 # Solving for Pt (stock acquisition)

I under stand most of this math excpet where does the 50% come from when solving for 21.66?

Gadgets N’ More has 78 million shares outstanding while World Beaters has 223 million shares outstanding. Gadgets N’ Mores stock was trading at a price of $20 per share pre-announcement while World Beater’s stock was trading at$43 per share. Clausen estimates the total present value of cost savings due to the merger to be $200 million. TP = PT – VT where PT = N x PAT for a stock acquisition. PAT = VAT / # of shares VAT = (223 million x$43) + (78 million x $20) +$200 million = $11,349 million. # of shares post-merger = 223 million + 78/2 million = 262 million PAT =$11,349 / 262 = $43.32 PT = 0.5 x 43.32 = 21.66 TP = 21.66 – 20 =$1.66 per share or 1.66/20 = 8.3%

So . . . two shares of G’N’M gets you one share of WB?

Or . . . to view it another way, one share of G’N’M gets you . . . wait for it . . . 0.5 shares of WB.

Maybe I’m confused, wasn’t that already taken into account in two steps above by the (78/2)? Or is the (78/2) the shares and the 21.66 is the earnings so you have to divide both by 2?

When you calculate $43.32 per share, that’s per share of WB. \left(\frac{$43.32}{1\ share\ WB}\right)\left(\frac{1\ share\ WB}{2\ shares\ G'N'M}\right)\ =\ \frac{$43.32}{2\ shares\ G'N'M}\ =\ \frac{$21.66}{1\ shares\ G'N'M}