What Is the ♎Calculating Compound Annual Growth Rate (CAGR)?꧅

The compound annual growth rate (CAGR) shows the rate of return of an i🐓nvestment 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 ജbetter but often at an uneven rate. The CAGR provides one rate that defines the return for the entire measurement period.

You may be presented with yeಌar-end prices for a stock like this:

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

The price appreciated by 20% ($10൲0 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-ov🥂er-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开奖号码历史查询:beginning value, its 澳洲幸运5开奖号码历史查询:ending value, and the time period expressed in years. Online tools, including Investopedia’s 澳洲幸运5开奖号码历史查询:CAGR calculator, wil🐬l give the CAGR when entering these three values. Th💙e 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 rate can be defined as 11.8% despite the fact that the stock’s price increased at different rates each year.

Tips and Tricks for Calculating CAGR

An easy🌃 mistake to make in figuring the CAGR is to incorrectly count the time period. There are three calendar years in the above example, but the data is presented as year-end prices, so we really only have two completed y♔ears. That’s why the equation reads 1/2, not 1/3.

Now let’s say we had a stock whose annual price data was pr🍷esented in percentages r𒆙ather 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 waღs 10%, the entire yearly return in 2022ﷺ was 15%, and the entire yearly return in 2023 was -4%. That means we would actually be working with a time period of three years when calculating the CAGR.

We would have to♛ convert these percentages into actual beginning and ending values. This is a good opp🌄ortunity 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 isꦚ the same as above: You need ending values, beginning values, and a length measured in years. Excel has a built-in formul🐬a, 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 annual growth rate of a company’s sales ov😼er 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 figure out the total completed years and add them to the partial year, called the✱ stub year.

Let’sไ take the same ☂figures, but they’re stock prices in this case:

Advantages and Disadvantages of CAGR

The CAGR is superior to other calculations, such as 澳洲幸运5开奖号码历史查询: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开奖号码历史查询:volatility. Let’s say you have an investm🌄ent that has posted these change🌜s 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 returns𓆏 is huge. The reality is that many investments 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 informs 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开奖号码历史查询:stock market or to include a year of strong performance.

The Bottom Line

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