How to Calculate CAGR Manually

When it comes to evaluating investment performance, one metric that stands out for its simplicity and effectiveness is the Compound Annual Growth Rate (CAGR). This financial indicator provides a smoothed annual growth rate over a specified period, which is especially useful for comparing different investments or assessing the growth of an investment over time. In this article, we'll walk through the manual calculation of CAGR, breaking down the process into digestible steps and offering practical examples to illustrate each point. By the end, you'll have a clear understanding of how to compute CAGR on your own and interpret the results for better investment decisions.

Understanding CAGR

CAGR represents the rate at which an investment grows annually to reach a given end value from its initial value, assuming the growth rate is compounded over the period. Unlike simple percentage growth calculations, CAGR provides a more accurate picture of an investment's performance by accounting for the effect of compounding.

The CAGR Formula

The formula for calculating CAGR is straightforward:

$\text{CAGR}={\frac{\text{Ending Value}}{\text{Beginning Value}}}^{\frac{1}{\text{Number of Years}}}-1$CAGR=Beginning ValueEnding Value​Number of Years1​−1

Here’s what each term means:

• Ending Value: The final value of the investment or asset at the end of the period.
• Beginning Value: The initial value of the investment or asset at the start of the period.
• Number of Years: The total duration of the investment period in years.

Step-by-Step Calculation

1. Identify Values and Period

   Suppose you have an investment that started at $1,000 and grew to $1,800 over 5 years. You need to determine the CAGR for this investment.

2. Apply the Formula

   Plug the values into the CAGR formula:

   $\text{CAGR}={\frac{1800}{1000}}^{\frac{1}{5}}-1$CAGR=10001800​51​−1

3. Perform the Calculation

   • Divide the ending value by the beginning value: $\frac{1800}{1000}=1.8$10001800​=1.8
   • Take the nth root of the result (where n is the number of years): $1.8^{\frac{1}{5}}\approx 1.1487$1.851​≈1.1487
   • Subtract 1 from the result: $1.1487-1=0.1487$1.1487−1=0.1487

   The CAGR is approximately 14.87%.

Practical Example: Investment in Stocks

Let’s say you invested in a stock that was worth $50 per share five years ago and is now worth $120 per share. To find the CAGR:

1. Plug Values into Formula

   $\text{CAGR}={\frac{120}{50}}^{\frac{1}{5}}-1$CAGR=50120​51​−1

2. Calculate

   • Divide: $\frac{120}{50}=2.4$50120​=2.4
   • Take the 5th root: $2.4^{\frac{1}{5}}\approx 1.1885$2.451​≈1.1885
   • Subtract 1: $1.1885-1=0.1885$1.1885−1=0.1885

   The CAGR is approximately 18.85%.

Why CAGR Matters

CAGR is invaluable because it provides a smoothed annual growth rate, making it easier to compare the performance of different investments regardless of the volatility within the period. It helps investors understand the average rate at which their investment has grown, which is crucial for long-term planning and decision-making.

Limitations of CAGR

While CAGR is a useful metric, it has its limitations:

• Assumption of Constant Growth: CAGR assumes that the growth rate is constant over the entire period, which may not reflect real-world fluctuations.
• No Insight into Volatility: It does not provide information about the volatility or variability of returns, which can be important for assessing risk.

Calculating CAGR in Excel

If manual calculations seem cumbersome, Excel provides a convenient way to calculate CAGR using the RATE function:

1. Open Excel and Enter Data

   Enter the beginning value, ending value, and number of years into separate cells.

2. Use the Formula

   The formula in Excel would look like this:

   $\text{=RATE(Number of Years, 0, -Beginning Value, Ending Value)}$=RATE(Number of Years, 0, -Beginning Value, Ending Value)

   For the stock example: $\text{=RATE(5, 0, -50, 120)}$=RATE(5, 0, -50, 120)

   This will return the CAGR as a decimal, which you can format as a percentage.

Conclusion

Understanding and calculating CAGR manually equips you with a powerful tool for evaluating investment performance. By applying the formula and interpreting the results, you can gain insights into how well your investments are performing and make more informed financial decisions. Whether you’re a seasoned investor or new to the game, mastering CAGR will enhance your ability to assess growth and plan for the future effectively.