Understanding the Calculation of Compound Annual Growth Rate (CAGR)- A Comprehensive Guide
How is Compound Annual Growth Rate (CAGR) Calculated?
The Compound Annual Growth Rate (CAGR) is a financial metric used to measure the average annual growth rate of an investment over a specific period of time. It is widely used to compare the performance of different investments or to track the growth of a business. Calculating the CAGR provides a more accurate representation of the investment’s growth than simply looking at the final value, as it takes into account the compounding effect of reinvesting the returns over the entire period.
To calculate the CAGR, you need the following information:
1. Initial value: The value of the investment at the beginning of the period.
2. Final value: The value of the investment at the end of the period.
3. Number of years: The total number of years over which the investment has grown.
The formula for calculating the CAGR is as follows:
CAGR = [(Final Value / Initial Value)^(1/Number of Years)] – 1
Let’s break down the formula and understand how it works:
1. Divide the final value by the initial value: This step gives you the growth factor, which represents how much the investment has increased in value.
2. Raise the growth factor to the power of 1 divided by the number of years: This step calculates the average annual growth rate. By raising the growth factor to the power of 1 divided by the number of years, you are essentially finding the geometric mean of the growth factor over the entire period.
3. Subtract 1 from the result: This step converts the growth factor into a percentage, representing the average annual growth rate.
For example, let’s say you invested $10,000 in a stock and after 5 years, it is worth $20,000. To calculate the CAGR, you would use the following formula:
CAGR = [(20,000 / 10,000)^(1/5)] – 1
CAGR = [2^(1/5)] – 1
CAGR ≈ 0.1487 or 14.87%
This means that your investment grew at an average annual rate of 14.87% over the 5-year period.
The CAGR is a valuable tool for investors and businesses, as it allows for a more accurate comparison of investments or growth rates. However, it is important to note that the CAGR assumes that the investment is compounded annually and that no additional investments or withdrawals are made during the period.
