How to Calculate Compound Annual Growth Rate (CAGR): A Comprehensive Guide for Investors and Businesses

What is Compound Annual Growth Rate (CAGR)?

Compound Annual Growth Rate (CAGR) is a financial metric that measures the annual growth rate of an investment or a company’s revenue over multiple years. It assumes that any profits are reinvested at the end of each period, which makes it more reflective of real-world investment scenarios compared to other metrics like Average Annual Growth Rate (AAGR) or Internal Rate of Return (IRR).

Unlike AAGR, which simply averages annual growth rates without considering compounding, CAGR provides a smoother and more consistent view of growth. Unlike IRR, which is more complex and sensitive to cash flow timing, CAGR offers a straightforward way to compare different investments or company performances.

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The CAGR Formula

The formula for calculating CAGR is straightforward:

[ \text{CAGR} = \left(\frac{\text{Ending Value}}{\text{Beginning Value}}\right)^{\frac{1}{\text{Number of Years}}} – 1 ]

Here’s what each component means:

• Ending Value: The final value of the investment or revenue at the end of the period.

• Beginning Value: The initial value of the investment or revenue at the start of the period.

• Number of Years: The total number of years over which the growth is being measured.

Step-by-Step Calculation of CAGR

Calculating CAGR involves a few simple steps:

1. Divide the Ending Value by the Beginning Value:

   [

   \frac{\text{Ending Value}}{\text{Beginning Value}}

   ]

2. Raise the result to the power of one divided by the Number of Years:

   [

   \left(\frac{\text{Ending Value}}{\text{Beginning Value}}\right)^{\frac{1}{\text{Number of Years}}}

   ]

3. Subtract one from the result:

   [

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   \left(\frac{\text{Ending Value}}{\text{Beginning Value}}\right)^{\frac{1}{\text{Number of Years}}} – 1

   ]

4. Multiply by 100 to convert to a percentage:

   [

   \left(\left(\frac{\text{Ending Value}}{\text{Beginning Value}}\right)^{\frac{1}{\text{Number of Years}}} – 1\right) \times 100

   ]

Example

Suppose you invested $1,000 in a stock that grew to $2,500 over five years.

1. Divide $2,500 by $1,000: (2.5)

2. Raise 2.5 to the power of (1/5): (2.5^{0.2} \approx 1.148698)

3. Subtract 1: (1.148698 – 1 = 0.148698)

4. Multiply by 100: (0.148698 \times 100 = 14.87\%)

So, the CAGR is approximately 14.87%.

Handling Non-Standard Time Periods

Sometimes investments span periods that are not whole numbers of years. To handle such cases, you need to convert days into years and adjust your calculation accordingly.

For example, if an investment lasted for 3 years and 6 months (or 3.5 years), you would use this adjusted number in your formula.

Applications and Benefits of CAGR

CAGR has several practical applications:

• Comparing Investment Performance: It allows investors to compare different investments on an apples-to-apples basis.

• Forecasting Future Values: By assuming a constant annual growth rate, businesses can forecast future revenues or investment values.

• Evaluating Company Revenue Growth: Companies use CAGR to evaluate their revenue growth over multiple years.

The benefits include:

• Smoothing Out Volatility: CAGR provides a consistent annualized rate of return, smoothing out year-to-year fluctuations.

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  Consistent Comparison: It enables consistent comparisons between different investments or company performances.

Limitations of CAGR

While CAGR is a valuable metric, it has some limitations:

• Assumption of Constant Growth Rates: It assumes that growth rates remain constant over the entire period, which may not always be true.

• Failure to Account for Non-Performance-Related Changes: CAGR does not account for changes in value due to non-performance-related factors such as market conditions or external events.

• Volatility Masking: It may mask the actual volatility of an investment by averaging out highs and lows.

Comparative Statistics and Examples

To illustrate how CAGR works in practice, let’s compare two investments:

Investment A

• Initial Value: $10,000

• Final Value after 5 years: $20,000

Investment B

• Initial Value: $5,000

• Final Value after 5 years: $15,000

Using the CAGR formula:

For Investment A:

[

\left(\frac{20,000}{10,000}\right)^{\frac{1}{5}} – 1 = 14.87\%

]

For Investment B:

[

\left(\frac{15,000}{5,000}\right)^{\frac{1}{5}} – 1 = 14.87\%

]

Both investments have the same CAGR despite different starting values.

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