Computing compound growth rates using CAGR

Learn about computing the key input for projecting the compound growth of your assets, the Compound Annual Growth Rate (CAGR).

The most fundamental input for projecting the compound growth of your assets is the annual growth rate. This growth rate can be easily computed by using the Compound Annual Growth Rate, or CAGR formula. In this article, we'll explore CAGR, how to use it in financial analysis, and how you can apply it to project the compound growth of your assets.

What is CAGR?

CAGR calculates the mean annual growth rate of an investment over a specified time period. Unlike simple averages, CAGR takes into account the effects of compounding, offering a more accurate representation of your investment's performance over time.

Calculating CAGR

CAGR formula is as follows:

CAGR = (Ending Value / Beginning Value)^(1/n) - 1

Where:

• Ending Value is the final investment value
• Beginning Value is the initial investment amount
• n is the number of years

For instance, if your investment of $10,000 grew to $15,000 over 5 years, CAGR would be:

CAGR = ($15,000 / $10,000)^(1/5) - 1 = 8.45%

Meaning that your investment grew at an average rate of 8.45% per year, accounting for compounding effects.

You can play around with computing the CAGR using this calculator:

CAGR and Compound Growth

Compound growth refers to the process where your investment generates returns not only on the initial principal but also on accumulated gains from previous periods. CAGR effectively captures this compounding effect, making it a key input for computing the compound growth of your assets.

To learn more about compound growth, check out our beginner's guide to compound growth.

Applying CAGR

Consider two investments:

1. Investment A: Grows from $10,000 to $20,000 in 10 years
2. Investment B: Grows from $10,000 to $25,000 in 10 years

Calculating CAGR for each:

• Investment A CAGR: 7.18%
• Investment B CAGR: 9.65%

The 2.47 percentage point difference in CAGR can lead to significantly different outcomes over extended periods, as illustrated in the simulation below.

Note while that a higher CAGR means a higher return, it doesn't mean that both investments will have the same risk profile. Investing in the higher CAGR investment could be more risky than the lower CAGR investment. Hence, CAGR is one metric for comparing investments, but it's not the only one.

Also, always make sure to use as much data as you can for your CAGR to prevent biases for short-term market trends.

Applications of CAGR

Investment Comparison

CAGR allows you to compare investments with different time horizons on an equivalent basis. This is useful when you're evaluating different asset classes (like stocks vs. bonds) or assets with in the same asset class (like MSFT vs. AAPL).

Financial Planning

Understanding CAGR can help you with setting realistic financial goals. By being concious of CAGR of your investments, you can determine the required monthly savings to achieve your financial goals. Subsequently, you can then optimize for more growth by either trying to increase CAGR by using different portfolio compositions, increasing your monthly investments, or by letting compound growth run for longer.

CAGR and Dividends

CAGR incorporates dividends in its calculation. When you calculate CAGR, you typically use the total return of an investment, which includes both price appreciation and dividends. This gives you a more comprehensive view of your investment's performance. If you reinvest dividends, they contribute to the compound growth, increasing your CAGR over time.

Limitations of CAGR

CAGR smooths out year-to-year fluctuations, potentially obscuring significant short-term drawdowns in your investments. It also assumes all returns are reinvested, which may not always reflect your actual investment behavior.

Another significant limitation is that CAGR doesn't account for inflation. When evaluating long-term investments, it's crucial to consider the real rate of return, which is CAGR adjusted for inflation. For example, if your investment has a CAGR of 7% but inflation is running at 2% annually, your real rate of return is only about 5%. This gives you a more accurate picture of your investment's purchasing power over time.

Lastly, remember that past CAGR doesn't guarantee future performance of your investments. CAGR is highly dependent on the amount of data that you feed in. For example, a CAGR that is computed over 30 years of data is more likely to be an accurate projection than a CAGR computed over 5 years of data. Past performance is never a guarantee of future performance.

Conclusion

CAGR is an essential tool for comparing assets, understanding your investment performance and projecting the compound growth of your assets. It helps you make more informed investment decisions by being able to compare assets and being able to project them into the future.

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