It is now January 1st, and I need to project the growth rate of my
firm's sales for this new year. All I know is that the sales grew by
12% in the first quarter of last year and that sales grow evenly
through the year. If I expect this year's sales growth to be the same
as last year's, what is this annual growth rate?

Hi Holla,

The annual growth rate of your firm in the upcoming year, given a
constant growth rate of 12% in all four quarters of the past year and
all four quarters of the upcoming year, would be 57.35%. In order to
allow you to make such calculations on your own in the future, I'm
including a step-by-step approach to calculating this this growth rate
(i.e., percentage):

It was derived by using the following formula:

(Upcoming Year's Sales - Previous Year's Sales)  x 100
___________________________________________________________

                     Previous Year's Sales

You can plug in numbers to get the percentage, but first you need to
calculate the previous year's sales and the upcoming year's sales.

You said that sales grew evenly at 12% - as in the first quarter of
year one. To make it easy math, assume that sales in the first quarter
were 1 dollar (you can use any figure here as an example, but the math
is easiest to explain with the number 1.) In the four quarters of year
one, with a steady 12% growth rate quarter over quarter, the quarterly
sales figures would be:

PREVIOUS YEAR...

Q1 = 1
Q2 = 1.2
Q3 = 1.2544
Q4 = 1.404928
__________________________________________
PREVIOUS YEAR's SALES TOTAL = 4.779328

For the upcoming year, you would use the same calculation, based on a
12% growth rate quarter over quarter, but instead of starting with 1
(the sales in the first quarter of year one) you would start with
1.404928 (the sales in the final quarter of the previous year) and
then add the 12% growth of Q4 to get 1.57351936 in Q1:

UPCOMING YEAR...

Q1 = 1.57351936
Q2 = 1.762341683
Q3 = 1.973822685
Q4 = 2.210681407
__________________________________________
UPCOMING YEAR's SALES TOTAL = 7.520365136


If you now plug in the previous year's sales total - 4.779328 - and
the upcoming year's sales total - 7.520365136 - into the formula
above, you get:

(7.520365136 - 4.779328)  x 100
____________________________________  = 57.35

                     4.779328


Thus the annual growth rate in sales, from the previous year to the
upcoming year - assuming a steady quarterly growth rate of 12% - would
be 57.35%.

Please note that as years pass on, you may be interested in
calculating your compounded annual growth rate (growth rate over many
years). As such, I have included a link below to a web site with a
special calculator that will let you quickly and easily plug in sales
figures and the number of years you are dealing with, so the
calculations won't get too difficult.

I hope this helps, and if you have any questions, please request a
question clarification before rating this answer.

Best,
Rippo

SEARCH STRATEGY:

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ADDITIONAL LINKS:

Online Investor's Guide to Calculating Annual Growth Rates:
http://www.fool.com/School/CalculatingGrowth.htm

Compounded Annual Growth Rate (CAGR) Calculator:
http://www.cpadvantage.com/onlinefinancialcalculators/cagr-calc.asp

Primer on Calculating CAGR:
http://www.investopedia.com/offsite.asp?URL=http://www.fool.com/workshop/2000/workshop000302.htm

For fun, here's what it look like to me but check with your CPA if the
result matters to you: If your sales started at 1 and rose 12 % in one
quarter to 1.12 and you want to know what they would be if that trend
continued for 4 quarters, then the answer you want is 1.12 x 1.12 x
1.12 x 1.12 which is the same as 1.12 to the power of 4 which is
1.57351936 or 57%+ per year. Projecting that growth out 20 years you
get 1.57 to the power of 20 which is 8,279 times more than you started
with. The calculation is trivial, the judgment to know it will not
happen may be harder.