Calculating and Estimating Internal Rate of Return

hoyer's picture
Rank: Senior Monkey | banana points 82

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-multipli...

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Comments (51)

Mar 26, 2010

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.

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Mar 29, 2010

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

    • 1
Mar 29, 2010
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.

Mar 29, 2010

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.

Mar 29, 2010

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.

  • Anonymous Monkey
  •  Dec 15, 2015

Can you please send that to me as well?

Mar 29, 2010

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...

Dec 15, 2015

Useful tool, yes. But being able to convert IRR to money multiple is about as impressive as being able to say that 100 / 10 = 10. Use it because the monkey in the next cube is using it, but don't get fooles that this will impress.

"Living the dream 24/7 on http://theallnighter.blogspot.com"

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Best Response
Mar 29, 2010

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.

    • 5
Dec 15, 2015

Pretty easy to do since the cash flow is constant and there is only a small gain on exit. They're not looking for an exact answer but a close approximation during interviews.

Think about it in terms of the yield you earn annually. You are getting $50 on a $100 investment, which is a 50% return annually. When you exit, you are making a small gain of $10 which would boost IRR just a tad higher. You could estimate IRR around 51 or 52%.

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    • 1
Dec 15, 2015

Thanks for the reply. I'm still not understanding how you got to an estimate of 51% - 52% though. In general, if the exit price is low and the number of years is 5 - 7, can you just assume the % is the same value as the cash flow?

I think I'm just stuck mathematically because I don't know how to work out the effect of the discount rate, especially when there are powers involved...

Dec 15, 2015
21:

Thanks for the reply. I'm still not understanding how you got to an estimate of 51% - 52% though. In general, if the exit price is low and the number of years is 5 - 7, can you just assume the % is the same value as the cash flow?

I think I'm just stuck mathematically because I don't know how to work out the effect of the discount rate, especially when there are powers involved...

There is no "effect of the discount rate". An IRR calculation aims to determine the discount rate required given a pre-identified PV. The question you posed could be rephrased as: "What discount rate would be required for a 7-year cash stream of $50 + a cash stream of $110 in year 7 to yield a PV of $100?"

Conceptually, it's very easy to prove that a perpetuity of $50 cash flows requires a 50% discount rate to yield a PV of $100 ($50 / 50% = $100). The $10 return in year 7 is negligible.

Dec 15, 2015

Ok, thanks for the answer. I'll try and get more familiar with the concept.

How does it work if the cash flow was $20 in perpetuity?

Dec 15, 2015

Then it would be ~20%.

As NorthSider mentioned, I think you may be confusing discount rates/DCF with IRR calculations. I'd recommend that you read into the basics of the LBO, specifically how one is structured/modeled, as this will probably better help you understand how the returns (IRR) are calculated and how the cash flow amount and timing will impact IRR.

Dec 15, 2015

Thanks for the reply. I will do that.

So just as a general rule, if the cash flow is 60 and the exit value is negligible, a close approximation of the IRR is 60%? Does this also apply if the time horizon is shorter or longer than 7?

Dec 15, 2015

You need to figure out the exit and entry equity values (you assume you're an investor). Then you figure out the IRR using the formula IRR = (FV/PV)^(1/years)-1. As NorthSider said, this formula allows you to find the discount rate at which the present value of all future cash flow is equal to the initial investment, i.e. if you rearrange the above formula, you get the formula to calculate future value: FV = PV*(1+IRR)^years. Since finding the nth root of a number is pretty tough to do in your head, most people just memorize an IRR table. Google these or simply use the formula above to create your own Excel version. Then memorize the 4-7 year columns.

For this case, assuming you're talking about equity values, you have +350 gain in equity from cash flow and +10 gain from multiple expansion. Thus, your exit equity is 460. Your multiple on invested capital is 4.6x, so your IRR formula should be 4.6^(1/7)-1. An IRR table will tell you that at 7 years, 4x MOIC is ~22% and 5x MOIC is ~26%, so you can approximate to ~24%. If you actually calculate this out, it comes out to 24.3%.

    • 2
Dec 15, 2015

But isn't (FV/PV)^(1/years)-1 the formula for CAGR which isn't the same as IRR if there are interim cash flows.

Dec 15, 2015
21:

But isn't (FV/PV)^(1/years)-1 the formula for CAGR which isn't the same as IRR if there are interim cash flows.

Correct, but it can typically give a decent enough approximation.

If there is one outflow and one inflow, CAGR = IRR.

Dec 15, 2015

I see.

So to confirm, in an interview situation, if I was asked to calculate the IRR. I could just use the CAGR formula?

Dec 15, 2015
iamfromcanada:

You need to figure out the exit and entry equity values (you assume you're an investor). Then you figure out the IRR using the formula IRR = (FV/PV)^(1/years)-1. As NorthSider said, this formula allows you to find the discount rate at which the present value of all future cash flow is equal to the initial investment, i.e. if you rearrange the above formula, you get the formula to calculate future value: FV = PV*(1+IRR)^years. Since finding the nth root of a number is pretty tough to do in your head, most people just memorize an IRR table. Google these or simply use the formula above to create your own Excel version. Then memorize the 4-7 year columns.

