I'm putting extra work into unit and UI testing to build a safety net so I can convince my CEO & other developers to let me carry out serious refactorings on ou

I'm putting extra work into unit and UI testing to build a safety net so I can convince my CEO & other developers to let me carry out serious refactorings on our code, like deleting large chunks that aren't used anymore, and changing objects that are used pervasively. We also have an increasingly broad application; as we add new features, I (as a developer) find that I don't visit older parts of the app, though of course the users still need them to work. Particularly when refactoring basic back end stuff that's called from lots of places, it's too tedious to manually track down every part of the UI that would need to be retested due to a given change (and then test it manually... ugh).