Cost is anything between 200 baht and a lifetime of (un)happiness

As for why it's called a fine, I believe it's an old tradition dating back hundreds of years to the Welsh.

Lonely young Welsh mountain men who couldn't find a woman, used to pay a sum of money to the village shepherd for a little warmth and comfort during the night.

In the morning when the Welshman came down the mountain, the shepherd would ask how was your night?

The sheep would say (you've guessed it) "baaaa" and the Welshman would say "fine". Hence the phrase was born. Not forgetting this is Thailand and we do things differently here.