Every time they make a lower offer counter with a higher price. They will soon learn what kind of person they are dealing with.
If they actually do come up with $120,000,000 - will at that point nobody will be surprised that you cashed out. They might be mad, but they won't blame you.
Case in point: Notch once said that his price for selling out Minecraft was $2B. When Microsoft eventually said "sounds fair" and gave it to him very few people found it easy to be mad at him.
My buddy loves buying and selling stuff from the local newspaper. Whenever people give a low ball offer he looks them directly in the face and in a very confident manner says: "I'm accepting asking price or anything higher!"
I sold a Chrome extension I wrote in the early days of extensions (for a lot less than $120M and with a lot less users, but meaningful numbers for both). It wasn't clear then just how bad the malware problem was.
In the joke, $1m was offered. I don't know when he made that joke, but since he died in 1948, that's somewhere over $15m now. And houses were ridiculously cheap by modern standards, so that would have been retirement money for sure.