Terminology question - Posted by BillOhio

Posted by ray@lcorn on October 23, 2003 at 09:47:40:


I disagree. If your comment regarding “99% of the deals made by people frequenting this forum” were made about the main newsgroup I would agree. There’s not much use in running the calculations on single-family lease options and flips. But I think you would be surprised to know the level of sophistication among the frequenters of this forum. I know for a fact that my deal volume isn’t as high as several others that post here.

This is not that complicated, and the results are invaluable in analyzing not only the performance of competing investments, but to offer indicators of where, how and when performance can be improved. The FMRR calculations are actually shortcuts to the very issues you are concerned with… cash flow, tax ramifications and the improvement of returns and asset value.

I would suggest you turn your thinking around, and instead of condemning the idea, ask yourself how you can use it to increase your skillset. Gross deal volume is not neccesarily an indicator of success. I’ve lost money on multi-million dollar deals that looked like sure bets.

I never stop learning. I want to know how to work smarter, not harder. That’s the purpose of this forum, and why I am here.


Terminology question - Posted by BillOhio

Posted by BillOhio on October 20, 2003 at 14:21:16:

When you invest in a commercial property, you can make money from 1. reduction of principal 2. inflation 3. cash flow and 4. taxes

What is this called IRR FMRR ROI ???

Re: Terminology question - Posted by ray@lcorn

Posted by ray@lcorn on October 20, 2003 at 19:11:22:


I’m not sure if you’re asking what the acronyms mean or how they relate to the four ways to make money from real estate. I’ll answer the former, and hope it explains the latter.

(This is an excerpt from my new book by the way… and don’t ask when it will be finished!)

Investor Rate of Return Measurements

Return on Investment- ROI: (also Cash-on-Cash Return) ROI provides a standard for comparison of the opportunity cost of your cash in investing in a specific project for a specific time, usually one year. That is to say that when you make a decision to invest capital in any particular investment, you have in essence given up your opportunity to invest it anywhere else. Therefore, a cash-on-cash return is a measure used to compare relative opportunities for investments, all other things being equal, which theyv rarely are. Leverage, risk, time, and opportunity can widely skew the results. It should be used as only one part of a conprehensive analysis of total returns (more below).

The formula is straightforward:

Annual pre-tax Net Income/Cash Investment = Cash on Cash Return (or ROI)

This measurement has meaning only as a comparison to competing investments.

Equity Dividend Rate: (also Return on Equity and Cash on Equity): This is a measure of performance that, like the cash-on-cash return, again offers a method of comparison to other investments. As defined above, the equity is stated as the difference between market value and debt. Critical to the calculation is an accurate estimation of value. It is calculated by dividing the pre-tax cash flow by the equity investment.

Pre-tax Cash Flow/Equity Investment = Equity Dividend Rate

Income Capitalization Rate: (also known as ?cap rate?): We will be discussing capitalization rates at length in a later chapter. Here we will look only at the traditional formula for the calculation of an overall capitalization rate. In its simplest form, the capitalization rate reflects the return the investor would receive over one year if the investment were purchased for all cash. In my opinion it is one of the most misused tools in the real estate industry, for reasons that will be explained at length in our later discussion. Used properly however, the cap rate can be a useful tool for determining value unique to the investor?s capacity and conditions.

This approach to establishing an estimate of value uses three factors; Income (NOI), Rate of Return, and Value. This formula is also known as the IRV formula, where ?I? represents income, ?R? represents rate, and ?V? represents value. If you know any two elements of the formula, you can solve for the third.

I/V = R

Example: A property has a Net Operating Income of $260,000. The asking price (value) is $3,000,000. The indicated capitalization rate would be 8.7%.

$260,000 (I)/ $3,000,000 (V) = .08666 (R)

Once you learn the method of deriving your own cap rate, then the formula will be solved for an indicated value. Assume that your minimum cap rate for an investment is derived to be 10.5%. With an accurate NOI of the property, you can then calculate the maximum price that can be paid to achieve that return.

$260,000 (I)/.105 (R) = $2,476,190 (V)

This is probably the most widely used measure of a property?s performance relative to value in use today. If you play around with the formula you will see that the higher the Cap Rate, the lower the indicated sales price. This is an important concept that will come into play on several levels before we are finished.

