Mistakes I see PM's make.The mistake I see PM's make is that they allow the Landlord to dictate to them how they want this or that.  

Your state laws probably dictate the manner in which they are held.

You should take this time to learn your local landlord/tenant laws, as they govern your business and will dictate much of what you do.

The other tenant (a new tenant) will have a lease that dictates they pay 1/8 of the water bill.  

Introduce yourself as the new owner, say you want to assure them that you are going to honor their leases at the current rate but that the cost of financing and maintaining the building dictates rents be raised to market rates at the end of their leases.

The applicant doesn't dictate the terms of your application and lease -- that's up to you.

The drawback is that increasing the rent comes with red-tape and the possibility that the rent will actually be LOWERED, if the market dictates it's too high. 

Be prepared to file the eviction within 3 days of the lease's expiration date (or whatever your lease and state laws dictate), and do not accept any money from her after the eviction is filed. 

Fair housing does not dictate that landlords do not have the right to choose based on qualifications. 

@John HodsonYou might let the market dictate what you do.