Forum Archive Index - March 2003

["tennyson@caverock.net.nz" <tennyson@caverock.net.nz>]

Hi Michael,



>
>
>Return on equity and earnings per share growth are not
>related to each other.
>
>Return on  equity is simply a measurement of how the net profit 
>performed against the equity employed. Earnings growth, on the 
>other hand, is an indication of how much net profit grew over the 
>past year or an average of , say, the last ten years. 
>



Imagine a company had shareholders equity of $1 per share.   Return 
on equity is 15% every year.  So net profit after tax was 15c 
per share after year one (after tax).  Now imagine all of those 
profits were reinvested.

Shareholders equity at the start of year 2 is $1.00 + 15c = $1.15.  
So return on this new total of shareholders equity is 
 $1.15 x 0.15 = 17.25c (after tax).   Again all of the profits are 
reinvested back into the business, so the net assets at the start of 
year three are $1.325.  Rather than go on like this, it is easier to 
see things in a table:


Year, Net Assets ps, eps, dps, retained earnings ps

2000, $1.00, 0.15, 0, 0.15
2001, $1.15, 0.175, 0, 0.175
2002, $1.325, 0.20, 0, 0.20
2003, $1.525, 0.23, 0, 0.23
2004, $1.755, 0.263, 0, 0.263
2005, $2.02


Notice here the pattern of earnings per share year after year:

0.15, 0.175, 0.20, 0.23, 0.263

Notice that each year earnings are growing at 15%.

0.15x 1.15= 1.175, 0.175 x1.15= 0.20, etc....

So while it is true to say that earnings per share and ROE are 
not dependent on each other (which means you can't figure out one 
from the other) I wouldn't say they are not connected.  It is the 
retained earnings that feed the equity base.  And it is the ROE that 
turns the equity base into earnings.

Furthermore, it is possible to have ROE and earnings per share growth 
the same value (in this case 15%) even if they are the same value 
'by chance', not because they are related.

If a company has an ROE of exactly 15% every year (after tax), then 
it cannot grow its earnings at more than 15% per year in the long 
term unless it reinvests all its profits.   

If a company has an ROE of more than 15% per year then it can pay out 
some of its earnings as dividends and still grow earnings at 15% per 
year.

If a company has a long term ROE of less than 15%, then it is 
impossible to grow earnings at 15% per year over the long term.


> 
> The more earnings retained the more
>difficult it is to maintain the same or better return in 
>future years.   
> 



Generally yes, but there is no mathematical reason why this has to be 
so.

What about 'the Warehouse'? 

SNOOPY


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