Week 5 Calculating Growth Rates
Calculating Growth Rates
Earlier we said that an important factor in producing a budget was summarizing what is known about how each item in the budget is expected to change in the future. This frequently involves looking at how various accounts have behaved in the past, and that frequently involves calculating growth rates.
To calculate growth rates accurately, many analysts turn to the Compound Annual Growth Rate (CAGR) formula, which is:
| where: | FV | = | the future, or ending value | |
| PV | = | the present, or starting value | ||
| n | = | the number of compounding periods, or years, between PV and FV. |
For example, take as look at the sales record for Amalgamated Hat Rack:
| Year | Sales |
| 2013 | $2,700,000 |
| 2014 | $2,820,000 |
| 2015 | $3,000,000 |
| 2016 | $3,200,000 |
Per the CAGR equation, Amalgamated’s averages sales growth per year between 2013 and 2016 was:
g = 1.185185185 .3333 -1
g = .0583, or 5.83% per year
Note that several calculators can be found on line. Below is a link to one of my favorites. Copy and paste in your browser. Note that N = 3.
http://www.investopedia.com/calculator/cagr.aspx
If you were forecasting Amalgamated’s sales for 2017 and you wanted to base your projection on the company’s past sales growth rate, you would estimate the sales for 2017 as follows:
| 2017 sales | = | 2016 sales | x | (1 + g) |
| 2017 sales | = | $3,200,00 | x | (1 + .0583) |
| 2017 sales | = | $3,386,560, rounded off to $3,386,500 | ||
You would generally round off to an even number because forecasting a very precise number implies you had very precise input data which is generally not the case.
Important Note: You should recognize that a growth rate is the same thing as a rate of return. Therefore, the CAGR equation above is equally useful for determining compound rates of return. Remember, this equation can be used to determine the rate of growth per period necessary to reach any ending value (FV) from any starting value (PV) in any given number of periods (n). It is, therefore, a very handy equation – burn it into your memory forever! The CAGR is just the manipulation of the formula we will use a lot-- FV = PV(1+i)n, where i=g!