Employee doing the work of 2 people asks company for a $40K raise: 'It would cost the company $120K to hire another employee to do my previous job.'

It doesn't matter if he tells them he's worth $40K more. They're not going to give it to him.

There's an art to asking for a raise. Unless you're getting a promotion, you can't really expect to get too big a raise every year. Or maybe you can, depending on your industry! It really depends on what company you work for. I've known people who have worked for a company for years without even getting a raise to keep up with inflation!  That's the kind of company that you can't justify staying at for a long time, unless you're in a terrible job market and can't find a new position anywhere. 

The best way to get a raise is to ask for a little bit more than you expect to receive, and hope that your employer meets you in the middle with the raise you expect. Anyone who says that there's no harm in asking for too big a raise has never encountered a young professional who has no sense of how much money is reasonable to ask for. If you really want to make $20K more than you made last year, the best way to ensure that is to get a new job. Even if you're going above and beyond at your company, the chance that they have that much wiggle room in the budget to give you such a raise within a year is slim to none.