What is Compound Annual Growth Rate (CAGR) and How to Calculate It?

The compound annual growth rate, commonly called CAGR, is the compounding of rates of return over a specified period.

It is useful for investors and businesses to compare the performances of different investments over the same period.

Let us discuss what is CAGR and how to calculate it along with its uses.

What is the Compound Annual Growth Rate – CAGR?

CAGR basically refers to the compound annual growth rate of investment or stock over a specified period.

It is the required rate of return of an investment if all profits were reinvested and compounded until the maturity date.

The CAGR when measured to forecast the future growth rate does not offer a real rate of return. Instead, it gives an idea of what investment could achieve if all of its profits were reinvested.

CAGR then takes the fluctuating rates of return out of the equation and offers a single and smooth rate of return for a single investment or a portfolio.

Like any other type of rate of return, there is no ideal CAGR. It will depend on the industry and investment size along with other factors.

However, generally, a CAGR of around 20% is considered a good result. It is important to mention here that the CAGR can also be a negative figure.

How to Calculate CAGR?

We can calculate the CAGR by using the following formula:

CAGR = [(EV/BV)1/n −1] × 100

Where:

• EV = Ending Value;
• BV = Beginning Value; and
• n= number of years

Here are a few simple steps to calculate the CAGR of an investment.

The first step is to find the beginning and ending values of the investment. These figures are usually readily available as the beginning and ending amounts of investments.

The second step is to divide the EV by the BV of the investment and take the exponential to one by nth power. Here “n” is the number of years for the investment period.

Then, deduct one from the result and multiply it by a hundred to get the compound annual growth rate in percentage terms.

Example

Suppose an investor buys ABC company’s shares worth \$ 10,000. The investor held this investment for 3 years and the value of the investment changed during this period.

• Beginning Value at Y1 = \$ 12,000
• Value at Y2 = \$ 14,000
• Ending Value at Y3 = \$ 15,000
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As we can see the initial investment had a steady growth rate. The growth rate for the first year was 20%, 16.67% for the second year, and 6.67% for the third year.

We can use the CAGR formula to get a compound annual growth rate for this investment as well.

CAGR = [(EV/BV)1/n −1] × 100

CAGR = [(\$ 15,000/\$ 10,000) 1/3 – 1] × 100

CAGR = 14.31%

Modifying CAGR Formula

In some cases, the investment period may not be given in terms of years. For instance, an investor may start investing in a stock in the middle of the year and may sell it before the last month of the year.

We can then modify the CAGR formula to convert these years into a uniform figure to avoid any miscalculations.

Continuing with our example above, suppose the investor invested on July 1 for the first year and disposed of the investment on October 1 in the third year.

It means the investor did not hold the investment for the full three years period.

We can modify the CAGR formula to calculate the rate again.

• Days for the First year = 184
• Days for the second year = 365
• Days for the Third Year = 276

The total number of days for the investment is 825. When we divide the number of days by 365, we’ll get the number of years 2.26.

We can use this period in the example above to find the CAGR again.

CAGR = [(\$ 15,000/\$ 10,000) ½.26 – 1] × 100

CAGR = 19.76%

We can see the actual CAGR is higher than the earlier calculation as the investment was held for a shorter period.

Uses of Compound Annual Growth Rate

CAGR can be used for comparing investment performances over a set period.

It brings annualized average returns to a consistent compound growth that makes it easy to compare different investments.

Smoothing the uneven and fluctuating rates of return is another typical use of the CAGR. It converts the changing rates into a single and consistent compounded rate of return.

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Although it does not forecast future returns, investors can use CAGR to analyze the historic returns of stocks and bonds. They can then use these results to forecast the future performance of potential investment options.

Businesses can use CAGR to compare the performance of different segments or a group of companies.

For example, if a business has several products, it can use the CAGR to compare the performances of these products.

In this way, the business can analyze its strengths and weaknesses in terms of financial performance.

The conventional approach of using the compound annual growth rate ignores investment risks. Also, you must use the same period when comparing different investment options.

CAGR also does not account for additional investments made by an investor. All these factors combined change the actual returns received by an investment.

One of the critical points is accommodating the volatility risk of the investment. In practice, investment returns are volatile as many factors affect the returns.

You can use the risk-adjusted CAGR to replace the conventional CAGR formula. For that, calculate the standard deviation of each investment under consideration.

If the standard deviation of an investment is zero, its expected CAGR and risk-free returns will be the same. Therefore, its risk-adjusted CAGR and CAGR will be the same. The formula for risk-adjusted CAGR is:

Risk-Adjusted CAGR = CAGR × (1 – Standard Deviation)

How Investors Can Use CAGR?

Investors can use the CAGR in different ways.

First of all, they can use it to compare the historic performances of different investments like stocks and bonds. They can then use the CAGRs of these investments to forecast future performance as well.

Secondly, investors can use the smooth CAGR formula to calculate an investment amount required after a specified period. Or conversely, they can use an investment amount required after a specific period to know the required rate of return now.

Suppose an investor needs \$ 50,000 after ten years and has only \$ 10,000 now. The investor is willing to reinvest all profits and compound them until ten years.

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What is the required rate of return that will yield \$ 50,000 in ten years?

We can use the CAGR formula to get the answer.

CAGR = [ (50,000/ 15,000) 1/10 – 1] × 100 = 12.79%

Now, the investor can find an investment that yield a CAGR of 12.79% for ten years to get the desired amount.

Put another way, the investor can increase the initial investment to reduce the required time or if the required rate of return is unavailable.

The compound annual growth rate is a useful tool with several advantages.

• It can be used to compare the investment performance over the same time.
• Businesses can use it to compare the performances of different products, segments, or divisions.
• Investors can analyze the historic performances of stocks and bonds.
• It converts the fluctuating annualized average returns into a smooth percentage figure for easy understanding.
• It can be adjusted for uneven investment time horizons too as we have shown in our example above.
• It is easy to calculate and can be understood easily.

Limitations of Using CAGR

Despite several uses and benefits, the compound annual growth rate has several disadvantages as well.

• It ignores the investment volatility that can change the investment returns significantly.
• It ignores the investment risks and does not consider the fluctuating returns due to these risks.
• CAGR can be adjusted to the standard deviation for volatility but it lacks authenticity with different assumptions.
• It is only useful for comparing the historic performances of investments over the same period and cannot be used for forecasting reliably.
• It also ignores the fact that the ending value of an investment can increase due to further investment by the investor.
• Smoothing of uneven averaging rates of return is also the limitation of CAGR as it hides the new investments injected into the previous pool of investment.
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