One other flaw with that sales plan is when buying the $156k car for $125k is the $31k below value of the sale becomes a gift as a matter of tax law. Without looking up the actual number for 2014, the gift tax is in the $14k range, leaving a $17k gift on which taxes are to be paid.
Not that the IRS could track or do anything about this, but by letter of the law, it's still another flaw.
I've wondered about winning cars, if a winner could get their local dealer to sell it on consignment. A dealer would make more money on that particular sale than other sales, and the contestant would still have a nice lump of cash.