Ask HN: How do you estimate cost of working on a legacy project?

I have been asked to evaluate an existing system written in Vanilla PHP. The current system is working as per client request but since code is not maintainable thus it needs to be changed. I have also been asked to use some MVC framework for the purpose. I have existing source code which is literally horrible and painful for eyes. I am not sure whether I learn system by looking into code or go thru the site. I would like to learn from community that how do you tackle such systems and how do you estimate? Should it be hourly or fixed rates? Thankyou