Welcome back to MrExcel Netcast, I am Bill Jelen. Well, year end is approaching. This is the time that we always want to see how bigger company grew or mutual funds grew or anything like that.
So let us talk about growth rates. Now there is a simple calculation to figure out growth rate of one year over the previous year. So here we have something, it was a 100 and went to a 120. That formula is the later year divided by the earlier year. Now that is going to give us a 120%. So you always need to subtract one, basically the 100%, so you subtract one and we want to see that is 20% growth.
Well this concept works great. But let us say we have a couple of years, so the later year divided by the earlier year minus one; we have 13% growth there and then copy down 27% growth the second year, but usually we are talking about not the average growth rate but something called a compounded growth rate. And this is a little bit more difficult to calculate.
Basically, what we want to do is we want to start up the same way. We want to take the latest year. So, in this case, year three divided by the earliest year, year one, and what we have to do is raise that to a fractional power. Raise that to a fractional power, so an exponent is the caret, Shift+6, and we are always going to put one divided by the number of years from the first year to the last year.
So, in this case, year one, year three is two years. We will raise it to the second power and then finally, again, this is going to give a number with a 100%, so subtract one and we see that that was 20% growth.
Now let us extend this. Let us say that we have 145,000 in year one, 615,000 in year five. What is the compounded growth rate over the four years? So we start out, last year divided by first year and we raise that in this case to the one fourth power because there is four years from year one to year five. So one divided by four and again subtract one and it says 43.5 %.
Now, how do we test this? Let us test and make sure that it is actually working. So we take the year one and we are just going to create a test calculation out here. Year one times 1.435 and we had 208,000 in the theoretical year two. We will do that again to get the theoretical year three and then the theoretical four and the theoretical year five 614,964.8; very close to the original number. Probably a rounding issue there on my first formula.
So when you are calculating compounded growth rate, how the math is a little bit tough, you always have to raise it to a fractional power and the denominator of that fraction has to be the number of years from the first year until the last year.
Note that it really does not matter to this compounded growth rate, what happens in the intervening years. It does not matter whether they grew fast early on or grew in the last year. This calculation is only looking at the earliest year and the latest year, how to figure the math.
Hey I want to thank you for stopping by. We will see you next time for another Netcast from MrExcel.
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