That's an unreasonably high estimate, and there is some data to support the idea that it's unreasonable[1].
Microsoft has been losing, at most, a few billion[2] a year on Bing. Assuming they've spent $45B since 2009, that's $6.4B per year spent on Bing. A net loss of $2B on Bing would mean Microsoft is making $4.4B per year, which isn't in the ballpark.
Even if the real number is only in the $20-30B range I'd still consider that "in the neighborhood" as I said. And they would have had a much stronger start by not having to build a brand from scratch.
I take your point, but I want to add a couple more things.
Buying a company costs a lot more than the purchase price. Due diligence, regulatory compliance, legal expenses, HR expenses, lost productivity due to changes, employee turnover, and other factors put a huge premium on top of that price.
Plus, a company that you buy has its own cash-flows, assets, and liabilities, and those might be costly, too. It's not always a good idea to buy a ship that's slowly sinking.
I think Microsoft has done incredibly well without Yahoo, and it's also using Bing in interesting ways that don't require direct competition with Google (powering Cortana, for example).
Microsoft has been losing, at most, a few billion[2] a year on Bing. Assuming they've spent $45B since 2009, that's $6.4B per year spent on Bing. A net loss of $2B on Bing would mean Microsoft is making $4.4B per year, which isn't in the ballpark.
1. http://www.businessinsider.com/chart-of-the-day-microsoft-on...
2. http://hal2020.com/2013/01/18/about-that-2b-annual-loss-from...