Formula Accounting Rate Of Return

Understanding and Applying the Formula Accounting Rate of Return (ARR)

The Accounting Rate of Return (ARR), also known as the Average Rate of Return (ARR) or the Simple Rate of Return, is a crucial financial metric used in capital budgeting. It helps businesses assess the profitability of potential investments by comparing the average annual net income generated by an asset to its average investment cost. This article delves deep into the ARR formula, its calculation, interpretation, advantages, disadvantages, and practical applications. Understanding ARR is vital for making informed investment decisions and maximizing returns.

What is the Accounting Rate of Return (ARR)?

The Accounting Rate of Return (ARR) is a financial ratio that calculates the percentage rate of return expected on an investment or asset. It expresses the average annual net income generated by an investment as a percentage of the average investment cost. In simpler terms, it shows how much profit an investment is expected to generate relative to its cost over its lifespan. This metric is particularly useful for evaluating the profitability of long-term assets like machinery, equipment, or property. It provides a straightforward way to compare the potential profitability of different investment opportunities.

The Formula for Calculating ARR

The ARR formula is relatively straightforward:

ARR = (Average Annual Net Income / Average Investment) x 100%

Let's break down each component:

• Average Annual Net Income: This is the total net income expected from the investment over its lifespan, divided by the number of years. This figure is derived from the projected income statement for the investment. It excludes non-cash expenses like depreciation, but includes any tax implications.

• Average Investment: This represents the average amount invested in the asset throughout its useful life. For investments with a consistent cost throughout, this is simply the initial investment. However, for projects with varying investments over time (e.g., additional capital expenditures during the project lifecycle), a more complex calculation is required, often using a weighted average approach. A common method to calculate this is: (Initial Investment + Salvage Value) / 2

Step-by-Step Calculation of ARR

Let's illustrate the calculation with an example:

Imagine a company is considering investing in new machinery costing $100,000. The machinery has a useful life of 5 years and is expected to generate the following annual net incomes (after tax):

• Year 1: $20,000
• Year 2: $25,000
• Year 3: $30,000
• Year 4: $25,000
• Year 5: $20,000

1. Calculate the Average Annual Net Income:

Total Net Income = $20,000 + $25,000 + $30,000 + $25,000 + $20,000 = $120,000 Average Annual Net Income = $120,000 / 5 years = $24,000

2. Calculate the Average Investment:

Assuming a salvage value (residual value) of $10,000 at the end of 5 years:

Average Investment = ($100,000 + $10,000) / 2 = $55,000

3. Calculate the ARR:

ARR = ($24,000 / $55,000) x 100% = 43.64%

Therefore, the Accounting Rate of Return for this investment is 43.64%.

Understanding the Implications of ARR

The ARR of 43.64% in our example suggests that, on average, the investment will yield a return of 43.64% per year on the average investment. This is a relatively high return, indicating that the investment may be worthwhile, depending on the company's required rate of return (hurdle rate). The hurdle rate is the minimum rate of return a company expects from an investment to consider it acceptable. If the ARR exceeds the hurdle rate, the investment is generally considered acceptable.

Advantages of Using ARR

• Simplicity: The ARR is relatively easy to understand and calculate, making it accessible to individuals with limited financial expertise.
• Clarity: It provides a clear percentage return on investment, facilitating easy comparison across different projects.
• Focus on Profitability: ARR directly focuses on the profitability of the investment, which is a primary concern for most businesses.
• Usefulness for Small-Scale Projects: ARR is particularly useful for evaluating smaller-scale investment projects where the complexity of other methods like Net Present Value (NPV) might be unnecessary.

Disadvantages of Using ARR

• Ignores the Time Value of Money: This is perhaps the most significant drawback. ARR doesn't account for the fact that money received today is worth more than money received in the future due to inflation and the potential for earning interest. This limitation can lead to inaccurate investment decisions, particularly for long-term projects.
• Sensitivity to Accounting Methods: The ARR is affected by the choice of accounting methods used to calculate net income. Different depreciation methods, for instance, can significantly impact the ARR calculation.
• Does Not Consider Project Size: ARR does not take into account the scale of the investment. A small project with a high ARR might be less profitable in absolute terms than a larger project with a lower ARR.
• Ignores Cash Flows Beyond the Initial Investment: ARR only considers the average annual net income, potentially overlooking important cash flow fluctuations during the project lifespan.

ARR vs. Other Capital Budgeting Techniques

ARR is often compared to other capital budgeting techniques, such as Net Present Value (NPV) and Internal Rate of Return (IRR). While ARR offers simplicity, NPV and IRR incorporate the time value of money, leading to more accurate and reliable investment decisions, especially for long-term projects. NPV determines the difference between an investment's present value of cash inflows and outflows, while IRR calculates the discount rate at which the NPV of an investment equals zero. Both NPV and IRR are more sophisticated than ARR but require a deeper understanding of financial concepts.

Practical Applications of ARR

ARR is widely used in various contexts, including:

• Capital Budgeting: Companies use ARR to evaluate and rank potential investment opportunities, including machinery purchases, building expansions, and new product development.
• Business Valuation: ARR can provide insights into the profitability of a business as a whole, assisting in valuation processes.
• Investment Analysis: Individuals can use ARR to assess the potential return on investments such as stocks, bonds, or real estate.
• Project Feasibility Studies: ARR is often incorporated into feasibility studies to determine the financial viability of projects.

Frequently Asked Questions (FAQ)

Q1: What is the difference between ARR and ROI?

While both ARR and Return on Investment (ROI) measure profitability, they differ in their scope and calculation. ROI typically focuses on a single period, while ARR considers the average return over the asset's entire lifespan. Moreover, ARR explicitly uses average net income and average investment values.

Q2: How do I choose between ARR, NPV, and IRR?

The best method depends on the specific investment and the investor's goals. ARR is suitable for simpler, shorter-term projects where the time value of money isn't a major concern. However, for long-term projects with complex cash flows, NPV and IRR, which incorporate the time value of money, are more appropriate.

Q3: Can ARR be negative?

Yes, an ARR can be negative if the average annual net income is less than zero. This indicates that the investment is expected to generate a net loss.

Q4: How do I account for salvage value in the ARR calculation?

Salvage value, the estimated value of an asset at the end of its useful life, is incorporated into the average investment calculation. It usually reduces the average investment, leading to a higher ARR.

Conclusion

The Accounting Rate of Return is a valuable tool for evaluating the profitability of potential investments. While its simplicity makes it easy to understand and apply, its limitations, particularly the neglect of the time value of money, must be carefully considered. For more complex projects or long-term investment decisions, a more comprehensive approach using NPV or IRR is generally recommended. However, ARR continues to hold relevance, especially for simpler investment scenarios and as a quick comparative tool for initial screening of potential investment opportunities. Remember to always consider the context, limitations, and complementary financial metrics when making crucial investment decisions. By understanding and properly applying ARR, alongside other financial tools, businesses and individuals can significantly improve their investment decision-making processes.