Uses of the Average Annual Growth Rate (AAGR)The AAGR is useful in assessing long-term trends. It is relevant to nearly any form of financial metric analysis, such as the growth rate of earnings, sales, cash flow, expenditures, etc., to give investors an indication of the direction in which the firm is going. The AAGR depicts, on average, what the annual returns have been. Show AAGR FormulaAnnual Average Growth Rate = [(Growth Rate)y + (Growth Rate)y+1 + … (Growth Rate)y+n] / NWhere:
How the AAGR is CalculatedThe AAGR is a benchmark for calculating the average return on investments over a number of years. Essentially, it is the basic average growth rates of return for a sequence of periods (years). To compute the average, the growth rate for each individual time period in the series must be computed. It can be done by using the basic formula below: Growth Rate Percentage = ((EV / BV) – 1) x 100%Where:
Once the growth rate percentages for each time period have been calculated, they are added together and divided by the total number of the time periods, giving the AAGR. One point to always take into consideration is that the periods used should be equal in length when calculating the growth rates. These time periods can be year-on-year, month-on-month, quarterly, etc., depending on the specific needs of the person or firm computing the growth rates. Step-by-Step ExampleGiven the following annual revenues for ABC Company: Year 1: $250,000 Year 2: $356,000 Year 3: $390,000 Year 4: $395,000 Year 5: $400,000 Year 6: $358,000 Year 7: $320,000 Using the growth rate formula above, the growth rates from Years 1 to 7 can be computed as: Y1: 0, because there is no preceding time period Y2: [(356,000/250,000)-1] x 100% = 42.4% Y3: [(390,000/356,000)-1] x 100% = 9.7% Y4: [(395,000/390,000)-1] x 100% = 101.3% Y5: [(400,000/395,000)-1] x 100% = 101.3% Y6: [(358,000/400,000)-1] x 100% = -10.5% Y7: [(320,000/358,000)-1] x 100% = -10.6% And the AAGR is calculated as: Sum of Growth Rates = [42.4 % + 9.7 % + 101.3 % + 101.3 % + (-10.5 %) + (-10.6 %)] = 233.6% AAGR = 233.6 % / 7 = 33.4% The average annual growth rate for ABC Company is 33.4%. Average Annual Growth Rate (AAGR) Restrictions in Financial AnalysisConsider a portfolio that grows by 25% in the first year and 12% in the following year. The average annual growth rate (AAGR) would be calculated as 18.5%. The fluctuations in the return rate of the portfolio between the start of the first year and the end of the year are not taking into consideration the average annual growth rate calculation. It can lead to certain mistakes in the estimation. Since AAGR is an average of the annual returns, the metric does not provide an estimate of the total risk associated with an investment, as estimated by the instability of its price. Basically, AAGR can be estimated for any investment; however, it will not provide any indication of the potential risk of the investment. Furthermore, AAGR does not accommodate the effects of compounding, as it is a linear metric. An analysis can show that an investment has grown by an average of n percent per year, whilst missing the fluctuations that may have occurred during the time period series. Ideal for showing trends, AAGR can also be deceptive to investors since it does not adequately reflect changing financial trends. Also, the growth of an investment can be overestimated. Additional ResourcesThank you for reading CFI’s guide on Average Annual Growth Rate. To keep learning and advancing your career, the additional CFI resources below will be useful:
The average annual growth rate (AAGR) reports the mean increase in the value of an individual investment, portfolio, asset, or cash flow on an annualized basis. It doesn't take compounding into account.
A A G R = G R A + G R B + … + G R n N where: G R A = Growth rate in period A G R B = Growth rate in period B G R n = Growth rate in period n N = Number of payments \begin{aligned} &AAGR = \frac{GR_A + GR_B + \dotso + GR_n}{N} \\ &\textbf{where:}\\ &GR_A=\text{Growth rate in period A}\\ &GR_B=\text{Growth rate in period B}\\ &GR_n=\text{Growth rate in period }n\\ &N=\text{Number of payments}\\ \end{aligned} AAGR=NGRA+GRB+…+GRnwhere:GRA=Growth rate in period AGRB=Growth rate in period BGRn=Growth rate in period nN=Number of payments The average annual growth rate helps determine long-term trends. It applies to almost any kind of financial measure including growth rates of profits, revenue, cash flow, expenses, etc. to provide the investors with an idea about the direction wherein the company is headed. The ratio tells you your average annual return. The average annual growth rate is a calculation of the arithmetic mean of a series of growth rates. AAGR can be calculated for any investment, but it will not include any measure of the investment's overall risk, as measured by its price volatility. Furthermore, the AAGR does not account for periodic compounding.
