Using the internal rate of return to measure performance of your investments

Overview of future value and present value

IRR can be confusing for those new to it, both mathematically and conceptually. In order to get a better feel for what IRR does, we need to spend a few minutes talking about the time value of money. The time value of money works in two directions: looking forward with “future value” and looking back with “present value.”

To determine the future value of an initial investment we apply a rate of return to the investment over the investment hold period. Table 1 below illustrates this concept on a $100 investment held for five years at a 5.0% annual rate of return. If $100 is invested today at an annual 5.0% interest rate, then the investment will grow at 5.0% each year and after four years the investment will have grown to $121.55. Thus, the future value of $100 invested at a 5.0% annual rate of return is $127.63.

Table 1: Future value

The present value calculation works in the opposite direction. Rather than asking how much an investment today will grow into in the future, we ask how much we must invest today at a given interest rate in order to achieve a specific future value amount.

Table 2 asks how much we must invest today at a 5.0% interest rate in order to have $100 five years from now. This calculation starts with $100 five years from now and incrementally works backwards until we see the amount that must be invested today, the present value, of $82.27 (represented by the arrows pointing to each previous year).

Table 2: Present value

Notice that both of these methods, future value and present value, require a rate of return in order to determine the respective answer. This is a great approach when the rate of return is known, but, as we’ll see in the explanation of the IRR below, what we often want to figure out is what return will be achieved from a given set of cash flows rather than what cash flows will be received from a given rate of return.

What is the internal rate of return?

Now that we’ve covered the basics of future and present value, we can take a closer look at the specifics of the IRR.

As mentioned in the previous paragraph, in real estate we’re often given a set of cash flows (in the form of rent rolls, expenses, etc. that are relatively static) and market conditions (market cap rate, for example) that determine the current “market value” of a property.

Although there are inefficiencies in the market that can be exploited by real estate operators, for the purpose of illustrating the use of IRR here we’ll assume an efficient market where rents, occupancy, and the given cap rate for a property are at market rates and no arbitrage opportunity exists.

A simplified explanation of IRR is that it takes two inputs: one is the set of assumed operating cash flows over the hold period and the other is the estimated initial cash outlay (purchase or acquisition price). The IRR calculation then discounts the assumed operating cash flow year-by-year and returns the rate of return that will be achieved on the given purchase/acquisition price. So, the IRR accounts for both the amount of the cash flow as well as for the timing of the cash flow.

Table 3 below provides a simple example of the IRR at work. In this example, an investor invested $100 at the beginning of year one and expects to receive $25 in cash flow at the end of each of the next five years. Given these assumptions, the investor should expect to achieve an annualized rate of return of 7.93% on the $100 investment.

Table 3: Internal rate of return

Caveat of the IRR calculation

The IRR approach to valuation is very useful, but the calculation itself has one drawback. The formula assumes that cash flows received earlier in the analysis are re-invested at the same rate of return as the rest of the cash flows.

This is often not the case because investors will sometimes reinvest funds in other projects at then-current market returns rather than reinvest funds in the same property. An analyst needs to be aware that this factor could cause the IRR to be slightly off from the actual return received.

Difference Between NPV and IRR

The two tables below will guide us through a discussion of the difference between the two methods. Keep in mind that these tables have been extremely simplified in order to illustrate the difference in the two approaches. In the “real world” you would use the Net Cash Flow (NCF) line item to perform NPV and IRR calculations (NCF is what’s left after deducting items such as capital expenditures, debt service, and other line items from the Net Operating Income (NOI)).

Table 4 below is an illustration of the NPV method. The NPV method was discussed in more detail in a previous article, so this article won’t dive into the details. As a refresher, though, the NPV valuation method uses the projected long-term cash flows from a property and applies a selected discount rate to those cash flows to determine how much an investor should pay for a property and its respective stream of cash flows (indicated by the red box with question marks).

Table 4: Net present value (NPV) method

Required rate of return = 10%

Suggested purchase price = Unknown

Table 5 uses the same property performance assumptions, but this time applies the IRR method instead of the NPV method. The difference here is that the investor assumes a purchase price for the property (the required initial cash outlay) and wants to know what rate of return will be achieved given the assumed cash flow and purchase price (indicated by the red box with question marks).

Table 5: Internal rate of return (IRR) method

Rate of return = 10%

Purchase price = $2,000,000

These two tables look very similar, but the difference between the two approaches is significant:

• The NPV method sets a rate of return in order to determine the purchase price of the property.

• The IRR method uses a purchase price to determine the likely rate of return given the assumed cash flows (both outflows and inflows).

Arguments for using IRR rather than NPV

While both the NPV and IRR methods are extremely useful, in practice the IRR method is generally a more viable approach. One of the reasons for this is that an investor rarely has the ability to change the purchase price as they see fit.

The purchase price is determined by the market and if the market price on a specific asset does not allow an investor to achieve the desired rate of return, the investor should move on to another property or rethink the rate of return they currently require.

The IRR method takes a more realistic approach to determining the expected yield given current market conditions and can be used to quickly figure out whether the combination of cash flows for a property and a probable purchase price offer the rate of return an investor finds acceptable. If an investor does not find this return acceptable, they can quickly move on to another property or market that does offer the desired rate of return.