For this case, assuming you're talking about equity values, you have +350 gain in equity from cash flow and +10 gain from multiple expansion. Thus, your exit equity is 460. Your multiple on invested capital is 4.6x, so your IRR formula should be 4.6^(1/7)-1. An IRR table will tell you that at 7 years, 4x MOIC is ~22% and 5x MOIC is ~26%, so you can approximate to ~24%. If you actually calculate this out, it comes out to 24.3%.

This is not correct.

The formula you are using is a shortcut that assumes all equity proceeds are received at exit. This shortcut can be relevant for a back-of-the-envelope IRR calculation for an LBO where we assume all interim cash flows received are swept to pay down debt.

But this is not the case here. We are receiving $50 equity cash flows every year until maturity. The IRR is 50.31% as stated above. Calculate yourself using the IRR function in excel if you don't believe.

OP, be careful when using the CAGR function to estimate IRR if there are interim cash flows. There is a massive difference between a 50% IRR and 24%.

    • 1
Dec 15, 2015

Pretty sure he's referring to a paper LBO, which is very standard in buyside interviews (which my method entails), but sure, do note the distinction.

    • 1
Dec 15, 2015

@new_analyst1: I still don't understand conceptually how you can just determine that the yield (50/100 or 20/100) would be equivalent to the IRR.

Dec 15, 2015

Very fair - and I definitely agree that the paper LBO method is much more common in interviews.

OP I don't know how to else to put it. If you gave me $100 and I offered to give you $50 in return every year what is your return? Ignore the $10 gain on exit. Let's say you invested in a bond. The bond is at par and you pay $100 for it. It pays you $50 annually until maturity. What would you say the interest rate on that bond is? 50%. It doesn't matter how long the maturity of the bond would be. The interest rate would always be 50%. Another way to think about it was mentioned above - what discount rate equates the future cash flows to the PV? 100 = 50 / x , solve for x = .50

Sometimes it's easier to think of IRR conceptually as an equivalent interest rate. So let's say you are valuing an LBO. Let's say it costs $1 billion to acquire the company and after 5 years you calculate an expected IRR of 20% (forget about cash flows received and exit price for now - all that matters is it returns 20%). Another way to think of that 20% is the rate you would require to be indifferent between two investments. So if you had the opportunity to invest that $1 billion today in a bond with equivalent maturity at a 20% interest rate, you would be indifferent towards buying the company or investing in the bond.

So in this case because the cash flow is constant, every year, calculating IRR is as easy as pretending it were a fixed income investment and determining what the interest rate would be.

You would not be able to use this as a shortcut if the cash flows were uneven. If CF in year 1 was $50, but then year 2 CF was $20, and then in year 3 CF was $40, etc. you would have to solve for this using excel or a financial calculator. You could set up the equation by hand but it would be near impossible for the average person to actually calculate it out by hand.

You would also not be able to use this as a shortcut if the investment was an LBO where CF is swept to pay down debt and equity is assumed to be received at exit. In this case you would use the MOC method and IRR tables that iamfromcanada mentioned. As he stated, these are the most common types of IRR questions in interviews. There are IRR "rules of thumb" that can be memorized (BIWS guides have them).

Just go into excel, set up a variety of different cash flow patterns and solve for IRR. The more you play around with it the quicker you'll understand it.

    • 2
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Mar 29, 2010

I wish there were a way to tag WSO posts to come up first in searches. Marcus' quick and dirty IRR calc is just a great post.

Dec 15, 2015

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

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

BUMP

Dec 15, 2015

BUMP

Dec 15, 2015

BUMP

Dec 15, 2015

( (5% * (sigma k=1 to 5 (1,1)^k) + 1,1^6 ) / 1,1) and all that to the power 1/5 then -1
Just simplify that equation and you got it

Dec 15, 2015

Ah, thank you.

That's a bit confusing but I'll try and work through it.

Thanks!

Dec 15, 2015

Wait, isn't that just the CAGR formula? I was under the impression that you can't use CAGR to work out IRR except in certain circumstances.

Dec 15, 2015
21:

Wait, isn't that just the CAGR formula? I was under the impression that you can't use CAGR to work out IRR except in certain circumstances.

You can use CAGR if it's just entry and exit. Your case has cash flow every period so you will need to account for that. Why not use XIRR in Excel?

Dec 15, 2015

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)

.

Dec 15, 2015

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

@new_analyst1 @NorthSider

Any thoughts on this?

Dec 15, 2015

As previously mentioned, if you want an exact answer, use XIRR excel formula

Dec 15, 2015

Result is c. 15%

Dec 15, 2015

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 26, 2010

Here's a list of IRRs that I found based on different cash multiples/years

http://tinyurl.com/37kk3w2

Dec 15, 2015

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.

"Success means having the courage, the determination, and the will to become the person you believe you were meant to be"

Dec 15, 2015

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
Dec 28, 2014
Dec 28, 2014