The compound annual growth rate, or CAGR for short, measures the return on an investment over a certain period of time. Below is an overview of how to calculate it by hand, and in Excel.
CAGR Defined
The concept of CAGR is relatively straightforward and requires only three primary inputs: an investment’s beginning value, ending value, and the time period. Online tools, including Investopedia’s CAGR calculator, will give the CAGR when entering these three values. The CAGR represents the growth rate of an initial investment assuming it is compounding by the period of time specified. Specifically, the formula is:
CAGR in Excel
The CAGR formula can be recreated in Excel. The formula to use is:
= ((FV/PV)^(1/n)) – 1
Where FV is the investment’s ending value, PV is its ending value, and n is the # of years.
The XIRR function in Excel also calculates an internal rate of return (IRR) that can also be used to calculate the CAGR. The XIRR function is:
XIRR(values,dates, guess)
Again, what is needed are the beginning and ending investing values, and date periods. This function is more flexible as it can include multiple values and dates beyond just the ending and starting value. The one rub to this approach is the user must enter an estimated CAGR value, but this also helps intuitively understand the return values.
A Brief Example of the CAGR Calculation
Assume an investment’s beginning value is $1,000 and it grows to $5,000 in 10 years. The CAGR calculation is as follows:
= ((5,000/1,000)^(1/5)) – 1
The CAGR is 17.4% and details that the investment grew at this annual rate for a decade.
Limitations of the CAGR
The CAGR is superior to average returns because it considers the fact that investment returns compound over time. One limitation is that it assumes a smoothed return over the time period measured. In reality, investments experience significant shortterm ups and downs. CAGR is also subject to manipulation as the time period used can be controlled by the user. For instance, a fiveyear return period can be shifted by a year to avoid a negative period (such as 2008), or to include a period of strong performance (such as 2013).
The Bottom Line
The CAGR helps frame the steady rate of return of an investment over a certain period of time. It assumes the investment compounds over the period of time specified, and it is helpful for comparing investments with different returns across periods, as well as for comparing investments in different asset classes.
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