I think that is going way out on a limb to build and install and not know what to charge. My question is what if you bill and your client doesn't like the price and says "I'm not paying" this leaves you really vulnerable.
What I usually do is discuss the project with the client. Have in mind the cost for materials, types of wood, plywood etc. Also have in mind what it cost for your time, electric, clean-up and dump fees. Do your home work and then quote before any of the work begins.
Example. Client A wants an alder entertainment center. He wants it to match existing cabinetry but would like a free standing unit.
Just looking before you design you fiqure you'll need approx. 200 bf alder for 5.60 a bd and 3 sheets 3/4 birch at 50.00 and 1 sheet 1/4 at 35.00 not to mention stain, finish, slides and hardware. This is your start for a ballpark price. Let the client make some decisions to narrow your price. When you both agree, ask for a 50% deposit down and a 50% completion. The half in the beginning allows you to buy material and components ie. bits and blades to match client's cabinets and pay your help. The check at the end is yours. You cover your suppliers and help in the beginning and pay yourself at the end. If the client defaults on the final payment, you don't owe anyone anything.
As for your project, I had a shop in Irwin, PA and was getting 300 to 500 a pop for custom tub skirts.
Hope this helps,
Nailgunner7