internal rate of return (IRR) is the interest rate at which the net present value of all the cash flows (both positive and negative) from a project or investment equal zero.

Internal rate of return is used to evaluate the attractiveness of a project or investment. If the IRR of a new project exceeds a company’s required rate of return, that project is desirable. If IRR falls below the required rate of return, the project should be rejected.

HOW IT WORKS (EXAMPLE):

The formula for IRR is:

0 = P0 + P1/(1+IRR) + P2/(1+IRR)2 + P3/(1+IRR)3 + . . . +Pn/(1+IRR)n

where P0, P1, . . . Pn equals the cash flows in periods 1, 2, . . . n, respectively; and

IRR equals the project's internal rate of return.

Let's look at an example to illustrate how to use IRR.

Assume Company XYZ must decide 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 annual profit 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 equipment purchase is a better use of its cash than its other investment options, which should 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 since this generates a 24.31% return for the Company --much higher than the 10% return available from other investments.

A general rule of thumb is that the IRR value cannot be derived analytically. Instead, IRR must be found by using mathematical trial-and-error to derive the appropriate rate. However, most business calculators and spreadsheet programs will automatically perform this function.

[Click here to see How to Calculate IRR Using a Financial Calculator or Microsoft Excel]

IRR can also be used to calculate expected returns on stocks or investments, including the yield to maturity on bonds. IRR calculates the yield on an investment and is thus different than net present value (NPV) value of an investment.