If you go much lower, shareholders become reluctant wondering if it's really worth it, or if the board are negotiating hard enough.

If you go much higher, shareholders start to wonder why someone is willing to pay so much for a stock. People start to get cagey and wonder what's going on. The sellers interest is to keep it lower as well.

It's just the region things have settled over time. It's generally enough that the board feel they're doing the right thing, it doesn't spook anyone, and it's what the buyer is expecting.

I don't think there's any more magic behind it, it's just what has become the norm over the years.

At 50% it might be easier to just buy up shares on the market til they have a controlling share. The number to do that sets a cap on what the buyer will pay. I don’t have numbers on-hand, but trying to move a majority of a company’s stock (buy or sell) can cause crazy swings. When I worked in hedge funds, it was a thing we worked around. Our larger trades would execute over the course of a day or several days to minimize our impact on pricing.

At 10%, many shareholders will feel that their risk-adjusted returns on the stock would do better than the buyout.

30% is likely below the costs to acquire a controlling share on the market, and above any reasonable belief in risk-adjusted returns for shareholders (barring exceptional companies).

A lot of it is wishy washy because it’s based on math, but math with presumptions baked in. How much do shareholders think their stocks are worth? How much would it cost to buy them on the open market? How much does the buyer think the stocks are worth? There are approximate answers to all of these, from which an even more approximate price needs to be determined.

It comes from the Doft (2004) ruling in Delaware courts that attaches a 30% control premium

If the last transaction was 30% the board as to explain why this one isn't 30% (either to the buyer if they are paying more; or to the shareholders if they are paying less).

> Maybe I'm missing something basic but that still doesn't explain why it's 30% and not 50%.

It's like tipping. There's no ideal value that can be picked; just agreed normal values. If 30% appears to work most of the time then that's probably why it's used.

Is there a way to search for lawsuits from shareholders when the price per share of going private was less than 30%? There's probably no mathematical model here but more a way for the sale to insulate itself from getting dragged into litigation.