I have been involved in several rewrite from scratch projects. The following projects are always more expensive than the original (probably less than the original counting all the maintenance - but a lot of weird bugs will take years of maintenance to clean up and that was done in the original so it is hard to count that). However once they are done the result is a lot more maintainable, and has a much better UI of a form that would be hard to retrofit to the old. Normally they are written in a better language an the original. (C++ with const correctness is better than C++ without!)

One key takeaway is we as an industry do not enough rewrites to get good at doing them. (I'm not sure that is a bad thing)