Chartered Financial Analyst specializing in investment performance metrics, simple vs. compound returns, and capital budgeting analysis.
The **Average Rate of Return Calculator** determines the arithmetic mean of the returns generated by an investment over a set period. Unlike the Compound Annual Growth Rate (CAGR), ARR ignores the effects of compounding, providing a straightforward metric for analyzing investment performance. Enter values for any three of the four core parameters (Initial Investment, Final Value, Time Period, or ARR) to solve for the missing one.
Average Rate of Return Calculator
Instructions: Enter values for any three of the four core parameters to solve for the missing one.
ARR Parameters
Average Rate of Return Formula
The Average Rate of Return ($ARR$) is based on the total net profit divided by the time period, then normalized by the initial investment:
Net Profit: $Profit = F_{final} – P_{initial}$
Average Rate of Return ($ARR$):
$$ARR = \frac{Profit / t}{P_{initial}}$$ Formula Source: InvestopediaVariables Explained (P, F, V, Q – Parameters)
- $P_{initial}$ (Initial Investment, $P$): The starting amount of the investment.
- $F_{final}$ (Final Value, $F$): The ending value of the investment after the time period.
- $t$ (Time Period, $V$): The duration of the investment, usually in years.
- $ARR$ (Average Rate of Return, $Q$): The arithmetic average return, calculated as a percentage. (Calculated Value)
Related Investment Performance Calculators
Compare arithmetic return to compound returns for a complete picture:
- Compound Annual Growth Rate Calculator (CAGR)
- Return On Investment Calculator (Simple ROI)
- Future Value Calculator
- Discount Rate Calculator
What is Average Rate of Return?
The **Average Rate of Return (ARR)** is a capital budgeting metric used to estimate the profitability of a potential investment. It’s the simplest measure of investment success because it focuses on the total arithmetic gain without taking into account the time value of money or compounding effects. This makes ARR easy to calculate and understand, particularly for short-term or simple comparison of projects with similar lifespans.
It is important to note that because ARR ignores compounding, it can sometimes present a misleading picture of long-term investment performance compared to metrics like CAGR. However, its simplicity makes it a valuable initial screening tool. A common application is assessing the returns on a fixed asset, such as machinery or real estate, over its useful life.
How to Calculate Average Rate of Return (Example)
Assume an Initial Investment ($P_{initial}$) of \$50,000, which grows to a Final Value ($F_{final}$) of \$75,000 over 5 years ($t$). We solve for the ARR:
- Step 1: Calculate Total Profit
$Profit = F_{final} – P_{initial} = \$75,000 – \$50,000 = \$25,000$.
- Step 2: Calculate Average Annual Profit
$Average Profit = Profit / t = \$25,000 / 5 = \$5,000$ per year.
- Step 3: Apply the ARR Formula
$$ARR = \frac{Average Profit}{P_{initial}} = \frac{\$5,000}{\$50,000} = 0.10$$
The **Average Rate of Return** is $0.10$, or $\mathbf{10.00\%}$.
Frequently Asked Questions (FAQ)
The main weakness is that ARR ignores the time value of money (TVM). It treats a profit earned in Year 1 the same as a profit earned in Year 10, which is financially inaccurate.
Use ARR when you need a simple, quick metric for initial project screening, or when comparing investments with very short, similar timeframes. Use CAGR when evaluating long-term, complex, or publicly traded investments where compounding is essential.
Yes. If the Final Value ($F_{final}$) is less than the Initial Investment ($P_{initial}$), the investment has generated a net loss, resulting in a negative ARR.
For a meaningful analysis, both the Initial Investment and Final Value should be calculated net of all relevant taxes and fees, meaning ARR should typically be calculated on an after-tax basis.