Time Value Methods of Return

Internal Rate of Return (IRR)
Most real estate books I have in my personal library avoid the discussion of explaining Internal Rate of Return calculations like the plague. After attempting (poorly, in my opinion) to explain the concept, one text even goes so far to say ?Confused? That?s why this subject is omitted here.? The reason is that it is a complicated formula to understand, and to try and teach the math is to run the risk of brain damage for both the teacher and the student. That same text then closes the discussion on the subject saying, ?The simplest definition I have been able to find to the term is from one of my old college financial management texts. The Internal Rate of Return is defined as the interest rate that equates the present value of the expected future cash flows to the initial cost outlay.? Now that we?ve seen that in terms no one can understand, let me see if I can explain the concept.

The idea is that every investment pays returns over time, and a dollar in the future is worth less than a dollar today. But at some discount rate, the value of that future dollar can be calculated in terms of today?s dollar. IRR is closely related to NPV, the net present value function. The rate of return calculated by IRR is the interest rate corresponding to a 0 (zero) net present value. In essence, there is a rate at which you can discount a stream of future cash flows that their value in today?s dollars would be zero. IRR finds that rate, and also includes in the calculation the costs of making the investment, and the recovery of the investment plus accrued appreciation on sale.

Let?s try a simple example. If I offered you $100 per year for five years, what would you be willing to pay for that income stream? Would you pay $500? If you paid $500 for the income stream, and received $100 per year for five years, then your return over the period would be 0%. However, there is more to the equation. Knowing that the inflation rate in recent years has been a low 3% or so, can you see that you would actually have less money than what you started with? Applying a 3% inflation rate, the five hundred dollars that you have at the end of five years would be worth about $429 in today?s dollars. So in fact our deal would produce a negative return, meaning you actually lost money, because the value of today?s dollar is greater than the dollar five years from now. But that?s not the only loss. Consider that by giving me the $500 now, you will not be able to invest that money in something else that would likely pay a positive return. That?s known as the opportunity cost of an investment. For example, you?ve lost the opportunity to get the kingly .75% the bank currently pays on a savings account. How do you compensate for that? Add to that the risk that I may not be able to pay the one hundred dollars every year. Are you now certain that you wouldn?t give me $500 in return for a promise to pay $100 per year for the next five years?

Bear with me; we?re almost there.

Now, do you think that there may be a lesser figure than $500 at which this deal could make sense for you? What if I told you that in return for $350, or $300, or whatever amount you choose today, I would pay you the $100 per year for five years? Is there a number at which you would get interested? If you said yes, then you?re thinking in the right context. An initial cost of $300 to you for the income stream would yield a 20% IRR over the five year holding period. That?s certainly above the rate of inflation, and possibly better than a mutual fund. We?ll see how it is calculated in just a minute.

There is one more factor to consider. Unlike our simple example above, most investments retain their value, and hopefully appreciate in value, over the time they are held. A property that appreciates five percent per year, with an original value of $100, would be worth $127 at the end of five years. That?s a profit of $27 that must be accounted for in figuring the total return on investment. In the terms of the IRR math, that?s known as the reversion value.

The actual formula for IRR looks like this:

(Note: Due to the formatting limitations of the newsgroup I cannot reproduce the formula for the calculation. It is essentially the net present value of the (after tax) cash flows for each year of the holding period, plus the reversion value.)

In this age of financial calculators, computers and custom software applications, there is no reason to go through the brain damage of mastering the formula. There are many fill-in-the-blank software applications that will perform the IRR calculation for you. However, if you have a computer with Microsoft Excel, the function is built right into the spreadsheet. There is a fairly simple way of calculating your own IRR numbers for any given project using this function.

By setting up a simple column of figures in Excel, you can plug in numbers to your heart?s content to show you your expected return. On an Excel worksheet, enter the original investment for a property in a cell, say its A2, as a negative number. (It?s a cash outlay, hence the negative entry.) Using our example above, enter the price that you think you would pay for the income stream; say $300, as a negative number. Now in the next five cells below this entry, enter the annual payments (cash flows) of $100. In the cell directly below the last payment entry, type the following formula:

=IRR (A2:A7)

Hit ?Enter?, and the calculation will run automatically. For the above example, you should have gotten the answer of 20%. If a ?#NUM!? entry appeared in the cell, go back and make sure you entered the initial cost as a negative number. If you still have problems, use the help function in Excel by typing ?IRR? in the search box. The program will walk you through the process.


