# CAGR - Compound Annual Growth Rate

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## What is CAGR?

Compound Annual Growth Rate (or CAGR) is a widely used measure of growth. It is used to evaluate anything that can fluctuate in value, such as assets and investments. CAGR takes the initial investment value and projects an ending investment value while assuming compound growth over a set period of time.

## Why CAGR Is So Useful

CAGR is used when looking at investments over any period of time, but usually for a period of at least 3 to 5 years. It provides the geometric mean return for investments over this time period while accounting for compound growth. If you’re analyzing investments, this number indicates the value of your investment at the end of that time period. This is useful information when comparing or evaluating historical returns of particular investments.

CAGR is a geometric average and provides a more accurate measure of investment than a simple arithmetic mean. CAGR represents the consistent rate at which an investment would have grown if the investment had compounded at the same rate each year. You should keep in mind that CAGR assumes a constant growth rate for the time period, which does not reflect the reality of most investment returns. CAGR is simply a way to calculate the internal rate of return, and does not incorporate or consider the variability or standard deviation of periodic returns.

## CAGR Formula

The CAGR formula provides a growth rate in the form of a percentage. You might use this formula to project the CAGR needed to achieve your investment goals or measure the return on existing investments.

You can calculate CAGR by using the following formula: where:

EV = Investment's ending value

BV = Investment's beginning value

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

### How to Calculate CAGR

As an example, let's say you invest \$1,000 in Fund X 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

You can calculate the CAGR of the investment as:

CAGR = (5,000 / 1,000)1/5 - 1 = .37973 = 37.97% Tip: If you’re using a financial calculator, use the yx button to raise (5,000 / 1,000) to the power of 0.20 (since 1 / 5 = 0.20 ).

If you need to plug CAGR into an Excel sheet, Excel Easy walks you through that process.  You can also use InvestingAnswers’ simple CAGR Calculator.

## How to Calculate Growth Rate for an Investment

When you’re considering an investment, you’ll want to look at the return from several different lenses (ie. using multiple formulas).

It’s common to use the Average Annual Return (AAR) when looking at mutual funds. This number can be helpful when looking at a long term investment. However,  CAGR is a better measure of an investment's return over time because it takes investment losses into consideration.

### CAGR Example of Return Over Time

For example, consider Year 1 and Year 2 of our hypothetical investment in Fund X.  At the end of Year 1, the portfolio value had fallen from \$1,000 to \$750 for a return of -25% [ (750 - 1,000) / 1,000 ]. By the end of Year 2, the portfolio value had grown by +33% [ (1,000 - 750) / 750 ].

Averaging Year 1 and Year 2 returns over two years gives us an average return of 4% [ (-25 + 33) / 2 ]. But that doesn't accurately reflect what has actually happened. Fund X began with \$1,000 and ended with \$1,000, which is a return of 0%.

This example shows why CAGR is a better measure of return over time. An average annual return (or arithmetic mean) ignores the effects of compounding and can overestimate growth. CAGR, on the other hand, represents a consistent rate at which the investment would have grown. CAGR will always be equal to or less than the arithmetic mean.

## CAGR vs. IRR

Let’s look at how Internal Rate of Return compares to CAGR.  Both of these formulas measure the returns of investments, but CAGR's formula only includes one initial investment (cash outflow) and one ending amount (cash inflow).

By contrast, IRR can have multiple cash inflows and outflows to measure an investment return.

Because of this versatility, IRR is often used to estimate whether proposed projects could generate a higher return than other investments. IRR is also commonly used by venture capital firms to analyze the growth of company acquisition targets.

## CAGR vs. Absolute Return

Absolute returns is a much simpler way to arrive at a total return. It doesn't take into account the rate of return over a period of time, making it easier to compare investments. Absolute value is like measuring how many miles you traveled while CAGR is like measuring how many miles per hour you traveled (aka the rate of speed) .

### Absolute Return Formula

The formula for absolute return is:

Absolute Return % = ((ending value - beginning value) / beginning value) x 100)

Say you invested \$50 and it evolved into \$100. That would make for an absolute return of 100% (or (100 - 50)/50 x 100 = 100%).

While that makes for an eye-popping return that's sure to impress, it may be hard to determine how valuable that is without involving a time element. Is that 100% over five years, or 100% over 20 years?

With the figures in the CAGR definition above, the absolute return would be 567% (or (5000 - 750) / (750) X 100) = 567). Using the Investing Answers CAGR calculator, the total was 37.97%.  This makes the CAGR a better measure of growth because it accounts for the 5 years of ups and downs.

Because CAGR measures returns for any time period, you can make equal comparisons of one investment's return to another investment's return.

Investing Answers is on a mission to help consumers build and protect their wealth through education. This is why our experts are here to answer your financial questions at the end of each article.

## Q: Who Uses CAGR?

CAGR is used by both investors and companies to provide hypothetical growth rates for investments over time. The number that CAGR provides is an easy metric to compare to other investments, which helps companies understand which one may provide higher returns.

## Q: Are CAGR and Average Annual Growth Rate the Same?

CAGR and average annual growth rate (AAGR) are not the same metric. CAGR is a growth statistic that measures the compound annual return of investments over a set period of time, assuming you reinvest your profits (i.e. compounding effect).

AAGR is a more simplistic growth metric and does not account for compounding. Instead, AAGR calculates the arithmetic average of an investment. It can be a good way to predict trends, but CAGR is superior for analyzing growth because it accounts for changing financials over time.

## Q: When are CAGR and AAGR appropriate to use?

Compound annual return is a better tool to describe the long-term, or historical, performance of an investment. It is best used for the purposes of comparison over longer terms (5-10 years).

Arithmetic average return (or AAGR) is best to estimate an investment’s expected, or future, return based on past performance. The AAGR in this way is an unbiased estimate of future returns.