This lesson examines the Internal Rate of Return method, its calculation, decision rules, and the specific problems that can arise when using IRR. The limitations of IRR—including the crossover problem, size problem, and reinvestment rate problem—are covered extensively in corporate finance curricula.

• The IRR Method: The internal rate of return is the discount rate that results in a net present value of zero. It equates the present value of future cash flows to the initial investment. The HSE course syllabus covers “Internal rate of return (IRR): methodology and limitations” as a core topic.

• The IRR Decision Rule: A project is accepted if its internal rate of return is greater than the required rate of return (hurdle rate). If the IRR is less than the required rate of return, the project should be rejected.

• Advantages of IRR: The IRR method:

  • Incorporates the time value of money

  • Considers all relevant cash flows

  • Provides a measure of profitability in percentage terms, which is intuitive for many managers

• The Crossover (Multiple IRR) Problem: If cash flows for a project change sign more than once (alternating between negative and positive), the IRR can have multiple mathematically valid solutions. The Business Finance Essentials text notes that “For projects with a crossover problem, the IRR cannot be used. For instance, consider a project with the following cash flow stream: CF0 = -$100, CF1 = $180, CF2 = $0, … CF7 = -$100. The project has two IRR’s (4.9% and 76.7%). With two solutions, it is unclear whether to accept or reject the project, so we use NPV analysis instead. IRR is unreliable in this situation”.

• The Size Problem and Reinvestment Rate Problem: When evaluating mutually exclusive projects, the IRR can provide invalid rankings due to two problems:

  • The Size Problem: When projects are of different sizes, IRR may rank a smaller project with a higher percentage return above a larger project with a lower percentage return but greater absolute wealth creation.

  • The Reinvestment Rate Problem: IRR assumes that cash flows from the project are reinvested at the IRR itself, while NPV assumes reinvestment at the discount rate.

• NPV vs. IRR: For mutually exclusive projects, NPV is generally preferred over IRR because it consistently selects the wealth-maximising alternative. The Coursera Corporate Finance Essentials course includes a module on “IRR vs. NPV Project Rankings” to address this issue.