The second requirement for a winning bid corresponds to
(3) PU y2/N + B2/NU,
where N,, is the number of voting shares. The bid for voting shares should at least be equal to the maximum price the other potential contender is prepared to pay for those shares. The contender's reservation price for all the voting shares is given by the fraction of income he obtains if he runs the company (No I Ny2), plus his private benefits of control (B2). This corresponds to a price per share equal to y2/N + B2/No.
If there is only one bidder interested in the company, then the winning bid has only to overcome the "free-rider" problem [Gross-
man and Hart 1980], that is, the smallest bid satisfying constraints
(1) and (2). In this case the bid will be
(4) PU = ylIN and Pm= yilN,
and the takeover price per share will be equal across classes.
On the other hand, whenever there is another potential bidder with a reservation value higher than the bidder's cash flow (h), the binding constraint in the voting class bid is given by inequality (3). As a result, the bid will be at the following prices:
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