Economic internal rate of return

What Is Economic Internal Rate of Return?

The economic internal rate of return (EIRR) is a metric used in financial analysis, particularly within the field of project appraisal, to evaluate the economic viability of a project from a societal perspective. It is the discount rate at which the net present value (NPV) of a project's economic benefits equals the present value of its economic costs, effectively making the NPV zero⁵⁴. Unlike the financial internal rate of return, which focuses on monetary returns to a specific entity or investor, the EIRR considers the broader impact on an economy by using "shadow prices" or "social prices" to reflect the true value of resources and outputs, rather than market prices which may be distorted by taxes, subsidies, or externalities⁵¹, ⁵², ⁵³. The EIRR is a key tool in public sector economics and development finance, guiding decisions on investments that aim to maximize overall societal welfare.

History and Origin

The concept of evaluating projects based on their societal impact, rather than just private financial returns, gained significant traction with the rise of development economics in the mid-20th century. Institutions like the World Bank played a pivotal role in popularizing the systematic use of economic analysis for projects, particularly in developing countries⁴⁸, ⁴⁹, ⁵⁰. The application of cost-benefit analysis, a foundational element for calculating EIRR, became an integral part of applied economic analysis in the 1960s⁴⁷. Early work by economists such as I.M.D. Little and J.A. Mirrlees, and institutions like the Organisation for Economic Co-operation and Development (OECD) and the United Nations Industrial Development Organization (UNIDO), contributed to the theoretical framework and practical guidelines for conducting economic appraisals. The World Bank's 1979 publication, "Economic Analysis of Projects," by Lyn Squire and Herman G. van der Tak, further solidified a comprehensive approach to economic analysis, including the consistent estimation and application of shadow prices to calculate social rates of return, thereby considering distributional effects alongside efficiency components⁴⁴, ⁴⁵, ⁴⁶.

Key Takeaways

• The Economic Internal Rate of Return (EIRR) assesses a project's viability from a societal viewpoint, considering its impact on the broader economy.
• It is the discount rate that equates the economic benefits and costs of a project, resulting in a net present value of zero.
• EIRR uses "shadow prices" instead of market prices to reflect the true economic value of inputs and outputs, accounting for externalities and market distortions.
• It is a crucial metric for public sector projects and development initiatives where maximizing social welfare is the primary objective.
• Projects with an EIRR exceeding the social discount rate are generally considered economically viable.

Formula and Calculation

The calculation of the Economic Internal Rate of Return (EIRR) involves finding the discount rate that satisfies the following equation:

Where:

• (B_t) = Economic benefits in year (t)
• (C_t) = Economic costs in year (t)
• (n) = Project's life in years
• (t) = Time period (year)
• (EIRR) = Economic Internal Rate of Return

Calculating the EIRR often requires an iterative process, as the formula cannot typically be solved directly for EIRR. This involves trying different discount rates until the net present value of the economic cash flows approaches zero. The "economic benefits" and "economic costs" are derived by adjusting market prices to reflect true societal values, often involving the use of shadow pricing for inputs like labor, foreign exchange, and capital⁴², ⁴³.

Interpreting the Economic Internal Rate of Return

Interpreting the Economic Internal Rate of Return (EIRR) involves comparing it to a predetermined social opportunity cost of capital or social discount rate⁴¹. If the calculated EIRR is greater than this social discount rate, the project is generally considered economically viable and desirable from a societal perspective⁴⁰. This suggests that the project generates benefits to society that outweigh its costs when all economic impacts are considered. Conversely, if the EIRR is lower than the social discount rate, the project may not be a worthwhile allocation of societal resources, as the capital could yield a higher return if invested elsewhere in the economy³⁹.

The higher the EIRR, the more economically attractive the project is perceived to be. However, the EIRR is an annualized percentage return and does not inherently reflect the absolute scale of the project's economic benefits³⁸. Therefore, for a comprehensive assessment, it is often used in conjunction with other metrics like economic net present value (ENPV), which directly measures the total economic value added by a project³⁷.

Hypothetical Example

Consider a hypothetical government project to build a new road in a rural area, aiming to reduce transportation costs and improve market access for farmers.

Project Details:

• Initial economic cost (Year 0): $100 million (includes construction, land acquisition, adjusted for shadow prices)
• Economic benefits (annual, Years 1-5): $30 million (estimated value of reduced travel time, lower vehicle operating costs, increased agricultural output, adjusted for social benefits)
• Project life: 5 years

To calculate the EIRR, we need to find the discount rate that makes the present value of benefits equal to the present value of costs.

We set up the equation:

By iteratively solving this equation (e.g., using financial software or a spreadsheet program), we find that the EIRR for this hypothetical project is approximately 15.24%.

If the government's social discount rate, reflecting the minimum acceptable economic return on public investments, is 10%, then an EIRR of 15.24% suggests that this road project is economically viable and beneficial to society. It indicates that the project generates a return exceeding the societal threshold for investment, justifying the allocation of public funds. This evaluation helps inform capital allocation decisions for public infrastructure.

