An Infinite Return On Investment Is Impossible, Even In Real Estate

2009 June 29
by Kyle Bumpus
from → Real Estate

Much-maligned real estate guru Robert Kiyosaki (of Rich Dad, Poor Dad fame) is often criticized for misleading aspiring real estate investors by giving advice that is either impractical, illegal, or downright inaccurate.  Many of these inaccuracies are harmless, but some cause real damage.  One of the ideas often attributed to Kiyosaki by his followers and critics is the idea that if you receive a positive cash flow on a property you acquired for no money down, meaning your revenue is higher than all your combined expenses associated with that property, you’ve just earned an infinite return on your investment.  This idea has been subsequently propagated all over the internet by mathematically-challenged individuals.  I’m sorry to burst Kiyosaki’s bubble, but an “infinite return” on any investment, including real estate, is a mathematical impossibility.

No Such Thing As An Infinite Return

To the uninitiated, the myth of the infinite return on investment at first seems plausible.  After all, if you were able to acquire a profitable asset without investing any of your own money, the profit on that investment would be infinite relative to the magnitude of that investment, right?  Wrong.

The utter ridiculousness of the myth of the infinite return on investment becomes obvious when one reflects on the meaning of the word “infinite.”  First, think of all the money in the entire universe that exists, has ever existed, or ever will exist.  Got a number in your head for how much that might be?  There’s no telling how large that number is but one thing is for certain:  it’s less than infinity.  There is a finite amount of money in the universe.  It might be an astronomical number, but its still a finite one.  When you say you’ve achieved an infinite return on an investment, what you’re really saying is that you received all the money in the universe and then some.  Did you receive all the money in the universe on your last investment?  The $20 bill in my wallet right now says you didn’t.  Unless you are the only one in the universe with any money, you didn’t earn an infinite return.

Remember Middle School Algebra?

The formula to calculate return on investment is simple:  ROI = (gain from investment – cost of investment ) / cost of investment.  If you bought a stock for $100 and by the end of the year it was worth $110, your ROI = ($110 – $100) / $100 = 10%.  The zero-down-infinite-return proponents will say “well wait a minute, if my investment is $0, that’s an infinite return!”  Wrong.  Let’s run the numbers using the above example except this time, the “cost of investment” is assumed to be $0.

ROI = ($110 – $0) / $0 = ???

Do you see the problem with the equation above?  The more mathematically-inclined among you will immediately note there is a $0 in the denominator.  This poses a problem since in math, division by zero is illegal.  You simply cannot do it.  Ever.  For any reason.  Thus, the correct thing to say is that in this case, the return on investment is undefined.  You can’t calculate what the return is but one thing is for certain:  it is not infinite.

Don’t believe me when I say you can’t divide by zero?  Just ask the U.S. Navy.  In 1997, the U.S. Navy aircraft carrier USS Yorktown’s propulsion system ceased to operate, rendering one of the mightiest ships in the history of the world dead in the water.  The reason?  An error in the ship’s database caused the on-board computer to attempt to divide by zero, crashing the entire system.  The ship had to be towed into harbor.  If the U.S. Navy can’t even divide by zero without catastrophic results, you haven’t got a prayer.

But The Return Is Still Huge, Right?

Hopefully by now I’ve managed to convince you an infinite return on investment is possible.  “Fair enough,” you might say, “but the financial rewards on the transaction is still huge.”  Well, maybe.  But probably not.

Zero-down deals are quite rare, and they are never easy.  If there really were plenty of zero-down properties out there that would yield positive cash flow right from the very beginning, everybody would be doing it.  Obviously, it’s not that easy.  In fact, it’s extraordinarily difficult.  It takes a lot of time, research, and careful calculation to find these deals and after closing, there’s often a lot of work that needs to be done, since the vast majority of these properties are fixer-uppers.  The financial investment required might be zero, but the labor and time investment required is huge.  Once you take the value of your time into account (and the associated opportunity cost of not being able to do something else), the picture changes dramatically.

An Example Of The Time Costs Involved In Real Estate Investing

Continuing the example above, let’s assume you are able to buy a $100,000 property with no money down that at the end of the year appreciates 4%.  Furthermore, let’s be generous and assume the above property yields $100 per month in positive cash flow after expenses, or $1200 per year.  Overall, the property returns $5,200 over the course of the first year, most of it unrealized appreciation.

