Throw a spanner in the works here.
I believe that normally the first year is free, then the luxury tax is due annually for the next five years, as stated above BUT if the vehicle is sold/bought during the first year, say at 6 month old, the new owner then pays the luxury tax from that date.
As the vehicle tax (zero) is cancelled when the vehicle is sold, the new owner needs to pay the vehicle tax for the remainder of the year (still zero), but the luxury tax then becomes due.
I think owners have been caught out with this when buying 'nearly new' cars.