# NPV, PI, IRR, FMRR, MIRR, CpA — Stirring the Alphabet Soup of Real Estate Investing, Part 2

#### IRR – Internal Rate of Return

Internal Rate of Return (IRR) seems to befuddle many investors, but if you understand Discounted Cash Flow and Net Present Value, then you already understand IRR. That’s because it is really the same process, but one where you are solving for a different unknown.

In DCF, you believe you know what the future cash flows will be, and you believe you know the rate at which those cash flows should be discounted. Your mission is to figure the Present Value of the cash flows.

With IRR, you still believe you know what the future cash flows will be, but now you know the Present Value and want to find the discount rate. How is it that you know the Present Value? This is a deal happening in the real world. The PV is the amount of cash you are paying for those future cash flows.

When you solve for the IRR, you are looking for the discount rate that accurately describes the relationship between those future cash flows and the money you put on the table on Day One.

When you’ve found the discount rate that makes the PVs of the future cash flow equal to your initial investment, you’ve found the IRR. You can express this another way: When you’ve found the discount rate that makes the NPV equal zero, you’ve found the IRR.

Admittedly, the math to find the IRR is ugly, but if you’re reading this then you probably have a computer (or a highly sensitive gold filling that also picks up the BBC on the Internet); there are plenty of tools, including Microsoft Excel and our own RealData software that will do the job for you.

IRR is the measurement of choice for many investors because it take into account both the timing and the magnitude of your cash flows. Consider this example:

You still have that \$300,000 to invest, and you can invest it in the property you saw in the first example, yielding these cash flows and IRR:

 Year 0 Initial Investment: (300,000) Year 1 Cash Flow: 10,000 Year 2 Cash Flow: 20,000 Year 3 Cash Flow: 25,000 Year 4 Cash Flow: 30,000 Year 5 Cash Flow: 385,000 (includes the proceeds of sale) IRR = 10.32%

Or you can acquire this property:

 Year 0 Initial Investment: (300,000) Year 1 Cash Flow: 80,000 Year 2 Cash Flow: 50,000 Year 3 Cash Flow: 30,000 Year 4 Cash Flow: 10,000 Year 5 Cash Flow: 300,000 (includes the proceeds of sale) IRR = 12.97%

If you add up the cash inflows and outflows for both properties, you will find that each has \$300,000 going out in Year 0, and a total of \$470,000 coming in over the next five years. However, the second property shows a significantly higher IRR. Both properties have the same total number of dollars going out and coming in over five years, but the second property shows a greater return on investment. Why?

Because IRR is indeed sensitive to both the timing and amount of cash flow. The first property has a big payday, but you have to wait five years to get the money. In the meantime, annual cash flows are relatively modest.

In the sale year the second property returns combined cash from operation and resale that is only as much as you originally invested to acquire the property. However, the intervening cash flows are much larger, especially the earlier ones. The early cash flows are especially valuable because you don’t have to wait long to receive them and therefore you don’t have to discount their values so greatly.

But Wait…

This sounds terrific; we’ve found the perfect way to measure our investment’s return. But wait – on closer inspection, IRR has a few warts. Sometimes its results are imperfect, sometimes even misleading. In the third installment of this series, we will look at the problems with IRR and at some potential solutions. We’ll examine FMRR and Modified IRR, and how they provide us with a means of dealing with the shortcomings.

—Frank Gallinelli

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