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Internal Rate of Return (IRR)

What is the Internal Rate of Return (IRR)?

The internal rate of return, or IRR, is one of the main measures used by investors and finance professionals to assess the profitability of an investment. In mathematical terms, the IRR is the discount rate that makes the net present value (NPV) of all future cash flows equal zero in a discounted cash flow analysis (DCF).

Private Equity (PE) investors find IRR particularly useful because of its focus on cash flows. Since PE managers deploy cash outflows in the initial stages of a project and then harvest cash inflows in later stages, calculating IRR in a PE context is relatively intuitive. One way to conceptualise IRR is as a growth rate that an investment generates annually. In this way, it is similar to a compound annual growth rate (CAGR).

Key Takeaways

  • IRR is derived directly from the cash flows associated with an investment.
  • Initial capital outlays are negative cash flows, while the eventual return cash flow streams are positive cash flows.
  • IRR is related to NPV, which in turn is dependent upon the investor’s required rate of return.
  • These measures have roots in the concept of time value of money, which has been cited in economics and philosophy for centuries.

IRR Formula and Calculation

The IRR is a discount rate. The differentiating feature of IRR from other discount rates, such as the required rate of return, is that we do not first calculate the IRR and subsequently apply it to a series of cash flows (as we do when calculating NPV, for example). We do the opposite. Given a series of cash flows, we derive the IRR by working backwards to develop the discount rate. 

IRR Equation:

0 = CF0 + CF1/(1+IRR) + CF2/(1+IRR)2 + CF3/(1+IRR)3 … CFn/(1+IRR)n

This is a generalised textbook formula for finding the internal rate of return. We are seeking the discount rate that makes the present value of a series of cash flows equal to zero. The left-hand side of the equation is therefore set to 0. On the right-hand side, we have the series of cash flows, beginning with the initial outlay at time zero, CF0. The remaining cash flows are denoted as CFx and in this formula, we have allowed for them to extend to n cash flows. 

The cash flows are derived either from actual results — free cash flow per year, for a period of years — or from a set of projected (pro forma) cash flows. We analyse quarterly or annual data, and the number of cash flows might range anywhere from three or four up to ten or fifteen periods. There is no hard and fast rule, and much depends on the investor’s time horizon.

The cash flows are the numerators of each entry in the equation, and the IRR is in the denominator. Therefore, we are discounting–as opposed to compounding–the cash flows. In contrast to the NPV, where we use a required rate of return for the discount rate, in the case of IRR we do not know our discount rate. We are finding the discount rate, which is the IRR.

An Example for Clarification

Start with a set of four basic cash flows to keep the example simple. The initial outlay of the investment period is $500. For each of the next three years, there is a cash flow at the end of the year: $200 after year 1; $350 after year 2; and $525 as the final cash flow, at the end of year 3.

On first reading over the numbers, this appears to be a good investment for a three-year timeline. Calculating an IRR will be helpful in distilling the cash flows down to a single measure, which provides a basis for comparison with other investments.

The equation now has some gaps filled in, as follows:

0 = -$500 + $200/(1+IRR) + $350/(1+IRR)2 + $525/(1+IRR)3

The first term, -$500, is the initial outlay for the investment. This explains why there is a negative sign on the first term. The subsequent terms in the equation place the yearly investment returns in the numerators.

The IRR takes into consideration the time value of money, the size of the cash flows, and the number of periods (in this case, years). Now that the equation has only one remaining unknown, the next step is to solve the equation for the discount rate, which is the IRR — 41.70% in this case.

The funds offered on Moonfare’s platform already have the IRR calculated and provided as part of the due diligence process in choosing investments.

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Why is the NPV set to zero?

Interpreting IRR on a stand-alone basis can be difficult in some cases, so understanding its context is important. The reason that NPV is set to zero is that the resulting discount rate for IRR – as calculated in the first example – is reliant purely upon the cash flows from the investment. NPV, on the other hand, may use the same set of cash flows but the discount rate is already included in the equation.

The discount rate used in NPV is often referred to as the required rate of return and can be arrived at in a number of ways. The discount rate in NPV is intended to capture the rate of return that an investor requires for a given project or investment. If the investor knows they can earn 10% on an alternative project, then they may use 10% as the discount rate for the NPV calculation. In this way, the resulting NPV must be positive to meet the required return.

If one sets NPV equal to zero and calculates IRR, then the IRR can be compared to the required rate of return. If the NPV calculation uses a discount rate of 15%, and the IRR calculation arrives at 22%, then the cash flow profile “beats” the required rate of return.

Why is IRR Important to Private Equity?

IRR can be used for a couple of primary purposes. One could compare the IRRs of two different private equity funds. For example, Fund A has consistently posted IRRs around 20%, or a bit higher than that. By comparison, Fund B yields IRRs of 30% and above. Assuming the funds have similar characteristics, then Fund B appears to be providing historically superior performance as measured by IRR.

Private Equity and IRR

The Internal Rate of Return (IRR) is a compelling metric in private equity, providing a comprehensive view of the potential profitability and efficiency of investments. It plays an indispensable role in decision-making processes, as it enables investors to compare different investment opportunities, assess their relative risk levels, and plan for optimal capital allocation. When looking at IRR, investors can predict the growth trajectory of their investments over time, providing a foundation for informed strategic decisions. Moreover, it allows for an unbiased comparison of PE funds by standardising returns despite different investment periods. IRR, therefore, offers a valuable lens through which to gauge the financial viability and long-term value creation of private equity investments.

Important notice: This content is for informational purposes only. Moonfare does not provide investment advice. You should not construe any information or other material provided as legal, tax, investment, financial, or other advice. If you are unsure about anything, you should seek financial advice from an authorised advisor. Past performance is not a reliable guide to future returns. Don’t invest unless you’re prepared to lose all the money you invest. Private equity is a high-risk investment and you are unlikely to be protected if something goes wrong. Subject to eligibility. Please see


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