Rate of Return Calculator
Calculate the rate of return for an investment using our ROR calculator.
Rate of Return:
Returns Over Time
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Joseph Rich holds a Bachelor's degree in economics and Master's degree in finance, and specializes in economics and investing analysis.
How to Calculate the Rate of Return
The rate of return (ROR) is the compounded rate earned over an investment’s life. It assumes a constant compounded growth rate, even though the investment probably didn’t grow at a constant rate.
The ROR can be positive or negative and can be calculated on any type of asset as long as there is a beginning and ending value and a time period. You can use the rate of return calculator above to calculate ROR if there are no cash flows during the time period.
Rate of Return Formula
There are two rate of return formulas. The first formula can be used only if the rate of return is compounded annually, while the second Rate of Return formula can be used for any growth compounds in a year.
Rate of Return Formula
Where:
BV = initial value
EV = final value
n = number of years
Rate of Return Formula with Regular Growth Compounding
Where:
BV = beginning value
EV = ending value
C = number of times growth compounds in period
n = number of years
You can see that with annual compounding (C = 1), the formulas remain the same. So if there is annual compounding, either formula can be used. But with any other frequency of compounding, only the second formula can be used.
It’s easiest to understand these formulas with an example. Let’s calculate the rate of return on an investment that started with $10,000 and ended at $30,000 12 years later.
We will assume annual compounding (C = 1) in the first example and monthly compounding (C = 12) in the second example.
Annual Compounding
Monthly Compounding
Here, we see that the monthly compounded rate of return is less than the annual compounded rate of return.
In both examples, the starting and ending points are the same, and since a monthly compounded rate compounds more often than an annually compounded rate, the monthly compounded rate must be slightly lower than the annually compounded rate to calculate the same ending value.
This will always hold true. The more frequent the compounding, the lower the rate of return. In this calculator, the compounding options are (from most to fewest number of times growth compounds in a year) continuous, daily, monthly, quarterly, semiannually, and annually.
ROR vs. CAGR, ROI & ROE
The ROR calculator and the CAGR calculator both yield the same result. They both have the same inputs of a beginning value, ending value, and time period in years, and compounding frequency.
The rate of return is sometimes used for only a one-year period. In this case, it would differ from the CAGR in that the CAGR annualizes the growth rate of a period of more than a year. However, in the calculator above, we use the rate of return and compounded annual growth rate interchangeably.
The rate of return can also be confused with the return on investment (ROI). The return on investment does not annualize the growth rate, and it does not take compounding into effect. Instead, it shows what the total return has been over the entire period.
The annual and monthly compounding examples above will produce the same return on investment value using the ROI calculator.
The formula for the ROI is shown below, and we can use it to calculate the ROI for our earlier example:
where:
BV = beginning value
EV = ending value
If we plug our values into the formula, we come up with an ROI of 200%.
The ROI calculator will calculate this answer as well, and it will also calculate the annualized ROI, which is the same as the rate of return.
There is also another calculator that calculates return as a percentage of equity. This is most often used for a business reporting to its shareholders how much net income it earned compared to the amount of total shareholder’s equity.
It is simply found by taking net income and dividing it by shareholder’s equity. The return on equity calculator will calculate these results.
Accounting for Discounted Cash Flow and Internal Rate of Return
The discounted cash flow and internal rate of return calculations are methods that account for compounding and can help a company determine if the rate of return on a particular investment is high enough for the owners of the business.
The discounted cash flow model takes future streams of cash inflows/outflows and calculates their present value using a certain discount rate. The discount rate is typically a company’s required rate of return.
So if a company’s shareholders seek a 10% return on investments, the company will set its discount rate at 10%.
The company can use this to determine if an investment makes sense or not. If the sum of all the discounted cash flows (including the cost of the initial investment) is greater than $0, the company should move forward with the project.
It will provide at least a 10% rate of return. However, if the amount is negative, it will fail to yield a 10% rate of return, and the business would be better off looking for a more profitable investment.
The internal rate of return (IRR) is the rate that sets the net present value (NPV) of a stream of cash flows for a project or investment to $0. The higher the IRR, the more profitable the project is.
The IRR needs to be higher than the company’s required rate of return in order for the company to move forward with the project.
The IRR is essentially the compounded annual growth rate that a project earns. If a project has an initial investment of $1,000 and earns a 10% internal rate of return for 5 years, it is equivalent to earning 10% over 5 years.
While this 10% is not earned consistently each year, the IRR just smooths out the return.