internal rate of return table below. Then you will be able to estimate IRR off of the top of your head!

Marcus-Halberstram - Industry CEO:
The best way to approximate IRR is by memorizing simple IRRs.
  • Double your money in 1 year, IRR = 100%
  • Double your money in 2 years, IRR = 41%; about 40%
  • Double your money in 3 years, IRR = 26%; about 25%
  • Double your money in 4 years, IRR = 19%; about 20%
  • Double your money in 5 years, IRR = 15%; about 15%

That's really all you need to know. So if you 1.5x you money in 2 years, you know that if you double your money in 2 years its a 40% return and if you only get your initial investment after 2 years, its a 0% return... mid-point of 0% and 40% is 20%... so your IRR is roughly 20%... now take into account that the 0% return scenario doesn't include any compounding... so you need to upwardly adjust that 20% figure... so make it 21 or 22%. Just did the IRR calc, what does it come out to? 22%.

No one expects you to be able to nail an IRR number in your head. But if you can get pretty close, you're fine.

IRR Table

  • X Axis: Number of Years
  • Y Axis: Multiple



1 Year2 Years3 Years4 Years5 Years
10.0%0.0%0.0%0.0%0.0%
2100.0%41.4%26.0%18.9%14.9%
3200.0%73.2%44.2%31.6%24.6%
4300.0%100.0%58.7%41.4%32.0%
5400.0%123.6%71.0%49.5%38.0%

View the full table at http://willprice.blogspot.com/2007/06/irr-multiplication-table.html

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Comments (51)

Mar 26, 2010 - 1:35pm

First, guesstimate IRR in your head. than pick a number lower than this presumed IRR and discount the cashflows, see what NPV you get. Send, pick another number, higher than your presumed IRR and discount the cashflows, note the NPV you get. Now you have to discount rates and 2 coresponding NPVs - you can linearly extrapolate this for NPV=0 and see what discount rate that yields. It will be a reasonable approximation of the IRR.

  • 1
Mar 29, 2010 - 4:54am
hoyer:
that must be a joke, whats the diff btwn running an NPV and an IRR calc in your head? seriously

someone has GOT to be most useful than that

Say you have a project that pays
t=0: -1000
t=1: 100
t=2: 1000

Can you guess or calculate the IRR in your head? I can't.

But NPV for d=0% is 100, and NPV for d=10% is -110 (100/1.1 is about 90, 1000/1.21 is about 800). Based on this I'd guess the IRR is about 5%. It so happens that it is exactly 5% in this example, but that doesn't matter.

If you find a better method please share.

  • 1
Mar 29, 2010 - 1:29am

Alright, I'll take a crack at the back-of-the-envelope approach. Take sale proceeds / initial investment in your head. Let's say that comes to 2.5. Take an approximate nth-root of that (e.g.. 5 year period, 5th root) and subtract 1.

Or, alternatively, calc some ballpark #s at some point and memorize them so you don't have to do the hard math - e.g. 2.5x = 20% for 5 years, etc.

  • 1
Mar 29, 2010 - 2:16am

I have just the academic paper you need to solve this problem. PM me.

After reading this puppy you will be able to work it out in your head in a matter of seconds.

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Mar 29, 2010 - 11:04am

tandaradei - your method would be needed for projects with more than 2 cash flows, but most IRR calcs are simply entry and exit from a sponsor's perspective (at least in theory). As such, you can simplify the calculation a bit...

Best Response
Mar 29, 2010 - 5:25pm

tandaradei thats a stupid approach. Primarily because you're guestimating the IRR to begin with... if you can guetsimate the IRR why would you need to go through your way of calculating NPV twice and triangulating what the actual IRR is?

In addition to that, your example is created to make NPV calculation easy. How about this...

CF0= -360
CF1= 0
CF2 = 0
Cf3 = 720

Discount rate is 7%

Do that NPV in your head and triangulate the IRR for me. Then change your discount rate and re-calculate in your head.

The best way to approximate IRR is by memorizing simple IRRs.

  • Double your money in 1 year, IRR = 100%
  • Double your money in 2 years, IRR = 41%; about 40%
  • Double your money in 3 years, IRR = 26%; about 25%
  • Double your money in 4 years, IRR = 19%; about 20%
  • Double your money in 5 years, IRR = 15%; about 15%

Thats really all you need to know. So if you 1.5x you money in 2 years, you know that if you double your money in 2 years its a 40% return and if you only get your initial investment after 2 years, its a 0% return... mid-point of 0% and 40% is 20%... so your IRR is roughly 20%... now take into account that the 0% return scenario doesn't include any compounding... so you need to upwardly adjust that 20% figure... so make it 21 or 22%. Just did the IRR calc, what does it come out to? 22%.

