Scenario: A company made an initial investment of $200 five years ago. By the end of year 4, the investment's book value depreciated to$ 100. In the 5th year, the net income generated from the investment was $50.

Calculation:

Using the formula: $R.O.R. = \frac{\text{Net Income in Period}}{\text{Book Value of Net Investment at Start of Period}}$

For this specific period: $R.O.R. = \frac{50}{100} = 0.5 = 50\%$

Interpretation: The investment generated a return equal to 50% of its book value at the beginning of that specific period.

References

Original Source

Interpretation and Considerations

The Accounting Rate of Return (ARR) provides a simple percentage-based measure of an investment's profitability based on accounting income, not cash flows. Its ease of calculation makes it useful for quick comparisons.

Key considerations:

Strengths: Simple to compute and understand; uses data readily available from financial statements.
Limitations: Ignores the time value of money (a dollar today is worth more than a dollar in the future); relies on accounting profit (net income), which can be affected by accounting policies and non-cash items like depreciation; does not consider the investment's overall lifespan or cash flow timing.
Decision Rule: A project is often considered acceptable if its ARR exceeds a company's predetermined minimum required rate of return.

Formula Variation

An alternative approach calculates ARR using the average investment over the period, which can provide a different perspective on the return.

The formula becomes: $ARR = \frac{\text{Average Net Income}}{\text{Average Investment}}$

Where:

Average Investment = (Initial Book Value + Final Book Value) / 2

This method smooths out the effect of depreciation on the investment base. Using the data from the example (Initial Value: 200, Final Value: 100, Net Income: 50):

$Average Investment = \frac{200 + 100}{2} = 150$ $ARR = \frac{50}{150} \approx 0.3333 = 33.33\%$

This yields a lower, more conservative return figure compared to the 50% calculated using the end-of-period book value. The choice of formula depends on the specific analytical context and the desired conservatism.

Additional Practical Example

Here's another example demonstrating the ARR calculation with depreciation:

The Accounting Rate of Return (ARR) can be calculated using the formula:

\text{ARR} = \frac{\text{Net Income in Period}}{\text{Book Value of Net Investment at Start of Period}}

Example: A company made an initial investment of 200 five years ago. By the end of year 4, the book value depreciated to 100 due to accumulated depreciation. The net income generated from this investment during year 5 is 50.

To find the ARR for year 5:

Book value at the start of year 5 (which is the end of year 4) = 100
Net income during year 5 = 50

\text{ARR} = \frac{50}{100} = 0.5 = 50\%

This result indicates a 50% return on the investment's book value for that period.

Note: It's crucial to use the book value at the beginning of the period for which you're calculating the return. In this case, the start of year 5 aligns with the book value at the end of year 4 after depreciation has been accounted for.

Accounting Rate of Return Formula

The core formula for the Accounting Rate of Return (ARR), also known as the Average Rate of Return or Return on Investment (ROI) for accounting purposes, is:

$ARR = \frac{\text{Average Annual Net Income}}{\text{Average Book Value of Investment}}$

This can also be expressed in its period-specific form as:

$R.O.R_{\text{period}} = \frac{\text{Net Income in Period}}{\text{Book Value of Net Investment at Start of Period}}$

Formula Components

Average Annual Net Income: The mean annual profit generated by the project after deducting all expenses, including depreciation, over the investment's useful life.
Average Book Value of Investment: Typically calculated as the average of the initial investment cost and the residual (salvage) value at the end of its useful life. For example, for an initial cost C and salvage value S over n years: Average Investment = (C + S) / 2.
Book Value of Net Investment (at Start of Period): The asset's book value at the beginning of the specific accounting period, which is its original cost minus accumulated depreciation up to that point.

Extended Practical Example

Using the data from the original example: an initial investment of $200 with a book value of$ 100 at the start of year 5 and a net income of $50 in year 5.

Period-Specific ARR Calculation (as in original text): $R.O.R_{\text{Year 5}} = \frac{\$50}{\$100} = 0.5 = 50\%$
Average ARR over Entire Life (assuming these are the only figures provided):
- Assumptions: Let's assume the investment has a 5-year life with a salvage value of $0 at the end (since book value depreciated to$ 100 by end of year 4, it may not be $0, but this is an illustrative assumption).
- Average Annual Net Income: Need total income over 5 years. We only have year 5 income ($50). This highlights a limitation—period-specific ARR does not equal the project's average ARR unless the net income is constant.
- Average Investment: (Initial Book Value + Salvage Value) / 2 = ($200 + $0) / 2 = $100.
- Illustrative Project ARR: If the $50 net income in year 5 were representative of the annual average, the project's average ARR would be `($ 50 / $100) = 50%`.

Simple ARR Calculation Example

The Accounting Rate of Return formula can be applied with this straightforward scenario:

Scenario:
A company made an initial investment of 200 five years ago. The book value of the investment depreciated to 100 at the end of year 4. Net income related to the investment in year 5 was 50.

Calculation: $ARR = \frac{\text{Net Income}}{\text{Book Value at Start of Period}} = \frac{50}{100} = 0.5 = 50\%$

Interpretation: The investment generated a 50% return relative to its depreciated book value during year 5.

Source: engineeringtoolbox.com