Compound Annual Growth Rate (CAGR)
The CAGR, or the compound annual growth rate, simply reflects the annualized return of a metric on a compounded basis, over a given period of time.
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CAGR Meaning & Definition
The Compound Annual Growth Rate (CAGR), is the annualized growth rate of return of the value of an investment or a financial metric over a given number of years and taking into account compound growth.
Growth of any metric can be volatile from year to year, sometimes fluctuating between positive and negative. CAGR "smooths out" this rate and presents growth as a number as if it were the same for each year over the period studied.
How CAGR Is Used by Investors
The CAGR allows investors to do the following:
- Analyze a Single Investment: The CAGR determines the average growth rate of a single investment.
- Compare the Performance of Different Investment Types: CAGR allows investors to compare the performance of different types of investment, such as those of bonds, stocks, real estate, or savings accounts over the same period.
- Compare Two Investments: Using CAGR, investors can compare the growth rates of two investments against one another, such as two stocks, or one stock against the performance of a market index.
- Compare Business Metrics: Investors can use the CAGR to analyze several business metrics within the same company; for example, the CAGR of the Return on Marketing Investment (ROMI) could be compared with that of the Net Sales Revenue, which is Gross Sales minus Discounts, Returns, and Costs Related to Discounts and Returns.
CAGR Formula
The formula for calculating the CAGR is:
CAGR = ([(Ending Value / Beginning Value) ^ (1 / # of years)] - 1) * 100
-the result of this calculation reflects a % value.
- Ending Value: Is the value of an individual investment, a portfolio, or a business metric at the end of the time period
- Beginning Value: Is the value of an individual investment, a portfolio, or a business metric at the beginning of the time period
- # of Years: Number of years of the study period (which can includes partial years converted into a decimal number)
Calculating CAGR for a Portfolio
To determine the starting and ending values of individual investments:
- For stocks, determine the price of each share on the starting date and multiply that by the number of shares. Do the same thing for the ending date.
- For certificates of deposit, either use their value at maturity or contact the certificates' issuer to find out their current value.
- For a 401k (or other account type), determine the starting and ending values, look at the first and last statements, or log into the online account.
Add up all the starting values to determine the portfolio's starting value, and add up all the ending values to determine its ending value. Be sure to include any quarterly dividends received during the period, and any taxes, fees, or penalties that would be incurred on the ending value.
Then, determine the number of years between those two dates.
Suppose a Mr. Smith invested $10,000 into a portfolio on January 1, 2018, and kept track of his returns over the next four years:
Mr. Smith's Portfolio:
| Date | Amount | Rate of Return |
| 1/1/2018 | $10,000 | |
| 1/1/2019 | $14,500 | 45% |
1/1/2020 | $15,200 | 4.8% |
| 1/1/2021 | $18,900 | 24.3% |
| 1/1/2022 | $26,100 | 34.1% |
We can easily see that the year-to-year growth rates of Mr. Smith's portfolio varied considerably, from 45% in the first year to 4.8% in the second, before rebounding during years three and four. The CAGR can tell us the average annual growth rate of Mr. Smith's portfolio over all four years:
CAGR = ([($26,100/$10,000) ^ 1/4]- 1) * 100 = 27.1%
Calculating CAGR for a Single Investment
To determine the CAGR for a single investment, determine its value on the starting date, its value on the ending date, then determine the number of years between the two dates.
5-year Microsoft share price chart (Seeking Alpha)
Suppose on 1/1/2018, Mr. Smith bought 116 shares of Microsoft Corp. (MSFT) at $86.35, spending $10,016.60. On 1/1/2022, Microsoft's shares were trading at $329.09, yielding $38,174.44. The calculation of the CAGR of Mr. Smith's Microsoft investment over four years is:
CAGR = ([($38,174.44 / 10,016.60) ^ 1/4] - 1) * 100 = 39.62%
Calculating CAGR in Excel/Sheets
If investors have 2 of the below 3 inputs, they can use a spreadsheet such as Excel to determine the value of the other input related to the CAGR formula:
- An ending value
- A starting value
- The number of years
Excel doesn't have a specific CAGR function, but one can use its pre-programmed RRI function instead as shown below:
Excel RRI Function (Wendorf)
One can also enter the CAGR formula manually as shown below:
Excel spreadsheet CAGR function (Wendorf)
Calculating CAGR for Partial Years
In reality, investments aren't held for an exact number of years. For example, if an investment of $10,000 was made on Wednesday, July 11, 2018, and the investor sells it on Monday, June 6, 2022, for $18,901, they would have held the stock for 1,426 days.
To find the CAGR:
1,426 / 365 days per year = 3.91 years
CAGR = ([($18,901/$10,000) ^ 1/3.91] - 1) * 100 = ~17.7%
Limitations of CAGR
- Portfolio Additions or Withdrawals: The CAGR for a portfolio doesn't consider account additions or withdrawals; if an investor adds funds to his portfolio but does not adjust the calculation for it, it will yield an inflated CAGR. If the investor deletes funds from his portfolio, the CAGR will be underreported.
- Actual CAGR Differing From Expected CAGR: While many investors use past growth rates to assess the future prospects for a portfolio or specific investment, actual returns will differ from those experienced in the past. Some securities, such as Certificates of Deposit, will yield a constant return rate each year, but that's not the case for many securities.
Bottom Line
Knowing what the CAGR is and how it is calculated is valuable to investors because it provides an accurate reflection the average compounded return of an individual asset over a period of time.
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