No one expects you to be able to nail an IRR number in your head. But if you can get pretty close, you're fine.

Array
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Dec 15, 2015 - 1:15pm

Mental calculation of IRR (Originally Posted: 10/12/2014)

I heard from a friend that in his interview, he got asked to calculate the IRR of an investment.

Assume initial investment is 100. Annual cash flow is 50. Exit after 7 years at 110.

How do you calculate the IRR for that in your head?

Dec 15, 2015 - 1:30pm

How to calculate IRR for a project? (Originally Posted: 09/28/2009)

How do you calculate IRR for a project assuming equity raise of 10mm and exit at 7x Ebitda multiple in 5 yrs? Do you take into consideration the cash -flows that the company gets in between or just do the IRR function in excel and put the $-10mm zeroes for the 5 yrs and the discounted cash flow net of taxes after exit?

Dec 15, 2015 - 1:31pm

The answer depends on where the cash flows go over those 5 years. IRR, in my opinion is only relevant in the context of who's return you are interested in. Assuming you are interested in returns to equity, you would have to be concerned with whether or not there is debt service (interest or amort.) that needs to come out first. Long story short, those cash flows are part of someone's return, so yes, they should be included and accounted for one way or another.

Mar 29, 2010 - 5:59pm

For shorter-term stuff, I will make a quick estimate by figuring out what the linear interest would be and then adjusting as necessary. Two years in fixed income analytics basically had me answer hundreds and hundreds of questions about "Does this number make sense?" For shorter-term stuff, you can get a decent estimate by figuring out the simple interest, guessing the impact of the compounding, and going from there. In Marcus's example, I'd take off 21% from the 720 and then adjust up maybe 1-2% to figure out the PV of the $720 cashflow. You can also invert this strategy to get a somewhat reasonable estimate of IRR/yield. There's also some similar mental tricks, of course, to look at a combination of an annuity and final cashflow. To get the IRR on -360 to 720 in three years, I'd look at 33% simple interest but then look quick look at the extra benefit from compounding and spread a reduction of (1.331.33-1.66~=10%)2=20% across the three years or about 26%.

It won't be exact, but 99% of the time, I'll be able to give the trader or researcher a definitive answer in five seconds rather than getting the TI-89 and pencil/paper out and taking five minutes.

For stuff with lots of compounding going on, you obviously go with the rule of 70/72 and then try and guess it by looking at squares or square roots. This method is less precise but you don't always have to be quite as exact for longer-term stuff.

Dec 15, 2015 - 1:32pm

IRR Calculation Question (Originally Posted: 10/11/2014)

How would you answer this?

If you make an investment, and pay 10% premium to book value and receive a 5% dividend, book value CAGR = 10% and you sell it at 10% premium after 5 years, what would your approximate IRR be?

Would it be 1.1^5*1.1+0.05-1.1?

Thanks!

Dec 15, 2015 - 1:40pm

JJSaurel put it all right.

Here are the separate items that will make it all clear:

1) Initial investment 1.1
2) Dividend income = 5%*1.1+5%*1.1^2+5%*1.1^3+5%*1.1^4+5%*1.1^5 = 5%*(sigma k=1 to 5 1.1^k)
3) Exit value = 1.1^5*1.1 = 1.1^6

IRR = ((Dividend income + Exit value)/Initial investment)^(1/5))

IRR = ((5%*(sigma k=1 to 5 1.1^k) + 1.1^6)/(1.1))^(1/5)

.
  • 1
Dec 15, 2015 - 1:41pm

Thanks for all the replies guys.

@HarvardOrBust: Thanks for the reply but that was the point I was trying to make - you can't use CAGR for this example. I can't use XIRR because I heard this was an interview question.

@WhatInTheName: Thanks for the reply but I don't think you can use the method to work out the IRR because it doesn't take into account the timing of the cash flows, right? It looks like the CAGR formula and HarvardOrBust made a point about that.

Dec 15, 2015 - 1:45pm

IRR Estimation (Originally Posted: 11/18/2017)

Is there a quick way to estimate how accretive or dilutive cash flow timing would be to your IRR without excel (just back of the envelope)? For example, say you have cash flows which look like the following:

100 = 10 / (1+IRR) + 10 / (1+IRR)^2 + 110 / (1+IRR)^3

The IRR above is 10%. Now if we assume we get $50 of the $110 in year 1 instead of year 3, roughly how accretive would the IRR be (without a calculator or excel):

100 = 60 / (1+IRR) + 10 / (1+IRR)^2 + 60 / (1+IRR)^3

Note total money received is unchanged, you simply get $50 earlier. What would be the best way to approximate this?

