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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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Rate of Return (RoR) | Definition, Formula, and Example 29 Jan 2024 · The rate of return, or RoR, is the net gain or loss on an investment over a period of time. It is expressed as a percentage of the principal of the investment. Calculating the rate of return gets the percentage change from the beginning of the period to the end. Formula for Calculating (RoR)

Introduction 11: Rate of Return Terminology 11.1 Basics of IRR Ex … Other types of rate of return External rate of return (ERR) uses external information about how funds reinvested Incremental rate of return methods recognize extra earnings due to additional investment IRR definition: interest rate that a bank account having the same cash flows would pay if its initial and final balances were $0, so root of 0 = 0 +

The External Rate of Return Method | PDF | Internal Rate Of Return ... The External Rate of Return (ERR) method directly takes into account the interest rate external to a project at which net cash flows can be reinvested or borrowed. It involves three steps: 1) discounting net cash outflows to the present, 2) compounding net cash inflows to the end period, and 3) determining the ERR.

Under what conditions should the External Rate of Return (ERR) … 14 May 2019 · NPW is the net discounted value of all the cash flows that occur throughout the life of project, while the discount rate is the MARR -- a rate that I have decided as a minimum rate of return for acceptance of a project. If NPW > 0, accept the project else reject.

Rate of Return (RoR): Formula and Calculation Examples - SoFi 2 Dec 2024 · Rate of return (RoR) is a measure of an investment’s gain or loss, expressed as a percentage of its initial value, over a given period of time. If calculated correctly, your rate of return will be expressed as a percentage of your initial investment.

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Rate of Return Calculator 18 Jan 2024 · The rate of return calculator allows you to find the annual rate of return of a given investment (see investment calculator), which is the net gain or loss through a given period expressed as a percentage of the initial investment cost.

Impact - Time Partners Time Partners created the External Rate of Return with the London School of Economics to measure a company or investment’s purpose and wider impact on society, the economy, and the environment. Promoting radical transparency, the ERR encourages companies to track and report the total external outcomes of their activities and act accountably.

Rate of return - Wikipedia To compare returns over time periods of different lengths on an equal basis, it is useful to convert each return into a return over a period of time of a standard length. The result of the conversion is called the rate of return. [2]

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THE External RATE OF Return - THE EXTERNAL RATE OF RETURN … It directly takes into account the interest rate (ε) external to a project at which net cash flows generated (or required) by the project over its life can be reinvested (or borrowed). If the ERR, which is usually the firm’s MARR, happens to equal the project’s IRR, then the ERR method produces results identical to those of the IRR method ...

External Rate of Return Method | PDF | Technology The External Rate of Return (ERR) method directly takes into account the interest rate external to a project to discount or compound net cash flows over the project's life. If the ERR equals the Internal Rate of Return (IRR), the results are identical to using the IRR method.

Rate of Return External rate of return (ERR). The investment will be attractive . Use incremental method to compare. Consider the following cash flow profile and assume MARR is 10% per year. a) Determine the IRR for this project. b) Is this project economically justified? MARR =10%, determine the IRR. (Same as data of problem 36), MARR=10%, determine the ERR.

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Rate of Return Formula, Definition & Example - InvestingAnswers 29 Sep 2020 · What is the Rate of Return? A rate of return is measure of profit as a percentage of investment. How Does the Rate of Return Work? Let's say John Doe opens a lemonade stand. He invests $500 in the venture, and the lemonade stand makes about $10 a day, or about $3,000 a year (he takes some days off).

“GROSS” PRESENT VALUE and “EXTERNAL” RATE OF RETURN … understanding of the External Rate of Return (ERR)! This paper also offers a set of concatenation statements which link the so noted financial measures of investment performance one to another, thereby making the pedagogy more robust!

The External Rate of Return: the next step - Mark Florman 17 Aug 2017 · This month I am delighted to announce the launch of a £2m fund from King’s College London to develop the External Rate of Return (ERR) into a fully functioning platform (summary here).

Rate of Return (RoR): Meaning, Formula, and Examples - Investopedia 20 Jul 2024 · A rate of return (RoR) is the gain or loss of an investment over a specified period of time, expressed as a percentage of the investment’s cost.

External Rate Of Return - icecreamtutor.com 31 Jul 2024 · The external rate of return (ERR) is the terminal value of the original investment of an investment plan The rate of return equal to the sum of the future values of net cash flows in each year calculated based on the benchmark rate of return or a set discount rate.