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

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 the asset, or related project. ARR does not consider the time value of money or cash flows, which can be an integral part of maintaining a business.

#### Rate of Return

## The Formula for ARR

A R R = A v e r a g e A n n u a l P r o f i t I n i t i a l I n v e s t m e n t ARR = frac

## How to Calculate Accounting Rate of Return

- Calculate the annual net profit from the investment, which could include revenue minus any annual costs or expenses of implementing the project or investment.
- 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.
- 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.

## What Does ARR Tell You?

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.

### Key Takeaways

- The accounting rate of return (ARR) formula is helpful in determining the annual percentage rate of return of a project.
- You may use ARR when considering multiple projects, as it provides the expected rate of return from each project.
- However, ARR does not differentiate between investments that yield different cash flows over the lifetime of the project.

## How to Use 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% (0.28 * 100)

## The Difference Between ARR and RRR

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 RRR can vary between investors as they each have a diffferent 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.

## Limitations of Using ARR

The accounting rate of return is helpful in determining a project’s annual percentage rate of return. However, the calculation has its limitations.

ARR doesn’t consider the time value of money (TVM). 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 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 year. In this case, the ARR calculation would not factor in the lack of cash flow in the first three years, and the investor would need to be able to withstand the first three years without any positive cash flow from the project.

is the minimum return in percentage that an investor must receive due to time value of money and as compensation for investment risks.

There are multiple models to work out required rate of return on equity, preferred stock, debt and other investments.

The most basic framework is to estimate required rate of return based on the risk-free rate and add inflation premium, default premium, liquidity premium and maturity premium, whichever is applicable.

The formula for the general required rate of return can be written as:

Required Return = r_{f} + IRP + DRP + LRP + MRP

Where, **r _{f}** is the real risk-free rate is the rate of return on Treasury inflation-protected securities.

**IRP**stands for inflation risk premium, the compensation for inflation risk;

**DRP**stands for default risk premium, the compensation for risk of investment loss due to default;

**LRP**stands for liquidity risk premium, the compensation for illiquidity and lack of marketability and

**MRP**stands for maturity risk premium, the compensation for higher interest rate risk and reinvestment risk that results from longer maturities.

## Required Return on Equity (i.e. Common Stock)

The required return on equity is also called the cost of equity. There are three common models to estimate required return on common stock: the capital asset pricing model, the dividend discount model and the bond yield plus risk premium approach.

### Capital Asset Pricing Model (CAPM) Formula

The capital asset pricing model estimates required rate of return using the following formula:

Required Return on Equity (CAPM)

= Risk Free Rate (r_{f}) + Equity Risk Premium

= Risk Free Rate (r_{f}) + Beta × Market Risk Premium

= Risk Free Rate (r_{f}) + Beta × (Market Return (r_{m}) − Risk Free Rate (r_{f}))

Where **r _{f}** is the nominal risk-free rate, beta coefficient is a measure of systematic risk and

**r**is the return on the broad market index such as S&P 500. Equity risk premium equals beta multiplied by market risk premium and market risk premium equals the difference between r

_{m}_{m}and r

_{f}.

### Dividend Discount Model (DDM) Formula

The dividend discount model (DDM) estimates required return on equity using the following formula:

Required Return on Equity (DDM) = | D_{0} × (1 + g) |
+ g |

P_{0} |

Where **D _{0}** is the current annual dividend per share,

**P**is the current price of the stock and

_{0}**g**is the growth rate of dividends. The growth rate equals the product of retention ratio and return on equity (ROE).

g = Retention Ratio × ROE

### Bond Yield plus Risk Premium Approach Formula

The bond yield plus risk premium approach adds a certain equity risk premium (based on historical analysis) to the yield on a company’s publicly-traded bonds.

## Required Return on Preferred Stock

Required return on preferred stock is also called cost of preferred stock and it equals the ratio of preferred dividends per share (**D**) to the current price of the preferred stock (**P _{0}**):

Required Return on Preferred Stock = | D |

P_{0} |

## Required Return on Debt

Required return on debt (also called cost of debt) can be estimated by calculating the yield to maturity of the bond or by using the bond-rating approach.

