You are still missing a step in your chain of logic. New shares...

You are still missing a step in your chain of logic. New shares are not being issued with no profit attached to them. It doesn't matter if you issue a trillion shares, if you are doing it to acquire earnings then it doesn't necessarily dilute the EPS, given both the numerator and denominator are changing. In your example, you are only changing the denominator which makes absolutely no sense..

The ABSOLUTE number of shares and EPS are NOT RELEVANT. This is why your BAL example is flawed. At a share price of $10 BAL needs $1 of EPS for a 10 P/E. At a share price of $0.045 LON needs $0.0045 EPS for a 10 P/E. They are both equally profitable (based on your definition) with WILDLY different EPS. The shares on issue means nothing.