Growth connotes progress, improvement and achievement. Measuring the increase of things, ranging from investment portfolios to populations, constitutes an essential part of many professions and trades. One such barometer of growth is the compound annual growth rate, or CAGR. Those who decide on business ventures, investments and public policy need to know how to calculate compound annual growth rate. Below you will find the CAGR formula, as well as an explanation of the concept and its practical applications.

## Understanding the Compound Annual Growth Rate

Generally, stock markets, labor markets, businesses, industries and population patters encounter periods of volatility. News, incidents and other forces cause growth or decline at least in the short-term. In other instances, growth can be concentrated at the beginning of a period or near the end.

With a CAGR calculation, you essentially ignore the volatility and curves in an upward trend. Thus, you will obtain a “smooth” rate of growth over a period of time. CAGR assumes that a particular value increases at the same rate each year over that interval. As such, CAGR is an imaginary or theoretical concept.

### What Types of Compound Annual Growth Rate Are There?

Ultimately, there is one type of Compound Annual Growth Rate. As the formula in the “How to Calculate Compound Annual Growth Rate” section explains, CAGR assumes exponential growth over an interval of years – even though the result is a “smooth” rate.

To understand how to calculate the compound annual growth rate, and what it means, consider the concept of simple growth. Such an annual simple growth rate assumes that a figure, such as population or revenue, increases by the same rate each year. By contrast, CAGR considers that growth likely does not occur at a constant rate, but can rise sharply or flatten or stall throughout a period.

## How to Calculate Compound Annual Growth Rate

### CAGR General Formula

The formula generally is expressed as:

**((Value (Present)-Value(Past)/Value Past)*100)/N (Number of years)**.

In other words:

- Divide the difference in Beginning and Ending Values by the Beginning Value.
- Multiply by 100 to get the Percentage Growth for the entire period.
- Divide by the number of years in the period.

### CAGR Formula for Regular Time Intervals

The CAGR calculation for regular time intervals involves using the below formula to isolate the “growth rate” variable:

***CAGR=((Ending Value/Beginning Value)^1/Compound Period)-1**

The **“Beginning Value”** represents the value or figure at the start of your compounding period. This can mean the price at which you bought stock or some other investment or the level of profits, revenues, employment or use of something in the first year of your examination. In the **“Ending Value”**, you take the relevant figure at the conclusion of the period.

In grasping how to calculate compound annual growth rate, the key lies in accurately stating the compound period. If data is reported on a yearly basis, **determine the “Compound Period” by subtracting the year for the ending value from the year for the beginning value**. For instance, you’re calculating the CAGR for revenues from 1998 to 2017. The compound period is 2017-1998, or 19 years.

When you’re given **a series of monthly figures**, you create a fraction with the number of months as the numerator and twelve (for the number of months per year) as the denominator. Then, invert that fraction because your exponent is one divided by the number of months/12 months per year. So, if you have 17 months of figures, your compound period is 17/12 years. The quotient of the ending value and beginning value would be raised in this example to 12/17.

##### So, to execute the formula, follow these steps:

- Divide the Ending Value by the Beginning Value.
- Raise the Quotient to the power of one divided by Compound Period in years.
- Subtract “1” from the Quotient raised to the power of one over the Compound Period.

## Applications of Compound Annual Growth Rate

Calculating the compound annual growth rate holds significant meaning for investors and those in the investment field. Those who pour money into stocks, bonds, mutual funds or other investments use CAGR to gauge present or past performance and predict future prospects. Investment houses post CAGR to allow investors to compare the performance and desirability of investments.

The CAGR extends beyond personal finance and investing. To companies, CAGR shows the growth over a relatively long-term the growth of revenues and profits and is a forecast tool From these rates, a manufacturer or retailer decides the whether to continue with a project or even a business.

Business or financial analysts also calculate CAGRs in net income and revenues across entire industries. For example, a study posted by the Stern School of Business of New York University showed CAGRs of 81.70% in net income in the “Green & Renewable Energy” sector over a five-year period. For “Oil/Gas (Production and Exploration)”, the five-year CAGR for next income was actually a decline of 14.02 percent.

Moreover, economists studying employment may find it helpful to know how to calculate compound annual growth rate. Published by the Harvard Business School in 2015, a report entitled Growth and Shared Prosperity included CAGRs for data such as job growth and real household incomes for various income distribution levels.

### Practical Example of Knowing Compound Annual Growth Rate

Transparency Market Research (TMR), a business information an analysis company, released in September 2016 a report about the “enterprise mobility market”. This sector consists of the use of laptops, smartphones, tablets and other wireless devices for communication between employers and employees. With this technology, employees can work away from offices and be available to employers at virtually any location and anytime.

The report based its CAGR calculation on TMR’s valuation of the enterprise mobility market at $86.6 billion in 2014 and a projected figure of $510.39 billion by 2022. The rise during the eight-year period amounts to $423.79 billion. TMR says the CAGR comes to the 24.7 percent predicted by TMR if the projection verifies.

The CAGR helps Transparency Market Research support with numbers and projections their assessment of the industry and its popularity. For individual and institutional investors, the CAGR guides decisions whether to buy stock in these companies, invest in mutual funds that include them, or start (or fund start-up) enterprise mobility companies.

## Conclusion

Knowing how to calculate compound annual growth rate can shape your analysis and decisions on your investments, savings and business operations. As a portrait of growth over multiple years, CAGR recognizes that factors such as the newness of a project, changing conditions or sudden events can produce different rates of growth (or decline) from year-to-year. By using CAGR, you’re more likely to avoid a short-term focus, and consider staying in an investment or business operation longer. Beyond finance and sales, calculating CAGR also helps those addressing population and employment trends. Please let us know whether and how you rely on compound annual growth rate calculations.

**Recommended read**: How to Calculate Net Present Value

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