After that long explanation of IRR, I have to warn you that there is an inherent flaw in the IRR formula. The basic assumption that skews the IRR as a measure of return is that the formula assumes that the cash outflows are reinvested at the same rate of return as the investment that produces the cash. This is only true if the cash thrown off the investment is reinvested in the project itself, or in another investment that returns the same as the subject investment. This is rarely (if ever) the case.

For a more accurate reflection of the total returns from an investment, there is a modification of this formula with which you can insert the actual rate of return on the reinvested funds. This is known as the Modified Internal Rate of Return (MIRR), also known as the Financial Management Rate of Return (FMRR).

The basic difference is that the calculation uses a predetermined rate (often called the safe rate, because it is usually pegged to CDs or T-bills) for the reinvestment of the cash flows. This removes the inflation of the return inherent in the IRR calculation. Again, there are many spreadsheet applications, including Excel, which can perform the calculations.

In using these formulae, one has to be aware that any error in the inputted data, i.e. the cash flows, tax rates and reversion value, will affect the answer. If the assumptions are significantly in error, then the result can be meaningless. Since the nature of real estate is that we have to project results based on varying assumptions, no calculation can be exact in projecting a return. Care must be taken to shape the assumptions as accurately as possible.

end of excerpt**

Hope that didn’t create more questions than it answered.


At the risk of further brain damage… - Posted by RobH_WA

Posted by RobH_WA on October 21, 2003 at 11:50:27:


Great job, as always.

  1. Suggestion - ROI/Cash-on-cash
    “This measurement has meaning only as a comparison to competing investments”. Maybe you could underline that the key issue here is the tax treatment. If the tax treatment is the same, and the holding period similar, this works. Ie you can compare two or more rehabs but not a rehab with a stock purchase or a rehab with a buy and hold property.

  2. Question
    Since you have opened the door a crack on MIRR can I ask you or someone else to explain what I am doing wrong with it. MIRR in Excel requires the list of values as per the IRR and two interest rates:
    Finance rate (FR) - the rate paid on the money used in the cash flows
    Reinvestment rate (RR)- The rate you receive on the cash flows that you reinvest.

My assumption is/was that the finance rate is the rate paid for the loan, or opportunity cost for your capital, on the original payment.

My problem is that whatever number I plug in for the FR has no impact on the result! The result will vary based on the interest rate assumed for RR.

Is my assumption wrong? Am I doing something wrong with the calculation?

Using $30 payment in year 0, and cash flow thereafter starting at 5 and rising by 1 per year to 11 in year 7 I get an IRR of 16%. Assuming FR of 10% and RR of 5% I get an MIRR of 11%. Whatever I do to the FR has no impact on the 11%, but the RR has an immediate impact.

Ouch! - Posted by ray@lcorn

Posted by ray@lcorn on October 22, 2003 at 09:09:03:


I am not a mathemetician, so don’t take this as being the definitive answer. In answering your question I ran into a conundrum of my own.

The FR only comes into play if one of the cash flows is negative. Take any of your cash flow numbers and make it negative. Then change the FR… you’ll see the change in the MIRR.

Since the initial investment that produces the cash flows is assumed to have a cost (whether the interest rate on a loan or required return on equity), then it is assumed that any subsequent negative cash flow would carry the same cost of funds.

Here’s the conundrum though… why does increasing the FR to very high levels (50% and more), cause the MIRR to rise? I don’t have the answer… I just noticed it as I was playing around with the numbers. Can anybody help?


Re: Ouch! - Posted by Jeff

Posted by Jeff on October 22, 2003 at 20:19:20:

This whole line of posts reeks of paralysis of analysis best left to esoteric Harvard MBA’s.

Most of the folks on this site don’t get involved with properties that require this much analysis.

Beyond all the due diligence checks and basic financial analysis, all we want to know is, does it cash flow and provide the tax consequences we are looking for.

