# Internal Rate of Return (IRR)

## What it is:

An investment's **internal rate of return (IRR)** is the discount rate that makes the net present value of the investment's cash flows equal to zero.

IRR calculates an investor's breakeven rate of return. If an investment's IRR exceeds the investor's required rate of return, the investment is considered acceptable. The investment should be rejected if the IRR is below the investor's required rate of return.

IRR is often used in capital budgeting, but its principles are also used to calculate expected returns on stocks or other security investments, including the yield to maturity on bonds. Note that the IRR method calculates a percentage return from an investment and is not the same as the Net Present Value method, which calculates a dollar yield.

The formula for IRR is:

*0 = P0 + P1/(1+IRR) + P2/(1+IRR) ^{2} + P3/(1+IRR)^{3} + . . . +P_{n}/(1+IRR)^{n}*

where P0, P1, . . . Pn = the cash payments in periods 1, 2, . . . n, respectively; and IRR = the investment's internal rate of return.

## How it works (Example):

Let's assume Company XYZ is deciding whether to purchase a piece of factory equipment for $300,000. The equipment would only last three years, but it is expected to generate $150,000 of additional profit per year during those years. Company XYZ also thinks it can sell the equipment for scrap afterward for about $10,000. Using IRR, Company XYZ can determine whether the purchase is a better use of cash than some of Company XYZ's other investment options, which return about 10%.

Here is how the IRR equation looks in this scenario:

*0 = -$300,000 + $150,000/(1+.2431) + $150,000/(1+.2431) ^{2} + $150,000/(1+.2431)^{3} + $10,000/(1+2431)^{4}*

The investment's IRR is 24.31%, which is the rate that makes the present value of the investment's cash flows equal to zero. From a purely financial standpoint, Company XYZ should purchase the equipment because doing so generates a 24.31% return on Company XYZ's cash--much higher than the 10% it could get elsewhere.

One benefit of the IRR method is that it can be performed without having to estimate the investor's cost of capital. However, IRR must be found iteravely, meaning that a method of mathematical trial-and-error is used to derive the appropriate rate. Most business calculators and spreadsheet programs automatically perform this function.

## Why it Matters:

IRR allows managers to rank projects by their overall rates of return rather than their net present values, and the investment with the highest IRR is usually most preferred. IRR's ease of comparison compels many investors to use IRR, but there are several limitations in the methodology that prevent investors from relying solely on IRR for decision-making purposes.

The Multiple Rates of Return Problem

In general, the IRR formula only works for investments that involve an initial cash outflow (the purchase of the investment) followed by one or more cash inflows. In circumstances where cash flows aren't conventional, i.e. there are inflows and outflows over the course of the investment, it is possible to calculate more than one IRR for an investment. In these cases, the maximum number of IRRs is equal to the number of times the cash flows change from positive to negative or negative to positive over the course of the investment, and the investor is forced to evaluate the investment over a range of IRRs.

*The Absolute-Size Problem*

IRR calculates a percentage return; it does not measure the absolute size of the investment or the return. This means that IRR can favor investments with high rates of return even if the dollar amount of the return is very small, and reject larger projects even though they may generate more cash for the investor. Thus, a $1 investment returning $3 will look more favorable than a $1 million investment returning $2 million. For this reason, many analysts use IRR in conjunction with net present value analysis when evaluating investments, rather than using IRR alone.

The Reinvestment Rate Problem

IRR is an accurate return measure only when the investment either has no interim cash flows or those interim cash flows can actually be reinvested at the investment's internal rate of return. This is not always a realistic assumption, especially for investments with an unusually high return. IRR can therefore materially overstate an investment's return if this reinvestment rate is not available to the investor. As a result, many investors use Modified IRR, which allows for a separate reinvestment rate in the calculations.

*A Final Note*

Because IRR is so influenced by cash flows, IRR comparisons are generally inappropriate between portfolios experiencing considerable contributions or distributions (like pension funds) and other portfolios or market indexes of different dollar size. Growth rates strongly influence portfolio IRRs, and managerial skill may therefore be distorted when comparing the IRRs of different-size portfolios.