compound_annual_growth_rate_cagr [CapiPedia]

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======Compound Annual Growth Rate (CAGR)======
Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period longer than one year. Think of it as the steady, imaginary rate at which an investment would have grown if it grew at the same rate every single year and the profits were reinvested at the end of each year. While real-world returns jump up and down, CAGR smooths out this [[Volatility]] to give you a single, easy-to-understand number that represents the overall growth. It's a foundational tool in [[Value Investing]] because it helps you look past short-term noise and measure the long-term performance of a business's [[Revenue]], profits, or an investment's value. It answers the simple but powerful question: "If my investment grew at a perfectly steady pace, what would that pace be?" This makes it incredibly useful for comparing the performance of different investments, like stocks or mutual funds, over time.
===== Why CAGR Matters to a Value Investor =====
For a value investor, CAGR is more than just a formula; it's a lens for assessing long-term business quality. [[Warren Buffett]] didn't build his fortune on one-year wonders. He focused on businesses that could compound capital at high rates over decades. CAGR is the perfect tool for this kind of analysis. It allows you to:
  * **Compare Apples to Oranges:** How do you compare a stock you've held for 3 years against one you've held for 10? CAGR puts them on a level playing field, showing the annualised growth rate for each.
  * **Cut Through the Noise:** A company's earnings might spike one year and dip the next. CAGR smooths these bumps, revealing the underlying growth trend of the business. Is the company truly growing its intrinsic value, or was last year a fluke?
  * **Set Realistic Expectations:** By looking at the historical CAGR of a company's [[Earnings per Share (EPS)]] or the broader market, you can form more realistic expectations for future returns, a cornerstone of disciplined investing.
===== Calculating CAGR: A Simple Guide =====
You don't need a math Ph.D. to calculate CAGR. The formula looks intimidating, but the concept is straightforward.
==== The Formula ====
CAGR = (Ending Value / Beginning Value)^(1 / Number of Years) - 1
==== A Practical Example ====
Let's say you invested $10,000 in a company, and after 5 years, your investment is worth $16,105. The annual returns were all over the place, but you just want to know the smoothed-out annual growth.
  - **Step 1: Divide the Ending Value by the Beginning Value.**
    * $16,105 / $10,000 = 1.6105
  - **Step 2: Raise the result to the power of (1 / Number of Years).**
    * The period is 5 years, so the exponent is 1/5, or 0.2.
    * 1.6105 ^ 0.2 = 1.10 (Most calculators have a `^` or `x^y` button for this)
  - **Step 3: Subtract 1 from the result.**
    * 1.10 - 1 = 0.10
  - **Step 4: Convert to a percentage.**
    * 0.10 x 100 = 10%
So, your investment's CAGR was 10%. It grew //as if// it had returned exactly 10% every year for five years.
===== The Pitfalls of CAGR: What It Doesn't Tell You =====
CAGR is a fantastic tool, but it's not a crystal ball. It's a simplified representation of the past and has important limitations.
  * **It Hides Risk and Volatility:** CAGR is a smooth line, but the journey is almost always a bumpy ride. Two investments could have the same 10% CAGR over a decade. One might have grown steadily, while the other experienced wild swings, including a 50% crash in the middle. CAGR won't show you this difference in risk, which is a crucial factor for any investor.
  * **It's a Hypothetical Number:** Remember, CAGR is an //imaginary// constant rate of return. Your investment did not actually grow by that exact percentage each year. It's a descriptive metric, not a reflection of the actual annual [[Return on Investment (ROI)]].
  * **It's Sensitive to Start and End Dates:** The calculated CAGR can change dramatically depending on the time frame you choose. A company's 5-year CAGR might look amazing if you start measuring from a market bottom, but terrible if you start from a market peak. Always consider the context of the period you're analysing.
===== CAGR vs. Average Annual Growth Rate (AAGR) =====
Don't confuse CAGR with the simple Average Annual Growth Rate (AAGR). AAGR is calculated by taking the average of the growth rates for each year. This method can be wildly misleading because it ignores the effects of compounding.
==== A Cautionary Tale ====
Imagine an investment starts at $100.
  * Year 1: It grows 100% to $200.
  * Year 2: It falls 50% back to $100.
  * **AAGR Calculation:** (100% - 50%) / 2 = 25% per year. This suggests you made a handsome profit!
  * **CAGR Calculation:** ($100 / $100)^(1/2) - 1 = 0% per year. This correctly shows that you broke even over the two years.
Always use CAGR for measuring multi-year investment returns. It's the only method that accurately accounts for the power (and sometimes pain) of compounding. While a more complex metric like the [[Internal Rate of Return (IRR)]] is needed to account for cash flows in and out of an investment, CAGR remains the go-to metric for a simple, powerful measure of point-to-point growth.