On the other hand, if you are one of those Harvard MBA’s more power to you, but you probably haven’t purchased any property because someone else will have closed escrow before you have completed your calculations.

Re: Ouch! - Posted by Jim Rayner

Posted by Jim Rayner on October 22, 2003 at 09:24:05:


the initial investment is always entered as a negative.

i’m still pondering your other question

Re: Ouch! - Posted by ray@lcorn

Posted by ray@lcorn on October 23, 2003 at 08:20:28:


I can understand your objection to learning anything new. It’s much easier to just do what you know.

But you did describe the discussion accurately…

es·o·ter·ic 1 a : designed for or understood by the specially initiated alone b : of or relating to knowledge that is restricted to a small group

And just so you know… in addition to being the host of this forum, I’ll close about $14,000,000 in deals this year. And that’s as a principal… I don’t do brokerage.

Happy returns,


Re: Ouch! - Posted by RobH_WA

Posted by RobH_WA on October 22, 2003 at 13:13:54:


I think I have discovered the answer(s).

The MIRR calculation works like this: Unlike IRR the cash flows are separated into two streams (negative and positive) and calculated differently.

All negative cash flows are calculated back to give a PV at year 0 using the FR. Since the initial (negative)payment is at year 0, this doesnt change when any change is made to the FR, and thus MIRR only changes with the FR when there are other/subsequent negative cash flows.

Positive cash flows on the other hand, are compounded to a FV at the last year based on the RR.

MIRR is then calculated based on the relationship between the PV of the outflows, and FV of the inflows, over the number of periods involved.

The reason why the MIRR rises when the FR falls is due to the way it is calculated, and it occurs all the time, not just when FR rises to a high level. This may not be obvious if the negative cash flow is relatively small and/or the answer is rounded off.

If, say, you had a negative cash flow in year 5, then the PV of that at year 0 would be higher if the FR is lower (less compounding is taking place.) $4 in year 5 is worth $2.72 at 8% in year 0, and $2.48 at 10%. Since the MIRR is the value of the positives at the end year over the value of the negatives at year 0, the rising FR will increase the MIRR.

Although the above may solve the technical questions over MIRR to me it does not replicate rational investor behavior. If an investor buys a property with a planned 7 year hold and with a projected negative in year 5 (roof replacement or whatever) their action would vary primarily on whether the FR is expected to exceed the RR at that time. If it is then the investor would either pre-fund from previous cash surpluses and/or pay back as rapidly as possible in subsequent years. If the RR was greater, then the rational thing to do is to fund the deficit from borrowing at the lower FR rate.


Re: Ouch! - Posted by ray@lcorn

Posted by ray@lcorn on October 22, 2003 at 12:15:12:

Hi Jim,

I should have been clearer in my comment… in addition to the initial investment which is always entered as a negative, if you enter a succeeding negative cash flow then the FR will change the MIRR. But an increase in the FR poroduces an increase in the MIRR. So the FR is not acting as a cost, but a return.

Enter the following calculation in an Excel spreadsheet:

10% (this is the finance rate)
12% (this is the reinvestment rate)
=MIRR(A2:A7,A8,A9) (this is the formula for MIRR)

The last cell will provide an MIRR of 13%

Now make the last cash flow negative i.e. -46,000

The MIRR is 3%.

Now increase the finance rate from 10% to 15%.

The answer I get is an MIRR of 4%. So intuitively I know that if I lost money in that last year of cash flows, and that money cost me more, then my return should be less. But the calculation is the opposite.

That means I must be misinterpreting the definition of Finance Rate? Excel defines FR as “the interest rate you pay on the money used in the cash flows”. Assuming the “cash flow” is after expenses and debt service, then why would the rate on the debt matter?


Re: Ouch! - Posted by Jeff

Posted by Jeff on October 23, 2003 at 09:19:32:

You are a much better deal maker than me. I only closed approximately 2.8Million in deals this year.

However, my point was that although your discussion was interesting, that degree of analysis probably doesnt factor into 99% of the deals made by people frequenting this forum.

Its not that we are not capable of running or understanding those formulas, its just not necessary with the great majority of our deals.