Compounded Annual Growth Rate (CAGR) [CAGR Formula]

What Is the Compound Annual Growth Rate (CAGR)?

CAGR stands for Compound Annual Growth Rate and is a measure of how an investment has grown over time.

It’s often used to calculate the percentage return on investments, such as stocks, bonds, mutual funds, among other assets.

To calculate CAGR, you take the beginning value of your investment, divide it by the ending value, and then raise that number to a fractional power equal to the number of years in your investment period.

For example, if you invest $100 at the beginning of Year 1 and it’s worth $150 at the end of Year 2, your CAGR would be ((150/100)^(1/2)) – 1 = 1.5^0.5 – 1, or 22.4%.

CAGR can be a useful measure for evaluating the performance of an investment, but it has some drawbacks.

One is that it smooths out the ups and downs of an investment’s return, so it may not give you an accurate picture of how your investment performed in any given year.

CAGR also assumes that your investment compounds, or grows at a constant rate, which may not be realistic.

Still, CAGR can be a helpful tool for comparing the performance of different investments over time.

And if you’re thinking about investing in something for the long term, CAGR can give you a sense of how much your investment could grow.

 

How to Find Compound Annual Growth Rate (CAGR)

To calculate CAGR, you’ll need three pieces of information:

  • The starting value of your investment
  • The ending value of your investment
  • The number of years you held your investment

Then, use this formula:

 

CAGR = (ending value / beginning value) ^ (1 / number of years) – 1

 

For example, let’s say you invested $10,000 in a stock five years ago and it’s now worth $25,000.

To find the CAGR, you would use this formula:

CAGR = ($25,000 / $10,000) ^ (1 / 5) – 1

CAGR = 2.5^0.2 – 1

CAGR = 1.20 – 1 = 0.2 or 20 percent per year

 

To find CAGR Using a Financial Calculator

Set the mode to “begin” or “end”. If you want to find CAGR for an investment that’s already been made, use the “end” mode. For an investment you plan to make in the future, use “begin”.

Enter the starting value of your investment.

Enter the ending value of your investment.

Divide the number of years you held the investment into 1. For example, if you held the investment for two years, enter 2 as 0.5.

Press the CAGR button and read the answer on the display.

 

What the CAGR Can Tell You

CAGR can give you a sense of how fast an investment is growing, but it’s just one tool you can use to evaluate an investment.

CAGR doesn’t take into account the volatility, or ups and downs, of an investment’s return.

So, if you’re looking at two investments with the same CAGR, the one with less volatility may be a better choice.

Also, CAGR assumes that your investment grows at a constant rate, which is rarely the case in the real world.

In reality, investments tend to have periods of strong growth followed by periods of slower growth or even decline.

CAGR can smooth out these ups and downs, so it’s important to look at other measures of performance, such as return on investment (ROI) or total return, when evaluating an investment.

Investors often use CAGR to compare the performance of different investments.

For example, you might compare the CAGR of a stock you’re thinking about buying with the CAGRs of similar stocks or with the CAGR of a benchmark index, such as the S&P 500.

You might also use CAGR to compare the performance of different investments in your portfolio.

For example, if you have your money in both stocks and bonds, you might want to know which asset class has grown more over time. CAGR can help you answer that question.

CAGR is just one tool for evaluating an investment. When you’re considering an investment, be sure to look at other measures of performance, such as ROI and total return.

And remember that CAGR smooths out the ups and downs of an investment’s return, so it may not give you an accurate picture of how your investment performed in any given year.

CAGR explained

 

CAGR vs. Compound Net Annual Rate (CNAR)

The CNAR is like CAGR, but it accounts for taxes. CAGR doesn’t take taxes into account, so it may overestimate the true return on your investment.

To find CNAR, you’ll need to know your tax rate and the CAGR of your investment.

Then, use this formula:

 

CNAR = CAGR x (1 – tax rate)

 

For example, let’s say you have an investment that grew by 10 percent last year and you’re in the 25 percent tax bracket.

To find the CNAR, you would use this formula:

CNAR = 10% x (1 – 0.25)

CNAR = 10% x 0.75

CNAR = 7.5%

 

CAGR vs. MWR vs. TWR

CAGR is the year-over-year growth rate of an investment.

The MWR is the average annual compound return of an investment over a holding period.

TWR is the total return of an investment, which includes both capital gains and income (dividends or interest).

To find CAGR, you divide the ending value of an investment by the beginning value and raise that number to the power of one divided by the number of years.

To find MWR, you add up all the individual yearly returns and divide by the number of years.

TWR is found by adding any income received from the investment (such as dividends or interest) to the ending value and then subtracting the beginning value.

CAGR is the best measure to use when you’re trying to find the average annual return of an investment over a period of years.

TWR provides investors with a good measure to compare the performance of a certain fund against other funds and against key asset class benchmarks (such as the S&P 500).

MWR provides investors with a good measure of the performance of their personal account, due to the timing of withdrawals and deposits.

 

CAGR vs. IRR

IRR is the internal rate of return of an investment. CAGR is the year-over-year growth rate of an investment.

To find CAGR, you divide the ending value of an investment by the beginning value and raise that number to the power of one divided by the number of years.

To find IRR, you need to know the cash flows from an investment over time. Then, you use a financial calculator or spreadsheet program to find the interest rate that makes the present value of the cash flows equal to the initial investment.

CAGR is best used to find the average annual return of an investment over a period of years. IRR is useful when comparing multiple investments and projects against each other or in cases where it is difficult to determine the appropriate discount rate.