Let’s assume the investor in question earns $50,000 per year at her day job, which equates to about $25 per hour (assuming two weeks vacation) and let’s furthermore assume it takes approximately 50 hours of work to locate, research, and renovate the property.  I believe 50 hours of work is a very reasonable assumption when you take into account the time spent on MLS websites looking at listings, visiting properties, negotiating, dealing with lenders, arranging inspections, attending closing, and a weekend renovating.  Nobody who has ever bought a property would balk at the 50 hour figure.  All told, 50 hours x $25 per hour equals $1,250.  This is the amount of your actual initial investment, not $0.  In the end, this works out to a 316% return on investment, which is nice but hardly anywhere close to infinite.  Looked at from another perspective, you earned approximately $104/hr on this real estate deal, which is over four times the hourly rate from your day job.

But wait, there’s more!  Rental properties don’t manage themselves.  Assuming it takes approximately 2 hours per month to manage your new property (24 hours per year), you’ve just added another $600 to your upfront investment, bringing your total to $1,850.  In the end, you get a 280% return on investment equating to just over $70/hr.  All in all, not a bad return, but it’s certainly nowhere near infinite.

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17 Responses
  1. 2009 July 7

    lim (a-> 0) (5 /a) = infinity, for all intents and purposes.

    The obvious problem is you are ignoring the amount of time; and the true cost isn’t 0.

  2. 2009 July 7
    Joe B permalink

    Dang SJ beat me to the limit.

    Kyle,

    You bring up an interesting point about the scammers. They claim an infinite return on investment, due to a $0 monetary investment. By that logic going to work has an infinite ROI, since it didn’t cost anything to go to work, except time.

    Maybe I should start selling a new infinite ROI program called, “NO MONEY DOWN JOBS!!!”, only 4 easy payments of $69.99

  3. 2009 July 7

    You’re being pedantic. For a given profit, the ROI increases without bound as the investment approaches zero. I’d imagine even the most stubborn mathematician would be satisfied with someone using “the ROI is infinite” as an informal shorthand for this.

  4. 2009 July 7

    Dang, forgot the other thing I wanted to say…

    Your own logic is even more faulty than Kiyosaki’s. You claim that an infinite ROI on a zero investment means that you get all the money in the world and more. However, you can’t claim that zero times an infinite quantity is infinite because it is undefined. I would be just as justified in claiming that zero times an infinite quantity equals five bucks.

  5. 2009 July 7

    “Pedantic” is just a fancy word for “correct.”

  6. 2009 July 7
    Paul permalink

    Obviously, no one can get infinite returns. I’ve done some “no money down” deals and in truth I’ve always had to come up with cash. Investment property requires cash for unexpected expenses. If you don’t have any cash for a down payment, it’s likely that if you lose a tenant for a long period or need a new roof you can be in deep trouble.

    Some people seem to think that if they buy property for no money down, that they can walk away if there are problems without any consequences. But if you default on a mortgage, consider your credit score. What is the return for the next seven years when you are paying a premium for any money you try to borrow? Maybe, it’s a negative infinite return :)

  7. 2009 July 8

    Nicely written and explained article.

  8. 2009 July 8

    Paul, thanks for pointing that out. Even if you put zero down, you still definitely need to hold cash in reserve to take care of unexpected expenses, which for all practical purposes is a form of “down payment” anyway. Returns in real estate can be large, but you’ve got to be realistic. Espousing “infinite returns” is irresponsible, in my opinion.

  9. 2009 July 8

    An infinite return DOES mean that you get infinite money if you ignore the practical element of the situation. In your arguement you point to the practical when it suits your arguement but fail to notice where it doesn’t.

    ROI as a metric in inherently flawed for this type of debate because it assumes linearity across all levels of investment. If instead I said given an investment you got a 10% ROI then you’d expect to get $1 if you invested $10, or $10 if you invested $100. However, even in the real world this doesn’t hold up for ANY investment. If I invest $1 trillion in a particular stock, I will not earn 100 billion because by that point I will either have exceeded the possible number of shares to own, or completely altered the financial situation that the ROI was based upon. On the opposite extreme it is doubtful I’d be allowed to purchase a stock at 1 cent or less…and if I did my 0.1 cent return would probably be rounded away into oblivion.

    However, if you took the ideal case of a company with infinite shares, with unlimited growth potential, then I should expect my ROI of 10% to hold up at any level. In the same way, if unlimited real estate was available for no money down, I could conceivably get infinite money.

