## What Is Compound Annual Growth Rate – CAGR?

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.

## Formula and Calculation of CAGR

\begin{aligned} &CAGR= \left ( \frac{EV}{BV} \right ) ^{\frac{1}{n}}-1\\ &\textbf{where:}\\ &EV = \text{Ending value}\\ &BV = \text{Beginning value}\\ &n = \text{Number of years} \end{aligned}CAGR=(BV EV)n 11where:EV=Ending valueBV=Beginning valuen=Number of years﻿

To calculate the CAGR of an investment:

1. 1.Divide the value of an investment at the end of the period by its value at the beginning of that period.
2. 2.Raise the result to an exponent of one divided by the number of years.
3. 3.Subtract one from the subsequent result.

### Key Takeaways

• CAGR is one of the most accurate ways to calculate and determine returns for anything that can rise or fall in value over time.
• Investors can compare the CAGR of two alternatives in order to evaluate how well one stock performed against other stocks in a peer group or against a market index.
• CAGR does not reflect investment risk.

## What CAGR Can Tell You

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.

## Example of How to Use CAGR

Imagine you invested $10,000 in a portfolio with the returns outlined below: • From Jan 1, 2014, to Jan 1, 2015, your portfolio grew to$13,000 (or 30% in year one).
• On Jan 1, 2016, the portfolio was $14,000 (or 7.69% from Jan 2015 to Jan 2016). • On Jan 1, 2017, the portfolio ended with$19,000 (or 35.71% from Jan 2016 to Jan 2017).

We can see that on an annual basis, the year-to-year growth rates of the investment portfolio were quite different as shown in the parenthesis.

On the other hand, the compound annual growth rate smooths the investment’s performance and ignores the fact that 2014 and 2016 were so different from 2015. The CAGR over that period was 23.86% and can be calculated as follows:

CAGR=\left(\frac{\$19,000}{\$10,000}\right )^{\frac{1}{3}}-1=23.86\%CAGR=($10,000 $19,000)3 11=23.86%﻿

The compound annual growth rate of 23.86% over the three-year investment period 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.

The compound annual growth rate can be used to calculate the average growth of a single investment. As we saw in our example above, 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.

### Compare Investments

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 five-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:

\text{Savings Account CAGR} =\, \left ( \frac{\$10,510.10}{\$ 10,000} \right )^{\frac{1}{5}}-1 = 1.00\%Savings Account CAGR=($10,000 $10,510.10)5 11=1.00%﻿

And:

\text{Stock fund CAGR} =\, \left ( \frac{\$15,348.52}{\$ 10,000} \right )^{\frac{1}{5}}-1 = 8.95\%Stock fund CAGR=($10,000 $15,348.52)5 11=8.95%﻿

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

### Track Performance

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.

### Detect Weaknesses and Strengths

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.

## Investor Use of CAGR

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:

\text{Required Return} =\, \left ( \frac{\$50,000}{\$ 15,000} \right )^{\frac{1}{18}}-1 = 6.90\%Required Return=($15,000 $50,000)18 11=6.90%﻿

## CAGR vs. IRR

The CAGR measures the return on an investment over a certain period of time. The internal rate of return (IRR) also measures investment performance but is more flexible than CAGR.

The most important distinction is that CAGR is straightforward enough that it can be calculated by hand. In contrast, more complicated investments and projects, or those that have many different cash inflows and outflows, are best evaluated using IRR. To back into the IRR rate, a financial calculator, Excel, or portfolio accounting system is ideal.

## Example of How to Use CAGR

Let’s say an investor bought 100 shares of Amazon.com (AMZN) stock in December 2015 at $650 per share, for a total investment of$65,000. After 3 years, in December 2018, the stock has risen to $1,750 per share, and the investor’s investment is now worth$175,000.﻿ What is the compound annual growth rate?

Using the CAGR formula, we know that we need the:

• Ending Balance: $175,000 • Beginning Balance:$65,000
• Number of Years: 3

So to calculate the CAGR for this simple example we'd enter that data into the formula as follows:

\text{CAGR for Amazon} =\, \left ( \frac{\$175,000}{\$ 65,000} \right )^{\frac{1}{3}}-1 = 39.12\%CAGR for Amazon=($65,000 $175,000)3 11=39.12%﻿
This tells us that the compound annual growth rate for the investment in Amazon is 39.12%.

CAGR is a measurement used by investors to calculate the rate at which a quantity grew over time. The word "compound" denotes the fact that CAGR takes into account the effects of compounding, or reinvestment over time. For example, suppose you have a company whose revenue grew from $3 million to$30 million over a span of 10 years. In that scenario, the CAGR would be approximately 25.89%.