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

The average annual growth rate (AAGR) is the average increase in the value of an investment, portfolio, asset or individual cash flow over a period of one year. It is calculated by taking the arithmetic mean of a series of growth rates. The average annual growth rate can be calculated for any investment, but it will not include any measure of the overall risk of the investment, as measured by its price volatility.

The average annual growth rate is used in many fields of study. For example, in economics, it is used to provide a better picture of changes in economic activity (for example, the growth rate of real GDP).

Key points to remember

- This ratio helps you determine the average return you have received over several periods.
- The AAGR is calculated by taking the arithmetic mean of a series of growth rates.
- The AAGR is a linear measure that does not take into account the effects of composition.

### The formula for the average annual growth rate (CAGR) is

The

$begin {aligned} & AAGR = frac {GR_A + GR_B + dotso + GR_n} {N} \ & textbf {where:} \ & GR_A = text {Growth rate over period A} \ & GR_B = text {Growth rate for period B} \ & GR_n = text {Growth rate for period} n \ & N = text {Number of payments} \ end {aligned}$TheAAgR=NOTgRAThe+gRBThe+…+gRnotTheTheor:gRAThe=Growth rate over period AgRBThe=Growth rate over period BgRnotThe=Growth rate over the period notNOT=Number of paymentsTheThe

### How to calculate AAGR

AAGR a standard for measuring average returns on investments over several periods. You will find this figure on the brokerage statements and it is included in the prospectus of a mutual fund. It is essentially the simple average of a series of growth rates for periodic returns. One thing to keep in mind is that the periods used must all be of equal duration, for example years, months or weeks – and not mix periods of different duration.

### What does AAGR tell you?

The average annual growth rate is useful for determining long-term trends. It is applicable to almost all types of financial measures, including growth rates in profits, revenues, cash flow, expenses, etc. to give investors a sense of where the business is headed. The ratio tells you what your average annual return was.

The average annual growth rate can be calculated for any investment, but it will not include any measure of the overall risk of the investment, as measured by its price volatility. In addition, the AAGR does not take into account the periodic composition.

### Example of using the average annual growth rate (CAGR)

AAGR measures the average return rate or growth over a series of equally spaced time periods. For example, suppose an investment has the following values over a four-year period:

- Starting value = $ 100,000
- Year-end value 1 = $ 120,000
- Year-end value 2 = $ 135,000
- Year-end value 3 = $ 160,000
- Year-end value 4 = $ 200,000

The formula for determining the percentage growth for each year is as follows:

- The$text {Simple percentage growth or yield} = frac { text {final value}} { text {initial value}} – 1$

Thus, the growth rates for each of the years are as follows:

- First year growth = $ 120,000 / $ 100,000 – 1 = 20%
- Second year growth = $ 135,000 / $ 120,000 – 1 = 12.5%
- Third year growth = $ 160,000 / $ 135,000 – 1 = 18.5%
- Fourth year growth = $ 200,000 / $ 160,000 – 1 = 25%

The AAGR is calculated as the sum of the growth rate of each year divided by the number of years:

- The$AAGR = frac {20 % + 12.5 % + 18.5 % + 25 %} {4} = 19 %$

In the financial and accounting parameters, the start and end prices are generally used, but some analysts may prefer to use average prices when calculating the AAGR based on what is analyzed.

### Average annual growth rate relative to the compound annual growth rate

The AAGR is a linear measure that does not take into account the effects of composition. The example above shows that investment has increased on average by 19% per year. The average annual growth rate is useful for showing trends; however, it can be misleading for analysts as it does not accurately represent the evolution of the financial statements. In some cases, it may overestimate the growth of an investment.

For example, consider a year-end value for the fifth year of $ 100,000. The percentage growth rate for year 5 is -50%. The resulting CAGR would be 5.2%; however, it is obvious from the start value of year 1 and the end value of year 5, the performance gives a return of 0%. Depending on the situation, it may be more useful to calculate the compound annual growth rate (CAGR). The CAGR smooths the returns on an investment or lessens the effect of volatility in periodic returns.

### The formula for CAGR is:

The

$CAGR = frac { text {End Balance}} { text {Beginning Balance}} ^ { frac {1} { text { # Years}}} – 1$VSAgR=Starting balanceClosing balanceThe# Years1The–1The

Using the example above for years 1 to 4, the CAGR is equal to:

**The**

**$CAGR = frac { 200,000 $} { 100,000 $} ^ { frac {1} {4}} – 1 = 18.92 %$**

**VSAgR=$100,000$200,000The41The–1=18.92%The **

During the first four years, the AAGR and the CAGR are close to each other. However, if year 5 were to be taken into account in the CAGR equation (-50%), the result would end up being 0%, which contrasts sharply with the AAGR result of 5.2%.

### Limits of the Average Annual Growth Rate (CAGR)

Because the AAGR is a simple average of periodic annual returns, the measure does not include any measure of the overall risk associated with the investment, as calculated by the volatility of its price. For example, if a portfolio grows 15% net one year and 25% the following year, the average annual growth rate would be calculated at 20%. For this purpose, fluctuations in the rate of return on investment between the start of the first year and the end of the year are not taken into account in the calculations, which leads to measurement errors.

A second problem is that as a simple average, it doesn’t care about the timing of returns. For example, in our example above, a sharp drop of 50% in the fifth year has only a modest impact on total average annual growth. However, timing is important, and therefore the CAGR can be more useful in understanding how time-related growth rates matter.