# Why is IRR used as a measurement of an investment's profitability?

I am new to money.SE so please forgive if this question is not in keeping with the norms of the site, and let me know how I can improve it.

I have a fundamental question about concept of internal rate of return (IRR). I just read the definition at Investopedia. As I understand it, we are supposing an investment where we know our initial outflow, and we have several projected inflows occurring at various points in the future. Then the IRR is the discount rate that would lead the net present value of the investment to be zero.

My question is about what the relevance of this number is, i.e. when people use it as a measure of the profitability of an investment, what do they think of it as telling them about the investment?

This much is clear to me: if the inflows are greater but occur on the same timeframe, then the IRR will be greater. But beyond that, the measure seems very indirect to me. If an investment claims a projected IRR of say 15%, this is not asserting that one is making %15 of anything in profit at any time, even on average, is it?

To sharpen the question:

I expect a measure called "rate of return" to mean something like "this is how much money, as a percentage of the investment, you can expect to make annually from the investment." When I attempt to undestand IRR in these terms, the best I have come up with is this:

"This investment has an IRR of 15%"

seems to me to mean the same thing as

"If there were a hypothetical money market account with a 15% interest rate, and I made the present investment, and reinvested the inflows from the investment into the money market account as they occurred, I would have the same amount of money in it at the end of everything as if I had just put the money in the money market account the whole time."

My questions are:

(A) Am I correct that the last paragraph is an accurate interpretation of the statement that the IRR is 15%?

and

(B) If I am, then since there is not really a 15% money market account, what do people think of this number as telling them about the investment?

The definition you cite is correct, but obscure. I prefer a forward looking definition.

Consider the real investment. You make an original investment at some point in time. You make a series of further deposits and withdrawals at specified times. At some point after the last deposit/withdrawal, (the "end") the cash value of the investment is determined.

Now, find a bank account that pays interest compounded daily. Possibly it should allow overdrafts where it charges the same interest rate.

Make deposits and withdrawals to/from this account that match the investment payments in amount and date.

At the "end" the value in this bank account is the same as the investment.

The bank interest rate that makes this happen is the IRR for the investment...

• Thanks. But I'm not sure I buy this. In a concrete case: suppose that there is an initial investment of \$100 and a payout of \$200 a year later, and that's the whole story. Then according to the definition of IRR at investopedia, the IRR is the solution in r to 200/(1+r) = 100, or r=100%. So, suppose I have a bank account with interest rate 100%. I put in \$100 at the beginning and take out \$200 a year later. The account balance is now zero. But it would be either unreasonable or tautological to say that the value of the investment is zero. Cont'd... Feb 11, 2017 at 16:54
• (Unreasonable because if I can double my money in a year then that's clearly good! But if you respond by saying, well, in this scenario there is a bank account that does that, so inflation is obviously wild, so doubling your money in a year is exactly zilch, then it's tautological: the existence of this bank account [in our hypothetical] came from the IRR calculation. IRR is supposed to measure a priorly-existing value of the investment in the real world, not the value of the investment in a counterfactual scenario built on the IRR itself.) Feb 11, 2017 at 17:07
• It still seems to me that the right hypothetical is the one in the OP: we suppose a bank account with interest rate the IRR, and then in one scenario we make the investment and put the withdrawals in the bank account as they come back to us (and if we have to make further deposits to the investment, take them from the bank account), while in the other, we put the money in the bank account and leave it there the whole time. For example: Feb 11, 2017 at 17:10
• Suppose a 100 initial investment and with 50 back after year one and 150 back after year two. Then the IRR is the solution to 150/(1+r)^2 + 50/(1+r) - 100 = 0. This is r=50%. So suppose a 50% bank account. In option A, we make the investment; when the 50 comes back after year 1, we put it in the bank. After year 2, we receive the 150 payout from the investment and 25 interest from the bak, and we now have 150 + 50 + 25 = 225. In option B, we put the initial 100 in the bank account, which receives 50 interest in year 1 and 75 interest in year 2, so at the end we have 100 + 50 + 75 = 225. Feb 11, 2017 at 17:20
• In both the real investment history and the hypothetical bank account, any withdrawals are removed from further calculations. Feb 11, 2017 at 17:41

Problem with deciding investments in a company is that you have multiple potential options, each with their projected returns, but each also has some hard-to-estimate risks. A further problem is that these opportunities arrive one-by-one, so you usually cannot compare project A vs. project B to decide which one is better.

