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# The IRR And Unsophisticated Investors

In mid market transitions you often come across inappropriate use of financial metrics, but none seems as prevalent as the Internal Rate of Return (NYSE:IRR). Despite a river of ink being spilt on the subject, it seems a sad fact that in many small and mid market transactions the IRR is still the preeminent metric in assessing projects. A lot of the inaccuracy can, if someone is determined to use it, be modified to represent a more reasonable figure. I refer to the Modified Internal Rate of Return (MIRR), while which not perfect, in practice, is normally more realistic and conservative than the IRR. Many of those that appraise investments regularly will already be familiar with the problematic issues relating to the IRR. However, for those of you that haven't yet wondered about the issues with this simple and elegant formula, then here's the problem (one of many I might add), it does not represent the real return on the investment, it merely represents the theoretical return an investor will get, assuming no risk in reinvesting those cash flow. Just to be clear, this is the discount rate at which the Net Present Value (NYSE:NPV) of the project would be zero, if that sounds a little convoluted let's look at an example to help highlight the issue. While IRR assumes the cash flow from a project could be reinvested at the same rate, the MIRR assumes that positive cash flows are reinvested at the firm's cost of capital, and the initial outlays are financed at the firm's financing cost.

The table below highlights the point in numbers, despite the two present value (PV) lines looking substantially different they are the same cash flows simply reinvested at different rates. One line shows the interim cash flow reinvested at the projects IRR of 10% and the other at the more realistic cost of capital. Just to be clear both lines have the same undiscounted cash flows, risk, and investment horizon and the same 10% IRR. If we use the IRR as our decision metric, we would not be aware of the substantial reinvestment risk. So in this case, an investment for \$100m with the same exit value, over a 15 year duration (and a flat 10% free cash flow yield), we would end up with an immense \$57m lower return then expected from the 10% IRR.

 Years 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sum Project cash flow 10 10 10 10 10 10 10 10 10 10 10 10 10 10 110 250 PV of the cash flows reinvested at the project IRR 28 25 21 19 16 14 11 9 8 6 5 3 2 1 0 168 PV of the cash flows reinvested at the cost of capital 18 16 14 12 11 9 8 7 5 4 3 2 2 1 0 111
Click to enlarge

In order to earn the stated return of a 10% IRR, the formula assumes that an investor can reinvest the interim cash flows through to the end of the investment horizon at a rate equal to that of the IRR. Even with the greater certainly of fixed income investments, this is practically impossible, and as a result, the investor would not earn the stated IRR on the investment.

Whenever the calculated IRR for a project is higher than the true reinvestment rate the investor can really achieve on the interim cash flows, the IRR formula will overestimate the return from the investment. This will pretty much always be the case for many of this type of investors that use IRR as their key metric. This is a more important issue for large corporations that tend to hold investments for a very long time and have low real reinvestment rate.

In practice, when the cost of capital (a proxy of the reinvestment return) is used instead of the IRR, a project's true IRR will fall considerably, this is particularly so with projects that forecast high IRRs, long durations or when the interim cash flows occur earlier in the investment horizon. If the executives making investment decisions are fully aware of these issues and/or can incredulously do the adjusting maths in their head then there's no problem. However, from experiences this is sadly not the case, and the discussions regarding project IRRs look as common as ever. Additionally none of the above takes account that the project cash flows also needs to be held for the duration of the project to achieve the IRR. If you are now wondering how to avoid the pitfalls of the IRR, then simply stop using it and use the NPV instead, which side steps this by simply discounting a projects cash flows at the cost of capital.