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Growth rate is the percentage change in a variable over a specific period of time. The growth rate can be positive or negative, depending on whether the size of the variable is increasing or decreasing over time.
Growth rate is the percentage change in a variable over a specific period of time. The growth rate can be positive or negative, depending on whether the size of the variable is increasing or decreasing over time. Growth rate was first used by biologists to study population size, but has since been widely used in the study of economic activity, business management, or investment returns.
For investors, growth rate often represents the compound annual growth rate of an investment, or a company's revenue, profits, or dividends. Growth rate is also applied to larger concepts such as gross domestic product (GDP) and unemployment. Expected forward-looking growth rates or historical growth rates are two types of growth rates commonly used when conducting analyses.
At its most basic level, growth rate is used to express annual changes in a variable as a percentage. For example, an economy's growth rate is based on the annual rate of change in GDP. This growth rate is used to measure an economy's recession or expansion. A country is considered to be in recession if its income falls for two consecutive quarters.
Conversely, if the country's revenue grows for two consecutive quarters, it is considered an expansion.
Growth rates can be calculated in a variety of ways, depending on the number you want to convey. A simple growth rate is the difference between the ending value and the beginning value divided by the beginning value, or (EV-BV)/BV. The economic growth rate of a country's GDP can be calculated as follows:
<!-- @@@ -->However, this approach may be too simplistic.
Compound annual growth rate (CAGR) is a variation of growth rate that is often used to evaluate the performance of an investment or company. CAGR is not a true rate of return, but rather describes the growth rate if an investment grew at the same rate each year with profits reinvested at the end of the year. The formula for calculating CAGR is:
<!-- @@@ -->The calculation of CAGR assumes that growth is steady over a specific period of time. Due to its simplicity and flexibility, CAGR is a widely used metric that many businesses use to report and forecast earnings growth.
Financial theory holds that a company's shares can be reasonably valued using the dividend discount model (DDM), with value based on current prices equal to the sum of the present values of all future dividend payments. Therefore, dividend growth rate is important for stock valuation.
The Gordon Growth Model (GGM) is a popular method for determining a stock's intrinsic value based on a series of future dividends growing at a constant rate. It is assumed that mature companies regularly seek to increase the dividends they pay to investors, so the dividend growth rate is a key input into stock valuation.
Growth rates are used by analysts, investors, and a company's management to regularly evaluate a company's growth and make predictions about future performance. Typically, growth rate calculations are used for a company's earnings, sales, or cash flow, but investors also look at growth rates on other metrics, such as price-to-earnings ratios or book value. When public companies report quarterly earnings, they typically disclose headline numbers for earnings and revenue, as well as growth rates on a quarterly or annual basis.
For example, Amazon reported full-year 2023 revenue of 514 billion in 2022. [1]
Internal growth rate (IGR) is a specific type of growth rate used to measure returns on investments or projects or a company's performance. It is the highest level of growth that a company can achieve without external financing, while a company's maximum IGR is the level of business operations at which it can sustain financing and growth.
Investors often look at rate of return (RoR) calculations to calculate the growth rate of their portfolio or investment. While this usually follows a growth rate or CAGR formula, investors may also want to know their actual rate of return or after-tax rate of return. Therefore, the investor's growth rate will be less the effects of taxes, inflation and transaction costs or fees.
Note: Because stock prices are thought to reflect the discounted value of a company's future cash flows, a rising stock market means an improvement in the company's forecast growth rate.
Specific industries also have growth rates. Each industry has a unique benchmark growth rate that is used to measure its relative performance. For example, companies at the cutting edge of technology are more likely to have higher annual growth rates than mature industries such as retail. Industry growth rates can be used as a comparison point for a company to evaluate its performance relative to its peers.
Using historical growth rates is one of the simplest ways to estimate an industry's future growth. However, high growth rates historically do not always imply high growth rates for the future, as industrial and economic environments are constantly changing and often cyclical. For example, the automotive industry has higher revenue growth during economic expansions, while during recessions, consumers tend to be more frugal and not spend their disposable income on new cars.
In addition to GDP growth, retail sales growth is another important growth rate for the economy because it can reflect consumer confidence and consumption habits. When the economy is good and people are confident, consumption increases and this shows up in retail sales. When the economy is in a recession, people spend less and retail sales decline.
For example, Ireland's Central Statistics Office reported on the country's retail sales growth over the past year in August 2023, showing that domestic retail sales had increased by 5.9% over the past twelve months. However, retail sales excluding automotive goods remained relatively flat, rising just 0.3%, indicating the relative importance of auto sales. Department stores, electrical appliances and food and beverage industries experienced negative growth. [2]
Suppose we are comparing the annual growth rates of GDP in two countries.
