# Internal Rate of Return: Understanding the Difference Between IRR, MIRR and FMRR

By definition, internal rate of return is the discount rate at which the present value of all future cash flows is exactly equal to the initial capital investment. To make the calculation, negative cash flows are discounted at the same rate (i.e., the IRR) as positive cash flows.

Let’s consider the following investment with the initial investment as CF0 (always a negative number because it is cash outflow) and subsequent cash flows as CF1, CF2, etc., with some negative and some positive.

CF0 -10,000

CF1 -100,000

CF2 50,000

CF3 -60,000

CF4 50,000

CF5 249,300

IRR = 30%

Seems all well and good, but the problem here is that the calculation assumes that the cash generated during an investment will be reinvested at the rate calculated by the IRR, which may be unrealistically high and therefore will overstate the return on initial investment. Likewise, since negative cash flows are also discounted at the IRR, if that rate is fairly high, the investor might not accurately estimate the cash required to meet those future negative cash flows.

To deal with this shortcoming many real estate analysts use a method known as MIRR (i.e., modified internal rate of return). In this approach, the assumption is that positive cash flows the investment generates during its life can be reinvested and earns interest at a “reinvestment rate”, and negative cash flows must be financed at a “finance rate” during the life of the investment. In other words, rather than simply using one rate (i.e., IRR) to deal with both negative and positive cash flows, MIRR introduces the option to use two different rates.

By applying a finance rate of 5% and a reinvestment rate of 10% here’s the result using the same investment criteria as we did earlier.

CF0 -10,000

CF1 -100,000

CF2 50,000

CF3 -60,000

CF4 50,000

CF5 249,300

MIRR = 18.75%

Okay, then along came the financial management rate of return (or FMRR). Though it also provides two separate rates to deal with negative and positive cash flows known as the “safe rate” and “reinvestment rate”, FMRR takes it a step further. The assumption here is that where possible, all future outflows are removed by using prior inflows. In other words, negative cash flows are discounted back at the safe rate and are either reduced or eliminate by any positive cash flow that it encounters. The remaining positive cash flows are compounded forward at the reinvestment rate.

We’ll apply a safe rate of 5% and a reinvestment rate of 10% to our investment criteria to show you the result. But this time we’ll also include a table to show you the adjusted cash flows.

CF0 -10,000

CF1 -100,000

CF2 50,000

CF3 -60,000

CF4 50,000

CF5 249,300

CF0 -111,717

CF1 0

CF2 0

CF3 0

CF4 0

CF5 304,300

FMRR = 22.19%

The financial management rate of return is difficult to compute, which is why most real estate investment software solutions opt for the modified internal rate of return (MIRR) calculation. But after learning about it from CCIM, I considered it a beneficial return for real estate investment analysis, so I included FMRR my ProAPOD real estate investment software as well as my ProAPOD mortgage calculator software. To learn more please visit the link provided below.

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