Incremental internal rate of return

What Is Incremental Internal Rate of Return?

The incremental internal rate of return (IIRR) is a capital budgeting metric used to evaluate the attractiveness of one investment project over another, particularly when comparing two or more mutually exclusive projects. It represents the discount rate at which the Net Present Value of the differences in cash flow between two projects equals zero. Essentially, it helps determine the return generated by the additional investment required by the more expensive project, aiding in sound investment decision making.

History and Origin

The concept of evaluating investment projects using discounted cash flow methods gained prominence throughout the 20th century. While the Internal Rate of Return (IRR) itself has theoretical roots tracing back to early economic thought, its widespread application in corporate financial management for project analysis solidified alongside the development of modern capital budgeting techniques. Economists and financial theorists sought robust methods to compare various investment opportunities, especially when projects differed significantly in scale or timing of cash flows. The need for a direct comparison metric between competing projects led to the development of incremental analysis, where the "extra" return from a larger or different investment could be quantified. The evolution of capital budgeting methods, including IRR and incremental analysis, has been a continuous process, adapting to the complexities of corporate decision making over time.³²

Key Takeaways

• Incremental internal rate of return (IIRR) evaluates the profitability of investing in a larger or alternative project over a smaller or baseline project.
• It focuses on the cash flow differences between two mutually exclusive projects.
• IIRR helps in making optimal capital allocation choices when conventional IRR might lead to incorrect conclusions due to scale differences or unconventional cash flow patterns.
• A positive IIRR greater than the cost of capital generally suggests the incremental investment is worthwhile.

Formula and Calculation

The calculation of the incremental internal rate of return involves determining the IRR of the differential cash flows between two projects. If Project B has a higher initial outlay than Project A, the incremental cash flow stream is derived by subtracting Project A's cash flows from Project B's cash flows. The IIRR is then the discount rate (r_{IIRR}) that makes the net present value of these differential cash flows equal to zero:

Where:

• (CF_B_t) = Cash flow of Project B at time (t)
• (CF_A_t) = Cash flow of Project A at time (t)
• (t) = Time period
• (n) = Total number of periods
• (r_{IIRR}) = Incremental Internal Rate of Return

It is critical to remember that underlying these calculations is the fundamental principle of the time value of money.³¹

Interpreting the Incremental Internal Rate of Return

Interpreting the incremental internal rate of return requires comparing it to the firm's cost of capital or required Return on Investment. If the IIRR is greater than the cost of capital, it indicates that the additional investment in the larger project yields a return that exceeds the firm's hurdle rate, making the incremental investment financially justifiable. Conversely, if the IIRR is less than the cost of capital, the additional investment is not generating sufficient returns, and the smaller, less expensive project may be preferred. This metric is particularly useful when the individual IRR for two mutually exclusive projects might lead to conflicting results if their initial investment costs or cash flow patterns differ significantly.

Hypothetical Example

Consider a company evaluating two mutually exclusive projects, Project X and Project Y.

Project X:

• Initial Outlay: $100,000
• Year 1 Cash Flow: $40,000
• Year 2 Cash Flow: $50,000
• Year 3 Cash Flow: $60,000

Project Y:

• Initial Outlay: $150,000
• Year 1 Cash Flow: $60,000
• Year 2 Cash Flow: $70,000
• Year 3 Cash Flow: $80,000

First, calculate the differential cash flows (Project Y - Project X):

• Year 0 (Initial Outlay): $150,000 - $100,000 = -$50,000 (Incremental Investment)
• Year 1: $60,000 - $40,000 = $20,000
• Year 2: $70,000 - $50,000 = $20,000
• Year 3: $80,000 - $60,000 = $20,000

Next, find the discount rate that makes the Net Present Value of these differential cash flows equal to zero. This is the incremental internal rate of return. Using financial software or a financial calculator, for the cash flow stream of (-$50,000, $20,000, $20,000, $20,000), the IIRR is approximately 7.2%.

If the company's discount rate (cost of capital) is, for instance, 6%, then since the IIRR (7.2%) is greater than the cost of capital, the incremental investment in Project Y is justified. This suggests Project Y, despite its higher initial cost, provides a superior return on investment compared to Project X for the additional capital deployed.

Practical Applications

Incremental internal rate of return is a valuable tool in corporate finance and capital allocation for several key applications:

• Evaluating Mutually Exclusive Projects: It is particularly useful when a company must choose between projects that compete for the same resources or fulfill the same need, such as choosing between different scales of a production facility or different technologies for a service.
• Capital Expenditure Planning: Businesses use IIRR to rank and prioritize potential capital expenditures, especially when budgets are limited and choices must be made between projects with varying initial costs and expected returns.
• Mergers and Acquisitions: While often complex, incremental analysis can be adapted to evaluate the financial benefits of acquiring a larger company or a specific asset compared to a smaller alternative, by focusing on the differential cash flows generated.
• Government and Public Sector Investments: Public entities may use incremental analysis to compare the efficiency and financial performance of different public works projects, though social benefits are often considered alongside financial metrics.

