Get a minimum of three estimates from licensed plumbers in your area and I suspect you will find that bid is very competitive.

I want to say it sounds high, but I also went with the first quote I was given. For 2 bathrooms, a kitchen, all new baseboard, and replacing all the cast iron pipes (which we removed ourselves) with pvc I paid 5k, in NJ.

To give you a comparison, we spent $15,000 on a remodeled bathroom in 2005. I have since found out you can save a lot by doing the demolition/tearout yourself. Our plumber worked with a contractor on our bath remodel. The contractor moved from NY to California. He may even be retired.