Quote from Hydroblunt:
You discount future cash flows by your own required return which is different for various people. That's how you figure out what the stock is worth to YOU. WACC is meant to evaluate projects by the company for the company, not to figure out the stock price for possible shareholders. WACC can change very often, a simple Moody's mood swing can change it significantly.
Actually, you are not entirely correct. One method of valuing a company is called the "free cash flow method", and it uses WACC as its discount rate. The theory behind doing so is that a company could arguably be broken down into a collection of projects.
So you basically discount the free cash flows by the firm's WACC, add and subtract a couple of things to get value of the overall equity of the firm, then divide by shares o/s to get a valuation per share. And yes, a change in ratings could increase the cost of debt for a firm, which would increase its WACC and therefore decrease the firm's value.