Old tub needs new tile. Need advice on edge of tub.

skits

We taken out the failed tile, removed everything to the studs. The depth of the cement backer board and tile do not come out to the edge of the tub. There is a horizontal wooden board running outside the tub butted to the studs. I don't want to lay the backer board on that wood because of the moisture problem. If we cut it out and make it level with the tub, we will have to shim all the studs. Is that what we want to do? Does the backer board sit on the upraised lip of the tub and the tile kind of go over the lip? Or is that filled with grout and eventually fail? I've added some photos.

Paul T.

In this situation in the past I have shimmed my studs and use hardie backer instead of the cement board. You will love working with Hardie backer rather than the cement board and it has more resistance to the water than the cement board. Hardie backer works the same as cement board and is easier to cut. All you need is a utility knife a straight edge and a solid surface to cut on. Score the board and snap to finish.
I would keep the hardie backer up off tub and us caulk at the bottom . Yes it is a maitence issue but it is alot cheaper than a new tile job.