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# Accounting Rate of Return (ARR)

## What Is the Accounting Rate of Return (ARR)?

The accounting rate of return (ARR) is a formula that reflects the percentage rate of return expected on an investment or asset, compared to the initial investment's cost. The ARR formula divides an asset's average revenue by the company's initial investment to derive the ratio or return that one may expect over the lifetime of an asset or project. ARR does not consider the time value of money or cash flows, which can be an integral part of maintaining a business.

### Key Takeaways

• The accounting rate of return (ARR) formula is helpful in determining the annual percentage rate of return of a project.
• ARR is calculated as average annual profit / initial investment.
• ARR is commonly used when considering multiple projects, as it provides the expected rate of return from each project.
• One of the limitations of ARR is that it does not differentiate between investments that yield different cash flows over the lifetime of the project.
• ARR is different than the required rate of return (RRR), which is the minimum return an investor would accept for an investment or project that compensates them for a given level of risk.
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## Understanding the Accounting Rate of Return (ARR)

The accounting rate of return is a capital budgeting metric that's useful if you want to calculate an investment's profitability quickly. Businesses use ARR primarily to compare multiple projects to determine the expected rate of return of each project, or to help decide on an investment or an acquisition.

ARR factors in any possible annual expenses, including depreciation, associated with the project. Depreciation is a helpful accounting convention whereby the cost of a fixed asset is spread out, or expensed, annually during the useful life of the asset. This lets the company earn a profit from the asset right away, even in its first year of service.

## The Formula for ARR

The formula for the accounting rate of return is as follows:

$ARR = \frac{Average\, Annual\, Profit}{Initial\, Investment}$

## How to Calculate the Accounting Rate of Return (ARR)

1. Calculate the annual net profit from the investment, which could include revenue minus any annual costs or expenses of implementing the project or investment.
2. If the investment is a fixed asset such as property, plant, and equipment (PP&E), subtract any depreciation expense from the annual revenue to achieve the annual net profit.
3. Divide the annual net profit by the initial cost of the asset or investment. The result of the calculation will yield a decimal. Multiply the result by 100 to show the percentage return as a whole number.

## Example of the Accounting Rate of Return (ARR)

As an example, a business is considering a project that has an initial investment of $250,000 and forecasts that it would generate revenue for the next five years. Here's how the company could calculate the ARR: • Initial investment:$250,000
• Expected revenue per year: $70,000 • Time frame: 5 years • ARR calculation:$70,000 (annual revenue) / $250,000 (initial cost) • ARR = 0.28 or 28% ## Accounting Rate of Return vs. Required Rate of Return The ARR is the annual percentage return from an investment based on its initial outlay of cash. Another accounting tool, the required rate of return (RRR), also known as the hurdle rate, is the minimum return an investor would accept for an investment or project that compensates them for a given level of risk. The required rate of return (RRR) can be calculated by using either the dividend discount model or the capital asset pricing model. The RRR can vary between investors as they each have a different tolerance for risk. For example, a risk-averse investor likely would require a higher rate of return to compensate for any risk from the investment. It's important to utilize multiple financial metrics including ARR and RRR to determine if an investment would be worthwhile based on your level of risk tolerance. ## Advantages and Disadvantages of the Accounting Rate of Return (ARR) ### Advantages The accounting rate of return is a simple calculation that does not require complex math and is helpful in determining a project's annual percentage rate of return. Through this, it allows managers to easily compare ARR to the minimum required return. For example, if the minimum required return of a project is 12% and ARR is 9%, a manager will know not to proceed with the project. ARR comes in handy when investors or managers need to quickly compare the return of a project without needing to consider the time frame or payment schedule but rather just the profitability or lack thereof. ### Disadvantages Despite its advantages, ARR has its limitations. It doesn't consider the time value of money. The time value of money is the concept that money available at the present time is worth more than an identical sum in the future because of its potential earning capacity. In other words, two investments might yield uneven annual revenue streams. If one project returns more revenue in the early years and the other project returns revenue in the later years, ARR does not assign a higher value to the project that returns profits sooner, which could be reinvested to earn more money. The time value of money is the main concept of the discounted cash flow model, which better determines the value of an investment as it seeks to determine the present value of future cash flows. The accounting rate of return does not consider the increased risk of long-term projects and the increased uncertainty associated with long periods. Also, ARR does not take into account the impact of cash flow timing. Let's say an investor is considering a five-year investment with an initial cash outlay of$50,000, but the investment doesn't yield any revenue until the fourth and fifth years.

In this case, the ARR calculation would not factor in the lack of cash flow in the first three years, while in reality, the investor would need to be able to withstand the first three years without any positive cash flow from the project.

Pros
• Determines a project's annual rate of return

• Simple comparison to minimum rate of return

• Ease of use/Simple Calculation

• Provides clear profitability

Cons
• Does not consider the time value of money

• Does not factor in long-term risk

• Does not account for cash flow timing

## How Does Depreciation Affect the Accounting Rate of Return?

Depreciation will reduce the accounting rate of return. Depreciation is a direct cost and reduces the value of an asset or profit of a company. As such, it will reduce the return of an investment or project like any other cost.

## What Are the Decision Rules for Accounting Rate of Return?

When a company is presented with the option of multiple projects to invest in, the decision rule states that a company should accept the project with the highest accounting rate of return as long as the return is at least equal to the cost of capital.

## What Is the Difference Between ARR and IRR?

The main difference between ARR and IRR is that IRR is a discounted cash flow formula while ARR is a non-discounted cash flow formula. A non-discounted cash flow formula does not take into consideration the present value of future cash flows that will be generated by an asset or project. In this regard, ARR does not include the time value of money whereby the value of a dollar is worth more today than tomorrow because it can be invested.

## The Bottom Line

The accounting rate of return (ARR) is a simple formula that allows investors and managers to determine the profitability of an asset or project. Because of its ease of use and determination of profitability, it is a handy tool in making decisions. However, the formula does not take into consideration the cash flows of an investment or project, the overall timeline of return, and other costs, which help determine the true value of an investment or project.

Article Sources
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1. University of Groningen-Pure. "Economic and Accounting Rates of Return," Page 3-5.

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