Super Gibo. I did MdS in 2006 so costs will have changed since then. At that time it was £2100 to enter. I think it is now £3000 but you can see easily by looking at the website.
I ran Badwater last year and can tell you that costs are a major issue. Firstly you have to have a crew and at least 1 support vehicle. Crew is between 2 and 6 people. You have to consider whether to get a locally sourced crew from the website who may be prepared to pay their own way, or whether you fly out with friends and pay for their accomodation. You will end up paying for the car. Hotels you need one night in Vegas and probably 4 - 5 in Death Valley/ Lone Pine for Before and After the race. These are not expensive but as I say if you pay for your crew, instead of $80 per night you'll be looking at twice that. You will also need to stock up on supplies at Wal mart (or a/n other) because you need 100+ litres of water and bags and bags of ice, plus food for during the race for you and the crew. I estimate I spent around £3000 but I paid for my crew hotel and had 2 cars (5 crew).
Entry: $800
Flight: £500 return to Vegas
Car Hire which is essential as you cannot race without a crew: £600 for the Friday - Wednesday (race start is Monday)
Hotels in Vegas (1 night) and Death Valley (4 nights) for you and your crew (2 - 6 people): £500
I think on a budget you could get it to work for as little as possible but the above costs you are not really going to be able to get away from. About £2100.