Practical Applications

The economic internal rate of return (EIRR) is extensively applied in various real-world scenarios, particularly in the realm of development economics and public finance. It is a fundamental tool for:

• Public Infrastructure Projects: Governments and international development agencies use EIRR to evaluate the societal benefits of large-scale infrastructure projects such as roads, dams, power plants, and irrigation systems³⁵, ³⁶. This ensures that projects contribute positively to overall economic welfare, even if they do not generate direct financial profits.
• Development Aid and Lending: Organizations like the World Bank and regional development banks regularly employ EIRR in their project appraisal processes for loans and grants to developing countries. This helps in allocating scarce resources to projects with the highest social and economic returns³³, ³⁴.
• Environmental and Social Impact Assessments: EIRR analysis can incorporate the economic valuation of environmental benefits (e.g., pollution reduction, ecosystem services) and social benefits (e.g., improved health, education) that are not typically captured by market prices. This allows for a more holistic evaluation of project impacts.
• Policy Analysis: Policymakers use EIRR to compare different policy interventions or investment programs, helping to prioritize those that offer the most significant net economic benefits to society. For example, evaluating investments in public health initiatives or educational reforms.
• Cost-Benefit Analysis in the Public Sector: EIRR is a key output of a comprehensive cost-benefit analysis for public sector undertakings, providing a clear percentage indicator of a project's societal profitability³². This framework assists in decision-making when there are no market prices, or when market prices do not reflect the true social costs and benefits³¹.

Limitations and Criticisms

While the economic internal rate of return (EIRR) is a valuable tool for evaluating public projects, it comes with several limitations and criticisms, many of which are similar to those faced by the financial internal rate of return (IRR).

One significant issue is the possibility of multiple EIRRs²⁹, ³⁰. For projects with unconventional cash flow patterns (e.g., alternating between positive and negative economic net cash flows over time), there can be more than one discount rate that makes the net present value zero, leading to ambiguity in interpretation²⁸. This problem often arises due to intermediate negative cash flows in the project's later stages, such as substantial maintenance costs or environmental remediation efforts.

Another criticism concerns the reinvestment assumption²⁶, ²⁷. The EIRR implicitly assumes that intermediate economic benefits generated by the project can be reinvested at the EIRR itself. In reality, finding other societal projects or opportunities that consistently yield the same high economic return can be challenging. If the actual reinvestment rate is lower, the true economic profitability of the project might be overstated²⁵.

Furthermore, the EIRR may not always be consistent with the economic net present value (ENPV) for mutually exclusive projects, especially when projects differ significantly in scale or duration²³, ²⁴. A project with a higher EIRR might have a lower ENPV, meaning it creates less total economic value for society²². This discrepancy suggests that relying solely on EIRR for ranking projects can lead to suboptimal resource allocation.

The accuracy of EIRR heavily depends on the quality and objectivity of shadow prices²¹. Determining appropriate shadow prices for goods, services, labor, and foreign exchange can be complex and subjective, requiring significant data and expert judgment¹⁹, ²⁰. Errors or biases in these estimations can significantly distort the calculated EIRR and lead to flawed investment decisions. For instance, critics argue that the World Bank's project analysis sometimes overestimates benefits or uses biased assumptions, impacting the reliability of the resulting EIRRs¹⁸.

Lastly, EIRR, like IRR, does not explicitly consider the size of the investment required¹⁵, ¹⁶, ¹⁷. A project with a very high EIRR might be a small project, while a larger project with a slightly lower EIRR could generate substantially more total economic benefit¹⁴. Therefore, using EIRR in isolation without considering the scale of the investment or capital constraints can be misleading when making investment decisions¹², ¹³.

Economic Internal Rate of Return vs. Financial Internal Rate of Return

The Economic Internal Rate of Return (EIRR) and the Financial Internal Rate of Return (FIRR) are both critical metrics used in capital budgeting and project evaluation, but they serve distinct purposes and are calculated differently. The primary distinction lies in their perspective: EIRR focuses on the societal and macroeconomic impact, while FIRR assesses the profitability from the viewpoint of a specific entity, such as a company or private investor.

The confusion between the two often arises because both are "internal rates of return" and use similar mathematical approaches to discount cash flows. However, their underlying inputs—the economic versus financial cash flows—are fundamentally different. FIRR uses actual money exchanged, such as revenue, operating expenses, and taxes, reflecting the financial transactions of a business. In¹¹ contrast, EIRR adjusts these monetary flows to reflect their real value to the economy, removing distortions caused by government interventions or market imperfections, and incorporating non-marketed benefits and costs. Fo⁹, ¹⁰r instance, a toll road might have a high FIRR for the private operator due to toll revenues, but its EIRR would also consider the broader economic benefits of reduced travel time and increased trade for the entire region, possibly also factoring in environmental costs.

FAQs

Why is Economic Internal Rate of Return (EIRR) important for public projects?

EIRR is crucial for public projects because it helps governments and international organizations assess whether an investment will genuinely benefit society as a whole, beyond just generating financial returns. It⁷, ⁸ considers broader economic impacts, such as job creation, environmental effects, and social welfare improvements, ensuring a more comprehensive evaluation of public investment decisions.

What are "shadow prices" in the context of EIRR?

Shadow prices are imputed values for goods, services, and factors of production (like labor or foreign exchange) that reflect their true economic cost or benefit to society, rather than their distorted market prices. Th⁵, ⁶ey are used in EIRR calculations to adjust for market imperfections, taxes, subsidies, and externalities, providing a more accurate measure of a project's societal impact.

How does EIRR relate to cost-benefit analysis?

EIRR is a key outcome of a cost-benefit analysis applied to public sector projects. In⁴ such an analysis, all economic benefits and costs are identified and quantified, and EIRR is the discount rate that balances these over the project's lifetime, helping to determine its overall economic viability.

Can EIRR be negative?

Yes, EIRR can be negative if the economic costs of a project consistently outweigh its economic benefits over its lifespan. A negative EIRR indicates that the project would destroy economic value from a societal perspective, suggesting it should generally not be undertaken.

#³## Is a higher EIRR always better?
Generally, a higher EIRR indicates a more economically attractive project, as it suggests a greater societal return on investment. However, it's important to consider the EIRR in conjunction with other metrics, such as the economic net present value (ENPV), especially when comparing projects of different sizes or durations, as a project with a lower EIRR might generate more total economic value.¹, ²