Question regarding acquisition of public company
I have a quick question regarding the acquisition of a public company. This is pretty basic, but one that I never figured out (and probably should ahead of upcoming interviews):
Using Softbank's acquisition of Sprint as an example, Softbank acquired 70% of Sprint last year (still awaiting regulatory approval).
Let's assume that they're paying for shares of Sprint all in cash, that Sprint isat $10/share, and their acquisition is at a price of $15/share.
Given the fact that these 70% shares of Sprint that Softbank is acquiring is held by the public, how exactly can Softbank say that they're acquiring 70% of Sprint? How do they know that the people holding onto shares of Sprint will actually sell their shares for $15/share?
Similarly, how do companies who buy out an entire public firm actually buy out 100% of the firm without any holdouts?
I feel like I'm missing a key piece of the puzzle here. Any explanation would be greatly appreciated.