Economic rate of return err; economic internal rate of return eirr

What Is Economic Rate of Return (ERR) and Economic Internal Rate of Return (EIRR)?

The Economic Rate of Return (ERR) and Economic Internal Rate of Return (EIRR) are critical metrics used in Investment Analysis and Project Evaluation to assess the societal profitability of projects, particularly those undertaken by governments or international development organizations. Unlike conventional financial metrics that focus on monetary returns to a specific entity, ERR and EIRR consider all benefits and costs to society as a whole, irrespective of who incurs them or receives them. This comprehensive approach falls under the broader discipline of Cost-Benefit Analysis, aiming to determine if a project generates a net positive impact on collective welfare.

ERR represents the discount rate at which the present value of economic benefits equals the present value of economic costs, resulting in a net present value of zero from a societal perspective. The ERR accounts for all relevant social costs and benefits, including those not reflected in market prices, such as environmental impacts or the provision of Public Goods. Similarly, the EIRR is essentially the internal rate of return calculated using these broader economic cash flows. Both ERR and EIRR are indispensable tools for sound Capital Budgeting decisions in the public sector, ensuring that investments contribute positively to national economic development and social well-being.

History and Origin

The foundational concepts underpinning the Economic Rate of Return and related economic appraisal methods trace back to the mid-19th century with the work of French engineer Jules Dupuit, who explored the concept of consumer utility in public works. Later, the British economist Alfred Marshall further formalized these ideas. However, the practical application and systematic development of cost-benefit analysis (CBA), from which ERR and EIRR evolved, gained significant traction in the United States in the 1930s. [The U.S. Army Corps of Engineers, through the Federal Navigation Act of 1936, was mandated to carry out waterway improvement projects only if their total benefits exceeded their costs, leading to the creation of systematic methods for measuring such benefits and costs.⁵ This marked a pivotal shift toward rigorous economic evaluation of public investments, recognizing benefits beyond direct financial returns.

Key Takeaways

• Societal Perspective: ERR and EIRR evaluate projects from the viewpoint of the entire economy and society, not just the direct investors.
• Comprehensive Scope: They incorporate all social benefits and costs, including non-market impacts and Externalities.
• Decision Criterion: A project is generally considered economically viable if its ERR or EIRR exceeds the prevailing social Discount Rate or social opportunity cost of capital.
• Public Sector Tool: These metrics are primarily used in the appraisal of public infrastructure projects, development programs, and policy interventions.
• Informational Value: ERR and EIRR provide a robust framework for comparing alternative projects and prioritizing those that offer the greatest collective welfare gains.

Formula and Calculation

The calculation of the Economic Internal Rate of Return (EIRR) is analogous to that of the conventional internal rate of return (IRR), but it uses economic benefits and costs instead of financial revenues and expenses. The EIRR is the discount rate (r) that makes the Net Present Value (NPV) of the project's economic cash flows equal to zero.

The formula for EIRR is:

Where:

• (B_t) = Economic benefits in year (t)
• (C_t) = Economic costs in year (t)
• (N) = Project lifetime in years
• (t) = Time period (year)
• (EIRR) = Economic Internal Rate of Return

To derive (B_t) and (C_t), a thorough Social Cost-Benefit Analysis is conducted, which often involves adjusting market prices to "shadow prices" to reflect true societal values, accounting for taxes, subsidies, and externalities. The determination of these economic flows requires careful consideration of the Opportunity Cost of resources from a national perspective.

Interpreting the Economic Rate of Return (ERR)

Interpreting the Economic Rate of Return (ERR) involves comparing the calculated rate against a predetermined social discount rate or the social opportunity cost of capital. If the ERR of a project is greater than this social discount rate, it implies that the project is economically viable and is expected to generate a positive net benefit for society. Conversely, if the ERR is lower, the project might not be considered economically desirable, as society's resources could likely be better allocated elsewhere.

For instance, an ERR of 15% on an Infrastructure Investment project, when the social discount rate is 10%, suggests that the project is expected to yield a 5% "excess" return to society above what is considered the minimum acceptable return for alternative uses of capital. ERR helps policymakers prioritize investments, guiding them toward projects that maximize collective welfare, even if they may not yield direct financial profits to the implementing agency. It shifts the focus from private gains to the overall economic impact and the efficient allocation of scarce resources across a nation.

Hypothetical Example

Consider a government agency evaluating a proposed national road construction project. The project has an initial cost (year 0) of $100 million. Over its useful life of 5 years, the estimated economic benefits are:

• Year 1: $20 million (reduced travel time, lower vehicle operating costs)
• Year 2: $30 million
• Year 3: $40 million
• Year 4: $35 million
• Year 5: $25 million

These benefits are "economic" because they include the value of time saved by commuters, reduced pollution from smoother traffic flow (a positive externality), and increased economic activity due to better connectivity, rather than just toll revenues.

