# IRR or Internal Rate of Return

IRR is a special application of the logic behind NPV or Net Present Value calculations. It is a commonly-used concept in project and investment analysis, including capital budgeting. The IRR of a project or investment is the discount rate that results in an NPV of zero.

Computing the IRR is a way to analyze an investment for which anticipated (or actual) returns vary from year to year or period to period. Except for debt instruments that yield a constant rate of return over their lives, such variation is the norm. The IRR methodology is a device to derive a single, average compound rate of return from such a scenario.

If the actual discount rate (which is the theoretic cost of funds to the company or investor in question) is lower than the IRR, the project or investment should be undertaken. It is the decision-making rule of thumb used when IRR is employed an analytic tool for evaluating projects or investments.

### Simple Numeric Example

You make a loan of $1,000 to someone. Per the terms of the loan, you will receive an interest payment of 11% ($110) at the end of the first year, and a 20% interest payment ($200) at the conclusion of the second year, at which time you also will receive your $1,000 principal back.

Your IRR, or Internal Rate of Return, on this loan, would be 15.1825%.

Here is the proof of that result:

The present value of $110 is $95.50, given a discount rate of 15.1825%.

That is, $110 / 1.151825 = $95.50

Meanwhile, the present value of $1,200 is $904.50, given a discount rate of 15.1825%.

Specifically, $1,200 / ((1.151825)^2) = $904.50

And, $95.50 + $904.50 = $1,000.00

### Computing IRR

The HP12c Financial Calculator is a classic tool, still in widespread use, for the computation of IRR, or Internal Rate of Return. Moreover, most spreadsheet programs, such as Microsoft Excel, offer the facility to calculate it.

### Uses of IRR

Internal Rate of Return is, as noted earlier, a time-honored tool in various areas of finance. In project analysis, for example, it is often used to determine whether a given project should be undertaken. However, as detailed in the next section, the use of IRR in such a forward-looking fashion has the limitation of being applied to forecasted figures, which may or may not come to fruition.

In a backward-looking fashion, IRR is used to assess the actual performance of investments. Investment funds, particularly hedge funds, habitually quote it as a key indicator of their track records.

In general, IRR is a commonly-used metric to assess actual or potential investments in which the returns have varied or are expected to vary over time. In the simple numeric example above, the potential lender is receiving an average compound annual return of 15.18% on his or her money and should compare this to other investment opportunities to judge its desirability.

### Limitations of IRR Analysis

Projected or forecasted returns may not materialize as anticipated.

A project or investment with a lower anticipated IRR may be preferable if that lower IRR can be earned on a larger principal amount. For example, an opportunity to earn 30% on a $100,000 investment brings greater absolute rewards than 40% on $1,000.

A project or investment with a lower anticipated IRR may be preferable if that lower IRR can be earned for a longer period. For example, earning a compounded 30% over four years, which nearly triples your investment, arguably is a better alternative than earning 40% for just one year and having highly uncertain prospects for reinvestment after that.

The overall IRR of an investment portfolio is not the average of the IRRs on each project, security or investment therein. Rather, the overall IRR of a portfolio with high initial returns of capital typically is greater than the overall IRR of a portfolio in which most gains come later, even if the latter has greater total gains over time. Thus, private equity managers often seek to produce a higher IRR on an investment portfolio by cashing out winning investments early while keeping losing investments longer.

For limitations of IRR analysis, an excellent discussion can be found in the article entitled "To rate a return, think of what you're missing" by John Kay, *Financial Times*, 9/8/2010.

**Also Known As - **Internal Rate of Return, Hurdle Rate, Compound Rate of Return, Compound Interest.