In today's dynamic economic environment, companies face complex capital allocation challenges amidst uncertainty, making robust evaluation techniques like IIRR crucial for navigating investment choices.³⁰

Limitations and Criticisms

Despite its utility, the incremental internal rate of return shares some of the limitations inherent to the standard Internal Rate of Return, as well as specific challenges. One primary criticism of IRR, which extends to IIRR, is the "reinvestment rate assumption." This assumption posits that all positive cash flows generated by a project can be reinvested at the calculated IRR itself. In reality, it is often unrealistic to expect to reinvest at such a high rate, especially for projects with very high IRRs. This can inflate the perceived profitability of the project.²⁹

Furthermore, the calculation of incremental internal rate of return can become problematic with unconventional cash flow patterns, where the differential cash flows switch from negative to positive more than once, potentially leading to multiple IIRRs or no real IIRR. When comparing projects of significantly different scales or durations, using IIRR alone can sometimes be misleading. For instance, a small project might have a very high IIRR on its small incremental investment, but the overall Net Present Value of the larger alternative project might still be greater, indicating higher absolute wealth creation. Therefore, it is generally recommended to use IIRR in conjunction with other capital budgeting methods like Net Present Value or Profitability Index for comprehensive project analysis.

Incremental Internal Rate of Return vs. Net Present Value

The incremental internal rate of return (IIRR) and Net Present Value (NPV) are both widely used capital budgeting techniques, but they approach investment evaluation from different perspectives. While IIRR calculates a rate of return on the difference between two projects, NPV directly calculates the absolute monetary value that a project is expected to add to the firm's wealth. The primary distinction lies in their output: IIRR provides a percentage rate, while NPV provides a dollar amount.

A key point of divergence arises when evaluating mutually exclusive projects. In some cases, the project with the higher IRR might not be the one with the higher NPV, especially when projects differ in scale or have different cash flow patterns. This conflict occurs because the IRR implicitly assumes reinvestment at the IRR, while NPV implicitly assumes reinvestment at the firm's cost of capital. For wealth maximization, financial theory generally suggests that NPV is the superior criterion for investment decision making, as it directly measures the increase in shareholder wealth. However, IIRR can still be a valuable supplementary tool for understanding the profitability of incremental investments, providing an intuitive percentage return that managers often find easier to grasp.

FAQs

Why is Incremental IRR used?

Incremental IRR is primarily used to compare and choose between mutually exclusive projects when the projects have different initial costs or cash flow patterns, and a simple comparison of individual IRRs might lead to an incorrect decision making. It helps quantify the return on the additional investment required by one project over another.

How does Incremental IRR differ from regular IRR?

Regular Internal Rate of Return calculates the return for a single project based on its own cash flows. Incremental IRR, on the other hand, calculates the return on the difference in cash flows between two competing projects. It's a comparative tool, not an absolute one for a single project.

When should Incremental IRR be considered?

It should be considered when a company faces a choice between two or more mutually exclusive projects and needs to determine if the additional investment in a larger or different project is justified by the extra returns it generates. It helps in assessing the value of "scaling up" or choosing an alternative investment.

Can Incremental IRR conflict with Net Present Value?

Yes, conflicts can arise between Incremental IRR and Net Present Value, especially when projects differ significantly in scale or have unconventional cash flows. When such conflicts occur, the Net Present Value rule is generally considered the more reliable criterion for maximizing shareholder wealth because it directly measures the dollar value added by a project.

Is Incremental IRR always reliable?

While useful, Incremental IRR is not always reliable on its own. It carries the same limitations as the regular Internal Rate of Return, such as the reinvestment rate assumption and potential for multiple IRRs with non-conventional cash flows. It is best used as a complementary tool alongside other capital budgeting techniques like Net Present Value.¹², ³, ⁴⁵, ⁶⁷, ⁸⁹, ¹⁰¹¹, ¹²¹³¹⁴, ¹⁵[¹⁶](https://analystprep.com/cfa-level-1-exam/corporate-issuers/net[²⁶](https://analystprep.com/cfa-level-1-exam/corporate-issuers/net-present-value-npv-and-internal-rate-of-return-irr/), ²⁷-present-value-npv-and-internal-rate-of-return-irr/)¹⁷, ¹⁸, ¹⁹²⁰, ²¹, ²²²³, ²⁴