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The big company is getting exactly the same as the small company; be wary of overcharging just because 'they can afford it' - they could be a long term partner ... or a once and never repeated opportunity.
[edited by: Quadrille at 1:15 pm (utc) on Sep. 1, 2008]
It's not perfect but it will give you an idea.
In the end, charge what YOU consider fair for your work/effort. If you aren't doing that already might want to rethink! :)
So, if you charge them a scaled-up version of what you'd charge for a smaller contract, be sure to specify what you provide along with that in terms of face time, phone time and reporting.
Above all I recommend that you require them to appoint a single point of contact within the company - all instructions and questions for you must go through that person - and all reporting by you must be accepted only by that person. I can't emphasise this enough - without a contractually defined single point of contact, dealings with a huge company could skin you alive.