In the scheweser notes it says that if (converted preferred divs/ converted preferred shares )< Basic EPS, then the convertibles are dilutive. Can someone please explain why?
\frac{Preferred\ Dividends}{Preferred\ Shares} < \frac{Earnings}{WACSO}
Because Preferred\ Shares and WACSO are positive, we can multiply both sides of the inequality by their product without changing the less-than sign:
\frac{Preferred\ Dividends}{Preferred\ Shares} × Pref\ Sh × WACSO < \frac{Earnings}{WACSO} × Pref\ Sh × WACSO
Preferred\ Dividends × WACSO < Earnings × Pref\ Shares
Adding Earnings × WACSO to both sides gives:
Pref\ Div × WACSO + Earn's × WACSO< Earnings × Pref\ Sh + Earn's × WACSO
\left(Preferred\ Dividends + Earnings\right)WACSO < Earnings\left(Preferred\ Shares + WACSO\right)
Now, we divide both sides by WACSO and by WACSO + Preferred\ Shares to get:
\frac{Earnings + Preferred\ Dividends}{WACSO + Preferred\ Shares} < \frac{Earnings}{WACSO}
QED
Truly a magician, just like the legend says!
Thank you very much! This is very helpful!
My pleasure.