## What is Growth Rate?

The **Growth Rate** reflects the percentage change in a metric, such as the population or sales, across a specified time frame.

How to Calculate Growth Rate

The term “growth rate” describes the rate of change in the value of a specific metric across a given period, expressed as a percentage.

Common examples of scenarios where the growth rate is often used are the following:

- Company Sales Growth Rate
- Population Growth Rate
- Gross Domestic Product (GDP) Growth Rate

Under the specific context of financial modeling, the growth rate is most frequently on a quarterly or annual basis (i.e. year-over-year).

For instance, more defensible predictions can be made about the future trajectory of the metric in question by determining the historical growth rate of a metric.

However, the metric’s usefulness is tied to the extent that the underlying drivers are identified and researched in-depth.

By itself, calculating the historical growth rates is not enough because what actually caused the past growth and which factors are likely to determine its future growth must be clearly understood.

## Growth Rate Formula

The following formula can be used to calculate the growth rate across two periods.

## Growth Rate Formula

- Growth Rate = (Ending Value ÷ Beginning Value) – 1

For example, if a company’s revenue was $100 million in 2020 and grew to $120 million in 2021, its year-over-year (YoY) growth rate is 20%.

- Growth Rate = ($120 million ÷ $100 million ) – 1 = 0.20, or 20%

But often, we’ll want to annualize the rate of growth (i.e. “smoothen” the growth rate across several periods), which is the use-case of the compound annual growth rate (CAGR) metric.

CAGR represents the annualized growth rate over a specified period, i.e. a single growth rate that treats all the past changes as if they occurred evenly across the entire duration covered.

Therefore, CAGR is conceptually the rate of return needed for the initial value of a metric to grow from its current value to its ending value between the two specified dates.

The three inputs necessary to compute the CAGR are listed below.

- Beginning Value
- Ending Value
- Number of Periods

Calculating the CAGR involves dividing the ending value by the beginning value, raising the resulting figure to the inverse number of periods (1 ÷ the number of periods), and subtracting by one.

Note that the number of periods refers to the number of compounding periods.

## CAGR Formula

- CAGR = (Ending Value ÷ Beginning Value) ^ (1 ÷ Number of Periods) – 1

## Growth Rate Calculator – Excel Template

We’ll now move to a modeling exercise, which you can access by filling out the form below.

## Population Growth Rate Example Calculation

Suppose we’re attempting to evaluate the past growth of the U.S. population.

The data set we’re working with here – pulled from Data Commons – can be found below.

Year | U.S. Population |
---|---|

2000 | 282,162,411 |

2001 | 284,968,955 |

2002 | 287,625,193 |

2003 | 290,107,933 |

2004 | 292,805,298 |

2005 | 295,516,599 |

2006 | 298,379,912 |

2007 | 301,231,207 |

2008 | 304,093,966 |

2009 | 306,771,529 |

2010 | 309,327,143 |

2011 | 311,583,481 |

2012 | 313,877,662 |

2013 | 316,059,947 |

2014 | 318,386,329 |

2015 | 320,738,994 |

2016 | 323,071,755 |

2017 | 325,122,128 |

2018 | 326,838,199 |

2019 | 328,329,953 |

2020 | 329,484,123 |

2021 | 331,893,745 |

Source: Data Commons

To calculate the year-over-year (YoY) growth rate, we’ll divide each year by the preceding year.

For example, the formula for calculating the growth rate in 2001 is the current population (284,968,955) divided by the population in 2000 (282,162,411), which is then subtracted by one.

- 2001 YoY Growth Rate = (284,968,955 ÷ 282,162,411) – 1 = 0.99%

The growth rates for each year are as follows.

- 2000 → 2001 = 0.99%
- 2001 → 2002 = 0.93%
- 2002 → 2003 = 0.86%
- 2003 → 2004 = 0.93%
- 2004 → 2005 = 0.93%
- 2005 → 2006 = 0.97%
- 2006 → 2007 = 0.96%
- 2007 → 2008 = 0.95%
- 2008 → 2009 = 0.88%
- 2009 → 2010 = 0.83%
- 2010 → 2011 = 0.73%
- 2011 → 2012 = 0.74%
- 2012 → 2013 = 0.70%
- 2013 → 2014 = 0.74%
- 2014 → 2015 = 0.74%
- 2015 → 2016 = 0.73%
- 2016 → 2017 = 0.63%
- 2017 → 2018 = 0.53%
- 2018 → 2019 = 0.46%
- 2019 → 2020 = 0.35%
- 2020 → 2021 = 0.73%

Next, the inputs used to calculate the CAGR are as follows.

- Number of Periods = 21 Years
- Beginning Value = 282,162,411
- Ending Value = 331,893,745

The CAGR of the U.S. population from 2000 to 2021 comes out as 0.78%.

- CAGR = (331,893,745 ÷ 282,162,411) ^ (1 ÷ 21 Years) – 1 = 0.78%