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The pool doesn't look to be in very bad shape

As long as the walls, floor and steps are sound (as well as the piping and filter equipment) this could run anywhere from $4000 to $8000, depending on your location and how much work needs to be done to make the pool 'new'.

I would have anyone giving you a quote, check the stair faceplates and gaskets, give an appraisal of the wall condition and the floor's condition. They should also measure the pool to insure that the new liner fits correctly! Before they drop the new liner, the lines should be pressure tested, it's better to fix plumbing issues before the new liner goes in.

I've done this more times than I can count. Get some quotes and run them by us and I'll tell you what to look for and watch out for.