    So yes, the text book ROI is definitely infinite…but does not define real world outcomes, anymore than a 10% ROI says anything about an investment as it approaches bounds of practical extremes.

  10. 2011 January 19
    Bob permalink

    Why so serious bro? Math is just a tool to help humans conquer nature, right?

  11. 2011 January 19

    No.

  12. 2011 May 20
    mike permalink

    The idea is that the amount you make is not limited by the amount of cash you have. Not limited by cash is an infinite return on capital, but not on other expenses such as time.

  13. 2011 May 20

    If you could do that deal over and over again, which theoretically you can, you are not limited by time. Of course, to be able to acheive that deal does take time. I don’t think Kiyosaki has ever downplayed the need for financial education and that it is a lifelong process, and that his advice is not for the average person. His only advice for the average person is “don’t be average”. many people looking to get rich quick just have a tendency to overlook some of these things.

    The vast majority will never put in the work to even come close to be able to invest like Kiyosaki.
    I mean he has a publishing business that can bring in lots of genius investors that also have careers in other area, form a corperation with those people working with him instead of costing expenses they share in the actual investment. So he pays $0 in management, in fact Ken McKelroy the manager of his properties puts his own money down along with kiyosaki so that they have more deals available to them. Normally what Kiyosaki advizes would be a huge expense and make positive cash flow very difficult, which is why not only “forming a team” of people that are also investors, but actually structuring that team as a corperation and pooling money and using their services for free rather than eat up expenses until positive cashflow disappears is crutial!

    Kiyosaki takes the time finding the deals, but many deals come to him because of relationships he has with bankers and lawyers that can give him deals that never hit the public. Overtime his actions compounds, but he dedicated the first half of his life to investing and now he is dedicating it to teaching.

  14. 2011 October 1

    You are confusing several issues. Firstly you’re confusing the value of the return with a ratio. Kiyosaki is saying that he receives an infinite Return On Iinvestment, not infinite money. ROI is the ratio of annual returns to the cash required to hold the investment. If no cash is needed, and the annual return is positive then the ROI is technically infinite, even though the earnings may only be one dollar.

    Secondly you are confusing the definition of ROI which does not calculate investment of time. The I part of ROI specifically refers to money, not time. Those who confuse the two have not studied it, and are not using the definition used by investors.

    Also I notice some people are suggesting that a job can somehow be an investment. But an investment results in returns that go on after you stop physically being productive. Working in itself is not an investment. If you build something which is productive after you stop working on it, then you have an investment.

  15. 2011 October 2

    CS, I am not confusing the issue. An infinite Return on Investment means infinite money. I made that statement as a way to highlight the ridiculousness of what Kiyosaki said. No, the ROI is NOT technically infinite if no cash is required. That is mathematically impossible. That’s like insisting that 2+2=5. It doesn’t and never will be.

    ROI refers to the return on your CAPITAL. Not all capital is monetary or represented by cash. To believe otherwise is to lie to yourself. Since time is money, time investment MUST be factored into any business endeavor, including investing in real estate, to get a true picture of how well you’re doing. That’s exactly why mutual funds are so popular: they don’t require any time or effort!

  16. 2013 June 28
    Anonymous permalink

    I think this article is more to do with someone mis-interpreting what was actually written by Kiyosaki and completely rehashing the context in which it was written.

    To go on to then argue and say that ‘infinite returns are impossible’ is therefore a mute point.

    In my experience of the property game, if after the hard slog of sweat equity/ time/effort/refurbishment/fees/mortgage payments/annual up keep/annual safety regs etc and I have none of my own cash left in a property that is then giving me a clear $150 per month in passive income (even after an agent has taken his cut for managing it for me)……then yes, I have an ‘infinite return on my investment’…..which really only needs to be 0.000000000000000000000000001 cent doesn’t it?

    Has nothing to do with the universe or all the money in the world. Unless you are prone to reading for context and comprehension issues.

  17. 2013 June 28

    No, I’m not mis-interpreting what was written. He LITERALLY wrote that his returns from real estate were LITERALLY infinite. In fact, there are MANY people who honestly believe infinite returns are possible as evidenced by comments and forum posts across the web. No, you do not have an ‘infinite return on your investment’ in that scenario. You just don’t. There are so many logical fallacies in that statement I don’t even know where to begin.

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