Adjusted growth irr

What Is Adjusted Growth IRR?

Adjusted Growth IRR, often referred to interchangeably with the Modified Internal Rate of Return (MIRR), is a sophisticated financial metric used in Capital Budgeting and Financial Analysis to evaluate the attractiveness of potential investments or projects. It refines the traditional Internal Rate of Return (IRR) by addressing its inherent limitations, particularly concerning the Reinvestment Rate assumption. This metric provides a more realistic annual rate of return by assuming that positive Cash Flow generated by a project is reinvested at the firm's Cost of Capital or a specified external rate, rather than at the project's own internal rate of return. The Adjusted Growth IRR aims to provide a clearer picture of a project's true profitability over its lifespan by accounting for the realistic cost of financing initial outlays and the actual rate at which generated funds can be reinvested.

History and Origin

The concept of the Internal Rate of Return (IRR) has roots tracing back to economists like John Maynard Keynes and Irving Fisher in the early to mid-22th century.¹⁴ While widely adopted for its intuitive percentage output, the traditional IRR method faced criticism due to its underlying assumption that all positive interim cash flows are reinvested at the IRR itself. This assumption often proves unrealistic, as a company may not always be able to reinvest funds at such a high rate, particularly if the IRR is exceptionally high.¹³

To overcome these theoretical shortcomings, the Adjusted Growth IRR, or Modified Internal Rate of Return (MIRR), was developed. Scholarly efforts, including those by Lin in 1976, introduced MIRR as a means to reconcile inconsistencies in project rankings between IRR and Net Present Value (NPV) by incorporating an externally determined reinvestment rate.¹² Academic discourse, as highlighted by ACCA Global, has long debated the drawbacks of IRR, noting that MIRR offers a more realistic assessment of reinvestment opportunities by typically aligning the reinvestment rate with the firm's cost of capital.¹¹ This evolution aimed to provide a more robust and practical measure for capital expenditure decisions.

Key Takeaways

• Adjusted Growth IRR (MIRR) is a profitability metric that addresses the flawed reinvestment rate assumption of traditional IRR.
• It assumes positive cash flows are reinvested at a more realistic rate, such as the firm's Cost of Capital or a specific Reinvestment Rate.
• Adjusted Growth IRR is typically used in Capital Budgeting to rank and select investment projects.
• Unlike IRR, Adjusted Growth IRR always yields a single solution, avoiding the issue of multiple internal rates of return for unconventional cash flow patterns.
• It provides a more accurate reflection of a project's true annual return under real-world financing and reinvestment conditions.

Formula and Calculation

The Adjusted Growth IRR is calculated in a way that separates the treatment of positive and negative cash flows. It involves discounting all negative cash flows to their Present Value at the firm's financing rate and compounding all positive cash flows to their Future Value at a specified reinvestment rate. The Adjusted Growth IRR is then the discount rate that makes the present value of the terminal cash flow equal to the present value of the initial investment.

The formula for Adjusted Growth IRR (MIRR) is expressed as:

Where:

• (FV_{positive}) = Future Value of positive cash flows, compounded at the Reinvestment Rate to the end of the project's life.
• (PV_{negative}) = Present Value of negative cash flows (initial investment and any subsequent outflows), discounted at the financing rate (usually the Cost of Capital) to time zero.
• (n) = Number of periods (years) over the project's life.

Spreadsheet software often includes a built-in MIRR function, simplifying the calculation by requiring inputs for the series of cash flows, the financing rate, and the reinvestment rate.⁹, ¹⁰

Interpreting the Adjusted Growth IRR

Interpreting the Adjusted Growth IRR involves comparing the calculated percentage to a company's target return or Hurdle Rate. A project is generally considered acceptable if its Adjusted Growth IRR is higher than the firm's Cost of Capital or the required rate of return. This indicates that the project is expected to generate a return exceeding the cost of funding it, thereby adding value to the company.

Because Adjusted Growth IRR accounts for a more realistic Reinvestment Rate, it provides a more conservative and often more accurate picture of a project's profitability than traditional IRR. When comparing mutually exclusive projects, the project with the higher Adjusted Growth IRR is typically preferred, assuming all other factors like risk are comparable. This metric helps decision-makers gauge how efficiently capital is expected to be utilized throughout the investment's lifecycle, considering the Time Value of Money.

Hypothetical Example

Consider a hypothetical project requiring an initial investment of $100,000, which is an outflow. It is expected to generate positive cash inflows of $40,000 in Year 1, $50,000 in Year 2, and $60,000 in Year 3. The company's financing rate (cost of capital) is 8%, and the assumed reinvestment rate for positive cash flows is 10%.

Step 1: Calculate the Present Value of Negative Cash Flows.
In this simple example, there's only one negative cash flow: the initial investment.
(PV_{negative} = $100,000) (at time 0)

Step 2: Calculate the Future Value of Positive Cash Flows.

