Internal Rate of Return (IRR) Definition

The internal rate of return (IRR) is a metric used in capital budgeting to estimate the profitability of potential investments. The internal rate of return is a discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. IRR calculations rely on the same formula as NPV does.

$\begin{aligned} &\text{IRR}=\text{NPV}=\sum_{t=1}^{T}\frac{C_t}{\left(1+r\right)^t}-C_0=0\\ &\textbf{where:}\\ &C_t=\text{net cash inflow during the period t}\\ &C_0=\text{total initial investment costs}\\ &r=\text{the discount rate, and}\\ &t=\text{the number of time periods}\\ \end{aligned}$​IRR=NPV=t=1∑T​(1+r)tCt​​−C0​=0where:Ct​=net cash inflow during the period tC0​=total initial investment costsr=the discount rate, andt=the number of time periods​

To calculate IRR using the formula, one would set NPV equal to zero and solve for the discount rate (r), which is the IRR. Because of the nature of the formula, however, IRR cannot be calculated analytically and must instead be calculated either through trial-and-error or using software programmed to calculate IRR.

Generally speaking, the higher a project's internal rate of return, the more desirable it is to undertake. IRR is uniform for investments of varying types and, as such, IRR can be used to rank multiple prospective projects on a relatively even basis. Assuming the costs of investment are equal among the various projects, the project with the highest IRR would probably be considered the best and be undertaken first.

IRR is sometimes referred to as "economic rate of return" or "discounted cash flow rate of return." The use of "internal" refers to the omission of external factors, such as the cost of capital or inflation, from the calculation.

There are two main ways to calculate IRR in Excel:

• Using one of the three built-in IRR Excel formulas
• Breaking out the component cash flows and calculating each step individually, then using those calculations as inputs to an IRR formula (As we detailed above, since the IRR is a derivation, there is no easy way to break it out by hand.)

The second method is preferable because financial modeling works best when it is transparent, detailed and easy to audit. The trouble with piling all the calculations into a formula is that you can't easily see what numbers go where, or what numbers are user inputs or hard-coded.

Here is a simple example of an IRR analysis with cash flows that are known and consistent (one year apart). Assume a company is assessing the profitability of Project X. Project X requires $250,000 in funding and is expected to generate $100,000 in after-tax cash flows the first year and grow by $50,000 for each of the next four years.

You can break out a schedule as follows (click on the image to expand):

The initial investment is always negative because it represents an outflow. You are spending something now and anticipating a return later. Each subsequent cash flow could be positive or negative – it depends on the estimates of what the project delivers in the future.

In this case, the IRR is 56.77%. Given the assumption of a weighted average cost of capital (WACC) of 10%, the project adds value.

Keep in mind that the IRR is not the actual dollar value of the project, which is why we broke out the NPV calculation separately. Also, recall that the IRR assumes we can constantly reinvest and receive a return of 56.77%, which is unlikely. For this reason, we assumed incremental returns at the risk-free rate of 2%, giving us an MIRR of 33%.

You can think of the internal rate of return as the rate of growth a project is expected to generate. While the actual rate of return that a given project ends up generating will often differ from its estimated IRR, a project with a substantially higher IRR value than other available options would still provide a much better chance of strong growth.

One popular use of IRR is comparing the profitability of establishing new operations with that of expanding existing ones. For example, an energy company may use IRR in deciding whether to open a new power plant or to renovate and expand a previously existing one. While both projects are likely to add value to the company, it is likely that one will be the more logical decision as prescribed by IRR.

IRR is also useful for corporations in evaluating stock buyback programs. Clearly, if a company allocates a substantial amount to a stock buyback, the analysis must show that the company's own stock is a better investment (has a higher IRR) than any other use of the funds for other capital projects, or than any acquisition candidate at current market prices.

In theory, any project with an IRR greater than its cost of capital is a profitable one, and thus it is in a company’s interest to undertake such projects. In planning investment projects, firms will often establish a required rate of return (RRR) to determine the minimum acceptable return percentage that the investment in question must earn in order to be worthwhile.

Any project with an IRR that exceeds the RRR will likely be deemed a profitable one, although companies will not necessarily pursue a project on this basis alone. Rather, they will likely pursue projects with the highest difference between IRR and RRR, as these likely will be the most profitable.

IRR can also be compared against prevailing rates of return in the securities market. If a firm can't find any projects with IRR greater than the returns that can be generated in the financial markets, it may simply choose to invest its retained earnings into the market. Although IRR is an appealing metric to many, it should always be used in conjunction with NPV for a clearer picture of the value represented by a potential project a firm may undertake.

IRR in practice is calculated by trial and error since there is no analytical way to compute when NPV will equal zero. Computers or software like Excel can do this trial and error procedure extremely quickly. But, as an example, let's assume that you want to open a pizzeria. You estimate all the costs and earnings for the next two years, and then calculate the net present value for the business at various discount rates. At 6%, you get an NPV of $2000.

