What is IRR and How Does it Work?

The internal rate of return (IRR) is a widely used investment performance measure in commercial real estate, yet it’s also widely misunderstood. What is IRR exactly? How is it used and what are its limitations? In this article we’ll discuss what IRR is and how it works. We will also identify some common misconceptions and finally clarify these ideas with some relevant examples.

What is IRR?

First of all, what is IRR? Simply stated, the Internal rate of return (IRR) for an investment is the percentage rate earned on each dollar invested for each period it is invested. IRR is also another term people use for interest. Ultimately, IRR gives an investor the means to compare alternative investments based on their yield.

Mathematically, the IRR can be found by setting the Net Present Value (NPV) equation equal to zero (0) and solving for the rate of return (IRR).

irr_formula

If the above equation scares you don’t worry, we will walk through a detailed example next that shows you exactly how IRR works and it will leave you with a solid intuition behind the internal rate of return.

Step-by-Step Example and Proof of IRR

Memorizing equations is one thing, but truly understanding what’s actually happening with IRR will give you a big advantage. Let’s walk through a detailed example of IRR and show you exactly what it does, step-by-step.

Suppose we are faced with the following series of cash flows:

what is irr example

This is pretty straightforward. An investment of $100,000 made today will be worth $161,051 in 5 years. As shown the IRR calculated is 10%. Now let’s take a look under the hood to see exactly what’s happening to our investment in each of the 5 years:

what is irr

As shown above in year 1 the total amount we have invested is $100,000 and there is no cash flow received. Since the 10% IRR in year 1 we receive is not paid out to us as an interim cash flow, it is instead added to our outstanding investment amount for year 2. That means in year 2 we no longer have $100,000 invested, but rather we have $100,000 + 10,000, or $110,000 invested.

Now in year 2 this $110,000 earns 10%, which equals $11,000. Again, nothing is paid out in interim cash flows so our $11,000 return is added to our outstanding internal investment amount for year 3. This process of increasing the outstanding “internal” investment amount continues all the way through the end of year 5 when we receive our lump sum return of $161,051. Notice how this lump sum payment includes both the return of our original $100,000 investment, plus the 10% return “on” our investment.

This is much more intuitive than the mathematical (and typical) explanation of IRR as “the discount rate that makes the net present value equal to zero.” While technically correct, that doesn’t exactly help us all that much in understanding what IRR actually means. As shown above, the IRR is clearly the percentage rate earned on each dollar invested for each period it is invested. Once you break it out into its individual components and step through it period by period, this becomes easy to see.

What IRR is Not

IRR can be a very helpful decision indicator for selecting an investment. However, there is one very important point that must be made about IRR: it doesn’t always equal the annual compound rate of return on an initial investment.

Let’s take an example to illustrate. Suppose we have the following series of cash flows that also generates a 10% IRR:

what is irr example 2

In this example an investment of $100,000 is made today and in exchange we receive $15,000 every year for 5 years, plus we also sell the asset at the end of year 5 for $69,475. The calculated IRR of 10% is exactly the same as our first example above. But let’s examine what’s happening under the hood in order to see why these are two very different investments:

 

what is irr 2

As shown above in year 1 our outstanding investment amount is $100,000, which earns a return on investment of 10% or $10,000. However, our total interim cash flow in year 1 is $15,000, which is $5,000 greater than our $10,000 return “on” investment. That means in year 1 we get our $10,000 return on investment, plus we also get $5,000 of our original initial investment back.

Now, notice what happens to our outstanding internal investment in year 2. It decreases by $5,000 since that is the amount of capital we recovered with the year 1 cash flow (the amount in excess of the return on portion). This process of decreasing the outstanding “internal” investment amount continues all the way through the end of year 5. Again, the reason why our outstanding initial investment decreases is because we are receiving more cash flow each year than is needed to earn the IRR for that year. This extra cash flow results in capital recovery, thus reducing the outstanding amount of capital we have remaining in the investment.

Why does this matter? Let’s take another look at the total cash flow columns in each of the above two charts. Notice that in our first example the total $161,051 while in the second chart the total cash flow was only $144,475. But wait a minute, I thought both of these investments had a 10% IRR?! Well, indeed they did both earn a 10% IRR, as we can see by revisiting the definition or IRR:

The Internal rate of return (IRR) for an investment is the percentage rate earned on each dollar invested for each period it is invested.

The internal rate of return measures the return on the outstanding “internal” investment amount remaining in an investment for each period it is invested. The outstanding internal investment, as demonstrated above, can increase or decrease over the holding period. It says nothing about what happens to capital taken out of the investment. And contrary to popular belief, the IRR does not always measure the return on your initial investment.

The Myth of The Reinvestment Rate Assumption

One of the most commonly cited limitations of the IRR is the so called “reinvestment rate assumption.” In short, the reinvestment rate assumption says that the IRR assumes interim cash flows are reinvested at the IRR, which of course isn’t always feasible. The idea that the IRR assumes interim cash flows are reinvested is a major misconception that’s unfortunately still taught by many business school professors today.