The yield to maturity is the internal rate of return of the bond i.e. the rate that equates the current price of the bond to its future cash flows based on the following equation:

Bond Price = c × F × | 1 − (1 + r) -t | + | F |

r | (1 + r) t |

Where, **c** is the periodic coupon rate which equals annual coupon rate divided by number of coupon payments per year, **F** is the face value i.e. principal amount, **t** is total number of coupon payments till maturity, and **r** is the periodic yield to maturity. Annual yield to maturity equals periodic yield to maturity multiplied by coupon payments per year.

Where the debt is not publicly traded, the required return on debt can be inferred from the yield to maturity of other marketable bonds which carry the same bond rating as the bond under consideration.

The build-up approach can also be used to estimate required return on debt. It involves adding inflation, default, liquidity and maturity premia to the real risk free rate.

If you have already studied other capital budgeting methods (net present value method, internal rate of return method and payback method), you may have noticed that all these methods focus on cash flows. But **accounting rate of return (ARR) method** uses expected net operating income to be generated by the investment proposal rather than focusing on cash flows to evaluate an investment proposal.

Under this method, the asset’s expected accounting rate of return (ARR) is computed by dividing the expected incremental net operating income by the initial investment and then compared to the management’s desired rate of return to accept or reject a proposal. If the asset’s expected accounting rate of return is greater than or equal to the management’s desired rate of return, the proposal is accepted. Otherwise, it is rejected. The accounting rate of return is computed using the following formula:

**Formula of accounting rate of return (ARR):**

In the above formula, the *incremental net operating income* is equal to *incremental revenues* to be generated by the asset less *incremental operating expenses*. The incremental operating expenses also include depreciation of the asset.

The denominator in the formula is the amount of investment initially required to purchase the asset. If an old asset is replaced with a new one, the amount of initial investment would be reduced by any proceeds realized from the sale of old equipment.

## Example 1:

The Fine Clothing Factory wants to replace an old machine with a new one. The old machine can be sold to a small factory for $10,000. The new machine would increase annual revenue by $150,000 and annual operating expenses by $60,000. The new machine would cost $360,000. The estimated useful life of the machine is 12 years with zero salvage value.

**Required:**

- Compute accounting rate of return (ARR) of the machine using above information.
- Should Fine Clothing Factory purchase the machine if management wants an accounting rate of return of 15% on all capital investments?

### Solution:

**(1): Computation of accounting rate of return:**

* *Incremental net operating income: *Incremental revenues – Incremental expenses including depreciation

$150,000 – ($60,000 cash operating expenses + $30,000 depreciation)

$150,000 – $90,000

$60,000

** The amount of initial investment has been reduced by net realizable value of the old machine ($360,000 – $10,000).

**(2)**. **Conclusion:**

According to accounting rate of return method, the Fine Clothing Factory should purchases the machine because its estimated accounting rate of return is 17.14% which is greater than the management’s desired rate of return of 15%.

## Cost reduction projects:

The accounting rate of return method is equally beneficial to evaluate cost reduction projects. The accounting rate of return of the assets that are purchased with a view to reduce business costs is computed using the following formula:

## Example 2:

The P & G company is considering to purchase an equipment costing $45,000 to be used in packing department. It would reduce annual labor cost by $12,000. The useful life of the equipment would be 15 years with no salvage value. The operating expenses of the equipment other than depreciation would be $3,000 per year.

**Required:** Compute accounting rate of return/simple rate of return of the equipment.

### Solution:

** Net cost savings: *$12,000 – ($3,000 cash operating expenses + $3,000 depreciation expenses)

$12,000 – $6,000

$6,000

## Comparison of different alternatives:

If several investments are proposed and the management have to choose the best due to limited funds, the proposal with the highest accounting rate of return is preferred. Consider the following example:

## Example 3:

The Good Year manufacturing company has the following different alternative investment proposals:

**Required:** Using accounting rate of return method, select the best investment proposal for the company.

### Solution:

If only accounting rate of return is considered, the proposal B is the best proposal for Good Year manufacturing company because its expected accounting rate of return is the highest among three proposals.