But, the NPV needs to be zero, so you try a higher discount rate, say 8% interest: At 8%, your NPV calculation gives you a net loss of −$1600. Now it's negative. So you try a discount rate in between the two, say with 7% interest: At 7%, you get an NPV of $15.

That is close enough to zero, so you can estimate that your IRR is just slightly higher than 7%.

Even though the internal rate of return metric is popular among business managers, it tends to overstate the profitability of a project and can lead to capital budgeting mistakes based on an overly optimistic estimate. The modified internal rate of return compensates for this flaw and gives managers more control over the assumed reinvestment rate from future cash flow.

An IRR calculation acts like an inverted compounding growth rate; it has to discount the growth from the initial investment in addition to reinvested cash flows. However, the IRR does not paint a realistic picture of how cash flows are actually pumped back into future projects.

Cash flows are often reinvested at the cost of capital, not the same rate at which they were generated in the first place. IRR assumes that the growth rate remains constant from project to project. It is very easy to overstate potential future value with basic IRR figures.

Another major issue with IRR occurs when a project has different periods of positive and negative cash flows. In these cases, the IRR produces more than one number, causing uncertainty and confusion. MIRR solves this issue as well.

The compound annual growth rate (CAGR) measures the return on an investment over a certain period of time. The IRR is also a rate of return but is more flexible than the CAGR. While CAGR simply uses the beginning and ending value, IRR considers multiple cash flows and periods – reflecting the fact that cash inflows and outflows often constantly occur when it comes to investments. IRR can also be used in corporate finance when a project requires cash outflows upfront but then results in cash inflows as an investment pays off.

The most important distinction is that CAGR is straightforward enough that it can be calculated by hand. In contrast, more complicated investments and projects, or those that have many different cash inflows and outflows, are best evaluated using IRR. To back into the IRR rate, a financial calculator, Excel, or portfolio accounting system is ideal.

Companies and analysts also look at the return on investment (ROI) when making capital budgeting decisions. ROI tells an investor about the total growth, start to finish, of the investment. IRR tells the investor what the annual growth rate is. The two numbers should normally be the same over the course of one year (with some exceptions), but they won't be the same for longer periods of time.

Return on investment – sometimes called the rate of return (ROR) – is the percentage increase or decrease of an investment over a set period of time. It is calculated by taking the difference between the current (or expected) value and original value, divided by original value and multiplied by 100.

While ROI figures can be calculated for nearly any activity into which an investment has been made and an outcome can be measured, the outcome of an ROI calculation will vary depending on which figures are included as earnings and costs. The longer an investment horizon, the more challenging it may be to accurately project or determine earnings and costs and other factors such as the rate of inflation or the tax rate.

It can also be difficult to make accurate estimates when measuring the monetary value of the results and costs for project-based programs or processes (for example, calculating the ROI for a human resources department within an organization) or other activities that may be difficult to quantify in the near-term and especially so in the long-term as the activity or program evolves and factors change. Because of these challenges, ROI may be less meaningful for long-term investments. This is why IRR is often preferred.

While IRR is a very popular metric in estimating a project’s profitability, it can be misleading if used alone. Depending on the initial investment costs, a project may have a low IRR but a high NPV, meaning that while the pace at which the company sees returns on that project may be slow, the project may also be adding a great deal of overall value to the company.

A similar issue arises when using IRR to compare projects of different lengths. For example, a project of short duration may have a high IRR, making it appear to be an excellent investment, but may also have a low NPV. Conversely, a longer project may have a low IRR, earning returns slowly and steadily, but may add a large amount of value to the company over time.

Another issue with IRR is one not strictly inherent to the metric itself, but rather to a common misuse of IRR. People may assume that, when positive cash flows are generated during the course of a project (not at the end), the money will be reinvested at the project’s rate of return. This can rarely be the case.

Rather, when positive cash flows are reinvested, it will be at a rate that more resembles the cost of capital. Miscalculating using IRR in this way may lead to the belief that a project is more profitable than it actually is. This, along with the fact that long projects with fluctuating cash flows may have multiple distinct IRR values, has prompted the use of another metric called modified internal rate of return (MIRR).

MIRR adjusts the IRR to correct these issues, incorporating the cost of capital as the rate at which cash flows are reinvested, and existing as a single value. Because of MIRR’s correction of the former issue of IRR, a project’s MIRR will often be significantly lower than the same project’s IRR.

The internal rate of return rule is a guideline for evaluating whether to proceed with a project or investment. The IRR rule states that if the internal rate of return on a project or investment is greater than the minimum required rate of return, typically the cost of capital, then the project or investment should be pursued. Conversely, if the IRR on a project or investment is lower than the cost of capital, then the best course of action may be to reject it.

While there are some issues with IRR, it can be a good basis for investments as long as the problems referenced earlier in the article are avoided. If you're interested in putting IRR into practice, you'll need to create a brokerage account to actually purchase the investments you're investigating. To help people along the research process of choosing a stockbroker, Investopedia has created a list of the best online stock brokers. From there you can decide what works best with your investment style.