What is Compound Annual Growth Rate (CAGR)?
The Compound Annual Growth Rate (CAGR) represents the rate of return required for an investment to grow from its initial balance to its ending balance, assuming the profits are reinvested at the end of each period.
Key Insights
- The CAGR is an accurate way to calculate and determine the returns of investments over time.
- It measures a smoothed rate of return, offering a clear growth depiction.
- Investors can compare different investments using CAGR to evaluate performance against benchmarks or peer groups.
- Note that CAGR doesn’t reflect investment risk.
How to Calculate Compound Annual Growth Rate (CAGR)
To calculate CAGR, follow these steps:
- Divide the ending value of the investment by its beginning value.
- Raise the result to the power of one divided by the number of years.
- Subtract one from the result.
- Multiply by 100 to convert the answer into a percentage.
Formula:
1\( C A G R = ( \frac{E V}{B V} ) ^{\frac{1}{n}} - 1 ) \times 100 \)
2
3where:
4- *EV* = Ending value
5- *BV* = Beginning value
6- *n* = Number of years
Understanding What CAGR Reveals
The CAGR isn’t a real rate of return but an assumption showing the rate at which an investment would have grown if profits were consistently reinvested yearly.
However, returns are rarely consistent in reality. CAGR smooths returns, making it easier to compare the performance of different investments.
Improved Example for How to Use CAGR
Consider a scenario where you invested $10,000 in a portfolio over three years. The portfolio grew to $13,000 in the first year (a 30% increase), to $14,000 in the second year (7.69% increase), and to $19,000 in the third year (35.71% increase). The CAGR for this period is 23.86% and is calculated as follows:
1\( C A G R = ( \frac{19,000}{10,000} ) ^{ \frac{1}{3}} - 1 ) \times 100 = 23.86 \%
Applications of CAGR
Comparing Various Investments
CAGR provides the geometric mean necessary to compare varied investment types more easily. For instance, $10,000 invested in a savings account at a 1% annual interest rate results in a balance of $10,510.10 after five years. Another $10,000 invested in a stock mutual fund might yield $15,348.52 with unequal year-to-year returns. Comparing CAGRs shows the difference in performance:
Savings Account CAGR: 1%
Stock Fund CAGR: 8.95%
Though the stock fund appears superior, the volatility or risk involved isn’t visible in CAGR figures.
Tracking Business Performance
Businesses can leverage CAGR to track growth across different performance metrics. Differing CAGRs within a company reveal strengths and weaknesses.
Identifying Competitive Strengths
Comparing similar activity CAGRs across different companies offers insights into competitive positioning. For instance, customer satisfaction rate comparisons can highlight industry positions.
Enhancing Investor Decision-Making with CAGR
The CAGR calculation is adaptable, serving as a foundation for estimating future returns or evaluating past performance against benchmarks.
Present vs. Future Value Calculations
Investors can rearrange the CAGR formula for use in present or future value calculations. For instance, an investor needing $50,000 for education in 18 years and starting with $15,000 can estimate necessary returns using CAGR.
Modification for Partial Years
In investments starting or ending mid-year, adjust for fractional periods. For example, holding an investment from June 1, 2013, to Sept. 9, 2018 (5.271 years), adjust n in the formula accordingly.
Formula for a Partial Period Example:
1\( C A G R = ( \frac{16,897.14}{10,000} ) ^{ \frac{1}{5.271}} - 1 ) \times 100 = 10.46 \%
Recognizing CAGR Limitations
- CAGR calculates smoothed growth, thus ignoring volatility, inflow, or outflow of funds during the period.
- Long-term CAGR projections based on short-term data may not represent future performance accurately.
- Partial historical data can misrepresent actual CAGR if information isn’t comprehensive.
CAGR vs. Internal Rate of Return (IRR)
While CAGR measures a straightforward return rate over time, Internal Rate of Return (IRR) offers more flexibility, making it suitable for complex investments with multiple cash flows. Calculating IRR requires more advanced tools, such as financial calculators or Excel.
Higher CAGR - Always Better?
A higher CAGR generally implies better performance, but it’s essential to consider both risk and industry benchmarks. Negative CAGR indicates losses, and comparison using risk-adjusted CAGR may be beneficial for risk assessment.
Conclusion
Understanding the Compound Annual Growth Rate (CAGR) helps demystify investment returns, track performance, and make informed comparisons. While useful, always consider its limitations and supplement the analysis with other financial metrics and risk assessment tools.
Related Terms: IRR, ROI, Growth Rate, Volatility, Risk, Standard Deviation.
References
- Yahoo Finance. “Amazon.com, Inc. (AMZN) Historical Data”.
