Inheriting Tenant Question

[Joshua Perelli]

Hello all, I am a new real estate investor and am in the process of purchasing my first duplex in Cleveland, OH.  I need some advice.  Both units are currently rented at below market rents ($600/mo per unit with the going rate of $800+ per unit).  While I've been doing my due diligence I had asked to see the current lease agreements and we have been told the current tenants have no lease agreement in place and have never paid a security deposit.  So basically, they are on a verbal lease.  

Once I take ownership I would like some advice on how I proceed.  I know they need to be on a lease. My idea would be to put them on my own lease agreement, making it a month to month at their current rent of $600 (trying to ensure I don't have immediate tenant turnover).  At the same time give them notice that the current rents are substantially below market and that in the near future the rents will be going up TBD.  My thought process here is at least they will be on some kind of lease to better protect myself and the property in the event an eviction or something needs to take place.

I feel like I'm walking a fine line here because they have been renting these units for the last 3 years and appear to be ok tenants as far as on time rent payments, tidiness, etc.  I wouldn't mind them staying and even let them have a discount on the going rents, like say $700/mo instead of the going rate of $800 so that I can at least approach my cashflow goals on the property.  And of course if I scare them off immediately I will have the added initial costs of the tenant turnover and getting each unit back up to rent ready standards after they move out, new tenant placement costs, etc.

Has anyone else inherited tenants on only a verbal lease with no paid security deposit etc?  And if so were you able to navigate through it successfully?   Any and all advice is welcome.