When evaluating the growth rate of an investment, the compound annual growth rate (CAGR) is an important indicator commonly used by many investors.。CAGR can calculate the average annual growth rate of an investment over a specific period of time through a simple formula, thus helping investors to initially judge the value of the investment。

Definition and formula of compound annual growth rate (CAGR)

CAGR is used to evaluate the annual average growth rate of an investment over a specific period. The formula is as follows:

For example, suppose an investor invested 1000 yuan in a company (let's call it "Company A") on January 1st of last year, and sold it for 1300 yuan on December 31st of this year. The calculation steps are as follows:

• End of period value: 1300 yuan
• Initial value: 1000 yuan
• Number of years: 2 years

CAGR is calculated as follows:

$\text{CAGR}={\left(\frac{1300}{1000}\right)}^{\frac{1}{2}}-1=14.02\mathrm{\%}$

This means that investment firm A has a CAGR of 14.02%.

Application Example: Calculating the CAGR of Company Performance

Using a company's net profit after tax as an example, assume that a company's net profit after tax over three years is as follows.

• 2 years ago: $10,000
• Last year: $8,500
• This year: $14,000

The calculation steps are as follows:

• Final value: $14,000
• Initial value: $10,000
• Number of years: 3 years

CAGR is calculated as follows:

$\text{CAGR}={\left(\frac{14000}{10000}\right)}^{\frac{1}{3}}-1=11.87\mathrm{\%}$

This indicates that the company's Compound Annual Growth Rate (CAGR) over the past three years is 11.87%.

It is important to note that CAGR focuses on the start and end values, without considering fluctuations during the period. Although the company's net profit decreased in the second year, CAGR still reflects its overall growth trend.

Scope and Limitations

The advantage of CAGR is its simplicity and intuition, which is suitable for evaluating high-growth companies. However, it also has some limitations:

1. Ignore period fluctuations: CAGR only considers values at the beginning and end of the period, ignoring period fluctuations.
2. Does not represent the future: CAGR is based on historical data and there is no guarantee that the same growth rate will occur in the future.
3. CAGR with a short time range is inaccurate: the calculation of CAGR in a short time may not be accurate enough, it is best to choose a longer time period.
4. Ignoring changes in cash flow during the period: If there are multiple cash flow changes during the investment period (such as additional investments or partial withdrawals), CAGR cannot accurately reflect the true growth rate.

Application Case: CAGR of Apple Inc.

For example, as of September 30, 2022, Apple Inc. (NASDAQ: AAPL) had a CAGR of 23.44%. However, during the same period, Apple's revenue growth rate was 7.79%, and its net profit growth rate was 5.41%. This disparity indicates that there can be a significant difference between CAGR and actual annual growth rates. Therefore, investors should consider other metrics in conjunction with CAGR for a comprehensive evaluation.

What is a good CAGR？

The quality of a CAGR needs to be judged in conjunction with the industry average. For example:

• The average CAGR for the telecommunications industry is 30%. If a company's CAGR in this industry is 20%, the company is performing relatively poorly.
• The entertainment industry's net income CAGR over the past five years is 21.75%, the food industry's is 3.54%, and Real Estate Investment Trusts (REITs) have a CAGR of 17.55%.

If a target company's CAGR is higher than the industry average, the company has good growth potential.

Advanced Applications of CAGR

In addition to assessing the growth rate of a single investment, CAGR can also be used in the following areas:

1. Investment Comparison: By comparing the CAGR of different investments, investors can decide which investment is more attractive. For example, if an investor is considering investing in bonds (with an average annual return of 3%) or stocks (with an ending value of 11,500 yuan), they can calculate:

   - The bond's CAGR is 3%- The stock's CAGR is 7.24%

2. The results show that the stock's CAGR is higher than the bond's, allowing the investor to make an informed investment decision.Analyzing Competitors: By comparing the CAGRs of competitors, investors can evaluate their competitive advantages. For example, if Company C has a CAGR of 1% and its main competitor has a CAGR of -1%, Company C is performing relatively better.
3. Calculating Required Return Rate: Suppose an investor plans to buy a car worth 50,000 yuan in five years and currently has 35,000 yuan. Using the CAGR formula, the required average annual return rate can be calculated as 7.39%.

Application of CAGR Formula for Investments of Less Than One Year

CAGR is typically calculated on an annual basis, but if the investment period is less than a year, the number of investment days can be converted into years. For example, if an investment runs from March 1, 2018, to April 1, 2022, the total number of days is 1,392, which is approximately 4.09 years:

$\text{Years}=\frac{1,392}{365}\approx 4.09$

If the beginning value is 46,500 yuan and the ending value is 58,900 yuan, the CAGR would be 5.95%. Even if the investment period is less than a year, you can calculate the CAGR by adjusting the number of years.

Difference Between CAGR and IRR

While CAGR can simply calculate the growth rate, the Internal Rate of Return (IRR) is more suitable for situations involving multiple cash flow changes. For example:

• Invest 10,000 yuan in the first year
• Invest an additional 5,000 yuan in the second year
• Withdraw 7,000 yuan in the third year
• The total value reaches 15,000 yuan in the fourth year

IRR can comprehensively account for all cash flows and accurately calculate the annualized return rate. However, calculating IRR is more complex and requires using financial software or Excel tools.

Conclusion

The Compound Annual Growth Rate (CAGR) is an important tool for evaluating investment growth. Its formula is straightforward and helps investors quickly understand the annual average growth rate of an investment. However, CAGR has its limitations, as it does not account for interim fluctuations and cash flow changes. Therefore, when using CAGR, investors should combine it with other financial metrics to ensure the accuracy and comprehensiveness of their investment decisions.