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What is the 'Compound Annual Growth Rate - CAGR'

The compound annual growth rate (CAGR) is the rate of return that would be required for an investment to grow from its beginning balance to its ending balance assuming the profits were reinvested at the end of each year of the investment’s lifespan.

To calculate the compound annual growth rate, divide the value of an investment at the end of the period by its value at the beginning of that period, raise the result to an exponent of one divided by the number of years, and subtract one from the subsequent result.

The formula for CAGR can be written as follows:

CAGR can also be calculated using Investopedia's own Compound Annual Growth Rate Calculator.

BREAKING DOWN 'Compound Annual Growth Rate - CAGR'

The compound annual growth rate isn't a true return rate, but rather a representational figure. It is essentially a number that describes the rate at which an investment would have grown if it had grown the same rate every year and the profits were reinvested at the end of each year. In reality, this sort of performance is unlikely. However, CAGR can be used to smooth returns so that they may be more easily understood when compared to alternative investments.

CAGR Example

Imagine you invested $10,000 in a portfolio on Jan 1, 2014 and by Jan 1, 2015, your portfolio had grown to $13,000. The investment then grew to $14,000 by the first day in 2016 and ended at $19,500 by Jan 1, 2017. The average (arithmetic mean) annual return for that period was 25.67%. The CAGR over that period was 24.95% because it smooths the investment’s performance and ignores the fact that 2014 and 2016 were so different than 2015.

The CAGR for this period can be calculated as follows:

A compound annual growth rate over a three-year investment equal to 24.93% can help an investor compare alternatives for their capital or make forecasts of future values. For example, imagine an investor is comparing the performance of two investments that are uncorrelated. In any given year during the period, one investment may be rising while the other falls. This could be the case when comparing high-yield bonds to stocks, or a real estate investment to emerging markets. Using CAGR would smooth the annual return over the period so the two alternatives would be easier to compare.

Uses of the Compound Annual Growth Rate (CAGR)

Most simply, CAGR can be used to calculate the average growth of a single investment. Due to market volatility, the year-to-year growth of an investment will likely appear erratic and uneven. For example, an investment may increase in value by 8% in one year, decrease in value by -2% the following year and increase in value by 5% in the next. CAGR helps smooth returns when growth rates are expected to be volatile and inconsistent.

CAGR can be used to compare investments of different types with one another. For example, suppose in 2013 an investor placed $10,000 into an account for 5 years with a fixed annual interest rate of 1% and another $10,000 into a stock mutual fund. The rate of return in the stock fund will be uneven over the next few years so a comparison between the two investments would be difficult.

Assume that at the end of the 5 year period, the savings account’s balance is $10,510.10 and, although the other investment has grown unevenly, the ending balance in the stock fund was $15,348.52. Using CAGR to compare the two investments can help an investor understand the difference in returns.

On the surface, the stock fund may look like a better investment with nearly nine times the return of the savings account. However, by smoothing the returns, CAGR cannot tell an investor how volatile or risky the stock fund was.

CAGR can also be used to track the performance of various business measures of one or multiple companies alongside one another. For example, over a five-year period, Big-Sale Stores’ market share CAGR was 1.82% but its customer satisfaction CAGR over the same period was -0.58%. In this way, comparing the CAGRs of measures within a company reveals strengths and weaknesses. Comparing CAGRs of business activities across similar companies will help evaluate competitive weaknesses and strengths. For example, Big-Sale’s customer satisfaction CAGR might not seem so low when compared with SuperFast Cable’s customer satisfaction CAGR of -6.31% during the same period.

Modifying CAGR in the Real World

An investment is rarely made on the first day of the year and then sold on the last day of the year. Imagine an investor who wants to evaluate the CAGR of a $10,000 investment that was entered on June 1st, 2013 and sold for $16,897.14 on September 9th, 2018.

Before the CAGR calculation can be performed, the investor will need to know the fractional remainder of the holding period. They held the position for 213 days in 2013, a full year in 2014, 2015, 2016, and 2017, and 251 days in 2018. This investment was held for 5.271 years which can be placed in the denominator of the exponent inside CAGR’s formula as follows:

Limitations of Compound Annual Growth Rate - CAGR

The most important limitation of CAGR is that because it calculates a smoothed rate of growth over a period, it ignores volatility and implies that the growth during that time was steady. Returns on investments are uneven over time, except bonds that are held to maturity, deposits, and similar investments.

Another limitation of using CAGR in assessing investments is that, no matter how steady the growth of a company or investment has been in the past, investors cannot assume the rate will remain the same in the future. The shorter the time frame used in the analysis, the less likely it will be for realized CAGR to meet expected CAGR when relying on historical results.

A third limitation of CAGR is a limitation of representation. Say that an investment fund was worth $100,000 in 2012, $71,000 in 2013, $44,000 in 2014, $81,000 in 2015 and $126,000 in 2016. If the fund managers represented in 2017 that their CAGR was a whopping 42.01% over the past three years, they would be technically correct. They would, however, be omitting some very important information about the fund’s history, including the fact that the fund’s CAGR over the past five years was a modest 4.73%.

Manipulating the CAGR Formula to Answer Other Questions About Growth

Understanding the formula used to calculate CAGR is an introduction to many other ways investors evaluate past returns or estimate future profits. The formula can be manipulated algebraically into a formula to find the present value or future value of money, or to calculate a hurdle rate of return.

For example, imagine that an investor knows that they need $50,000 for a child’s college education in 18 years and they have $15,000 to invest today. How much does the average rate of return need to be in order to reach that objective? The CAGR calculation can be used to find the answer to this question as follows:

This version of the CAGR formula is just a rearranged present value and future value equation. For example, if an investor knew that they needed $50,000 and they felt it was reasonable to expect an 8% annual return on their investment, they could use this formula to find out how much they needed to invest to meet their goal.

Summary

The compound annual growth rate (CAGR) helps investors understand their investment performance if they assume returns are consistent and profits are reinvested at the end of each year during the investment period. It can also be used to compare investments or other growth rates. One of the most significant risks of using CAGR to evaluate an investment return is that it ignores the volatility and risk of an investment’s return.

For more on the Compound Annual Growth Rate (CAGR), see: Compound Annual Growth Rate: What You Should Know.

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