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# Growth Rates: Formula, How to Calculate, and Definition

## What Are Growth Rates?

Growth rates refer to the percentage change of a specific variable within a specific time period. Growth rates can either be positive or negative depending on whether the size of the variable is increasing or decreasing over time. Growth rates were first used by biologists studying population sizes, but have since been brought into use in studying economic activity, corporate management, or investment returns.

For investors, growth rates typically represent the compounded annualized rate of growth of an investment, or a company's revenues, earnings, or dividends. Growth rates are also applied to more macro concepts, such as gross domestic product (GDP) and unemployment. Expected forward-looking or trailing growth rates are two common kinds of growth rates used for analysis.

### Key Takeaways

• Growth rates are used to express the annual change in a variable as a percentage.
• A positive growth rate indicates a variable is increasing over time; a negative growth rate that it is decreasing.
• Growth rates can be beneficial in assessing a company’s performance and to predict future performance.
• Growth rates are computed by dividing the difference between the ending and starting values for the period being analyzed and dividing that by the starting value.
• Time periods used for growth rates are most often annually, quarterly, monthly, and weekly.
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## ﻿Understanding Growth Rates

At their most basic level, growth rates are used to express the annual change in a variable as a percentage. An economy's growth rate, for example, is derived as the annual rate of change at which a country's GDP increases or decreases. This rate of growth is used to measure an economy's recession or expansion. If the income within a country declines for two consecutive quarters, it is considered to be in a recession.

Conversely, if the country has grown its income for two consecutive quarters, it is considered to be expanding.

## How to Calculate Growth Rates

Growth rates can be calculated in several ways, depending on what the figure is intended to convey. A simple growth rate simply divides the difference between the ending and starting value by the beginning value, or (EV-BV)/BV. The economic growth rate for a country's GDP can thus be computed as:

\begin{aligned} &\text{Economic Growth} = \frac { \text{GDP}_2 - \text{GDP}_1 }{ \text{GDP}_1 } \\ &\textbf{where:} \\ &\text{GDP} = \text{Gross domestic product of nation} \\ \end{aligned}

This approach, however, may be overly simplistic.

### CAGR

The compound annual growth rate (CAGR) is a variation on the growth rate often used to assess an investment or company’s performance. The compound annual growth rate (CAGR), which is not a true return rate, but rather a representation that describes the rate at which an investment would have grown if it had grown at the same rate every year and the profits were reinvested at the end of each year. The formula for calculating CAGR is:

\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}

The CAGR calculation assumes that growth is steady over a specified period of time. CAGR is a widely used metric due to its simplicity and flexibility, and many firms will use it to report and forecast earnings growth.

### Dividend Growth and Securities Valuation

Financial theory suggests that a company's shares can be fairly valued using a dividend discount model (DDM), based on the hypothesis that present-day price is worth the sum of all of its future dividend payments when discounted back to its present value. As a result, dividend growth rates are important for valuing stocks.

The Gordon Growth Model (GGM) is a popular approach used to determine the intrinsic value of a stock based on a future series of dividends that grow at a constant rate. This dividend growth rate is assumed to be positive as mature companies seek to increase the dividends paid to their investors on a regular basis. Knowing the dividend growth rate is thus a key input for stock valuation.

## Using Growth Rates

### Company and Investment Growth Rates

Growth rates are utilized by analysts, investors, and a company's management to assess a firm's growth periodically and make predictions about future performance. Most often, growth rates are calculated for a firm's earnings, sales, or cash flows, but investors also look at growth rates for other metrics, such as price-to-earnings ratios or book value, among others. When public companies report quarterly earnings, the headline figures are typically earnings and revenue, along with the growth rates—quarter over quarter or year over year—for each.

Amazon, for example, reported full-year revenue of $232.89 billion for 2018; this represented growth of 30.93% from 2017 revenue of$177.9 billion. Amazon also reported that its earnings totaled $10.07 billion in 2018, compared to$3.03 billion in 2017, so the firm's growth rate for earnings on a year-over-year basis was a whopping 232%.

The internal growth rate (IGR) is a specific type of growth rate used to measure an investment's or project's return or a company's performance. It is the highest level of growth achievable for a business without obtaining outside financing, and a firm's maximum internal growth rate is the level of business operations that can continue to fund and grow the company.

Investors often look to rate of return (RoR) calculations to compute the growth rate of their portfolios or investments. While these generally follow the formulae for growth rate or CAGR, investors may wish to also know their real or after-tax rate of return. Thus, growth rates for investors will net out the impact of taxes, inflation, and transaction costs or fees.

Because stock prices are thought to reflect the discounted value of a firm's future cash flows, a rising stock market implies improving forecasted growth rates for the company.

### Industry Growth Rates

Specific industries also have growth rates. Each industry has a unique benchmark number for rates of growth against which its performance is measured. For instance, companies on the cutting edge of technology are more likely to have higher annual rates of growth compared to a mature industry such as retail. Industry growth rates can be used as a point of comparison for firms seeking to gauge their performance relative to their peers.

The use of historical growth rates is one of the simplest methods of estimating the future growth of an industry. However, historically high growth rates do not always indicate a high rate of growth looking into the future as industrial and economic conditions change constantly and are often cyclical. For example, the auto industry has higher rates of revenue growth during periods of economic expansion, but in times of recession, consumers are more inclined to be frugal and not spend disposable income on a new car.