To calculate the EIRR, we set the net present value of these economic cash flows to zero:

Solving this equation (typically requiring iterative methods or financial software), we might find the EIRR to be approximately 18.5%. If the government's social discount rate, representing the Monetary Value of alternative investment opportunities for society, is 10%, then an EIRR of 18.5% indicates that this road project is economically beneficial and should be considered for implementation.

Practical Applications

Economic Rate of Return (ERR) and Economic Internal Rate of Return (EIRR) are predominantly applied in public sector investment decisions and development Project Finance. Governments, multilateral development banks (such as the World Bank, Asian Development Bank), and international organizations widely use these metrics to appraise large-scale projects that have broad societal impacts, often beyond direct financial returns.

Key practical applications include:

• Infrastructure Development: Evaluating major infrastructure projects like roads, railways, ports, power plants, and water supply systems, where significant public benefits (e.g., improved productivity, health, access to services) are not captured by market prices alone.
• Social Programs: Assessing the economic viability of public health initiatives, education reforms, and poverty reduction programs by quantifying their broader societal gains.
• Environmental Projects: Determining the overall benefit of conservation efforts, pollution control measures, and renewable energy projects by valuing environmental improvements and avoided damages.
• Policy Formulation: Informing government policy decisions by analyzing the economic efficiency and welfare impacts of different regulatory approaches or public expenditure priorities.
• International Development Assistance: Guiding the allocation of funds by international bodies like the International Monetary Fund (IMF) and the European Investment Bank (EIB) to ensure that financed projects contribute effectively to a country's economic and social development. For example, the IMF's Public Investment Management Assessment (PIMA) framework includes "Project Appraisal" as a key institution, emphasizing rigorous technical, economic, and financial analysis for major capital projects.⁴ The European Investment Bank (EIB) also explicitly uses economic appraisal to judge whether an investment project will contribute to the economic growth and cohesion of the EU and its partners.³ The Organisation for Economic Co-operation and Development (OECD) provides extensive guidance and standards to help governments create an enabling environment for public and private infrastructure investment, highlighting the need for strategic, integrated investment approaches that consider long-term economic, environmental, and social objectives.²

Limitations and Criticisms

While ERR and EIRR provide a vital societal perspective in Project Appraisal, they are not without limitations and criticisms. One significant challenge lies in the accurate valuation of non-market benefits and costs, such as environmental impacts, public health improvements, or the value of life. Assigning a precise Monetary Value to these intangibles can be subjective and prone to debate, potentially leading to inflated benefits or underestimated costs.

Another criticism revolves around the selection of the appropriate social discount rate. A slight change in this rate can significantly alter a project's ERR, influencing its perceived viability. There is no universal consensus on how to determine this rate, leading to potential inconsistencies across different evaluations. Furthermore, the accuracy of ERR and EIRR depends heavily on the quality and reliability of the underlying data and assumptions used in the Financial Analysis. Errors in forecasting costs, benefits, or project timelines can lead to misleading results, potentially justifying projects that are not truly economically efficient. Issues like "optimism bias" and lack of transparency have been identified in the appraisal of public projects.¹ These inherent challenges necessitate thorough Sensitivity Analysis and robust Risk Assessment to understand how changes in assumptions might affect the calculated ERR or EIRR.

Economic Rate of Return (ERR) vs. Financial Internal Rate of Return (FIRR)

The primary distinction between the Economic Rate of Return (ERR) and the Financial Internal Rate of Return (FIRR) lies in the perspective from which a project's profitability is evaluated.

Confusion often arises because both metrics use the concept of an internal rate of return. However, their scope and purpose are fundamentally different. FIRR tells an investor if a project is financially attractive for them, based on direct cash flows. ERR tells a government or society if a project is economically attractive for the entire nation, considering all benefits and costs, even those without a direct market price. A project might have a low FIRR (not attractive for a private investor) but a high ERR (highly beneficial for society), making a case for public funding or subsidies.

FAQs

What is the main difference between ERR and IRR?

The main difference is the perspective of analysis. ERR (or EIRR) evaluates a project's profitability from society's viewpoint, considering all economic benefits and costs, including those not traded in markets. In contrast, the standard Internal Rate of Return (IRR) assesses profitability from a private financial perspective, focusing only on the direct monetary cash flows to a specific investor or entity.

Why are ERR and EIRR important for public projects?

ERR and EIRR are crucial for public projects because many public goods and services (like clean air, public health, or improved infrastructure access) do not generate direct revenue streams but provide substantial societal benefits. These metrics ensure that public investments are made where they generate the greatest overall economic welfare for the nation, guiding the efficient allocation of public funds and resources. They are core to Cost-Benefit Analysis in the public sector.

How are non-market benefits valued in ERR/EIRR calculations?

Valuing non-market benefits in ERR/EIRR calculations often involves specialized economic techniques. This can include "shadow pricing" (adjusting market prices to reflect true economic values), stated preference methods (e.g., surveys to determine willingness to pay), or revealed preference methods (inferring value from observed behavior, such as property values near green spaces). While challenging, including these valuations is essential for a comprehensive Social Cost-Benefit Analysis.