# Better way to calculate earning growth rate to have quick glance on company earning quality

I was wondering, what is a better way, to calculate earning growth rate, to have a quick glance on company earning quality?

In ycharts, according to https://ycharts.com/glossary/terms/eps_growth , the mentioned way is

``````Compounded EPS Growth = (EPS this period/EPS t periods ago)^(1/t) - 1
``````

However, it only consider EPS during starting period and ending period. It doesn't take consideration into EPS in between the period.

Let's look at both company A and company B.

``````Company A
=========
Year    EPS    "EPS Growth Rate"

2017    6.00   (6.0/4.9 - 1) = 0.22
2016    4.90   (4.9/3.5 - 1) = 0.40
2015    3.50   (3.5/2.2 - 1) = 0.59
2014    2.20   (2.2/1.0 - 1) = 1.20
2013    1.00

Compounded EPS growth rate = (EPS in year 2017 / EPS in year 2013) ^ (1/4) - 1
= (6.00 / 1.00) ^ (1/4) - 1
= 0.56 = 56%

I try to take account into EPS in between period too, by using the following calculation.

Average EPS growth rate = Sum of "EPS Growth Rate" / 4
= (0.22 + 0.40 + 0.59 + 1.20) / 4
= 0.60 = 60%
``````

``````Company B
=========
Year    EPS    "EPS Growth Rate"

2017    6.00   (6.0/0.3 - 1) = 19.0
2016    0.30   (0.3/0.4 - 1) = -0.25
2015    0.40   (0.4/0.5 - 1) = -0.2
2014    0.50   (0.5/1.0 - 1) = -0.5
2013    1.00

Compounded EPS growth rate = (EPS in year 2017 / EPS in year 2013) ^ (1/4) - 1
= (6.00 / 1.00) ^ (1/4) - 1
= 0.56 = 56%

Average EPS growth rate = Sum of "EPS Growth Rate" / 4
= (19.0 - 0.25 - 0.2 - 0.5) / 4
= 4.5 = 450%
``````

We can observe the following.

1. Company B has more "bumpy" earning than company A. `Compounded EPS growth rate` unable to reflect such, as it only take consideration into EPS during starting period and ending period.

2. Although company B has higher `Average EPS growth rate`, it doesn't indicate that it has higher earning quality. The higher value, is caused by a sudden spike jump from 2016 EPS to 2017 EPS. Before 2017, company B EPS is in decreasing trend.

I was wondering, given data of earning history, which is a better way to calculate earning growth rate, to better reflect company earning quality?

• One option would be to show the calculation done for year 1,2,3,and 4 separately. Show that the growth rate is very inconsistent between years (if you want, do some type of trend analysis for the year-over-year change in the compounded growth rate). As a single number it may be difficult to get exactly what you want, because you are doing a relatively non-standard calculation, so an observer won't have a natural reference point of understanding without you 'showing your work'. – Grade 'Eh' Bacon Dec 11 '17 at 13:29

Your formula for compound growth is slightly off:

``````                                             |*****|
(EPS in year 2017 / EPS in year 2013) ^ (1/4) - 1
= (6.00 / 1.00) ^ (1/4) - 1
= 1.565 - 1 = 56.5%
``````

So the compound growth is much closer to the arithmetic average growth in the first case (60%), but still does not match the second case. However, the geometric average is more appropriate to use when taking about compounding growth since growth is a multiplicative function.

The geometric average in the first case would be

``````( 2.20 * 1.59 * 1.4 * 1.22 ) ^ (1/4) = 1.565
``````

and in the second case it would be:

``````( 0.50 * 0.80 * 0.75 * 20 ) ^ (1/4) = 1.565
``````

so you get the exact same answer regardless of method.

That said, looking at the actual periodic values will tell you about the variance of annual growth. Certainly the wide difference in the second case needs further analysis - is it due to a product that was released after 4 years of development that could be sustained going forward? Or does it indicate a highly volatile business?

• Thanks for the great explanation. It seem that is it better for me to use "geometric average". As, the \$ company earn this year, can be used as capital for next year, to further accelerate more earning. However, what's your view on calculation on "dividend growth". Should I use "arithmetic average" instead? My view is that, dividend a company pay this year, has no correlation with the dividend next year. – Cheok Yan Cheng Dec 11 '17 at 17:04
• Well, they are correlated since the \$/share is typically constant from year to year, but yes an arithmetic average is appropriate since dividends do not "compound" like returns do. Plus you don't usually see huge swings in dividend rates that you do in rates of return. – D Stanley Dec 11 '17 at 17:37
• Thanks for the great explanation, I understand why EPS growth rate should use "geometric mean" to get the compound growth rate. But how about I have "Debt-to-Equity ratio" of last 5 years, how do I calculate whether it has increased / decreased? Is it appropriate to use "geometric mean" method? – Shuwn Yuan Tee Dec 13 '17 at 11:23
• @shuwnyuantee If you are calculating an average percentage increase over the prior period, then yes a geometric mean is appropriate, but I can't see how that would apply to D/E ratio, or how would tell you if it has increased or decreased. – D Stanley Dec 18 '17 at 14:40
• @DStanley Do you think EXCEL's LOGEST (least square regression on log) is a better way over geometric mean? As, it does consider values in between the period. GuruFocus website seems to be using LOGEST method too. I post my findings, and my implementation here - github.com/yccheok/logest – Cheok Yan Cheng Dec 20 '17 at 19:08