 

Modifying the CAGR Formula

For example, if you’ve held an investment for between 5 and 6 years, calculating your CAGR isn’t most accurately estimated only using the whole integers.

Instead, you have to figure it down to a more accurate decimal point.

For example, if you bought something on the first of January between 5 and 6 years and it’s now August 4, that means you’ve owned it for 216 days of the year (217 in leap years), so that fraction of a year is 0.59 (216 divided by 365).

So if you bought it at $100 per share and it’s now $170 per share (assume no dividends or distribution paid out), that means your CAGR is:

CAGR = (170/100)^(1/5.59) – 1

CAGR = 1.0996 – 1 = 0.0996 or 9.96 percent

 

CAGR Limitations

CAGR can be a useful tool for estimating the average return of an investment, but it has its limitations. CAGR doesn’t take into account the timing of cash flows, so it may overestimate the true return on your investment.

To get a more accurate picture of your investment’s return, you need to look at the overall rate of return, which takes into account both the CAGR and the timing of cash flows.

CAGR also assumes that you reinvest all your profits back into the investment, like in the case of stocks that have dividends. If you don’t, CAGR will overestimate your investment’s true return.

And finally, CAGR doesn’t take into account the riskiness of an investment. A higher-risk investment may have a higher CAGR, but it may also be more volatile and more likely to lose money.

When using CAGR to estimate the return on an investment, keep these limitations in mind and use other measures of performance as well to get a complete picture.

 

Compounded Annual Growth Rate (CAGR) – FAQs

What Is Considered a Good CAGR?

There’s no simple answer to this question since a “good” CAGR depends on your investment goals and the level of risk you’re comfortable with.

If you’re investing for retirement, you may be willing to accept a lower CAGR if it means less volatility in your portfolio.

On the other hand, if you’re investing for a short-term goal, you may be willing to accept a higher CAGR even if it means more volatility.

It’s also important to compare your investment’s CAGR to its benchmark.

For example, if you’re invested in a stock that has a CAGR of 5 percent but the stock market as a whole has a CAGR of 7 percent, your investment is underperforming.

Conversely, if your stock has a CAGR of 10 percent but the market has a CAGR of 7 percent, your investment is outperforming.

Keep in mind, though, that past performance is no guarantee of future results. Just because a stock has outperformed in the past doesn’t mean it will continue to do so in the future.

What Is CAGR Used for?

CAGR can be used for a number of different purposes, including estimating:

  • The return on an investment over time (most common)
  • The growth rate of an economy or market
  • The growth rate of inflation
  • The population growth rate
  • The average rate of return on a car loan or mortgage repayment for a lender

Is CAGR the Same as Average Annual Return?

No, CAGR is not the same as average annual return. CAGR takes into account the compounding of returns, while average annual return does not.

CAGR is therefore a more accurate measure of an investment’s true return.

What Is the Difference Between CAGR and IRR?

The main difference between CAGR and IRR is that CAGR takes into account the compounding of returns, while IRR does not.

CAGR is often considered a more accurate measure of an investment’s true return.

The IRR is a metric used in financial analysis to estimate the profitability of potential projects or investments.

Can the CAGR Be Negative?

Yes, CAGR can be negative. This happens when the investment loses money over the time period in question.

For example, let’s say you invest $10,000 in a stock on the first day of Year 1.

The stock goes down 10 percent in value in Year 1, then up 20 percent in Year 2, and finally down 25 percent in Year 3.

The CAGR for this investment would be:

CAGR = (0.9 * 1.2 * 0.75)^(1/3) – 1 = 0.932 – 1 = -0.068 = minus-6.8 percent

What Is a Good CAGR for an Industry?

It depends on the industry and asset class.

For example, most who invest in tech stocks expect a higher CAGR because those securities are more volatile.

Those who invest in utilities or consumer staples might be content with a lower return because the cash flows in those industries are more stable.

Moreover, those who invest in stocks expect a higher return those who invest in bonds, who expect a higher return than those who put money into cash or money market funds.

And those who invest in venture capital and private equity expect to be compensated more than public market investors due to the illiquidity of their investment.

What Is Risk-Adjusted CAGR?

Risk-adjusted CAGR is a CAGR that has been adjusted to account for the investment’s risk.

There are a number of different ways to adjust CAGR for risk.

A common, basic way to calculate the risk-adjusted CAGR is to multiply the CAGR by one minus the investment’s standard deviation (a proxy for volatility, which is a form of risk).

The higher the standard deviation the lower the risk-adjusted CAGR.

How to Calculate CAGR in Excel?

This video gives a good overview of how to calculate CAGR in Excel.

CAGR Function and Formula in Excel | Calculate Compound Annual Growth Rate

 

Summary – Compounded Annual Growth Rate (CAGR)

The CAGR formula is a way to calculate the average annual return of an investment over a period of time. CAGR stands for Compounded Annual Growth Rate.

It takes into account the compounding of returns, which is why it’s often considered a more accurate measure of an investment’s true return.

CAGR can be used to estimate the return on an investment, the growth rate of an economy or market, the growth rate of inflation, the population growth rate, or the average rate of return on a loan.

CAGR is not the same as the average annual return. CAGR takes into account the compounding of returns, while average annual return does not.

The main difference between CAGR and IRR is that CAGR takes into account the compounding of returns, while IRR does not. CAGR is often considered a more accurate measure of an investment’s true return.

 

 

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