As shown in the step-by-step approach above, the IRR makes no such assumption. The internal rate of return is a discounting calculation and makes no assumptions about what to do with periodic cash flows received along the way. It can’t because it’s a DISCOUNTING function, which moves money back in time, not forward.

This is not to say the the IRR doesn’t have some limitations, as shown in the examples above. It’s just to say that the “reinvestment rate assumption” is not among them. Should you take into account the yield you can earn on interim cash flows that you reinvest? Absolutely, and there have been various measures introduced over the years to turn the IRR into a measure of return on the initial investment. Some of the more popular approaches include the modified internal rate of return (MIRR), the capital accumulation method, and the external rate of return (ERR). These approaches are beyond the scope of this article, but will be explored in the near future.

Conclusion

The Internal Rate of Return (IRR) is a popular measure of investment performance. While it’s normally explained using its mathematical definition (the discount rate that causes the net present value to equal zero), this article showed step-by-step what the IRR actually does. What is IRR? Once you walk through the examples above this question becomes much easier to answer. It also becomes clear that the IRR isn’t always what people think it is. That is, it isn’t always the compound annual return on the initial investment amount. Understanding what IRR is at an intuitive level will go a long ways towards improving your ability to analyze potential investments.

  • Gary Schreiber

    Doesn’t the operating agreement determine whether the $5000 in example 2 is considered “return of capital” or “profit”? The IRR would then be different in that case and not 10%

    • Rob

      What exactly would be the difference in your view?

  • gary schreiber

    disregard my last comment. The IRR remains 10%. The risk is different in the second case due to earlier return of capital

  • Zaw Zaw Oo

    Thank you!

    • Rob

      Sure, glad you found it helpful.

  • Hank Chang

    I am a retired research engineer and studying/learning finance for my hobby. I found this article not help me but confuse me furthermore. It is your fault. I need to learn finance English more than finance Math. And change my “brain” into finance oriented.
    Both examples add up money amounts at different years. I does not make sense to do so since one dollar at different years are not equivalent. Adding apples and oranges together make thing more messy.

    • Rob

      Can you re-phrase your question and make it more specific? Happy to help, but not sure I can follow your question here.

  • vostok

    I think the theory of the reinvestment rate refers to deferred cash flows and not cash flows paid current. IRR by its inherent calculation is the discount rate on the cash flows received that set the NPV to 0 for an investment/project. Thus, for cash flows received, the return assumes nothing regarding the reinvestment of those cash flows since those would be outside the current project and into another asset, which would be outside of the scope of the project you’re discounting. For deferred cash flows, it makes 100% reason to assume that an investor would require the same yield on deferred cash flows into a project with respect to the initial investment. A Deferral is in essence a reinvestment into the same project as the project keeps those cash flows and doesn’t return it back to the investor, presumably to reinvest back into the project. Thus, why would you expect a different yield? The only basis I can think of is if the deferred cash some how super-primes the cash flow returns to the initial investment or if they are gauranteed by some 3rd party, in which case they can be considered less risky computed at a different rate, which would drop the IRR. On the other hand, if they are riskier than the initial investment cash flows in any type of subordination, then the IRR would go up, since the yield would be reflective of the repayment of these riskier cash flows. But undoubtedly, deferred cash flows have to be reinvested at some rate and it makes 100% sense that that rate is the same as the initial investment, and thus it must be taken into account when computing IRR.

  • Rob

    I have an investment where we invested $440,000 up front – a year later we returned to the investors $678,500 – yet the IRR calculation is 54% – it would seem to me the IRR would be infinite as we gave the investors there original money back and $238,500 in “interest” or gain – at the end of year 2 we returned another $50,000 and the IRR dropped to 45% – but I don’t understand what it is calculating against? the investment is returned with a healthy gain a year earlier?

    • Rob

      Can you post the entire set of cash flows you’re working with? I can gather the following from your comment: [-$440,000, $678,500, $50,000]. Are there any others?

      • Rob

        the 3rd year the return to investors was $140,000
        the project could now be sold in the 4th year for a net return to investors of $2,260,000 – this yields an IRR of ~100%
        but the question remains – why would it not be infinite with the return of cash year 1 far exceeding the expected interest rate return of the investors?

        • Rob

          Remember the definition of IRR – IRR is the percentage rate earned on each dollar invested for each period it is invested. Now, check this chart of your cash flows. Make more sense?

          • Rob

            Thanks Rob – makes sense – also points out the limitations of IRR as the investors are not expecting an interest rate return of 117% per annum.

        • Donna Roberts

          Hmm can I get in on that investment with $25K?

  • Roy

    Thank you for your article and make me see another point of view of IRR.
    Can you advise to calculate IRR if the cashflow was daily/monthly base?
    I have some difficulties for calculate the analysis for project in my office which is run for short term. i was in Freight Forwarding company.

