It will help rankings, read up on http://www.blackhatworld.com/blackhat-seo/black-hat-seo/579328-learn-how-easily-bypass-google-hit-position-one-any-keyword-using-301-redirects.html, it won't boost PR immediately if it even does, but in 7-14 days it will usually give good results.Good insight nullfo, I appreciate it!
By the way, here is my question to you -> By redirecting (301) an expired high PR domain (with a clean backlink profile) to a newly registered domain, will the PR gets boosted for new domain? And what about the PA and DA? How many redirects needed for a fresh website to outrank the good old ones in the same niche?
Make sure the backlink profile is clean though, check ahrefs with www. and without, check archive and recheck the DA/PA/PR.