One small thing that might make the business world just a tiny bit better is all of us agreeing how we measure growth.
I hesitate to wade into this subject because so many people have so many definitions. And you’d think it was obvious, but then suddenly I find myself in meetings, or on the phone, and I’m wondering whether we’re all on the same page. And the point here isn’t exactly getting something right or wrong, but having growth percentages mean the same thing to everybody. Let’s get on the same playing field.
Here’s a quick quiz:
- sales grow from $100 in one year to $150 in the next. How much growth is that?
- And what if sales grow from $100 to $150 over three years. How much growth is that?
Maybe I’m wrong, but I’ve had what I learned in business school confirmed for me many times by accountants and analysts.
Calculating Simple Growth
To calculate simple growth, subtract the final number from the starting number and divide the result by the starting number. Then multiply by 100 if you want to show it in percentage. So, for the example above:
(150-100)/100 = 50/100 = .5
((150-100)/100)*100 = 50%
And you can see that as a spreadsheet here to the right. C2 shows 50 because it’s the product of subtracting A2 from B2. Then the formula divides that by A2, to generate .50. Or, if you multiply by 100, 50%.
There is also a simpler formula that also works. Divide the more recent by the previous, and subtract 1. That gives the same result.
You can see that in the second illustration here.
Calculating Compound Growth (CAGR)
CAGR stands for compound average growth rate. The active word there is “compound.” It means that the growth accumulates, like interest. So if you grow 10% per year over four three years you’ve actually grown from 100 in the first year to 133 in the fourth.
There’s a formula that calculates the CAGR over a period of years (or months). It’s hard to explain, but easy to use. What’s especially awkward is the ^ sign in spreadsheet formulas stands for “raised to the power,” so 4^2 (four squared, which is four raised to the second power) is 16, and 2^3 (two cubed, which is two raised to the third power) is 8.
When the CAGR formula is written out, it’s:
(last number/first number)^(1/periods)-1
Which is probably easier to see if you look at the spreadsheet illustration here to the left. The first row has the first year and last year plus the CAGR formula. The second row shows the result when 100 grows at 22.47% over three years. And the combination illustrates and awkward point about how many years are involved: it would be easy to call that two years of growth, but the “periods” number here is three, not two. And you can see the spreadsheet formula clearly here, I hope. And the 22.47% growth from 100 to 122.47, and then again to 150.
Maybe it helps on that point to show the same thing for growth from 100 to 150 over four years. That’s another simple spreadsheet, and the calculation shows that the CAGR for growth from 100 to 150 over four years as 14.47% per year.
Conclusion: maybe it’s just that I like numbers, maybe that I use them a lot, perhaps too much … but it’s nice when the growth figures we talk about mean the same thing to one and to all.