@Vincent Lattuca
First, you're gonna be bound to whatever their lease states. Maybe they just renewed their lease and they have 10 months left at the current rent. Maybe it is a month-to-month lease and you can give them a 30-day notice. Maybe they don't have a lease at all, in which case you might want to talk to an attorney to see what legal issues (eviction rights / squatter rights) you could face as the possible new owner.
Second, take into account what type of tenant they are. Most (not all) long term tenants are LONG term because they are good tenants and pay. Maybe they take really good care of the property and don't cause extra hassle to you or your PM. Those are big bonus points in my book.
Third, you'll want to figure out what your break-even numbers are gonna be. Take into account if the properties current rental income can support the listed purchase price and new taxes/insurance. If they can, then you have some time to slowly raises rents, if you choose. If not, then you know you absolutely have to raise rents right from the start.
All in all, here are the two most likely scenarios.
1) Tenants are great and you'd like to keep them. Raise rents 2-5% each year. Tenant is fine with that and stays.
2) You don't really care whether the tenant stays or not. Raise rents to market value. Tenant moves out. Consider how much you'll spend on a turnover (paint, flooring, touch-up, cleaning, etc) and how long your property might stay vacant for and how long this 'Lost Income' will take to makeup with the new tenant vs. keeping the old tenant at a lower rent.
Hope this helps.
-Troy