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# Internal Rate of Return IRR: Formula and Examples

August 6, 2024
Bill Kimball

The example above illustrates the basic principles of disaggregating IRR, which ideally should be done before any comparison of different investments. Consider, for example, two investments by a large private-equity fund, both of them businesses with more than €100 million in annual revenues (Exhibit 2). Each had generated healthy bottom-line returns for investors of 20 percent or more on an annualized basis.

## Multiple IRRs

Therefore, the internal rate of return may not accurately reflect the profitability and cost of a project. IRR, or internal rate of return, is a metric used in financial analysis to estimate the profitability of potential investments. IRR is a discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis.

## Is Using the IRR Rule the Same as Using the Discounted Cash Flow Method?

However, being an expert salesperson, you could sell the van for \$25,000, \$7,000 more than your initial investment. Calculating it is very similar to calculating the net present value of an investment. The difference is that, in calculating this rate, we are setting NPV equal to zero. Practically, such an interest rate guarantees that the money you would invest in such a project today will earn you precisely \$0.

## IRR and Investment Returns

These include building out new operations, improving existing operations, making acquisitions, and so on. IRR can help determine which option to choose by showing which will have the best return. Within its realm of uses, IRR is a very popular metric for estimating a project’s annual return; however, it is not necessarily intended to be used alone. IRR is typically a relatively high value, which allows it to arrive at an NPV of zero. The IRR itself is only a single estimated figure that provides an annual return value based on estimates. Since estimates of IRR and NPV can differ drastically from actual results, most analysts will choose to combine IRR analysis with scenario analysis.

To make a decision, the IRR for investing in the new equipment is calculated below. Any project with an IRR that exceeds the RRR will likely be deemed profitable, 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 will likely be the most profitable. In capital planning, one popular scenario for IRR is comparing the profitability of establishing new operations with that of expanding existing operations. For example, an energy company may use IRR in deciding whether to open a new power plant or to renovate and expand an existing power plant. If applied iteratively, either the secant method or the improved formula always converges to the correct solution.

## Internal rate of return

The term internal refers to the fact that the calculation excludes external factors, such as the risk-free rate, inflation, the cost of capital, or financial risk. In order to calculate the multiple-of-money (MoM), or multiple on invested capital (MOIC), we’ll calculate the sum of all the positive cash inflows from each holding period. In capital budgeting, senior leaders like to know the estimated return on such investments. The internal rate of return is one method that allows them to compare and rank projects based on their projected yield. The investment with the highest internal rate of return is usually preferred. The Internal Rate of Return (IRR) is the discount rate that makes the net present value (NPV) of a project zero.

Recognizing the differences in the assumptions is the only way to compare products accurately. The internal rate of return (IRR) is a metric used to estimate the return on an investment. As the same calculation applies to varying investments, it can be used to rank all investments to help determine which is the best. The CAGR measures the annual return on an investment over a period of time.

In this case the NPV of the payment stream is a convex, strictly decreasing function of interest rate. Any fixed time can be used in place of the present (e.g., the end of one interval of an annuity); the value obtained is zero if and only if the NPV is zero. Based on the completed output for our exercise, we can see the implied IRR and MoM at a Year 5 exit – the standard holding period assumption in most LBO models – is 19.8% and 2.5x, respectively. Note that for the formula to work and be dragged down, the date selection must be anchored in Excel, i.e. fixed (Press F4).

1. An investment creates value when its market value exceeds the cost of acquiring the project.
2. Suppose a private equity firm made an equity investment of \$85 million in 2022 (Year 0).
3. Companies and investors can compare it to other projects and investments that are under consideration.
4. So there is no squabbling over who gets which project, they are each happy to choose different projects.

In general the IRR equation cannot be solved analytically but only by iteration. The IRR is an indicator of the profitability, efficiency, quality, or yield of an investment. This is in contrast with the NPV, which is an indicator of the net value or magnitude added by making an investment. Since the investment represents an outflow of cash, we’ll place a negative sign in front of the figure in Excel.

This can give investors in private-equity funds a deeper understanding when making general-partner investment decisions. Specifically, this occurs when a project has non-conventional cash flows. This means the cash flow changes from positive to negative throughout the investment. Note that this method is the least efficient way of calculating the internal rate of return. There are other more effective ways, such as using a financial calculator.

However, a company might prefer a project with a lower IRR because it has other potential benefits, such as contributing to a larger strategic plan or impeding competition. Disaggregating the effect of IRR’s various components can help managers and investors alike more accurately assess past results and contribute to future investment decisions. With unconventional cash flows, calculating the rate will become more complicated, as we usually end up with more than one answer. Another advantage is that using tNPV requires deciding upon a discount rate.

Regardless, the internal rate of return (IRR) and MoM are both different pieces of the same puzzle, and each comes with its respective shortcomings. In the commercial real estate (CRE) industry, the target IRR on a property investment tends to be set around 15% to 20%. Level up your career with the world’s most recognized private equity investing program. Companies take on various projects to increase their revenues or cut down costs. A great new business idea may require, for example, investing in the development of a new product. A company is deciding whether to purchase new equipment that costs \$500,000.

The IRR is also an annual rate of return; however, the CAGR typically uses only a beginning and ending value to provide an estimated annual rate of return. Whether you’re an individual investor or run a company, it’s important to deploy your investment capital in a way that makes sense. The internal rate of return rule can be a useful tool for comparing your different options. However, the rule has some downsides that can lead to flawed results, and you don’t want to follow it blindly because there may be other issues to consider that it doesn’t account for. Private-equity investments typically rely on high amounts of debt funding—much higher than for otherwise comparable public companies.

In the spreadsheet, project A results in an IRR of 17%, and project B results in an IRR of 5%. Given that the company’s cost of capital is 10%, management should proceed with Project A and reject Project B. Get instant access to lessons taught by experienced private equity pros and bulge bracket investment bankers including financial statement modeling, DCF, M&A, LBO, Comps and Excel Modeling.

The IRR method of evaluating an investment or a project is very similar to the NPV method. However, instead of having a certain discount rate for calculating the NPV, we now have to find the discount rate that makes the NPV equal to 0. As a simple example, suppose a \$1,000 investment today results in a \$1,100 cash flow in one year. Maximizing total value is not the only conceivable possible investment objective. An alternative objective would for example be to maximize long-term return.