We did this as part of a larger remodel. It wasn't over a vaulted ceiling, just a regular 8' ceiling. I can't remember the exact size since we sold the house a couple of years ago, but I think the room it was around 13'x20' and included a walk in closet and a regular closet and some built ins. We didn't have to raise the roof but did add a dormer. Our attic had 2x6 joists and hosted hvac and water heater, which both had to be moved to a different location in the attic. Joists had to to be replaced with 2x12, which also meant all of the sheet rock ceiling below had to be replaced as well. We already had a walk in door to the attic from a second floor landing, so adding a short hallway to the new room wasn't super complicated other than the floor level between the landing and new room/hallway were about 1/2" different.
I don't remember the cost of adding the room, but it was easily the most value add part of our reno. All in we spent around $125k and that included doing two complete bathrooms, flooring and shower in 1 bathroom, partial kitchen reno, sand and refinish wood flooring and replace kitchen flooring with matching wood, full interior repaint, new hvac, replacement of all recessed lighting, new interior and exterior doors, all new siding, roof, and gutters, and a good deal of framing work. Also had to add a couple of beams to facilitate the new room and remove a couple of walls in the downstairs. I'm sure there were a few other things that I can't recall.
The room addition couldn't have added more than $30k to the cost if that, but that was likely due to all of the other work we were already doing. The new room easily added more value than anything else we did, but that said, it probably wouldn't have been as cost effective if it was the only thing we did.
eta: We had a structural engineer look at the foundation first because it was a 75 year old house that had already had a foundation addition and we wanted to make sure it was capable of supporting what we wanted to do. After that we got rough quotes from 2 GCs and and after we picked one, had an architect draw everything up to get a more final quote. Some would say start with an architect, but we found having the GC weigh in on how the design would impact cost helped a lot with making sure the architect didn't draw something up that was beautiful, but ridiculously expensive to build.