Hey mate - although not the MR, the charity version of the MR - Mongolia Charity Rally run by UK registered charity Go Help, has a good page listing costs here;
http://mongolia.charityrallies.org/costs
The costs are vastly different depending on whether you take a decent car (which becomes a decent donation on arrival) or a POS which breaks down everywhere. I broke down in 17 countries and the cost of getting the car repaired was high, and to be honest, although taking a banger sounds fun, it would have actually been a much better trip in a decent 4x4 or station wagon/van where we could sleep (lowering cost) and not break down (lowering cost and allowing us to spend more time enjoying the incredible places we visited).
Be smart about your fundraising and get guys to donate for charity to your justgiving account, and set up a paypal account where guys can e.g. buy cans of petrol for your trip, which will lower the overall cost. Book your return flight well in advance, and the train from UB.
Good luck driving to Mongolia!
Best regards,
Dave @ Charity Rallies
[email protected]
