# Compound Annual Growth Rate (CAGR)

**AJIT KUMARWISDOM IAS, New Delhi.**

The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets one from the initial investment value to the ending investment value if one assume that the investment has been compounding over the time period. The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer than one year.

To calculate compound annual growth rate, divide the value of an investment at the end of the period in question by its value at the beginning of that period, raise the result to the power of one divided by the period length, and subtract one from the subsequent result.

The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially an imaginary number that describes the rate at which an investment would have grown if it had grown at a steady rate, which virtually never happens in reality. You can think of CAGR as a way to smooth out an investment’s returns so that they may be more easily understood.

The formula for CAGR is:

CAGR = ( EV / BV)1 / n - 1

where:

EV = Investment's ending value

BV = Investment's beginning value

n = Number of periods (months, years, etc.)

Let's assume you invest $1,000 in Fund "A"for five years. The year-end value of the investment is listed below for each year. Year Ending Value

1 $ 750

2 1,000

3 3,000

4 4,000

5 5,000

We can calculate the CAGR of the investment as: CAGR = ( 5,000 / 1,000)1/5 - 1 = .37973 = 37.97%

Thus, the compound annual growth rate of your fice-year investment is equal to 37.97%, representing the smoothed annualized gain you earned over your investment time horizon.

Uses of CAGR

CAGR is a relatively simple metric, since it merely measures the average rate of an investment’s growth over a variable period of time. Because of this simplicity, this metric is a flexible one and thus has a variety of uses.

Most simply, CAGR can be used to calculate the average growth of a single investment. Because of marketvolatility, the year-to-year growth of an investment may be difficult to interpret. For example, an investment may increase in value by 8% in one year, decrease in value by 2% the following year and increase in value by 5% in the next. With inconsistent annual growth, CAGR may be used to give a broader picture of an investment’s progress.

CAGR may also be used to compare investments of different types with one another.

CAGR can also be used to track the performance of various business measures of one or multiple companies alongside one another.

Like any metric, CAGR should not be used alone, but rather should be used alongside other metrics as well. This is because, like any metric, CAGR is not without its drawbacks.**Wednesday, 16th Dec 2015, 11:55:56 PM**