- ARR = (Average Accounting Profit) ÷ (Initial Investment)
- ARR = (Average Accounting Profit) ÷ (Average Investment)
- ARR = (Net Profit After Taxes) ÷ (Initial Investment)
- ARR = (Total Revenue) ÷ (Average Investment)
- ARR = (Cash Inflows – Depreciation) ÷ (Initial Investment)
Correct Option:
The correct formula for the Accounting Rate of Return (ARR) is:
ARR = (Average Accounting Profit) ÷ (Average Investment).
This formula reflects the return expected from an investment in terms of accounting profit, considering the average amount invested.
What is the Accounting Rate of Return (ARR)?
The Accounting Rate of Return (ARR) is a financial ratio that compares the average accounting profit generated by an investment to the average amount of capital invested. This method is especially useful for businesses looking to assess the financial viability of projects or investments without relying solely on cash flow metrics.
ARR provides a simple yet effective measure of profitability, focusing on accounting data rather than cash flow. It is a critical tool in project appraisal, often used alongside other methods like Net Present Value (NPV) and Internal Rate of Return (IRR).
Formulas to Calculate the Accounting Rate of Return
There are several ways ARR is expressed, leading to common questions about its exact formula. Below are the key variations:
1. ARR = (Average Accounting Profit) ÷ (Initial Investment)
This formula is straightforward, comparing the average accounting profit to the initial amount invested.
Key Use Case: Suitable for investments where initial capital is a major focus.
2. ARR = (Average Accounting Profit) ÷ (Average Investment)
Correct Option: This is the most widely accepted formula for ARR.
Explanation: The average investment accounts for depreciation and other reductions in investment value over time. It provides a more accurate representation of profitability when assets depreciate over the project lifecycle.
Example:
If an investment of $100,000 depreciates by $10,000 annually over 5 years, the average investment is: Average Investment=Initial Investment + Residual
Average Investment = Initial Investment + Residual Value / 2 = 100,000 + 50,000 / 2 = 75,000.
ARR can then be calculated using average profits over the same period.
3. ARR = (Net Profit After Taxes) ÷ (Initial Investment)
- Focuses on post-tax profits relative to initial investment.
- Key Use Case: Often used when tax considerations are central to investment decisions.
4. ARR = (Total Revenue) ÷ (Average Investment)
- Measures the return based on total revenue instead of profits.
- Key Use Case: Less common and generally avoided as it doesn’t consider costs.
5. ARR = (Cash Inflows – Depreciation) ÷ (Initial Investment)
- Considers cash inflows adjusted for depreciation.
- Key Use Case: When businesses prioritize cash flow but also need to account for depreciation.
Correct Formula for ARR
The most accurate and widely accepted formula for ARR is:
How to Calculate ARR: Step-by-Step
To calculate ARR effectively, follow these steps:
1. Calculate the Average Accounting Profit
Sum up the expected accounting profits for the investment period and divide by the number of years.
Example: If profits over 3 years are $30,000, $40,000, and $50,000:
2. Determine the Average Investment
Average investment accounts for the decline in value over time.
Formula:
Example: If the initial investment is $100,000 and the residual value is $50,000:
3. Apply the ARR Formula
Plug the values into the formula:
Example: Using the above values:
Advantages of ARR
- Simplicity: Easy to calculate and understand.
- Accounting Focused: Relies on familiar financial statements.
- Decision-Making: Provides a quick estimate of an investment’s profitability.
Limitations of ARR
- Ignores Time Value of Money (TVM): Doesn’t account for the value of money decreasing over time.
- Based on Accounting Data: Relies on profits rather than cash flows, which might distort reality.
- Residual Value Impact: Sensitive to the choice of residual value.
Applications of ARR
- Project Appraisal: Evaluating new investments or capital projects.
- Performance Comparison: Comparing the profitability of different investments.
- Budgeting Decisions: Assists in deciding which projects to prioritize.
Conclusion
To answer the question, “The formula to calculate the accounting rate of return is:”, the correct option is:
ARR = (Average Accounting Profit) ÷ (Average Investment).
ARR is a valuable metric for assessing profitability, offering insights into how effectively an investment will generate accounting profits. While simple and straightforward, remember its limitations and use it alongside other evaluation tools like NPV or IRR for a comprehensive investment appraisal.
By understanding ARR in-depth, businesses can make informed, data-driven decisions to maximize their financial success.
