Calculating Compound Annual Growth Rate (CAGR): Step-by-Step

The Compound Annual Growth Rate (CAGR) is a measure of the annual growth rate of an investment or asset over a specified period, assuming that the investment has been compounding over that time frame. It provides a smoothed annualized rate of return, which takes into account the compounding effect. Here's a step-by-step guide on how to calculate CAGR:

Formula for CAGR:

The formula for calculating CAGR is as follows:

$CAGR = \left(\frac{EV}{BV}\right)^{\frac{1}{n}} - 1$

Where:

• CAGR is the Compound Annual Growth Rate.
• EV is the ending value or the final value of the investment or asset.
• BV is the beginning value or the initial value of the investment or asset.
• n is the number of years over which the growth occurred.

Step-by-Step Calculation:

1. Determine the Beginning and Ending Values:

   • Identify the initial value (BV) of the investment or asset at the beginning of the period.
   • Determine the final value (EV) of the investment or asset at the end of the period.

2. Determine the Number of Years (n):

   • Calculate the number of years (n) over which the growth occurred. This is the time period between the initial and final values.

3. Apply the CAGR Formula:

   • Plug the values of EV, BV, and n into the CAGR formula.
   • Calculate the expression inside the parentheses first ($EV/BV$), and then raise the result to the power of $\frac{1}{n}$.
   • Subtract 1 from the result to get the CAGR.

Example:

Let's say you invested $1,000 in a stock, and after 5 years, it has grown to $1,500. To calculate the CAGR:

• Beginning Value (BV) = $1,000
• Ending Value (EV) = $1,500
• Number of Years (n) = 5

Using the CAGR formula:

$CAGR={\left(\frac{1,500}{1,000}\right)}^{\frac{1}{5}}-1$

1. Calculate the expression inside the parentheses: $\frac{1,500}{1,000} = 1.5$
   
2. Calculate the CAGR: $CAGR=1.5^{\frac{1}{5}}-1$

Now, calculate the CAGR:

$CAGR = 0.1487 \text{ or } 14.87\%$

So, the CAGR for this investment over 5 years is approximately 14.87%.

CAGR is a valuable metric for evaluating the annualized growth rate of investments, particularly when comparing different investments or assessing the performance of assets over time. It provides a more accurate representation of the annual growth, accounting for the compounding effect.