If you're summing up the cost of items in a webshop, then you're in the domain of accounting. If the result appears to be off by a single cent because of a rounding subtlety, then you're in trouble, because even though no one should care about that single cent, it will give the appearance that you don't know what you're doing. Not to mention the trouble you could get in for computing taxes wrong.
If, on the other hand, you're doing financial forecasting or computing stock price targets, then you're not in the domain of accounting, and using floating point for money is just fine.
I'm guessing from your post that your finance people are more like the latter. I could be wrong though - accountants do tend to use Excel.