Given that a publically funded manned Mars mission would be at least $10B, a private mission would be difficult even if the cost were reduced 10x. And SpaceX can't even reduce orbital launch costs by 10x over today's gold standard; according to Wikpedia, the Russians have the currently cheapest operational LEO system on a per kilogram basis. Meanwhile, SpaceX's costs are 2x over original estimates. While the Space Shuttle was such a boondoggle that almost anyone could reduce costs as compared to it, contemporary Russian programs are not nearly as poorly designed and executed.