## What is internal rate of return?

**Internal Rate of Return **(**IRR**) is a financial metric for cash flow analysis, often used for evaluating investments, capital acquisitions, project and program proposals, and business case scenarios.

Like other cash flow metrics (net present value, payback period, and return on investment), IRR takes an "investment view" of expected financial results. This means, essentially, that the magnitudes and timing of cash flow returns are compared to cash flow costs. Each of these financial metrics compares returns to costs in its own way and each carries a unique message about the value of the action.

IRR analysis begins with a cash flow stream, a series of net cash flow figures expected from the investment (or action, acquisition, or business case scenario).
The expected cash flows for IRR analysis might appear as shown below. In the figure, each
bar represents the net of cash inflows and outflows for one two-month period.
Positive values are net inflows and negative values are net outflows. The complete set of net cash flow events is a **cash flow stream**.

This stream shows expected results from one action, and another stream for a different action might show a different cash flow profile. IRRs for each stream can be compared and, other things being equal, the proposed action with the higher IRR is viewed as the better choice.

Notice especially the shape, or *profile* of this example stream. The figure shows a typical "investment curve." Net cash outflows at the outset and net cash inflows in later periods mean that costs initially exceed incoming returns, but if results appear as expected, returns eventually outweigh the
costs. The IRR metric, in fact, "expects" this kind of cash flow profile—early costs and later benefits. When the cash flow stream has this profile, an IRR can probably be found and usefully interpreted. When the stream deviates substantially from this profile, however, it may not be possible to find an IRR for the stream. Or, other strange IRR results may appear, such as multiple IRRs for the same stream, or a negative IRR for the stream. In such cases, the resulting IRRs are either very difficult to interpret or meaningless.

Most people in business have heard of "internal rate of return." Some are required by their financial officers to produce an IRR to support budget requests or action proposals. IRR is in fact a favorite metric of many CFOs, Controllers, and other financial specialists. Many in the financial community believe, for instance, that IRR is a more "objective" metric than NPV, because NPV depends on an arbitrarily chosen discount rate, while IRR is determined entirely by the cash flow figures and their timing. Many also believe that IRR allows returns to be compared readily with inflation, current interest rates, and financial investment alternatives. Organizations sometimes establish an IRR hurdle rate, that is, an IRR rate that must be reached or exceeded by incoming proposals before approval and funding.

It should be no surprise to learn that most business people who are not in finance have a limited or poor understanding of IRR and its meaning. It may be more surprising, however, to learn that research on professional competencies finds consistently that most financial specialists who require IRRs with proposals or funding requests are themselves largely unaware of IRR's serious deficiencies and unprepared to explain its meaning and proper use.

This article puts a special emphasis on understanding IRR meaning and interpretation, as well as common misconceptions and misuses of IRR. This article also compares IRR to other financial metrics and presents the **modified internal rate of return** (**MIRR**), a more easily interpreted alternative to the better known IRR.

## Contents

- What is internal rate of return?
- How is internal rate of return IRR defined? Illustrated example.
- IRR re-defined: Why is it called
*internal*rate of return? - Is modified internal rate of return (MIRR) a better metric than IRR?
- How does Internal rate of return compare to NPV, ROI, and other financial metrics?
- Is IRR appropriate for lease vs. buy analysis? What are other problem IRR results?

- What is internal rate of return?
- How is internal rate of return IRR defined? Illustrated example.
- IRR re-defined: Why is it called
*internal*rate of return? - Is modified internal rate of return (MIRR) a better metric than IRR?
- How does Internal rate of return compare to NPV, ROI, and other financial metrics?
- Is IRR appropriate for lease vs. buy analysis? What are other problem IRR results?

## How is internal rate of return IRR defined? Ilustrated example.

As the word "return" in its name implies, an IRR view of the cash flow stream is essentially an investment view: paid out funds are compared to returns. The best known IRR definition explains this comparison in terms that call for a basic understanding of discounted cash flow concepts present value, net present value (NPV), and the role of the discount rate (interest rate) in determining NPV:

IRR Definition 1 (textbook definition): The internal rate of return (IRR) for a cash flow stream is the interest rate (discount rate) that produces a net present value of 0 for the cash flow stream.

That definition, however, can be less than satisfying when first heard. Many ask:

What does *that* tell me about returns and costs?

A first interpretation of IRR meaning is illustrated with an example.

Consider two proposed investments competing for funding: Case Alpha and Case Beta. The expected net cash flow streams for Alpha (A) and Beta (B) are as shown.

Alpha

Beta

**Total**

**200**

**240**