AAGR is a standard for measuring average returns of investments over several time periods on an annualized basis. You'll find this figure on brokerage statements and in a mutual fund's prospectus. It is essentially the simple average of a series of periodic return growth rates. One thing to keep in mind is that the periods used should all be of equal length—for instance, years, months, or weeks—and not to mix periods of different duration. The AAGR measures the average rate of return or growth over a series of equally spaced time periods. As an example, assume an investment has the following values over the course of four years:
The formula to determine the percentage growth for each year is: Simple percentage growth or return = ending value beginning value − 1 \text{Simple percentage growth or return} = \frac{\text{ending value}}{\text{beginning value}} - 1 Simple percentage growth or return=beginning valueending value−1 Thus, the growth rates for each of the years are as follows:
The AAGR is calculated as the sum of each year's growth rate divided by the number of years: A A G R = 20 % + 12.5 % + 18.5 % + 25 % 4 = 19 % AAGR = \frac{20 \% + 12.5 \% + 18.5 \% + 25 \%}{4} = 19\% AAGR=420%+12.5%+18.5%+25%=19% In financial and accounting settings, the beginning and ending prices are usually used. Some analysts may prefer to use average prices when calculating the AAGR depending on what is being analyzed.
As another example, consider the five-year real gross domestic product (GDP) growth for the United States over the last five years. The U.S. real GDP growth rates for 2017 through 2021 were 2.3%, 2.9%, 2.3%, -3.4%, and 5.7%, respectively. Thus, the AAGR of U.S. real GDP over the last five years has been 1.96%, or (2.3% + 2.9% + 2.3% + -3.4% + 5.7%) / 5. AAGR is a linear measure that does not account for the effects of compounding. The above example shows that the investment grew an average of 19% per year. The average annual growth rate is useful for showing trends; however, it can be misleading to analysts because it does not accurately depict changing financials. In some instances, it can overestimate the growth of an investment. For example, consider an end-of-year value for year 5 of $100,000 for the AAGR example above. The percentage growth rate for year 5 is -50%. The resulting AAGR would be 5.2%; however, it is evident from the beginning value of year 1 and the ending value of year 5, the performance yields a 0% return. Depending on the situation, it may be more useful to calculate the compound annual growth rate (CAGR). The CAGR smooths out an investment's returns or diminishes the effect of the volatility of periodic returns. C A G R = Ending Balance Beginning Balance 1 # Years − 1 CAGR = \frac{\text{Ending Balance}}{\text{Beginning Balance}}^{\frac{1}{\text{\# Years}}} - 1 CAGR=Beginning BalanceEnding Balance# Years1−1 Using the above example for years 1 through 4, the CAGR equals: C A G R = $ 200 , 000 $ 100 , 000 1 4 − 1 = 18.92 % CAGR = \frac{\$200,000}{\$100,000}^{\frac{1}{4}}- 1 = 18.92\% CAGR=$100,000$200,00041−1=18.92% For the first four years, the AAGR and CAGR are close to one another. However, if year 5 were to be factored into the CAGR equation (-50%), the result would end up being 0%, which sharply contrasts the result from the AAGR of 5.2%. Because AAGR is a simple average of periodic annual returns, the measure does not include any measure of the overall risk involved in the investment, as calculated by the volatility of its price. For instance, if a portfolio grows by a net of 15% one year and 25% in the next year, the average annual growth rate would be calculated to be 20%. To this end, the fluctuations occurring in the investment’s return rate between the beginning of the first year and the end of the year are not counted in the calculations thus leading to some errors in the measurement. A second issue is that as a simple average it does not care about the timing of returns. For instance, in our example above, a stark 50% decline in year 5 only has a modest impact on total average annual growth. However, timing is important, and so CAGR may be more useful in understanding how time-chained rates of growth matter.
The average annual growth rate (AAGR) identifies long-term trends of such financial measures as cash flows or investment returns. AAGR tells you what the annual return has been (on average), but it does not take into account compounding.
AAGR may overestimate the growth rate if there are both positive and negative returns. It also does not include any measure of the risk involved, such as price volatility—nor does it factor in the timing of returns.
Average annual growth rate (AAGR) is the average increase. It is a linear measure and does not take into account compounding. Meanwhile, the compound annual growth rate (CAGR) does and it smooths out an investment's returns, diminishing the effect of return volatility.
The average annual growth rate (AAGR) is calculated by finding the arithmetic mean of a series of growth rates. |
What is the simple average yearly percentage increase in production percent over the period shown
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