Compound Annual Growth Rate

Compound Annual Growth Rate (CAGR) is the magic wand of investment metrics. Imagine you're on a roller coaster of an investment journey, with thrilling highs and stomach-churning dips. The CAGR is the smooth, straight line that tells you the average yearly growth rate from your starting point to your destination, as if the ride had been a calm, steady ascent instead. It is a hypothetical measure that effectively irons out the market's volatility to reveal a single, representative growth number. For believers in value investing, the CAGR is indispensable. It cuts through the short-term noise and helps evaluate the long-term performance of an investment, which is crucial for assessing the real growth of a business or your portfolio. This focus on a smoothed, long-term rate of compounding is precisely what helps investors like Warren Buffett gauge the underlying success of their holdings over many years.

Think of CAGR as the great equalizer in the world of investment analysis. Its primary power lies in its ability to make performance comparable. Did your stock in a tech startup outperform your cousin’s investment in a blue-chip company over the last five years? Calculating the CAGR for both will give you a clear, apples-to-apples answer, even if the investments had very different journeys year to year. But its use extends far beyond your personal portfolio. Value investors use CAGR to analyze the health and growth of a business itself by applying it to key metrics:

• Sales Growth: What is the CAGR of a company's revenue over the last decade? A steady, positive number is a great sign.
• Earnings Growth: Are the profits, often measured by earnings per share (EPS), growing consistently? CAGR tells the story.
• Dividend Growth: For income-focused investors, tracking the CAGR of dividends shows if the company is increasingly rewarding its shareholders.

In essence, CAGR provides a standardized lens to measure the growth of almost anything over time, from a single stock's share price to the gross domestic product of an entire country.

While it might sound intimidating, calculating CAGR is straightforward once you break it down. You don't need a PhD in mathematics, just a basic calculator.

The formula looks like this: CAGR = ( (Ending Value / Beginning Value) ^ (1 / Number of Years) ) - 1 Let's unpack that piece by piece:

1. Step 1: Find the Growth Factor. Divide the final value of your investment (Ending Value) by its initial value (Beginning Value). This tells you how many times your money has multiplied.
2. Step 2: Annualize the Growth. Raise the result from Step 1 to the power of (1 divided by the Number of Years). This mathematically complex-sounding step is what “smooths out” the growth into a yearly figure. On most calculators, you'll use the '^' or 'xʸ' button.
3. Step 3: Convert to a Percentage. Subtract 1 from the result of Step 2, and then multiply by 100 to get the final percentage rate.

Let's say you invested $10,000 into the fictional “Capipedia Value Fund” five years ago. Today, your investment is worth $16,105.

1. Step 1: Find the Growth Factor.

$16,105 / $10,000 = 1.6105

1. Step 2: Annualize the Growth. The time period is 5 years, so we need to calculate 1 / 5 = 0.2.

1.6105 ^ 0.2 ≈ 1.10

1. Step 3: Convert to a Percentage.

1.10 - 1 = 0.10

  0.10 x 100 = 10%

The CAGR of your investment is 10%. This means that, on average, your money grew by 10% every single year for five years to reach its final value. A quick mental check using the Rule of 72 (72 / 10 = 7.2 years) tells you that at this rate, your money would double in about 7.2 years.

This is one of the most important distinctions in finance. New investors often confuse CAGR with the simple average return (also known as the arithmetic mean), but they are worlds apart. The simple average can be dangerously misleading because it ignores the effect of compounding. Let's look at a volatile two-year investment:

• You invest $100.
• Year 1: The investment soars by +50%. Your $100 becomes $150.
• Year 2: The investment crashes by -50%. Your $150 becomes $75.
• Simple Average Return: (50% - 50%) / 2 = 0%. This suggests you broke even.
• CAGR: ( ($75 / $100) ^ (1 / 2) ) - 1 = (0.75 ^ 0.5) - 1 ≈ -0.134, or -13.4%.

The CAGR correctly shows that you actually lost 13.4% per year. The simple average completely failed to capture the painful reality of your loss. This is because CAGR is a geometric mean, which properly accounts for volatility and the compounding base from one year to the next.

For the value investor, CAGR is a trusted ally. Since value investing is a long-term game, we need tools that measure performance over the long haul. CAGR is perfect for this. It helps us answer fundamental questions about a business:

• Has this company demonstrated a consistent ability to grow its earnings over the last 5, 10, or 20 years?
• How does its growth compare to its direct competitors?
• Is the current return on investment (ROI) an anomaly, or is it in line with its long-term CAGR?

By focusing on the smoothed, annualised growth rate, an investor can better judge the quality and consistency of a company's management and business model, separating truly great businesses from those just having a lucky year.

As powerful as CAGR is, it's not a crystal ball. Remember these key points:

• It's Historical: CAGR tells you what has happened in the past. It offers no guarantee of future performance.
• It's Sensitive to Endpoints: The result can be skewed if your start or end date happens to fall on a day of an extreme market high or low. It's always wise to calculate CAGR over several different time frames.
• It Assumes Reinvestment: The basic CAGR formula for a stock doesn't include the impact of dividends. For a truly accurate picture of total return, you must assume dividends were reinvested when calculating your Ending Value.

Ultimately, CAGR is a single number that tells a big story. Use it to understand the past, compare opportunities, and build a clearer picture of an investment's journey. But always use it as part of a broader analysis, not as the sole reason to buy or sell.