In addition to GDP growth, retail sales growth is another important growth rate for an economy because it can be representative of consumer confidence and customer spending habits. When the economy is doing well and people are confident, they increase spending, which is reflected in retail sales. When the economy is in a recession, people reduce spending, and retail sales decline.

For example, Q2 2016 retail sales growth for Ireland was reported in July 2016, revealing that domestic retail sales flatlined through the second quarter of the year. It is believed that political instability within the country, combined with the results of the Brexit vote in June 2016, caused Ireland's sales to stall. While some industries, such as agriculture and garden, showed positive growth, other industries within the retail sector counteracted that growth. Fashion and footwear had negative growth for the quarter.

## Example of a Growth Rate

Say that we are comparing the annual growth rates of two countries' GDP.

• Country A is a developed economy with a large, skilled population and a high degree of technology. It had a GDP over three years of:
• year 1: $1.20 trillion • year 2:$1.26 trillion (growth y1 to y2 = 6/120 = 5.0%)
• year 3: $1.29 trillion (growth y2 to y3 = 3/126 = 2.4%) • Country B is a developing economy with a rapidly growing population of unskilled but cheap labor and only a moderate degree of technology. Its GDP over the same period was: • year 1:$20 billion
• year 2: $25 billion (growth y1 to y2 = 50/200 = 25.0%) • year 3:$35 billion (growth y2 to y3 = 100/250 = 40.0%)

First, we can look at the annual growth rates of each country for the first two years. Country A is growing at a modest rate that is declining over the three years. Country B is growing rapidly and at an increasing rate. This is not unusual for large mature countries and emerging markets economies, respectively. But also notice that in year 3, the size of Country A's economy is still more than 36x larger than it.

We can also consider the CAGR of the two countries over the two-year period taking place between years 1 and 3. We then get

• CAGRA = (1.29/1.20)1/2 - 1 = 3.68% per year
• CAGRB = (35/20)1/2 - 1 = 32.29% per year

Note that the CAGR annualized rates are slightly lower than the arithmetic average of the two years' individual growth rates.

## Limitations of Growth Rates

While growth rates are important for understanding how things change over time, they do come with some important limitations. First, the growth rate only considers the net change between two points in time, but says nothing about the price movements or volatility that may have occurred in between. For instance, if some variable has a value of 10.00 today and 10.00 as well in a year from now, the growth rate is zero. However, it could have fluctuated wildly - or not at all - during those twelve months. The annual growth rate, in this case, cannot tell us anything about that.

Growth rates also ignore the nominal amounts involved. For instance, Company A's earnings may grow from $100,000 per year to$150,000 per year, representing 50% growth, but only a \$50,000 change. A much larger Company B's earnings may only grow at, say 5% a year (10x less in terms of the growth rate), but amount to several millions of dollars in the company's coffers.

Finally, growth rates are hard to compare across industries or other unlike variables. A 5% rate of growth for a company may be relatively good or bad depending on if it is a growth-oriented tech start-up versus a large, incumbent consumer staples manufacturer. Likewise, a 4% decline in unemployment does not necessarily carry the same impact as a 4% increase in GDP.

## How Do You Calculate GDP Growth Rate?

The GDP growth rate, according to the formula above, takes the difference between the current and prior GDP level and divides that by the prior GDP level. The real economic (GDO) growth rate will take into account the effects of inflation, replacing real GDP in the numerator and denominator, where Real GDP = GDP / (1 + inflation rate since base year).

## What Is a Normal Growth Rate For a Company?

What is considered to be a good growth rate for a company will depend on several factors such as the industry it is in, whether it is new or well-established, the size of the company, and the overall condition of the economy. In general, a company's growth rate should exceed the rate of nominal GDP growth as well as the rate of inflation. Newer companies in riskier industries will require a higher rate of growth to satisfy investors.

Taking all of this into account, the Harvard Business Review suggests that most companies should grow at between 10% and 25% per year.

## What Is a Good Growth Rate for a Startup?

Startup companies, especially those in high-tech industries, are expected to grow quite rapidly. For Y Combinator companies (a well-known tech incubator), a good growth rate is considered to be 5 to 7 percent per week of revenues, while an exceptional growth rate is 10 percent per week. Thus, a startup may grow by 150% and more over the first few months. As the company matures, the growth rate will decrease.

## How Do You Calculate Growth Rate in Excel?

Since growth rate calculations follow a fairly straightforward formula, they can be easily transported into a spreadsheet program like MS Excel in order to speed up calculations and remove the chance of human error. You will simply need to provide the beginning values, ending values, and the number of periods (if using CAGR, for instance). Note that newer versions of Excel also have a built-in rate of return function that can compute CAGR in one step, known as [RRI]. Still, the RRI function uses three arguments: number of periods, start value, and end value.

## How Do You Calculate the Growth Rate of a Population?

Like any other growth rate calculation, a population's growth rate can be computed by taking the current population size and subtracting the previous population size. Divide that amount by the previous size. Multiply that by 100 to get the percentage.

## The Bottom Line

Growth rates measure how quickly variables increase or decrease, showing the net change in value over some period of time. First applied to the study of biological populations and diseases, growth rates today are an important factor for economists, policymakers, company managers, entrepreneurs, and investors. Calculating a growth rate is simply achieved by dividing the difference in value observed over some period (such as a year) by the starting value.

Article Sources
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1. Amazon. "2018 Amazon Annual Report," Page 17.

2. Grant Thornton. "Grant Thornton REI Irish Retail Industry Productivity Review Q2 2016."

3. Paul Graham (of Y Combinator). "Startup = Growth."