Formula to Calculate CAGR (Compounded Annual Growth Rate)
CAGR (Compounded Annual Growth Rate) refers to the rate of return that is 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 and it is calculated by dividing the value of the investment available at the period’s end by its beginning value and then raising the resultant to the exponent of the one divided by a number of the years and from further resultant subtract one.
The formula 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.
where Absolute ROI = (Ending value – Beginning value) / Beginning value
Calculation of CAGR (Step by Step)
The compounded annual growth rate can be calculated 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.
- 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
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.
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Use the following data for the calculation of CAGR.
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 = [($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.
Example #2
Let us take an example of an equity portfolio that 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%.
CAGR 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 |
Uses of CAGR
It is important for the analyst to understand the concept of the compounded annual growth rate 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 the 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 article has been a guide to CAGR Formula. Here we learn how to calculate the compounded annual growth rate of the portfolio with examples and a downloadable excel template. You can learn more about financing from the following articles –
- Return on Investment Formula
- Formula of Effective Annual Rate
- Calculation of Growth Rate
- Formula to Calculate Interest Rate
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