Compound Annual Growth Rate (CAGR): A Complete Guide

The Compound Annual Growth Rate, commonly abbreviated as CAGR, is a single, constant rate that describes the rate at which an investment would have grown if it had grown at a steady rate on an annually compounded basis. CAGR is widely used by investors, analysts, and business leaders to compare returns across investments and to measure historical performance in a way that accounts for compounding.

Why CAGR Matters

CAGR compresses a multi-period growth pattern into a single number that is easy to compare. When you want to compare the performance of two investments over different time frames, or evaluate a company's revenue growth without the volatility of year-to-year changes, CAGR provides a normalized view.

The CAGR Formula

The mathematical expression for CAGR is simple and powerful. If you know the beginning value (BV), the ending value (EV), and the number of periods (N in years), the formula is:

CAGR = (EV / BV)^(1 / N) - 1

Expressed in words, you divide the ending value by the beginning value, take the Nth root, and subtract 1 to convert the factor into a percentage growth rate per year.

Step-by-Step Calculation

Step 1: Identify the beginning value and the ending value. Step 2: Count the number of years between the two values. Step 3: Divide EV by BV. Step 4: Raise the result to the power of 1 divided by N. Step 5: Subtract 1 and convert to a percentage.

Example: If you invested $10,000 and after 5 years it became $16,105, then BV = 10,000, EV = 16,105, N = 5. Compute CAGR = (16105 / 10000)^(1/5) - 1 = 1.1 - 1 = 0.10 or 10% per year.

Manual and Excel Calculations

Manual calculation follows the formula. In Excel, use the POWER function or the RATE function. Example with POWER: =POWER(EV/BV,1/N)-1. If EV is in cell B2, BV in B1, and N in B3, the formula is =POWER(B2/B1,1/B3)-1.

Alternatively, use =RATE(N,0,-BV,EV) when cash flows are only the initial investment and the final value; understand that RATE returns a decimal that you multiply by 100 to get a percent.

Practical Examples

Example 1: Stock Investment. You buy shares at $50 and sell five years later for $120. CAGR = (120/50)^(1/5)-1 = (2.4)^(0.2)-1 ≈ 0.190 or 19.0%.

Example 2: Revenue Growth. A company's revenue increases from $2.5 million to $4 million over 3 years. CAGR = (4.0/2.5)^(1/3)-1 ≈ 0.170 or 17.0% per year.

When to Use CAGR

CAGR is appropriate when you need a smoothed annual growth rate over multiple periods and when you assume compounding. It's useful for comparing funds, evaluating business growth over time, modeling financial projections, and summarizing historical returns.

Limitations and Common Pitfalls

CAGR hides volatility because it represents a hypothetical steady growth rate. Two investments with the same CAGR can have very different year-to-year returns and risk profiles. CAGR does not reflect interim cash flows, drawdowns, or sequence-of-returns risk. Avoid using CAGR alone when volatility, periodic withdrawals, or irregular cash flows matter.

CAGR vs. Other Metrics

CAGR is not the same as arithmetic average return or average annual return. The arithmetic mean adds annual returns and divides by years, which ignores compounding. CAGR accounts for compounding and therefore will generally be lower than the arithmetic average when returns vary year to year.

Use CAGR when you want a compounded, smoothed measure. Use the internal rate of return (IRR) when there are multiple cash flows at different times. Use annualized volatility and drawdown metrics to assess risk.

How to Interpret CAGR in Context

A high CAGR indicates strong compounded growth but always inspect the underlying data. Ask whether growth was steady or driven by a single outlier year. Check absolute values: a small base can produce a high CAGR that may be misleading. Consider margins, cash flow, and market factors alongside CAGR.

FAQ

Q: Can CAGR be negative? A: Yes. If the ending value is lower than the beginning value, CAGR will be negative, indicating compounded decline.

Q: Is CAGR suitable for short periods? A: CAGR can be used for any period length but is less informative for very short periods because compounding has limited effect and volatility may dominate.

Q: How do I handle partial years? A: Use fractional values for N. For example, 18 months equals 1.5 years, so use N = 1.5 in the formula.

Quick Checklist Before Relying on CAGR

Confirm the timeline and data accuracy. Verify that there are no significant interim cash flows that alter the analysis. Compare CAGR against volatility measures and absolute returns. Use CAGR with other financial metrics to form a complete picture.

Key takeaway: CAGR is a concise way to express compounded annual growth over time, but it should be used alongside volatility and cash flow analysis to fully understand performance.

Summary

CAGR is a fundamental metric for investors and business analysts. It provides a normalized, compounded annual rate that simplifies comparison across investments and time periods. Learn the formula, practice with real examples, and remember the limitations: CAGR smooths volatility and omits interim cash flows. Combine CAGR with risk and cash flow metrics for better-informed decisions.