Take-over either has to be accepted by the board and/or shareholders. Why would either accept at a low price? If you look at the takeover history of Medarex (public information) - BMY actually did lowball when the markets crashed last year (but still at a premium to current stock price). The ensuing negotiation resulted in a substantially higher price that was acceptable to MEDX's board. Board has a duty to maximize shareholder value and in EXEL's case, lots of institutional ownership that would demand it as well. So BMY can try to lowball, but for all intents and purposes, it has to be a negotiation that revolves around both parties trying to get to fair market value.
SO to answer your question, $4 takeout could never succeed as easily as you imply (without some sort of disastrous result hampering the overall value of Exel).