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External Rate Of Return

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Understanding the External Rate of Return (ERR)



The External Rate of Return (ERR), also known as the modified internal rate of return (MIRR), is a crucial financial metric used to evaluate the attractiveness of capital investment projects. Unlike the Internal Rate of Return (IRR), which suffers from certain limitations, the ERR addresses these shortcomings by providing a more realistic and reliable assessment of profitability, especially in scenarios with multiple cash flows and varying reinvestment rates. This article aims to provide a comprehensive understanding of the ERR, outlining its calculation, advantages, limitations, and practical applications.

Understanding the Limitations of IRR



Before diving into the ERR, it's essential to understand why a modified approach is necessary. The IRR assumes that all intermediate cash flows are reinvested at the same rate as the project's IRR. This assumption is often unrealistic. In reality, funds generated by a project may be reinvested at the company's cost of capital or at a prevailing market rate, which is likely different from the project's IRR. This discrepancy can lead to an overestimation or underestimation of the project's true profitability when using IRR alone.

Calculating the External Rate of Return



The ERR calculation involves two key steps:

1. Determining the Future Value of Cash Inflows: This step involves calculating the future value of all positive cash inflows (receipts) at the project's reinvestment rate (typically the cost of capital or a predetermined hurdle rate). This rate reflects the return the company can achieve on its funds.

2. Calculating the ERR: Once the future value of the cash inflows is determined, the ERR is calculated by finding the discount rate that equates the present value of the initial investment (outflow) to the future value of the positive cash inflows. This can be solved using financial calculators, spreadsheet software (like Excel's `IRR` or `MIRR` function), or iterative numerical methods.


Example:

Let's consider a project with an initial investment of $10,000 and the following cash flows:

Year 1: -$2,000 (negative as it's an expense)
Year 2: $5,000
Year 3: $8,000

Assume a reinvestment rate of 8%.

Step 1: Future Value of Cash Inflows:

Year 2 inflow: $5,000 (1 + 0.08) = $5,400
Year 3 inflow: $8,000
Total Future Value: $5,400 + $8,000 = $13,400

Step 2: Calculating ERR: We need to find the discount rate that makes the present value of $13,400 equal to $10,000 (initial investment). Using Excel's `RATE` function or a financial calculator, we find the ERR to be approximately 11.7%.


Advantages of Using ERR



Realistic Reinvestment Assumption: The ERR assumes a more realistic reinvestment rate, usually the company's cost of capital, providing a more accurate reflection of project profitability.
Improved Decision Making: By providing a more accurate picture of profitability, ERR improves the decision-making process regarding project selection and capital budgeting.
Avoids Multiple IRRs: Unlike the IRR, the ERR avoids the problem of multiple IRRs (which can occur with unconventional cash flows), providing a single, unambiguous result.

Limitations of ERR



Sensitivity to the Reinvestment Rate: The choice of reinvestment rate significantly impacts the calculated ERR. An inappropriate rate can lead to inaccurate conclusions.
Complexity: The ERR calculation is slightly more complex than the IRR, requiring more steps and potentially specialized software.


Conclusion



The External Rate of Return provides a significant improvement over the traditional IRR by addressing the unrealistic reinvestment rate assumption. By using a more appropriate reinvestment rate (typically the cost of capital), ERR offers a more accurate and reliable measure of project profitability, leading to better investment decisions. While slightly more complex to calculate, the benefits of a more realistic assessment often outweigh the increased computational effort.


FAQs



1. What is the difference between IRR and ERR? The IRR assumes reinvestment at the IRR itself, while ERR uses a more realistic reinvestment rate, typically the cost of capital.

2. Which is better, IRR or ERR? ERR is generally preferred due to its more realistic reinvestment assumption, leading to a more accurate assessment of project profitability.

3. How do I choose the reinvestment rate for ERR? The reinvestment rate should reflect the return the company can realistically achieve on its funds, often the cost of capital or a hurdle rate.

4. Can ERR be negative? Yes, a negative ERR indicates that the project is expected to generate a return lower than the reinvestment rate, suggesting it is not a worthwhile investment.

5. What software can calculate ERR? Spreadsheet software like Microsoft Excel (using the `MIRR` function) and dedicated financial calculators can easily compute the ERR.

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