# Compound Annual Growth Rate (CAGR)

## What is the Compound Annual Growth Rate (CAGR)?

The Compound Annual Growth Rate (CAGR) is a measure of a company, asset, or investment's performance expressed as a percentage change over the number of years over which it is held.

By taking the geometric mean, it provides an **average growth rate** for all of the years being measured, rather than an average of the separate growth rates from each year.

## Formula for Compound Annual Growth Rate (CAGR)

The mathematical formula for CAGR is as follows:

$CAGR = \frac{(Ending\ Value/Starting\ Value)^{1/N} - 1}{N}$

Where:

- Ending Value = Value at end of interval
- Starting Value = Value at start of interval
- N = Number of years

## Example of CAGR calculation

For example, let's say a company had $100 in assets in 2018, and in 2022 it had a total of $200 in assets (4 years later).

The CAGR for the four-year period will be :

$CAGR = \frac{(200/100)^{1/4} - 1}{4} = 0.47 = 47\%$

## When to use CAGR?

CAGR is a valuable benchmark used to compare the rates of return from different investments over different time periods.

### Benchark the performance of assets

CAGR gives a more accurate indication of the true growth, as it levels out the erratic fluctuations in short-term growth or decline. It is very useful for benchmarking investments. For example, if the S&P 500 is showing a 10-year CAGR of 8%, investors can compare their portfolio's performance against the return of the S&P 500 and develop more meaningful expectations for their investments.

### Compare to historical performance

It's also helpful to compare the growth of a company over multiple years or to measure the success of a given project during a specific period. As the CAGR provides an average growth rate, it takes into account different rate of growth from each year and allows for an easy comparison.

### Compare the performance of industries

When analysing different industries or asset classes, the CAGR is a useful way to make judgments about investments and determine which investments are most likely to produce profitable results in the long run.

## Differences between Compound Annual Growth Rate (CAGR) and Internal Rate of Return (IRR)

While CAGR measures the average return of an asset, the Internal Rate of Return (IRR) is a measure of the average return over a rolling period.

With CAGR, investors compare the starting and ending points with no consideration of the cash flows reinvested along the way, and CAGR is a better measure of the average growth rate of the investments without making the assumption of reinvestment.

However, with IRR, the reinvestments are taken into consideration and it also takes into account any intervening cash flows. The IRR is a better measure of the returns of the investment and is preferred over the CAGR as it takes into account the costs of investing and the timing of when the returns are generated.