    • Rob

      It would be the same analysis as above, except in your case “Periods” would be daily or monthly rather than yearly. This would also make the resulting IRR daily or monthly since IRR is the percentage rate earned on each dollar invested for each period it is invested.

  • murali mohan

    Excellent article, which has given me a good insight about IRR. In our business investment decisions, we generally rely on IRR figures and not on Total Cash flows. From the 2 scenarios you have illustrated in the article, which is the best (preferred) investment option and why?

    • Rob

      I suppose it depends on your goals, but there is no silver bullet, so why not use all of them in making your decision?

  • Shane

    great article, thank you!

  • Abhishek

    sir if in your example my required return would have been 20% and cashflows still continue to be 15000 then what would have been my irr ?

  • DANISH

    SIMPLY AMAZING!!!! I COULD NOT UNDERSTAND IT BEFORE WATCHED MANY VIDEOS AND RED MANY COLUMNS BUT THE ARTICLE PROPERTYMETRICS.COM SHARED HERE IS SIMPLY MING BOGGLING, IT MADE EASY NOT TO SOLVE PROBLEM ONLY BUT AM ABLE TO UNDERSTAND THE SPIRIT OF IRR.

  • Villma

    Thanks for your article. One question: if the IRR is the discount rate which mathematically sets the NPV of your investment to zero, then this means that it is the maximum discount rate you could plug in before the investment becomes unworthy. I.e. if you use a higher discount rate the NPV becomes negative, right? Following this logic, the higher the IRR, the better the investment opportunity since it gives you more leeway to a negative NPV, right? Now how does this fit with your definition: the IRR is the percentage rate earned on each dollar invested for each period it is invested?

  • himal gurung

    really helping,, thankyou so much,but please can you help me further more,, how IRR is calculated??? and IRR is only best choice for investor or rate more than IRR can be the best decision???

  • Gnv Raghavan

    hi rob – if a loan given out by a bank, is looked at as an investment, the lending rate and the IRR do not match. I’m not able to understand this.

  • vostok

    I think what b-schools are thinking with respect to re-investment rate of cash flows relates to the carried return, and not actual free cash flows being paid out. Thus, if for ex in 1 period, there is no cash flow that can be paid out but the investor is owed a divident or a payout, then those cash flows are accrued/re-invested into the company/project at the same rate as their required return. This applies primarily to investments senior to equity in the capital structure, namely debt/subordinated and preferred equity.

    -Kellogg MBA

    • Toussaint

      I agree. To illustrate, I had to analyze a preferred equity investment to help fund ground up construction. In the development model the investment would continue to accrue interest on the reinvested basis until there was enough cash flow after debt service to make a distribution to the preferred equity. A similar calculation was used for the subordinated limited partners’ equity with interest building in their capital accounts until enough cash flow occurred to pay off the preferred equity position. To Rob’s point- that scenario, however, differs from a straight equity investment in a property which yields enough after debt service cash flows to enable a distribution which returns a portion of the investors’ initial capital.

  • Bandit

    Please explain the return of investment of $76795 in the second example. Your examples have given me insight as to why an audit of Federal Government is impossible. Too many interpretations of posted numbers.

  • Bandit

    Please explain the return of investment of $76795 in the second example. Your examples have given me insight as to why an audit of Federal Government is impossible. Too many interpretations of posted numbers.

  • DERICK

    THANKS….. IT IS HELPFUL

  • Priyank

    Thank you so much for the clear explanation. Can you please tell what is going on in the following two cash flows. With one XIRR is 172.3% and with other is is 9%. Though at the end of both the periods what one earns is 9 points.

    31-Dec-14 -100
    31-Jan-15 109
    30-Dec-15 -109
    31-Dec-15 109
    XIRR 172.30%

    31-Dec-14 -100
    31-Jan-15 0
    30-Dec-15 0
    31-Dec-15 109
    XIRR 9.00%

  • K

    If a 24 month investment gave an IRR of 10,64%, do you have to calculate the annual IRR separately? That is, by calculating the monthly IRR and converting it to annual as follows:

    Monthly IRR

    = 24√(1+ .1064) – 1

    = .004221866

    Annual IRR

    =(.004221866+1)^12 – 1

    = 5,19%

  • Sepik

    Nice and simple to understand. thank you

  • Suv Sach

    What exactly is return of investment and return on investment?

  • Gene Mack

    I took your whole CRE course and benefited hugely. Working on lender comparisons right now to refinance some properties. Can you help me understand the relationship between IRR and cash-on-cash return? On some loans, the difference between the cash-on-cash return and a five-year IRR is minimal. On others, it’s wildly different. I understand both metrics; I just can’t put my finger on what drives cash-on-cash and IRR to be close on some loans and far apart on others. Thx!

  • Hamid

    Hi everyone, I have a question and appreciate it if someone who knows finance would help me.
    If I make a contribution every year for $500 for 10 years, I will be returned $1,500 for that specify year but I’m not allowed to touch the money until next 10 years, in other words after 10 years overall I pay $5000 and by year 10 I can take my own money and also $10,500 of return. Is this a good investment to go?