Old finished basement. Tear it down?

[Aref Shehadeh]

Will begin working on a rehab soon, the basement has me a bit perplexed.

3 bedroom 1.5 bath (2.5 if you count one full bath in the basement) single family home. 1200 sq/ft. + basement is 760 sq/ft. 

The basement is some what finished, contains a full bathroom and several closets and what not. But, it is all crap. The walls had to be done 20 years ago. Bathroom is falling apart- old small tile shower, broken floor tiles. Walls have mold on it, ceiling consists of old ripped up hanging tiles. 

My initial thought is to demo it all with the exception of the bathroom, but maybe keep it a half bath and leave the plumbing for the shower. I've been reading and have spoken to an appraiser and I've gathered that basements really don't add value. The full bath is the biggest consideration really. 

Any experiences and/or thoughts?