A few factors in play here.
1) How likely is it that those same customers will simply go to the other salon after you close anyway? A) Are there a lot of similar salons in the immediate area? B) Is there something unique or different about your salon?
2) What kind of loyalty is there typically in the tanning business? ie: A tanning bed is a tanning bed, etc.
3) How current is your list? A) Have people moved away, moved on to other shops, died, etc.
4) Are there minutes left on some clients cards that will pretty much insure that they will go to the salon that purchases the list? Will they promote or honor those minutes paid or not?
5)You could go on and on about this. A good way to think about it is to place yourself in the other persons shoes. What questions would you ask, what would be your concerns?