The simple rate of return is calculated by taking the annual incremental net operating income and dividing by the initial investment. When calculating the annual incremental net operating income, we need to remember to reduce by the depreciation expense incurred by the investment.

### Watch IT

Let’s take a look at an example.

Hupana Running Company is looking at adding a stitcher that will add $40,000 to the revenues of the company per year. The incremental (additional) cash operating expenses of this piece of equipment would be $5,000 per year, and the equipment has a cost of $100,000 with a 5 year life and no salvage value. So let’s pop these numbers into the formula:

Hupana Running Company—Stitcher Purchase | |
---|---|

Annual incremental revenue | $40,000 |

Annual incremental operating expense | $5,000 |

Annual depreciation ($100,000/5 years) | $20,000 |

Annual incremental expenses | $25,000 |

Annual incremental net operating income/(loss) | $15,000 |

So the simple rate of return would be: annual incremental net operating income/ initial investment cost

$15,000/$100,000= 15% simple rate of return

So it looks like the stitcher would be a good investment! What if we change up the numbers a bit. The stitcher will still add the $40,000 to revenues, but will add $10,000 to annual operating costs and only have a useful life of three years.

Hupana Running Company—Stitcher Purchase | |
---|---|

Annual incremental revenue | $40,000 |

Annual incremental operating expense | $10,000 |

Annual depreciation ($100,000/ years) | $33,333 |

Annual incremental expenses | $43,333 |

Annual incremental net operating income/(loss) | −$3,333 |

We now have a negative rate of return, so would probably pass on making this purchase. This brings home the point of how important it can be to know your numbers and do your research! Also noting, a small difference, can make a huge difference in the decision to make a capital budgeting decision, so as a manager, be clear on your information and perhaps use several of the available methods before making a final decision or before taking your analysis to your supervisor!

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## What is the Accounting Rate of Return?

The accounting rate of return is the expected rate of return on an investment. The calculation is the accounting profit from the project, divided by the initial investment in the project. One would accept a project if the measure yields a percentage that exceeds a certain hurdle rate used by the company as its minimum rate of return. The formula for the accounting rate of return is:

Average annual accounting profit ÷ Initial investment = Accounting rate of return

In this formula, the accounting profit is calculated as the profit related to the project using all accruals and non-cash expenses required under the GAAP or IFRS frameworks (thus, it includes the costs of depreciation and amortization). If the project involves cost reduction instead of earning a profit, then the numerator is the amount of cost savings generated by the project. In essence, then, profit is calculated using the accrual basis of accounting, not the cash basis. Also, the initial investment is calculated as the fixed asset investment plus any change in working capital caused by the investment.

The result of the calculation is expressed as a percentage. Thus, if a company projects that it will earn an average annual profit of $70,000 on an initial investment of $1,000,000, then the project has an accounting rate of return of 7%.

## Problems with the Accounting Rate of Return

There are several serious problems with this concept, which are:

*Time value of money*. The measure does not factor in the time value of money. Thus, if there is currently a high market interest rate, the time value of money could completely offset any profit reported by a project – but the accounting rate of return does incorporate this factor, so it clearly overstates the profitability of proposed projects.

*Constraint analysis*. The measure does not factor in whether or not the capital project under consideration has any impact on the throughput of a company’s operations.

*System view*. The measure does not account for the fact that a company tends to operate as an interrelated system, and so capital expenditures should really be examined in terms of their impact on the entire system, not on a stand-alone basis.

*Comparison*. The measure is not adequate for comparing one project to another, since there are many other factors than the rate of return that should be considered, not all of which can be expressed quantitatively.

*Cash flow*. The measure includes all non-cash expenses, such as depreciation and amortization, and so does not reveal the return on actual cash flows experienced by a business.

*Time-based risk*. There is no consideration of the increased risk in the variability of forecasts that arises over a long period of time.

In short, the accounting rate of return is not by any means a perfect method for evaluating a capital project, and so should be used (if at all) only in concert with a number of other evaluation tools. In particular, you should find another tool to address the time value of money and the risk associated with a long-term investment, since this tool does not provide for it. Possible replacement measurements are net present value, the internal rate of return, and constraint analysis. This measure would be of the most use for reviewing short-term investments where the impact of the time value of money is reduced.

