# Compound Annual Growth Rate (CAGR)

## What is the Compound Annual Growth Rate (CAGR)?

The Compound Annual Growth Rate (CAGR) is a measurement used to assess the annualized growth rate of an investment or metric over a specified period longer than one year.

It represents the steady pace of growth that would produce the same cumulative result if compounding occurred annually. CAGR helps smooth out volatility in growth rates over time and helps illustrate the performance of a given investment to make objective comparisons.

## What Does the CAGR Measure?

CAGR measures the annual growth as if growth was constant over the analysis period. It assumes reinvestment of returns and compounding of previous gains each period.

For example, an investment that grew from \$100 to \$150 over 2 years would have a CAGR of 22.5%. This is because a 22.5% compound growth each year would turn \$100 into \$150 over the 2-year period.

CAGR helps normalize returns over time, smoothing out volatility. An investment could grow 50% one year but decline 25% the next. The arithmetic average return would be 12.5%, but CAGR considers the compounding effect, which lowers the return.

## Calculating the CAGR

It is calculated by using the following formula:

CAGR = (End Value / Start Value)(1/N) – 1

Where:

• End Value = Ending value of the investment after N years.
• Start Value = Beginning value.
• N = Number of years considered for the analysis.

For example, if an investment grew from \$10,000 to \$15,000 over 5 years:

CAGR = (\$15,000 / \$10,000)(1/5) – 1 = 8%

This means that the investment had an 8% CAGR over that 5-year period.

### CAGR Example

ABC Company had annual revenues of \$100 million five years ago. In the current year, revenues reached \$150 million.

CAGR = (\$150 million / \$100 million)(1/5) – 1 = 8%

This means that revenues grew at a compound annual growth rate (CAGR) of 8% over this 5-year period.

ABC Company can compare their 8% revenue CAGR to industry averages and specific competitors to evaluate their performance.

The historical 8% CAGR could also provide an estimated growth rate assumption for revenue projections.

## Why Use the Compounded Annual Growth Rate

CAGR serves various useful purposes in financial analysis, including the following:

• Assess Growth Performance: It provides a straightforward way to evaluate and compare growth rates over time across various assets.
• Project Future Value: CAGR can be used to project the expected future value of an investment based on past growth trends.
• Benchmark to Goals: Companies can use the compounded annual growth rate as a benchmark for their performance to incorporate this variable to set organizational growth goals.
• Smooth Volatility: CAGR normalizes spikes and dips in individual annual growth rates to illustrate an underlying steady rate.
• Model Forecasts: Historical CAGR figures serve as assumptions for forecasting models to project future performance.

## CAGR vs. Average Return

CAGR differs from calculating a simple arithmetic average return on investment (ROI) as this metric adjusts for compounding effects over time.

For example, consider two investments with the following annual returns over 3 years:

 Year Investment 1 Investment 2 1 10% 40% 2 -20% -20% 3 20% 10%

Investment 1 has an average return of 3.33% derived from (10% + -20% + 20%) / 3

Investment 2 has an average return of 10% derived from (40% + -20% + 10%) / 3

However, the CAGR figures are:

Investment 1 CAGR: 1.83%

Investment 2 CAGR: 7.20%

The CAGR shows the impact of compounding and reflects a more accurate annual growth rate in both investments.

## Limitations of the CAGR

While useful, it does have some limitations that analysts must consider:

• Smooth Volatility: It may mask investment risk if high volatility exists during the measurement period.
• Assumes Reinvestment: CAGR calculations assume that profits are reinvested each period, which may not be true in reality.
• Varies with Timeframes: Its figures can differ significantly depending on the start and end dates used.
• Ignores External Changes: It only considers growth and does not reflect external contributions or withdrawals.
• Not Forward Looking: Historical CAGR is not a guarantee of similar future growth rates.

## Real-World Applications of the CAGR

The compound annual growth rate has several common business and investing applications, including the five mentioned below:

CAGR is useful for evaluating past growth performance. Companies can compare historical revenue or profit CAGR to industry averages or growth goals. Changes in CAGR over time can indicate improving or worsening trends.

2. Projection of Future Values

The historical CAGR of metrics like profits or market size can serve as assumptions to forecast future values. CAGR provides an expected growth rate that can be used to project results.

3. Investment Analysis

For investors, CAGR reveals a “smoothed” annual return rate on assets like stocks, bonds, or portfolio investments. It measures performance by adjusting for compound growth over time.

4. Benchmarking Investment Options

An investor can compare CAGR figures across multiple investments to gauge historical returns. Higher CAGRs indicate better compound growth performance across different investments.

5. Evaluating Fund Managers

CAGR provides a simple metric to evaluate investment fund managers. Comparing a manager’s CAGR to pre-selected benchmarks reveals if they have historically beaten or underperformed these returns.

## Best Practices to Consider When Using CAGR

To effectively apply CAGR:

• Use consistent time frames when comparing CAGRs for multiple investments or businesses.
• Confirm that its figures align with intuition. Significant deviations could indicate unrealistic assumptions.
• Reference CAGR trends over sequential time frames rather than a single snapshot figure.
• Consider both CAGR and the standard deviation of returns for insights into growth and volatility.
• Avoid placing excessive weight on historical CAGR when projecting future values or performance.

## The Bottom Line

CAGR measures annualized growth over a multi-year horizon, adjusting for compounding. It offers a straightforward way to evaluate growth, smooth volatility, project future values based on historical trends, and compare performance across investments or financial metrics.

While the CAGR calculation relies on various assumptions, it remains a widely used indicator of growth. Applying CAGR appropriately provides useful insights into both historical growth and potential future trajectory.