# The IRR, MIRR, and FMRR Approaches to Investment Analysis by James Kobzeff
May 22, 2018

IRR, MIRR, FMRR are three investment analysis methods used by real estate investors to explore the potential profitability of a real estate investment based upon evaluation of the entire length of the property's proposed or anticipated holding period.

1. IRR - Internal Rate of Return
2. MIRR - Modified Internal Rate of Return
3. FMRR - Financial Management Rate of Return

To do this, the three methods equate the discounted present value of future cash inflows to the present value of cash flow derived from the real estate investor's initial cash investment (e.g., down payment and closing costs). The major benefit being that they each account for the timing of the expected cash flows, since it is known that the value of money received in the future is worth less than money available today.

In this article we'll consider how each investment analysis method is formulated to help you understand how each works and thereby how the resulting rate produced by each might affect your real estate investing objective.

The basic internally rate of return method (IRR) is discussed first, followed by an extension of that method (with increasing complexity and analytical power) in the modified internal rate of return method (MIRR) and the financial management rate of return method (FMRR).

## IRR

By definition the internal rate of return (IRR) 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. Or if you wish, think of it simply as the percentage rate earned on each dollar invested for each period it is invested.

### Formulation:

1. All projected future cash flows (both negative and positive) are discounted at a rate that makes the total present value of those cashflows equal to the investor's initial cash investment.
2. The resulting rate is the internal rate of return.

### Example:

Let's assume we project the following cash flows illustrated in the schema below. In this case CFO reflects the initial cash investment, CF1-CF5 reflects subsequent periodic cash flows, and CF6 reflects both a subsequent cash flow and proceeds collected from a sale.

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%

### Explanation:

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.

### This Method's Assumption

That the IRR reflects the rate for both the reinvestment of positive annual cash flows and the cost of short-term borrowing needs required to cover negative annual cash flows.

## MIRR

This method is a "modified" internal rate of return that was derived to address what many regard as an unrealistic assumption made by the IRR: that periodic positive cash flows get reinvested at that rate and loans needed to cover negative cashflows get financed at that rate.

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:

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

### Example:

Using the same cashflows as we did to create the schema in the previous method, let's assume a 10% finance rate and 10% reinvestment rate and create a modified schema to compute our return.

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)

CF0 -106,910
CF1 0
CF2 0
CF3 0
CF4 0
CF5 0
CF6 237,801

MIRR = 14.25%

### Explanation:

First, we discount back all the negative revenues at the finance rate (in this case, just CF4) and add that present value sum to the initial investment (CF0). Then we compound forward the annual positive revenues at the reinvestment rate toward our sale year (CF6) and add each to our cashflow and sales proceeds. Then we solve for IRR to arrive at a MIRR of 14.25%.

### This Method's Assumption

That the rate is more likely to mirror real-world investment returns when the cost of short-term borrowing required to cover negative annual cash flows, as well the rate analysts expect reinvested positive revenues to earn, are designated by the investor.

## 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. It also requires two additional rates for discounting and compounding loosely explained this way.

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

### Formulation:

1. 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.
2. 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.
3. The IRR is then computed to determine the financial management rate of return.

### Example:

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 (initial cash investment)
CF1 8,792
CF2 9,700
CF3 10,480
CF4 -2,472
CF5 12,093
CF6 12,780 + 169,408 (sale)

CF0 -105,222
CF1 0
CF2 0
CF3 0
CF4 0
CF5 0
CF6 234,667

FMRR = 14.30%

### Explanation:

First, we discounted back the negative outflow (CF4) at the safe rate and eliminated it by the positive inflow in CF3. Then we compounded all the positive annual amounts at the refinance rate and added them to our cashflow and sales proceeds in CF6. Then we solve for IRR to arrive at a FMRR of 14.30%.

### This Method's Assumption

That two different rates (like in the MIRR method) would separately be used to deal with negative and positive annual cash flows. But unlike that method, FMRR also makes the assumption that positive cash flows occurring prior to negative cash outflows will be used to cover that negative outflow.

## So You Know

All three returns are included in the following ProAPOD solutions:

Pro RE Calculator
Compute it quickly and easily.
Executive 10
Computed and posted in all appropriate reports automatically. James Kobzeff is a former realtor with over thirty years of investment property experience and is the owner/developer of ProAPOD Real Estate Software.