## Terms Similar to Accounting Rate of Return

The accounting rate of return is also known as the average rate of return or the simple rate of return.

Internal Rate of Return (IRR) is a discount rate that is used to identify potential/future investments that may be profitable. The IRR is used to make the net present value (NPV) of cash flows from a project/investment equal to zero.

In simpler terms, the IRR is used to determine what percentage return of an investment is necessary for it to break even when adjusted for the value of time and money involved. This is often considered the minimum acceptable return on investment, as most companies want to do more than just break even.

Internal Rate of Return is also sometimes referred to as the “discounted cash flow rate of return” or the “economic rate of return”. The “internal” part of the name refers to the fact that external factors such as inflation or the cost of capital are not included in the calculation.

## IRR Formula

- NPV = Net present value
- CF = Cash flow per period
- r = Internal rate of return

Put simply, the IRR is determined by experimenting to find the rate which cause the NPV of a series of payments to equal $0. The above formula is a derived version of the NPV formula:

If the payments for each cash flow are expected to be the same, you can also use the simpler NPV formula:

$$NPV = CF times dfrac<1-(1+r)^<-n>>

From this point, the only variable that needs to be calculated is the IRR itself. This is done in Microsoft Excel in most instances but can be done manually if need be as shown below. It can take a bit of trial and error when calculated but is certainly possible.

## IRR Example

The IRR is presented as a percentage. In this instance, the found IRR is 10%. Assuming that the business is lower than 10%, this would represent a good investment. If the ending NPV does not equal zero, the percentage must be adjusted accordingly until that goal is reached. The return rate, after properly calculated, can be compared to other investments to determine what is ultimately worth the money.

As mentioned above, finding the exact rate that balances to 0 can take a bit of trial and error, and programs such as Microsoft Excel are commonly used to make this task easier.

## IRR Analysis

The IRR can be used for just about any potential investment, including the stock market, equipment, and other capital investments. While the projected amount of future cash flow is not always accurate due to a variety of factors, the IRR is a great jumping off point when considering any sort of future investment.

The IRR is also commonly used when comparing if it will be more profitable to open a new branch of business within a company or expand the operations of an existing one. An example of this would be a paper company deciding whether to open a new mill or simply expand an existing one. Both would certainly add value to the company, but the IRR could give a good indication of which is the more profitable decision in the long term.

The IRR is also useful in helping corporations evaluate stock buyback programs. Similarly to the new mill vs expanding a current mill example used above, the IRR analysis must show that buying back the company’s own stock is ultimately a better investment than using that funding elsewhere.

One limitation of the IRR is that it can tend to favor smaller investments with shorter-term returns over larger ones with longer-term returns. Whereas a $600 investment that returns $1800 per year appears to have a more favorable IRR than a $15,000 investment that returns $30,000 per year, the larger investment ultimately brings much more value.

## IRR Conclusion

- Internal Rate of Return is a metric used to indicate the rate of growth a project can be expected to generate.
- The IRR is presented as a percentage.
- The IRR helps in deciding whether or not a project is worth investing in.
- The IRR is generally the minimum accepted return on a project or investment. The goal of a company is often to do more than break even.
- The IRR helps a company determine which investments would be profitable, including aiding in decisions of expansion of existing assets or the purchase of new equipment.
- IRR

## IRR Calculator

You can use the calculator below to calculate the IRR. You will need to experiment with the interest rate value to find the correct rate which discounts the Net Present Value back to 0.

So, for example, if your cash flow was one period, for $105, and the initial investment was $100, then to get an NPV of $0 you would need an interest/discount rate of 5%. That is your internal rate of return.

Like net present value method, **internal rate of return (IRR) method** also takes into account the time value of money. It analyzes an investment project by comparing the internal rate of return to the **minimum required rate of return** of the company.

The **internal rate of return** sometime known as **yield on project** is the rate at which an investment project promises to generate a return during its useful life. It is the discount rate at which the present value of a project’s net cash inflows becomes equal to the present value of its net cash outflows. In other words, internal rate of return is the discount rate at which a project’s net present value becomes equal to zero.

