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What is CAGR Formula (Compounded Annual Growth Rate)?
The term “CAGR” which is also known as “compounded annual growth rate” refers to the rate of return that has been achieved by an investment by growing from its beginning value to its ending value, based on the assumption that the profits during the tenure of the investment were reinvested at the end of each year. The formula for CAGR is derived by dividing the ending value of an investment by its beginning value, then raise the result to the power of reciprocal of the tenure if investment and then finally subtract one.
Mathematically, Compounded Annual Growth Rate Formula is represented as,
The formula for CAGR can also be expressed by adding one to the absolute return on investment (ROI), then raise the result to the power of reciprocal of the tenure if investment and then finally subtract one.
Mathematically, Compounded Annual Growth Rate Formula is represented as,
where Absolute ROI = (Ending value – Beginning value) / Beginning value
Explanation of the Compounded Annual Growth Rate Formula
The formula for the calculation of CAGR can be derived by using the following steps:
Step 1: Firstly, determine the beginning value of the investment or the money that was invested at the start of the investment tenure.
Step 2: Next, determine the final value of the investment at the end of the tenure of investment or the ending value.
Step 3: Next, determine the tenure of the investment i.e. number years from the start of the investment to the end of the same.
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Step 4: Next, divide the ending value of the investment by the beginning value and then raise the result to the power of reciprocal of the tenure of investment. Finally, subtract from the result and express in percentage terms to derive the Compounded Annual Growth Rate Formula as shown above.
Examples of CAGR Formula (with Excel Template)
Let’s see some simple to advanced examples of Compounded Annual Growth Rate Formula to understand it better.
CAGR Formula – Example #1
Let us take an example of David who invested $50,000 in a portfolio on Jan 1, 2015, and the following portfolio return has been outlined below:
- On Jan 1, 2016, the value of the portfolio stood at $60,000
- On Jan 1, 2017, the value of the portfolio was $73,000
- On Jan 1, 2018, the value of the portfolio was $70,000
- On Jan 1, 2019, the value of the portfolio was $85,000
Based on the given, determine the yearly return and the CAGR for David’s investment portfolio.
Use the following data for the calculation of CAGR Formula.
Return for the 1^{st} year
- Return for 1^{st} year = [(Ending value / Beginning value) – 1] * 100%
- = [($60,000 / $50,000) – 1] * 100%
- = 20.00%
Return for 2^{nd} year
- Return for 2^{nd} year = [($73,000 / $60,000) – 1] * 100%
- = 21.67%
Return for 3^{rd} year
- Return for 3^{rd} year = [($70,000 / $73,000) – 1] * 100%
- = -4.11%
Return for 4^{th} year
- Return for 4^{th} year = [($85,000 / $70,000) – 1] * 100%
- = 21.43%
Now, let us do the calculation of the CAGR in excel based on the given information,
- CAGR Formula = [($85,000 / $50,000) ^{1/4 }-1] * 100%
CAGR will be –
- CAGR = 14.19%
Therefore, the above example shows how CAGR encapsulates all the growth and de-growth during the investment period and provides an average annual growth rate during the investment tenure.
CAGR Formula – Example #2
Let us take an example of an equity portfolio who has value growth such that the absolute return over the period of five years stood at 57%. Do the calculation for the CAGR of the portfolio.
Therefore, the calculation of CAGR of the portfolio can be done as,
- CAGR = [(1 + Absolute ROI) ^{1/ Number of years} – 1] * 100%
- = [(1 + 57%) ^{1/5} – 1] * 100%
CAGR will be –
- CAGR = 9.44%
Therefore, the CAGR of the equity portfolio after five years stood at 9.44%.
Compounded Annual Growth Rate Calculator
You can use the following CAGR Calculator.
Ending Value | |
Beginning Value | |
No. of Years | |
CAGR Formula = | |
CAGR Formula = | [(Ending Value / Beginning Value)^{1/No. of Years}- 1] * 100% | |
[(0 / 0)^{1/0}-1] * 100% = | 0 |
Relevance and Use of CAGR Formula
It is important for the analyst to understand the concept of Compounded Annual Growth Rate Formula because it can be used to calculate the average growth of an investment. Under certain circumstances, the market becomes volatile and as such the year-to-year growth of an investment may appear uneven and erratic. In such a case, the CAGR helps in smoothening the erratic growth rates that are expected due to market volatility and inconsistency.
Another use of CAGR equation is that it can be used for comparison of investments of different types. Nevertheless, the CAGR has its own drawback that by smoothening the erratic returns on investment, the CAGR conceals from the investor the fact of how risky or volatile the portfolio has been during its investment tenure. However, despite the drawback, the CAGR remains a very useful performance indicator for investors and analysts.
Recommended Articles
This has been a guide to CAGR (Compounded Annual Growth Rate) Formula. Here we discuss how to calculate CAGR of the portfolio with examples and downloadable excel sheet. You can learn more about financing from the following articles –
- Portfolio Return Formula
- What Does Rate Formula do in Excel?
- What is Return on Investment Formula?
- Steps to Calculate Percent Error
- Dividend Growth Rate Formula
- Sustainable Growth Rate Calculation
- Required Rate of Return Calculation
- Effective Annual Rate Formula
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