The internal rate of return is a rule-of-thumb like way to make these decisions. The company board may set an IRR target of e.g. 15%, and each executive will compare their projects against that target. They'll execute only the projects that are projected to give a good return, but some of these projects will end up failing. Thus the real average profit will not be equal to IRR.

Important thing is that this target number gives ways to compare projects, and also for the board to control the investments. If the company has a good track record of being successful at projects, the board might set an IRR target of 10% and expect to get e.g. 8% return on their investment. However, if the company has a much larger risk of projects failing, they might demand a predicted IRR of 20% to account for the risk.

Ultimately if the IRR target is set too high, the company will find no projects it considers profitable to invest in. In practice if this happens, the company owners are better off taking out the cash as dividends and investing it elsewhere.

• Dear @jpa, thank you for this. I understand you to be saying that in practice, the IRR is used only in a comparative capacity: higher IRR means better return. Am I right in understanding that the uses you mentioned (compare projects / account for risk) do not really go beyond this? My question was about what the number itself means, so I take you to be indicating that the answer is "not much, except for how it compares to other IRRs..." Am I parsing you correctly? Feb 11, 2017 at 17:30
• @benblumsmith That is my understanding, yes, but I'm pretty much novice at this also so perhaps someone else can confirm.
– jpa
Feb 12, 2017 at 6:28

IRR is the acronym for internal rate of return. And it appears that you do understand how it works.

It's not the phrase most investors use for their own returns. I'd typically talk about my own return last year, or over the last decade, etc, as well as what the S&P did during that time, and might even use the term CAGR, compound annual growth rate, although I wouldn't pronounce it 'kegger' or anything like that. Aside from discussing company investments in some MBA class, the only time I'd use IRR is in an excel spreadsheet to calculate the return over time of a series of my own investments.

The nothing magic about this, it's a function of an initial dollar investment, time passing, and the final value. All else is addition complexity based on multiple deposits/withdrawals, etc. If I deposit \$100 and get back \$200 in a year, it's a 100% IRR.

Disclosure - I am no fan of Investopedia or re-explaining its wording on these topics. I've caught multiple errors in their articles, and unlike the times I've emailed my friends at the IRS who quickly fix typos and mistakes I've caught, Investopedia authors are no better than bloggers (which I am) who take offense at any criticism (which I do not).

• In the particular case at hand - the definion of IRR - are you saying that the Investopedia is materially incorrect? I am finding the same definition at Wikipedia and InvestingAnswers.com. Feb 11, 2017 at 21:11
• No. In fact, I didn't read it until this moment. Had I read it first, I'd have been inclined to close the question as "accounting questions are off topic". The article is fine, the concept is more used in business than PF, and my last paragraph was just my opinion, a gut reaction. Feb 11, 2017 at 21:17
• Is there a more appropriate place on the SE network for questions of this kind? Feb 11, 2017 at 21:22
• No. This is the correct place. In the case of accounting, there's often a fine line between business and personal finance. IRR straddles that line in my opinion. Feb 11, 2017 at 22:03

Your hypothetical money market account parallel basically nails it. You understand exactly how the math works. IRR computes a rate at which your money market account would have to pay interest in order to match whatever investment you are comparing to.

That said, there are two major complicating factors to consider:

1. Your hypothetical account would have to not only pay interest, but also lend money, at exactly the IRR rate. In reality of course, it never happens this way. You may be able to lend (invest) at x, but to borrow you're going to have to pay y. IRR simplifies away that issue in order to give us a single number. That number can be very handy for comparison to other competing hypothetical investments, but it does not capture that fundamental issue of lending rate vs. borrowing rate.

2. An IRR calculation assumes implicitly that all cash flows, outgoing and incoming, are known and fixed; that is, risk-free. It makes no allowance whatever for risk, and all investments have some level of risk. Two investments that compute to the same IRR might have hugely different risk around their cashflows, and so not be a close decision at all. To compare those investments, you might go to a measure like RAROC-- risk-adjusted return on capital. But that's much harder, and more subjective, because it requires some numerical measurement of risk.