Compound Annual Growth Rate (CAGR)

What is CAGR?

The compound annual growth rate (CAGR) is the annualized rate at which an investment would have grown from its beginning value to its ending value over a specified period, assuming profits are reinvested and growth is compounded each year. It smooths varying year-to-year returns into a single representative growth rate.

Formula and calculation

CAGR = (EV / BV)^(1 / n) − 1

where:
– EV = ending value
– BV = beginning value
– n = number of years

To calculate:
1. Divide the ending value by the beginning value.
2. Raise the result to the power of 1/n.
3. Subtract 1 and multiply by 100 to express as a percentage.

Example:
– Beginning value = $10,000
– Ending value = $19,000
– Period = 3 years

CAGR = (19,000 / 10,000)^(1/3) − 1 = 0.2386 → 23.86%

Common uses

• Comparing performance of different investments over the same period (stocks, funds, savings accounts).
• Estimating a required average return to reach a future financial goal (rearrange the formula to solve for BV, EV, or n).
• Tracking business metrics (revenue, market share) to compare growth rates across companies or divisions.

Example (required return):
If you need $50,000 in 18 years and have $15,000 now:
Required annual return = (50,000 / 15,000)^(1/18) − 1 ≈ 6.90%

Adjusting for non-integer holding periods

When the holding period is not an exact number of years, compute n as total days held ÷ 365 (or use exact year fraction). For example, a 1,924-day holding period = 1,924 / 365 = 5.271 years. Plug that n into the CAGR formula.

What is a “good” CAGR?

“Good” depends on context—industry averages, opportunity cost, and risk. Higher is generally better, but compare against relevant benchmarks and consider volatility and risk profile.

Limitations

• Smooths volatility: CAGR represents a steady compound rate and hides year-to-year fluctuation.
• Ignores cash flows: Deposits or withdrawals during the period distort CAGR. Use IRR or time-weighted returns when there are multiple cash flows.
• Can be misleading over short periods: Short-term CAGRs are less reliable as predictors of future performance.
• Selective reporting: Presenting a high CAGR for a short subperiod can omit unfavorable earlier results.

CAGR vs. IRR

• CAGR measures growth between two balances over time with no intermediate cash flows.
• Internal Rate of Return (IRR) handles multiple inflows and outflows and finds the discount rate that sets net present value to zero. Use IRR for projects or investments with varying cash flows.

Risk adjustment

A simple risk-adjusted approach is to reduce CAGR by a function of volatility (for example, multiplying CAGR by (1 − standard deviation)), but this is crude. Use more formal risk-adjusted metrics (Sharpe ratio, MAR, etc.) for robust comparisons.

Quick FAQs

• Can CAGR be negative? Yes — a negative CAGR indicates a decline in value over the period.
• How is CAGR different from a simple growth rate? CAGR assumes compounding and smooths annual rates; a simple growth rate is just the raw percentage change over the period without annualization.
• When should I not use CAGR? Avoid CAGR when there are intermediate cash flows or when volatility and timing of returns are critical to the analysis.

Bottom line

CAGR is a useful, easy-to-calc metric for comparing average annual growth across investments or business metrics. It provides a simplified, annualized view of performance but omits volatility, timing of cash flows, and risk. Use CAGR alongside measures that capture risk and cash-flow timing for a complete evaluation.