# Internal Rate of Return

The Internal Rate of Return (or IRR for short) is a way of evaluating the return rate that an investment is expected to produce. It is used to decide whether a given investment is worth making, and for comparing the expected returns between alternative investments. You feed in the amounts you are investing and the returns you expect to get for each period, and the result is a percentage which is the rate at which your investment grows if you undertake the project.

The IRR is often used to decide whether a project is worth undertaking. If the IRR is greater than the returns which could be achieved elsewhere (for example, by investing in a different project, or by investing in the stock market) then the investment is worth making.

## IRR Formula

The IRR is defined as the discount rate at which the NPV of all cash flows is zero.

NPV = sum_(n=0)^NC_n/(1 + r)^n = 0

where N is the total number of periods, C_n is the cash flow at period n, and r is the internal rate of return.

When r is the IRR, the NPV as shown above will be 0. Unlike many other formulas, this can't usually be solved by rearranging the equation to find r. Instead, you need to use trial and error to find the answer. This basically involves guessing at a value for the IRR, then calculating the NPV for that rate and improving the guess until you have a rate for which the NPV is 0. The IRR Calculator on this site can do this for you. There are also desktop financial calculators available as well as functions in spreadsheets such as Excel for calculating the IRR.

## Example

A company is deciding whether to build a new factory producing widgets. The initial cost of building the factory will be $100,000, and they expect to make$16,000 every year until the factory closes after 10 years.

NPV = -100000 + 16000/(1 + r)^1 + 16000/(1 + r)^2 + ... + 16000/(1 + r)^10 = 0

Solving through trial and error shows that the NPV is 0 when the IRR = 9.61%.

When comparing projects that require different up-front investments, IRR may not be a good choice. For example, if you are comparing investing $100 in one project with an IRR of 10% with investing$1000 in a project with an IRR of 5%, you should invest in the \$1000 project, because you will make more profit overall. In these types of cases, you should compare the NPV of the two projects.

It's not always possible to calculate a single IRR value. Depending on the values used for the cash flows, you may get 0 IRRs, or more than 1. In these cases, using the IRR to determine the attractiveness of an investment is probably meaningless.

## Also Known As

The Internal Rate of Return is also known as:

• Economic Rate of Return (ERR)
• Discounted Cash Flow Rate of Return (DCFROR)
• Effective Interest Rate