i just returned from the Danakil Desert this past weekend and hope the following information helps...
we were able to do a 2-day trip for 4,400 birr (divided by our group of 3); this did not include the hike to the volcano, which would add 2 more days AND require (if you're sensible) the 2nd 4x4 vehicle. we took in the amazing geothermals, camel caravans, "red mountain," & the salt excavations.
for the trip, including the volcano, we were quoted 17,000 birr - including everything but food, water, meal stipend for 2 hired men (a policeman & a militia man with gun...you pay for 3, but may be allowed to carry only 2, depending how much space you have in the vehicle), & water for everyone else in the vehicle. we booked in mekele (travel agent rec'd in the LP & the Mekele Tourism Office, though I can't recommend them). the sights make the visit worthwhile, but the organization of the trip is poor & unprofessional -- you will pretty much be on your own, as far as any service or explanations of what you're seeing go -- but transport is covered.
a local guide rode along to lead us to the geothermals, though spoke no English.
we didn't have to pay for extra tires, but it was also disconcerting that our driver refused to carry extra water in case the engine overheated!
we didn't have any "bagshist" issues with the tribes & didn't pay them anything.
logistics of such a trip are not detailed much in the '03 LP.