Understanding the Accounting Rate of Return (ARR) Formula

The accounting rate of return (ARR) is a formula that measures the net profit or return expected on an investment compared to the initial cost. It is an important financial metric used by businesses to evaluate the profitability of a project or investment.

What Is the Accounting Rate of Return (ARR)?

The accounting rate of return (ARR) is a financial metric used to measure the profitability of an investment. It calculates the average annual net profit as a percentage of the initial investment. ARR is expressed as a percentage and is commonly used by businesses to assess the potential profitability of projects.

The Formula for ARR

The formula for calculating the accounting rate of return (ARR) is:

ARR = Average Annual Net Profit / Initial Investment

The average annual net profit is calculated by dividing the total net profit over a specific period by the number of years in that period. The initial investment refers to the total cost of the project or investment.

How to Calculate ARR

To calculate the accounting rate of return (ARR), follow these steps:

1. Calculate the average annual net profit. This can be done by dividing the total net profit over a specific period by the number of years in that period.
2. Calculate the initial investment. This refers to the total cost of the project or investment.
3. Divide the average annual net profit by the initial investment and multiply by 100 to get the ARR as a percentage.

Example of the ARR

Let's consider an example to illustrate how the accounting rate of return (ARR) is calculated:

Company XYZ invests $100,000 in a project. Over a period of 5 years, the project generates a total net profit of $50,000. To calculate the ARR:

1. Calculate the average annual net profit: $50,000 / 5 = $10,000.
2. Calculate the initial investment: $100,000.
3. ARR = $10,000 / $100,000 * 100 = 10%.

In this example, the ARR for the project is 10%, indicating that the project is expected to generate a 10% return on the initial investment.

Accounting Rate of Return vs. Required Rate of Return

The accounting rate of return (ARR) is often compared to the required rate of return (RRR) to assess the profitability and viability of an investment. The required rate of return is the minimum rate of return that an investor or business expects from an investment to compensate for the risk.

If the ARR is higher than the RRR, it indicates that the project is expected to generate a return higher than the minimum expected return and may be considered profitable. On the other hand, if the ARR is lower than the RRR, it suggests that the project may not be as profitable as expected.

Advantages and Disadvantages of the ARR

The accounting rate of return (ARR) has several advantages and disadvantages:

Advantages

• Simple and easy to calculate: The ARR formula is straightforward and can be easily calculated using basic financial information.
• Provides a percentage-based measure: The ARR is expressed as a percentage, making it easy to compare different projects or investments.
• Considers the entire project lifespan: The ARR takes into account the average annual net profit over the entire project lifespan, providing a comprehensive measure of profitability.

Disadvantages

• Does not consider the time value of money: The ARR does not take into account the time value of money, which means that it does not consider the impact of inflation or the opportunity cost of capital.
• Relies on accounting profit: The ARR is based on accounting profit, which may not accurately reflect the economic profitability of a project.
• Does not consider the risk factor: The ARR does not consider the risk associated with an investment, which may result in misleading profitability estimates.

How Does Depreciation Affect the Accounting Rate of Return?

Depreciation is an accounting method used to allocate the cost of an asset over its useful life. It affects the accounting rate of return (ARR) by reducing the net profit and, consequently, the ARR. Depreciation expense is subtracted from the net profit when calculating the average annual net profit.

What Are the Decision Rules for Accounting Rate of Return?

When using the accounting rate of return (ARR) to make investment decisions, businesses often follow certain rules:

• If the ARR is higher than the required rate of return (RRR), the project is considered profitable.
• If the ARR is lower than the RRR, the project is considered unprofitable.
• Projects with higher ARR values are generally preferred over projects with lower ARR values.
• The ARR is compared to the RRR to assess the profitability and viability of an investment.

What Is the Difference Between ARR and IRR?

The accounting rate of return (ARR) and the internal rate of return (IRR) are both financial metrics used to evaluate the profitability of an investment. However, there are some key differences between the two:

• The ARR is based on accounting profit, while the IRR is based on cash flows.
• The ARR calculates the average annual net profit as a percentage of the initial investment, while the IRR calculates the discount rate at which the net present value (NPV) of cash flows is equal to zero.
• The ARR does not consider the time value of money, while the IRR takes into account the time value of money by discounting cash flows.

In general, the IRR is considered a more comprehensive and accurate measure of investment profitability compared to the ARR.

The Bottom Line

The accounting rate of return (ARR) is a formula used to measure the net profit or return expected on an investment compared to the initial cost. It is an important financial metric used by businesses to evaluate the profitability of a project or investment. While the ARR has its advantages and disadvantages, it provides a simple and percentage-based measure of profitability. However, it should be used in conjunction with other financial metrics and factors to make informed investment decisions.