What is CAGR and Its Formula?

 

CAGR is a useful measure of growth over multiple time periods. It represents one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time. It is especially useful for comparing the growth rates of different investments or business metrics over time.

Definition:

CAGR is the mean annual growth rate of an investment over a specified period of time longer than one year. It represents one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time.

Formula:

The formula for CAGR is:

$\text{CAGR} = \left( \frac{\text{Ending Value}}{\text{Beginning Value}} \right)^{\frac{1}{n}} - 1$

Where:

• Ending Value is the value of the investment at the end of the period.
• Beginning Value is the value of the investment at the start of the period.
• n is the number of years.

Steps to Calculate CAGR:

1. Identify the Beginning Value: This is the initial value of the investment or metric at the start of the period.
2. Identify the Ending Value: This is the final value of the investment or metric at the end of the period.
3. Determine the Time Period (n): This is the number of years over which the growth is being measured.
4. Apply the Formula: Use the CAGR formula to calculate the growth rate.

Example:

Suppose you invested $1,000 in a stock, and after 5 years, the investment is worth $2,000. To calculate the CAGR:

1. Beginning Value: $1,000
2. Ending Value: $2,000
3. Number of Years (n): 5

Plugging these values into the formula:

$\text{CAGR} = \left( \frac{2000}{1000} \right)^{\frac{1}{5}} - 1$

$\text{CAGR} = (2)^{0.2} - 1$

$\text{CAGR} = 1.1487 - 1$

$\text{CAGR} = 0.1487$

So, the CAGR is approximately 14.87%.

Interpretation:

• CAGR of 14.87% means that the investment has grown at an average annual rate of 14.87% over the 5-year period.
• CAGR is useful because it smooths out the volatility in period-to-period growth rates, providing a more consistent measure of performance over time.

Importance of CAGR:

1. Comparability: CAGR allows investors and businesses to compare the growth rates of different investments or projects on a like-for-like basis.
2. Performance Measurement: It provides a clear picture of how investments or business metrics have performed over a specific period.
3. Decision Making: Helps in making informed decisions based on the historical growth rates.

See also: app for mutual funds

Limitations:

1. Does Not Account for Volatility: CAGR does not reflect the investment's volatility over the period. Two investments with the same CAGR could have different levels of risk.
2. Past Performance: Like any metric based on historical data, CAGR is not necessarily indicative of future performance.