I met the director of a market research department for a large trade publisher recently and she revealed a very interesting client-side perspective to me. This executive has a half million dollar annual budget for "consultants" and she’s not afraid to spend it.
Most charge $1000/day and she’s fine with that. But, she said, sometimes she deals with consultants who are new or unsure of themselves and who don’t ask for enough money. With them, depending on many factors (including whether she likes them) she will offer a higher fee than she knows they’ll request.
So forget your worries and fears about asking for too much money. And remember that when you’re dealing with large corporations, they have already allocated money for your services. And if you don’t get the work, someone else will.