What Is the Calculating Compound Annual Growth Rate (CAꦺGR)൩?

The compound annual growth rate (CAGR) shows the rate of return of an investment over a period of time. It’s expressed in 𝄹annual percentage terms and can be calculated by hand or by using Microsoft Excel.

The easiest way to think of the CAGR is to recognize that the value of something may change over a number of years, hopefully for the better but oftenܫ at an uneven rate. The CAGR provides one rate that defines the⭕ return for the entire measurement period.

You may be presented with year-end prices for a stock like t༒his:

• 2021: $100
• 2022: $120
• 2023: $125

The price appreciated by 💯20% ($100 to $120) from year-end 2021 to year-end 2022, then by 4.17% ($120 to $125) from year-end 2022 to year-end 2023. These growth rates are different on a year-over-year basis, but we can use a formula to 🍰find a single growth rate for the time period.

The CAGR requires three inputs: an investment’s 澳洲幸运5官方开奖结果体彩网:beginning value, its 澳洲幸运5官方开奖结果体彩网:ending value, and the time period expressed in years. Online tools, including Investopedia’s 澳洲幸运5官方开奖结果体彩网:CAGR calculator, will give the CAGR when entering these three values.💜 The formula♈ is:

$\begin{aligned} &CAGR=\left(\frac{EB}{BB}\right)^{\frac{1}{n}}-1\\ &\textbf{where:}\\ &EB = \text{Ending balance}\\ &BB = \text{Beginning balance}\\ &n = \text{Number of years} \end{aligned}$​CAGR=(BBEB​)n1​−1where:EB=Ending balanceBB=Beginning balancen=Number of years​

Plugging in the above values, we get [(125 / 100)^(1/2) - 1] for a CAGR of 11.8%. Its overall growth rat🌠e can be defined as 11.8% despite the fact that the stock’s price increased at dif꧃ferent rates each year.

Tips and Tricks for Calculating CAGR

An easy mistake to make in figuring the C🌌AGR is to incorrectly count the time period. There are three calendar years in the above example, but the data is presented as yea🅠r-end prices, so we really only have two completed years. That’s why the equation reads 1/2, not 1/3.

Now let’s say we had a stock whose annual price data was presen꧒ted in percentages rather than dollar terms:

• 2021: 10%
• 2022: 15%
• 2023: -4%

The data is shown from the beginning of the year in this case: The entire yearly return in 2021 was 10%, the entire yearly return in 2022 was 15%, and the entire yearly return in 2023 was -4%. That means we would actually be 𝔍working with a time period of three years when calculating the CAGR.ꦜ

We would have to convert theseܫ percentages into actual beginning and ending values. This is a good opportunit🤪y to use a spreadsheet because it’s easy to add a helper column to convert the percentages into values.

Calculating CAGR in Excel

The math formula is the same as above: You need ending values, beginning values, and a length measured in years. Excel has a built-in fo𝔉rmula, but it’s far from ideal.

Financial modeling best practices require calculations to be transparent and auditable. The trouble with piling all the calculations into a formula is that you can’t easily see what numbers go where or what numbers are user inputs or hard-coded. You can set this up in Excel to have all the data in one table, then break out the calculations line by line.

Let’s derive the compound an꧑nual growth rate of a company💯’s sales over 10 years:

The CAGR of sales for the decade is 5.43%. But a more complex situation arises when the measurement period is not in even years. With annual sales figures, this is not a problem. With investment returns, it becomes an issue. The solution is to figuꦇre out the total completed years and add them to the partial year, called the stub year.

Let’s take the same figures, but they’re stock prices in t🅺his case:

Advantages and Disadvantages of CAGR

The CAGR is superior to other calculations, such as 澳洲幸运5官方开奖结果体彩网:average returns, because it takes into account that values compound over time.

On the downside, the CAGR dampens the perception of 澳洲幸运5官方开奖结果体彩网:volatility. Let’s say you h🤪ave an investment that has posted these changes 💜over three years:

• 2021: 25% gain
• 2022: 40% loss
• 2023: 54% gain

That’s actually a 4.9% CAGR, but the year-over-year volatility in those returns is huge. The reality is that many investme🐓nts experience significant short-term ups and downs. The CAGR might give a numerically accurate but emotionally misleading impression of performance when smoothing them out. It’s like a map that correctly infor🌃ms you that your destination is only five miles away without indicating the bumpy condition of the roadway.

The CAGR is also subject to manipulation depending on the measurement period, which is ultimately and often arbitrarily selected. A CAGR can be shifted to avoid a negative year in the 澳洲幸运5官方开奖结果体彩网:stock market or to include a year of strong performance.

The Bottom Line

The CAGR helps identify the ste💙ady rate of return oꦯf an investment over a period of time. It assumes that the investment compounds over the period of time specified and is helpful for comparing investments with similar volatility characteristics.