• Year 1 inflow: $40,000 compounded for 2 years at 10% = ( $40,000 \times (1 + 0.10)^2 = $40,000 \times 1.21 = $48,400 )
• Year 2 inflow: $50,000 compounded for 1 year at 10% = ( $50,000 \times (1 + 0.10)^1 = $50,000 \times 1.10 = $55,000 )
• Year 3 inflow: $60,000 compounded for 0 years at 10% = ( $60,000 )
• Total (FV_{positive} = $48,400 + $55,000 + $60,000 = $163,400 )

Step 3: Calculate the Adjusted Growth IRR.
Using the MIRR formula:

The Adjusted Growth IRR for this project is approximately 17.8%. This value can then be compared to the company's Hurdle Rate to determine if the project is a worthwhile undertaking.

Practical Applications

The Adjusted Growth IRR is a versatile tool with numerous practical applications across various financial domains. In Capital Budgeting, corporations routinely use this metric to evaluate and rank potential investment opportunities, such as expanding production facilities, investing in new technology, or launching new product lines. By comparing the Adjusted Growth IRR of different projects, companies can make informed decisions about Capital Allocation to maximize shareholder value.⁶

In Private Equity, Adjusted Growth IRR (often referred to as MIRR) is crucial for assessing the performance of fund investments and individual deals. It helps private equity firms understand the true profitability of their ventures by factoring in acquisition costs, operational expenses, and eventual exit proceeds, while allowing for different financing and reinvestment assumptions. For instance, McKinsey & Company highlights how disaggregating IRR, which MIRR facilitates, can provide a deeper understanding of value creation from various drivers in private equity investments.⁵ This enhanced clarity supports strategic decision-making and helps attract potential investors by demonstrating more transparent historical returns.

Furthermore, real estate investors, infrastructure project managers, and government agencies also utilize Adjusted Growth IRR for comprehensive Financial Analysis and project evaluation, especially for long-term projects with complex cash flow patterns.

Limitations and Criticisms

Despite its improvements over the traditional Internal Rate of Return, Adjusted Growth IRR is not without its limitations. One primary criticism is that while it resolves the multiple IRR problem and offers a more realistic Reinvestment Rate assumption, it can still lead to erroneous rankings when comparing mutually exclusive projects of different scales or lives. A project with a lower Adjusted Growth IRR might actually generate a higher Net Present Value and thus be more valuable to the firm, particularly if it's a larger-scale investment.², ³, ⁴

Academics and practitioners suggest that relying solely on a single metric, even Adjusted Growth IRR, for complex investment decisions can be misleading. Issues related to capital rationing, project independence, and inherent differences in Risk Management profiles can still complicate direct comparisons based solely on a percentage return. The Institute for Transport Studies at the University of Leeds, for example, points out that while Adjusted IRR gives a better estimate of the true rate of return when benefits are not fully reinvestible at the project's internal rate, it's still crucial to consider other metrics like Net Present Value for a holistic view.¹ Therefore, financial professionals typically use Adjusted Growth IRR in conjunction with other Capital Budgeting techniques to ensure robust decision-making.

Adjusted Growth IRR vs. Internal Rate of Return (IRR)

The core distinction between Adjusted Growth IRR and the traditional Internal Rate of Return (IRR) lies in their underlying assumptions about reinvestment.

The confusion between the two often arises because both are percentage-based metrics aiming to assess investment profitability. However, the Adjusted Growth IRR was specifically designed to rectify the theoretical flaws of IRR, making it a preferred metric for many practitioners seeking a more accurate and reliable assessment of project returns.

FAQs

Why is Adjusted Growth IRR considered "adjusted"?

Adjusted Growth IRR is considered "adjusted" because it modifies the primary problematic assumption of the traditional Internal Rate of Return. While IRR assumes that intermediate cash flows are reinvested at the project's own rate, Adjusted Growth IRR allows for a more realistic Reinvestment Rate, often the firm's Cost of Capital. This adjustment provides a more accurate reflection of what the company can realistically earn on reinvested funds.

When should I use Adjusted Growth IRR instead of traditional IRR?

You should typically use Adjusted Growth IRR, or MIRR, when evaluating projects with complex Cash Flow patterns, particularly those with alternating positive and negative cash flows that might result in multiple IRRs. It's also preferred when the implicit reinvestment assumption of traditional IRR (reinvesting at the IRR itself) is unrealistic given current market conditions or the firm's actual investment opportunities. Adjusted Growth IRR offers a more conservative and often more reliable estimate of a project's true profitability.

Does Adjusted Growth IRR solve all problems of investment evaluation?

No, Adjusted Growth IRR significantly improves upon traditional IRR but does not solve all problems of investment evaluation. For instance, it can still lead to suboptimal decisions when comparing projects of significantly different sizes or durations. Like any single financial metric, it should be used in conjunction with other Capital Budgeting tools, such as Net Present Value, to gain a comprehensive understanding of a project's financial viability and its impact on overall firm value.

Can Adjusted Growth IRR be negative?

Yes, Adjusted Growth IRR can be negative. A negative Adjusted Growth IRR indicates that the project is expected to lose money, even when accounting for a realistic Reinvestment Rate and financing costs. In such cases, the project would generally be considered financially unviable and should be rejected, as it would erode shareholder value.