Dividing closing costs by monthly savings is the version everyone uses. It is also the version that overstates the benefit of restarting a 30-year term.
Compare total remaining interest on your current schedule against total interest on the new schedule plus costs. If you are eight years into a loan, resetting the clock can erase the monthly savings entirely.
The refinance still makes sense when you shorten the term, remove mortgage insurance, or convert an adjustable rate before reset.
From the book
This topic is covered in depth in Mortgage Intelligence: A Mortgage Guide to Success. A free sample chapter is available.