For purposes of my decreasing mobility we have to convert one of our bedrooms into a bathroom with no sill shower and hydro therapy tub. We will be ripping out the carpeting and walls to replace them with appropriate walls and tiles anyway so I thought it may be necessary to add insulation to the walls that are on exterior exposure and in contact with tub and shower. We would probably need to add 2x4's for this but one wall (with tub) has a window so it would need a sill? Question: the walls already have white styrofoam like insulation. What insulation would be best suited for bathroom? Would closed cell foam have more R value/inch than Roxul insulation R14?