You're over-thinking it.

The only math needed is to decide how much benefit is lost using Goodsearch vs. whatever search engine you currently use—if it's slower, less effective relevant-stuff-finding engine, etc, then it might very well not be worth it. Maybe Goodsearch is like AOL circa 1997? Or equivalent to Asking Jeeves?

You could also—even if it's a best-in-the-market engine functionality wise—decide whatever advertising you are exposed to has some negative value, but I'd take that to be largely preferential if there was no loss of performance.

If Goodsearch is an equally valuable search tool to your current, then switch. It would be like refusing to put a Goodgarbage or Goodvaccum or Goodkitchentable in your home that promised to yield $0.01 to charity per use.

It's just a search engine. Assuming it's functionality remains equal to other leading search engines (maybe a big "if"), then it's a simple, one-time 10-minute switch in exchange for an ongoing $0.01 per search...or $XX.XX per year.

It seems to me this would be a pretty effective little fund-raising tool for a large(r) organization. Get a church congregation or school to change their search engines over to Goodsearch and fund charitable projects each year.

Unless Goodsearch is not a good search engine...