Compound Annual Growth Rate (CAGR) Guide: Formula, Excel Models & Real Examples

1. What Is Compound Annual Growth Rate (CAGR)? In finance and corporate strategy, **Compound Annual Growth Rate (CAGR)** is the geometric progression ratio that measures the constant rate of return required for an asset to grow from its initial starting value to its final terminal balance over multiple annual periods.

Where: - $\text{Ending Value}$ = Terminal value of the portfolio or asset - $\text{Beginning Value}$ = Initial invested capital or starting balance - $t$ = Total holding period duration in years

Unlike simple or arithmetic averages that assume returns are independent and isolated, CAGR recognizes the power of exponential compounding—where returns earned in Year 1 generate incremental gains in Year 2 and beyond.

2. The Mathematical CAGR Formula Explained Consider the fundamental compounding equation:

Solving algebraically for $r$ (the annualized compound growth rate): 1. Divide both sides by $\text{Beginning Value}$: $$(\text{Ending Value})/(\text{Beginning Value)} = (1 + r)^t$$ 2. Raise both sides to the power of $(1)/(t)$: $$\left((\text{Ending Value})/(\text{Beginning Value)}\right)^{(1)/(t)} = 1 + r$$ 3. Subtract 1 to isolate $r$: $$r = \left((\text{Ending Value})/(\text{Beginning Value)}\right)^{(1)/(t)} - 1$$

3. Step-by-Step Numerical Example Suppose an entrepreneur purchases a commercial real estate property or equity portfolio for **$50,000**. Five years later, the asset is appraised at **$120,000**.

1. Calculate the Total Return Multiple: $$\text{Multiple} = ($120,000)/($50,000) = 2.40\times$$ 2. Apply the 5-Year Time Horizon ($t = 5$): $$2.40^{(1)/(5)} = 2.40^{0.20} = 1.19135$$ 3. Subtract 1: $$\text{CAGR} = 1.19135 - 1 = 0.19135 = \mathbf{19.14\%}$$

The investment yielded a true compound annual growth rate of 19.14% per year.

4. CAGR vs. Arithmetic Mean: Why Volatility Drag Distorts Returns A frequent trap among corporate analysts is using arithmetic average return (AAR) instead of CAGR. The arithmetic mean consistently overstates realized investment performance due to **volatility drag**.

In the volatile scenario, the investor has exactly $0.00 in net profit, yet the arithmetic average claims a +25% return. CAGR accurately reflects the real economic truth: 0.00%.

5. Calculating Doubling Time & The Rule of 72 To determine how many years an investment takes to double at a given CAGR, use the logarithmic doubling formula:

For fast mental calculation, the Rule of 72 provides a close approximation:

• At 8.0% CAGR: $72 \div 8 = 9.0$ years to double.
• At 12.0% CAGR: $72 \div 12 = 6.0$ years to double.

6. How to Calculate CAGR in Excel & Google Sheets In spreadsheet software, you can calculate CAGR using either of two formulas:

1. Direct Formula: `=(End_Cell / Start_Cell)^(1 / Years_Cell) - 1` 2. Using the RRI Function: `=RRI(nper, pv, fv)` Example: `=RRI(5, 50000, 120000)` returns `19.14%`.