We can also consider the CAGR between the first and third years of both countries. We get:
Note that the annualized CAGR rate is slightly lower than the arithmetic mean of the two years' respective growth rates.
Although growth rates are important for understanding how quickly things change over time, they also have some important limitations. First, growth rates only focus on the net change between two points in time, without taking into account price changes or fluctuations that may have occurred in between. For example, if a variable has a value of 10.00 today and is still 10.00 one year from now, the growth rate is zero. However, during this 12-month period, it can fluctuate wildly or be completely motionless. In this case, the annual growth rate tells us nothing relevant.
Growth rates also ignore the nominal amounts involved. For example, a company's earnings might grow from 150,000, representing a 50% increase but only a $50,000 change. On the other hand, a larger Company B's earnings may only grow 5% per year (10 times lower in growth), but that could mean millions of dollars in revenue.
Finally, growth rates are difficult to compare across industries or other different variables. A company's 5% growth rate can mean very different things whether it's a growth-focused tech startup or a large, traditional consumer products manufacturer. Likewise, a 4% drop in unemployment does not necessarily have the same impact as a 4% increase in GDP.
According to the above formula, the GDP growth rate is calculated by finding the difference between the current and previous GDP levels and then dividing it by the previous GDP level. The real economic (real GDP) growth rate will take into account the effects of inflation, replaced by real GDP in the numerator and denominator, with the formula: real GDP = GDP / (1 + inflation rate since the base year).
What is considered a good company growth rate will depend on several factors, such as its industry, whether it is start-up or mature, the size of the company, and the overall state of the economy. Generally speaking, a company's growth rate should exceed nominal GDP growth and inflation. New companies in riskier industries require higher growth rates to meet investor expectations.
Start-ups, especially those in high-tech industries, are often expected to grow quite rapidly. For Y Combinator, a well-known technology incubator, good growth is considered to be 5% to 7% revenue growth per week, while excellent growth is 10% per week[3]. As a result, a startup may grow 150% or more in the first few months. As the company matures, the growth rate will decrease.
Because the growth rate calculation follows a relatively simple formula, it can be easily imported into a spreadsheet program such as Microsoft Excel to speed up calculations and reduce human error. Just provide the beginning value, the ending value, and the number of periods (for example, when using compound annual growth rate [CAGR]). It’s worth noting that the new version of Excel also has a built-in rate of return (RoR) function that can calculate CAGR in one step, called [RRI]. However, the RRI function takes three parameters: number of periods, starting value, and ending value.
Similar to other growth rate calculations, the growth rate of a population can be calculated by subtracting the previous population size from the current population size. Then, divide that value by the previous scale and multiply by 100 to get the percentage.
Growth rate measures how quickly a variable increases or decreases, showing the net change in value over a period of time. Originally applied to the study of biological populations and diseases, growth rates are now an important consideration for economists, policymakers, corporate managers, entrepreneurs, and investors. The growth rate is calculated simply by dividing the difference in value changes over the observation period (e.g. one year) by the starting value.
[1] Yahoo Finance. "Amazon: Financials."
[2] Central Statistics Office. "Retail Sales Index July 2023 (Provisional) and June 2023 (Final)."
[3] Paul Graham (of Y Combinator). “Startup = Growth.”
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不过，这种方法可能过于简单。
复合年增长率（CAGR）是增长率的一种变体，通常用来评估投资或公司的表现。CAGR 不是一个真正的回报率，而是描述投资如果每年以相同的速度增长且年末利润再投资的情况下的增长率。计算CAGR的公式为：
增长率是指在特定时间段内某个变量的百分比变化。增长率可以是正值也可以是负值，这取决于该变量的规模是随时间增加还是减少。增长率最早是由生物学家用来研究种群规模的，但随后被广泛应用于经济活动、企业管理或投资回报的研究中。
对于投资者来说，增长率通常代表投资的年均复合增长率，或公司的收入、利润或股息。增长率还被应用于更宏观的概念，如国内生产总值（GDP）和失业率。预期的前瞻性增长率或历史增长率是进行分析时常用的两种增长率。
在最基本的层面上，增长率用于以百分比形式表达变量的年度变化。例如，一个经济体的增长率是根据GDP的年变化率得出的。这个增长率用于测量经济的衰退或扩张。如果一个国家的收入连续两个季度下降，就被视为处于衰退中。
相反，如果该国的收入连续两个季度增长，则被视为扩张。
增长率的计算方法有多种，取决于所要传达的数字。一个简单的增长率是将期末值与期初值之差除以期初值，即 (EV-BV)/BV。一个国家GDP的经济增长率可以这样计算：
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