I hate estimating projects. Face it, unless you've done the same job a statistically significant number of times before, there isn't an estimate on the planet worth the bits in it.
They tell me there are two basic philosophies of estimation. There is the American way of over-estimating and then joyously coming in under budget. And then there's the way I'm told is currently in vogue among the off-shores where the initial estimate is absurdly low, and creeps up and up and up and up as the client is drawn more and more into their commitment to the investment.
I prefer the former :) The rule I like to use is almost universally both right on the mark and initially completely, categorically and flatly rejected, the Fahrenheit-to-Celsius rule:
Take my best estimate (say $24k, double it and add 10% ($52.8k) and take away 32 comparable-sized units, usually of the next lower order of magnitude ($52.8k - 3.2k = $49.6k).
That said, I wouldn't want to ask for $50k up front; I'd instead prefer maybe 20% up front to get us rolling, prime the dev environment and then involve them in all facets of the progress as soon as we have even a few pages to show, and keep the discussions in the open, making sure everyone knows where we are at all times so we can manage the burn rate to hopefully get to the destination state way under that price.
It's like the game we used to play with art installation funding with the Canada Council: They offered some cash sum for some certain kind of event, we'd target that sum in our proposal, then pay our musicians, technicians, suppliers and artists out of that account, and everything left over by the end was a bonus (usually paid for opening night pizza).
But, really, realistically -- asking us for our estimate is all backwards. A client should be preparing to wager some fraction of their ROI, some sum that says unspoken, "If it's headed higher than this, we need to bail." Their return on this wager/investment is the only true bottom line -- if the return is $1M/year, then it's worth half that to build a truly stunningly brilliant design; if the return is only $10k/year, then it makes more sense to cobble it on the dirt-cheap from spare parts and student volunteers.
'Course, you can I both know that no one wants to face this reality, and without that basic bit of realism, we're all still stuck with that old smoke and mirrors cat-and-mouse game of "how much does it cost?" vs "how much are you willing to pay?" :)