Each search = predictable $$. Spending $100M will increase searches and ad clicks. Which means they will get some, or even more, of that money back. (Could $100M get a higher ROI elsewhere? maybe, but unless you know the revenue per query MSFT makes I wouldn't call the marketing campaign a mistake).
There is also the aspect of trying to catch up to Google, even if it isn't a great investment they may see it as there last real chance to catch Google. Customers probably wouldn't respond well to another rebranding in future.
Theres also the emotional aspect, you'd imagine Steve Ballmer would like nothing more than to take Google down a couple of pegs.