Dec 15, 2015 - 1:46pm

jllx, pure crickets, that's where I come in. Any of these useful?

  • IRR vs. Compound Return Rate internal rate of return measures the return on the outstanding "internal" investment amount ... gives a positive NPV and an IRR of 5.5% even though the investment has a compounded return rate of 5%. ... Investopedia's IRR article says "One of the disadvant
  • internal rate of return vs. "simple rate of return" to me) yield different rates of return? Many thanks! IRR Return ... annual rate of return of this investment. My first simple approach only considers one period as follows: ... Then it is a cash flow). Rate of return: 530 Euros / 14.000 Euros = 3.8% (which I intuitively ...
  • Internal Rate of Return Questions rate of return is 25%? I appreciate any and all responses. IRR DCF ... trouble wrapping my head around this concept. I understand that IRR is the discount rate that makes your ... COC, but an NPV of 0 at your IRR. Maybe I am just thinking about this the wrong way, but I just do not ...
  • IRR to overall return I couldn't find a straight answer anywhere so here it is My understanding is that IRR is internal rate of ... return (i think it gives annualised return for everydollar (internally invested- used with where periodic ... hell is average IRR? OR average XIRR? THANKS IN advance IRR TO total return or overall return<
  • Relationship among Cap Rate, IRR, Discount rate and NPV context, but has a different meaning when discussing return (IRR is effectively the blended rate of the ... is defined as the annual rate of return that generates NPV of zero. The formula of net present value ... Seeking a high-level explanation to explain the relationships among cap rate, IRR, discount
  • Is there an IRR formula formula to find internal rate of return when number of cash flows exceed 5? For example, is it possible to ... I am told there are no IRR formulas when number of cash flows excess 5 Is it so? Is there an IRR ... find IRR of the following investment using a "formula" rather than "iterative ...
  • Advice for summer and return offer rate? I have a tendency to worry that I won't get the return offer since there are so many interns and ... group is fairly large with a big intern class. Does anyone have any specific advice for the summer? ... because of how competitive it may be. summer internship ...
  • Debt fund returns / IRR of 2-4% and potential additional upside to IRR from warrants, etc. My question is HOW can they ... achieve 15+% IRRs while providing debt at c.10% coupon? Would their returns not be limited to the coupon ... early stage companies ($15-30MM tickets). They talk about 15+% gross IRR (YTM) (before carry and ...
  • More suggestions...

No promises, but maybe one of our professional members will share their wisdom: NiuShi Chaunce TudorM

You're welcome.

Dec 15, 2015 - 1:47pm

IRR Calc for purchase (Originally Posted: 02/22/2014)

I'm trying to calculate IRR on purchase of business. 5 yr NPV of cash flows below, with 70 paid as purchase of private co, fully funded by term debt.

Yr 0 Yr 1 Yr 2 Yr 3 Yr 4 Yr 5
-70 23 20 14 11 7

Questions:
1. Do I use -70 in calculation if fully funded (this is the purchase price), not included additional debt required for transaction fees?
2. In order to arrive at NPV of cash flows (used DCF calculation), I used 35% tax rate but company is C Corp. Do I use this tax rate when running projections or do I use 0 since equity holders will pay individually for profits? Or do I not understand this correctly.
3. What about any terminal value - is this normally included to arrive at IRR?

Clearly I dont fully understand mechanics to run this, appreciate any advice - as well as beyond questions. Hopefully I've included enough info to answer.

Dec 15, 2015 - 1:48pm

your IRR is infinite in the case you described
you spend 0 of your own money (100% debt and no equity) and you make money.

why would anybody lend you 100% of a purchase price? this situation doesn't make much sense...

not entirely sure that I understand your second question, but if you buy the company, you are the 100% equity holder. if this is the case, you'll have to pay taxes one way or another before you can pocket the cash.

yes, you include TV in your IRR calc.

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Dec 15, 2015 - 1:49pm

Thx PSD92
So how should I view the required return if these are my cash flows and the deal is going to cost me 70? Lender has secured position on assets, gets its interest payments at a high rate, and believes the business has ability to payback in 5 yrs. how do I show TV does it go in yr 6? Appreciate help, I'm an ops guy trying to at least understand finance folks.

Oct 23, 2014 - 12:44am

Thanks for the post Marcus this is really helpful! One part I didn't understand:

now take into account that the 0% return scenario doesn't include any compounding... so you need to upwardly adjust that 20% figure...

Anyone want to take a stab?

Dec 28, 2014 - 5:42pm

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