# CAGR - Compound Annual Growth Rate

## What is CAGR?

CAGR, or compound annual growth rate, is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.

## CAGR Formula and Example

You can calculate CAGR by using the following formula:

**CAGR = ( EV / BV) ^{1 / n} - 1**

where:

EV = Investment's ending value

BV = Investment's beginning value

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

As an example, let's say you invest $1,000 in Fund XYZ 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%

TIP: If you are using a financial calculator, use the y^{x} button to raise ( 5,000 / 1,000) to the power of 0.20 (since 1 / 5 = 0.20 ).

[Our easy to use CAGR Calculator can help you project the CAGR needed to achieve your investment goals or measure the return on existing investments.]

## How to Calculate Growth Rate for an Investment

Although average annual return is a common measure for mutual funds, CAGR is a better measure of an investment's return over time because it takes investment losses into consideration.

For example, consider Year 1 and Year 2 of our hypothetical investment in Fund XYZ. 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 the 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 happened. We 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. Average annual return ignores the effects of compounding and it can overestimate the growth of an investment. CAGR, on the other hand, is a geometric average that represents the one, consistent rate at which the investment would have grown if the investment had compounded at the same rate each year.

While both IRR and CAGR can both measure the returns of investments, CAGR's formula only includes one initial investment (cash outflow) and one ending amount (cash inflow) to find out an investment's return. By contrast, IRR can have multiple cash inflows and outflows to measure an investment return.

Because of its multiple cash flow versatility, IRR is often used to estimate if proposed projects within an organization could generate a higher return than an organization's other investments. IRR is also commonly used by venture capital firms to decide which company acquisition targets could provide the highest returns.

Absolute return is a much simpler way to arrive at a total return, but it doesn't take into account the rate of return over a period of time which makes it easier to compare investments on an apples-to-apples basis. In simple terms, absolute value is like measuring how many miles you traveled while CAGR is like measuring how many miles per hour (the rate of speed) you traveled along the way.

The formula for absolute return is simply:

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

So if you invested $50 and it turned into $100, that would make for an absolute return of % (or (100 - 50)/50 x 100 = 100%).

While that makes for an eye-popping return that's sure to impress colleagues, it may be hard to know how valuable that is without the time element. Is that a 100% over five years, or 100% over 20 years? The time part can make a big difference when comparing returns between investments that have made returns over different lengths of time.

Let's try an example with the figures in the CAGR definition above. The absolute return would be 567% (or (5000 - 750) / (750) X 100) = 567). The CAGR, as we went through in the definition, came out to 37.97%, which takes the time element into account, and is expressed on an annual basis.

Because CAGR allows us to measure returns on a per year basis (or any time period), we can make an apples-to-apples comparison of one investment's annual return to any other investment's annual return.

### Learn more about CAGR:

CAGR vs. Average Annual Return: Why Your Advisor is Quoting the Wrong Number