# Change in Growth Calculation

Yesterday while speaking with our new contributor, Aaron Horvitz, the topic of calculating growth came up.Â  The calculation of a forecasted growth rate is one of the most significant variables in any company valuations.Â  Growth is often miscalculated, leading to an inaccurate calculation of intrinsic value.

We believe that growth is best forecasted using historical data from the company at question.Â  Since the variable is so important to the calculation, it is important for the intelligent investor to avoid any speculation that comes from using subjective judgment to simply forecast what a company may achieve in terms of growth in the future.

Previously we had been calculating growth by taking an average of the annual growth in net income.Â  Aaron suggested we take the approach of a Compound Annual Growth Rate, which eliminates the statistical error inherent in a simple average.Â  For example, if a company grows earnings from \$10 to \$20, there is a 100% increase.Â  If the following year the earnings drop back to \$10, it shows a 50% decrease.Â  Using a strict average of the two year’s growth would give an average growth of 25% per year.Â  However, the actual growth achieved by the company would be 0% using a compound annual growth rate method.

So the suggestion from Aaron was to use the earnings per share 5 years ago and the current earnings per share to calculate the growth over the 5 year period, then divide that by 5 to get the average per year.Â  This would be a very good approach except for the fact that you are stuck with the possibility of using years that abnormally reflect the company’s performance.Â  Perhaps the company’s earnings were affected by a down year in the business cycle.

I decided to compensate for cyclical problems the same way we do with our calculation of PE (see our methods) – by using a weighted average of the previous 5 years of earnings per share.Â  This allows us to gauge the growth rate that has been historically achieved without worrying about cyclical changes in the annual performance.

As a result of this change, a few of our recent analyses and valuations have been changed.Â

What other methods of determining growth do our readers use?Â  What do you think of our method?Â  Do you think we’re on the right track or do you have a suggestion for us to improve the calculation even further?Â  Let us know by leaving a comment below.Â  Your thoughts are always appreciated.

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### 7 responses to “Change in Growth Calculation”

1. djam

You could used the 5years back earnings as the PV(present value) and the current years earnings as the FV (future value) put in 5 as the number of years and calculate the annual compounded growth rate using any finacial type of calculator.
Example PV=2.3,FV=4.6,N=5 ?Calc.i=14.87%.
The growth over the period is 100% and if you devide this by 5 you get 20% wich is the wrong way of calculating this.
Doing the weighted average and using the every year number is also wrong because the years in between do not realy matter.
Your earning can double in a volatile way or in a steady way(at14.87%).
The earnings pattern should be as steady as possible in any case because forcasting from a volatile pattern of earnings is not reliable at all.

2. Djam,

That’s a good method to use too. Thanks for submitting it.

However, I do think that using the weighted average for the earnings per share is a good way to smooth out the cyclicality of many companies. Over the long term I don’t care if a firm has a bad year here or there as long as they are growing earnings overall.

3. buffetteer17

While it is good to look at the past, you have to consider whether it indicates anything about the future. To paraphrase Warren Buffett, “If past performance was all there was to investing, librarians would be rich.”

For Garmin, I used the Logistics curve (S-curve) to predict growth of the automotive segment. See wikipedia for the math and some discussion. In brief, the S-curve models the growth of an epidemic, a new technology, or any exponential growth situation constrained by limited resources.

I put a formula for the curve in Excel and fiddled with the parameters to fit 4 years of prior data. The interesting thing about new technology like portable GPS units is that sales grow fast for while, but at some point sales fall off due to market saturation. I was interested in when such saturation might happen, so I could get out of Garmin beforehand. My model predicted 2008-2009 in Europe and 2009-2010 in the USA for sales to begin to decline.

4. lppm05

Hello,
It is rather difficult to follow your musings without actual relative values inserted in formulas. Tryng to describe a weighted average can be subjective in only written words. As you know, written words do not always convey full thought process. It would help to see your point if you illustrated the values mentioned above. Thanks.

5. Costantino

The best way to estimate the growth rate without to be biased by an abnormal beginning or end value is by log-linear least squares regression. Another vantage is that the Coefficient of Determination (R2) of the regression gives you a measure of how constant und predictable the estimated growth rate is.
In Excel you can compute it i.e. with the function SLOPE(LN(A2:A7),B2:B7) while R2 ist RSD(LN(A2:A7),B2:B7).

Compliments for the site and let me know, if you need more details.

1. Constantino, Thanks for the suggestion. I’ll look into that.

6. Costantino

I forgot to mention, that to apply the growth rate to the original data (before the log transformation), one has to apply the following formula: EXP(x) – 1, where i.e. x = SLOPE(LN(A2:A7),B2:B7)

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