Do You Use IRR to Evaluate Projects? Consider This:
Many financial professionals use the Internal Rate of Return (IRR) for project evaluation, but it can be highly misleading. Despite its ease of use, there are significant drawbacks to relying solely on IRR.
The main issue with IRR is that it assumes reinvestment of positive cash flows at the IRR itself, which is often unrealistic. Mathematically, several nuances arise:
1. Comparing Projects: It’s possible for Project A to have a better Net Present Value (NPV) while Project B has a higher IRR. The rational choice is Project A because it accounts for the Opportunity Cost of Capital (OCC):
2. Cash Flow Sign Changes: When a project’s cash flows change signs (positive to negative or vice versa) multiple times, there can be two, several, or even no IRRs.
3. Inverted Cash Flows: For projects with initial positive and subsequent negative cash flows, the project with the lower IRR might be preferable (depending on whether you are borrowing or lending).
4. Multiple Discount Rates: Occasionally, the correct discount rate for a single project may vary. For instance, with a long-term contract where revenues are fixed, differing long-term and short-term interest rates may lead a manager to discount 1-5 year cash flows at one rate and 5-15 year cash flows at another. In such cases, IRR is less useful:
5. Different Discount Rates for Revenues and Expenses: In some evaluations, cash inflows and outflows need to be discounted at different rates due to operational leverage. IRR fails to accommodate this complexity.
Due to these shortcomings, a new metric, the Modified Internal Rate of Return (MIRR), has been developed. MIRR accounts for the reinvestment of positive cash flows at the company’s OCC and discounts negative cash flows at the rate needed to finance the specific project.
P.S.
What Is the Underlying Reason for Such Shortcomings?
IRR inherently assumes that positive cash flows are reinvested at the same IRR. It is as if the positive cash flows are temporarily placed in a deposit account that earns the same IRR until they are needed again for the project, while negative cash flows are financed with loans at the same IRR.
This assumption might be reasonable when the IRR is relatively modest, and reinvesting dividends from the project at the same rate is not an issue. However, for projects with a high IRR, you would likely agree that this assumption is unrealistic.
Due to such shortcomings, a new metric was introduced: MIRR (Modified Internal Rate of Return). MIRR considers that:
- Positive cash flows are reinvested at the company’s Opportunity Cost of Capital (OCC).
- Negative cash flows are financed at the borrowing rate required for the specific project.
Excel provides a formula for MIRR, and its logic is as follows:
Now, let’s assume you have a 10-year project where positive cash flows arise along the way, but you cannot reinvest these elsewhere (due to legal or other constraints). Instead, you can only place them in a bank deposit earning 3% annually. Meanwhile, the project is primarily financed with debt, which costs 9% per year, and you need additional funding at times.
Let’s compare how IRR and MIRR differ in this scenario:
On the right side of the table, you will see a transformed cash flow, which in some sense is more realistic. This is because:
- Until the project is completed, you cannot actually withdraw the money.
- Every additional cash deficit requires you to pay interest.
Notice that the IRR of this adjusted cash flow is equal to the MIRR of the original version.
inspired by:
Principles of Corporate Finance – by F. Allen, R. A. Brealey, & S. Myers.