Following these instructions I am having the same problem as jstep1.
jstep1's post wasn't exactly informative as to what "doesn't work".
I delete my old m4p files, go to purchased songs and download them again only to find that the new files are still m4p files.
And they will always download as m4p (unless Apple makes a big gift to everybody). They are protected files. The only way to get unprotected copies is to either do as was suggested 3.5 years ago and burn them to CD, or to do as was suggested 4 years ago and subscribe to iTunes Match and re-download them: About iTunes Plus - Apple Support