The **minimum required rate of return** is set by management. Most of the time, it is the cost of capital of the company.

Under this method, If the internal rate of return promised by the investment project is greater than or equal to the minimum required rate of return, the project is considered acceptable otherwise the project is rejected. Internal rate of return method is also known as *time-adjusted rate of return method*.

To understand how computations are made and how a proposed investment is accepted or rejected under this method, consider the following example:

## Example:

The management of VGA Textile Company is considering to replace an old machine with a new one. The new machine will be capable of performing some tasks much faster than the old one. The installation of machine will cost $8,475 and will reduce the annual labor cost by $1,500. The useful life of the machine will be 10 years with no salvage value. The minimum required rate of return is 15%.

**Required:** Should VGA Textile Company purchase the machine? Use internal rate of return (IRR) method for your conclusion.

### Solution:

To conclude whether the proposal should be accepted or not, the internal rate of return promised by machine would be found out first and then compared to the company’s minimum required rate of return.

The first step in finding out the internal rate of return is to compute a discount factor called *internal rate of return factor*. It is computed by dividing the *investment required for the project* by *net annual cash inflow* to be generated by the project. The formula is given below:

**Formula of internal rate of return factor:**

In our example, the required investment is $8,475 and the net annual cost saving is $1,500. The cost saving is equivalent to revenue and would, therefore, be treated as net cash inflow. Using this information, the internal rate of return factor can be computed as follows:

Internal rate of return factor = $8,475 /$1,500

After computing the internal rate of return factor, the next step is to locate this discount factor in “present value of an annuity of $1 in arrears table“. Since the useful life of the machine is 10 years, the factor would be found in 10-period line or row. After finding this factor, see the rate of return written at the top of the column in which factor 5.650 is written. It is 12%. It means the internal rate of return promised by the project is 12%. The final step is to compare it with the minimum required rate of return of the VGA Textile Company. That is 15%.

**Conclusion:**

According to internal rate of return method, the proposal is not acceptable because the internal rate of return promised by the proposal (12%) is less than the minimum required rate of return (15%).

Notice that the internal rate of return promised by the proposal is a discount rate that equates the present value of cash inflows with the present value of cash out flows as proved by the following computation:

This rate of return calculator estimates the profitability of a business or investment measured by its discount rate which is also known as compound annual growth rate. There is in depth information on how to determine this financial indicator below the tool.

## Other Tools You May Find Useful

■ Business Loan Calculator

■ Modified Adjusted Gross Income Calculator for Business

## How does this rate of return calculator work?

The rate of return is an important financial figure each investor is looking at before deciding to invest or not in a new or existing opportunity. This application requires the value of the initial investment or the so called starting principal (present value – PV), the total return of the investment at the end of the period (future value – FV) and the term of the investment in years.

The algorithm behind this rate of return calculator uses the compound annual growth rate formula, as it is explained below in 3 steps:

- First divide the Future Value (FV) by the Present Value (PV) in order to get a value denoted by “X”.
- Then raise the “X” figure obtained above by (1/ Investment’s term in years. More specific: X^(1/Investment’s term) – where ^ is the sign for power. After this calculation a new value will be obtained which is denoted with “Y”.
- Finally subtract 1 from “Y” and then multiply the resulting figure by 100 to obtain the rate of return in percentage format.

## How to calculate return rate

Let’s us assume the following example:

-Present Value (PV) = $20000

-Future Value (FV) = $80000

-Investment’s term = 10 years.

Step 1: 80000/20000=4

Step 2: 4^(1/10)=4^0.1= 1.148698355

Step 3: (1.148698355-1)*100=14.87%.

## Understanding the usability of the rate of return

Usually investors compare the rate of return of an investment with the annual inflation rate or with the effective interest rate bank offers on deposits in order to check whether the investment’s return covers or not the inflation within the time frame given.

Since this figure indicates how profitable can a business be, the higher the rate of return the better for the investor is. Please keep in mind that usually high levels of ROI are associated with a high risk profile of the investment in question.

Typically the higher the risk is the higher the rate of return, and so when assessing an opportunity it is important that the investor analyses both the associated risk and its likelihood and its rate of return level.