# What IRR, MIRR, FMRR Provide Real Estate Investors

**IRR, MIRR, FMMR** are acronyms for three different rates of return available to real estate investors
that can help him or her measure the potential profitability of real estate investment properties.

Otherwise known as Internal Rate of Return, Modified Internal Rate of Return and Financial Management Rate of Return, the three returns, although with diverse mathematical formulations, do share a similar model. They each account for the time value of money and thereby provide a rate of return that links the real estate investor's initial cash investment to the "present and future value" of revenue streams derived from the investment.

In this article I'll show you how each method is formulated so you understand how each can help you determine their benefit to your real estate investing objective.

## IRR

By definition internal rate of return is the discount rate at which the present value of all future cash flows produced by an income-producing property is exactly equal to the real estate investor's initial capital investment.

### Formulation

All projected future cash flows (both negative and positive) are discounted at the same rate; which in this case is the IRR.

For example, let's assume the following cash flows as illustrated in the schema below. In this case, CFO reflects the initial cash investment and CF6 reflects both a cash flow and proceeds collected from a sale. The IRR reflects the rate at which all future cash flows must be discounted to exactly equal the amount of the initial cash investment.

CF0 -105,222 (initial cash investment)

CF1 8,792

CF2 9,700

CF3 10,480

CF4 -2,472

CF5 12,093

CF6 12,780 + 169,408 (sale)

IRR = 15%

Result: The total present value for the amounts in CF1 through CF6 will exactly equal the amount in CF0 when discounted at 15%. In other words, the investor could expect to get a 15% yield on his or her cash investment based upon the projected cash flows listed above.

## MIRR

This method is a modified internal rate of return. It was derived because many argued that it's not reasonable to assume that periodic annual cash flows are reinvested at the IRR or that the real estate investor will have to cover negative cash flows at the IRR.

To overcome this shortcoming, MIRR makes the assumption that negative cash flows generated during the life of the investment would be financed at a "finance rate" and positive cash flows can be reinvested (and earning interest) at a "reinvestment rate".

### Formulation

- All cash outflows (negative amounts) are discounted to present value at the finance rate and added to the initial investment.
- All cash inflows (positive amounts) are compounded to future value at the reinvestment rate and added to the expected sales proceeds, if any.
- The internal rate of return is then computed to derive MIRR.

Let's apply this method to the same cash flows illustrated above and assume a 5% finance rate and a 10% reinvestment rate. The negative revenue is discounted back at 5% and the positive revenues are compounded forward at 10% resulting in the schema below which, when IRR is computed, determines the MIRR.

CF0 -107,256

CF1 0

CF2 0

CF3 0

CF4 0

CF5 0

CF6 237,801

MIRR = 14.19%

## FMRR

The financial management rate of return goes even a step further with the additional assumption that where possible, all future negative cash outflows will be removed by prior positive cash inflows. Otherwise, it also requires two additional rates for discounting and compounding loosely explained this way.

- A "safe rate" for funds assumed to be available to service periodic negative cash flows (discounting).
- A "reinvestment rate" for funds that one might expect to receive from average investments of intermediate duration (compounding).

### Formulation

- All negative flows are discounted back at the safe rate and are either reduced or eliminated by any prior positive cash flow. Along the way, if the negatives are not eliminated completely they are discounted back to present value and added to the initial investment.
- Any remaining positive flows are then compounded forward at the reinvestment rate to their future value and added to the expected sales proceeds, if any.
- The IRR is then computed to determine the financial management rate of return.

If we apply this model to the cash flows illustrated earlier with a 5% safe rate and 10% reinvestment rate we create this schema which, when IRR is computed, determines the financial management rate of return.

CF0 -105,222

CF1 0

CF2 0

CF3 0

CF4 0

CF5 0

CF6 234,667

FMRR = 14.30%

## So You Know

ProAPOD's Executive 10 real estate investment analysis software solution and iCalculator, its online suite of real estate calculators, compute IRR, MIRR and FMRR.