The stockholders do not enter the equation, but do negotiate the price of their shares. The interesting aspect is the way Lehman can come up with a sum large enough to cover all of the stockholders' financial demands. Leverage buyout! It may use junk bonds issuing (bonds at high interest rate) and then cover up the loan from the profits made in the deal.

Negotiations with each important stockholder in part are commenced and continue at an incredible pressure. The problem for each stockholder in part is when to sell. If they sell too soon, then they will not benefit from the subsequent new offer that Lehman is most likely to come up with if it is refused. If they sell too late, Lehman will already have a majority and will no longer need the shares from other stockholders. In an obvious minority, they will need to sell at a much lower price.

The management, who is facing a job loss situation, need to come up with different investment plans and convince the stockholders that it is better to stick with the current team and attack future possible businesses than sell right away. As I have said, for Lehman, pressure comes from the profit it will later make: if it has to raise the price offer too much, then the profit will be lower and it will not cover the debt that Lehman has to return, plus the interest rate.

Of course, inside information...

As such, many of the important financial characters of the 80s served some time in prison on this account. Although it was not the case for people at Lehman Brothers, it nevertheless became a victim of its own maneuvers.
As we have seen from the book, the two factions that fight for the bank's leadership end up tearing the company apart and making it vulnerable to the attack of a much smaller raider company, Shearson/American Express, using much the same tactics Lehman had in the past. The scenario presented previously works great in Lehman's decline as well.

3. In order to form the equation, we will be noting X and Y, where X = the some borrowed through the junk bond mechanism and Y the price the company needs to pay in order to acquire the majority shares.

This would mean that X + (x/100)*X needs to be compared with Y, where x is the interest rate the company needs to pay.

Hence, X*((100+x)/100) - Y = Z, where Z. is the profit from the deal.

It is quite easy to manage this equation. X and x are fixed (sum borrowed and interest rate on junk bonds), but Y can vary (price offered to stockholders. The problem is how much we can vary Y in order to have a Z. high enough.