If you're really bullish on the market's long term outlook and/or current rents are way below market, I would accept a lower going-in cash flow (that is still positive) with the anticipation of raising rents at the next lease renewal. 

I just renewed my CA RE Brokers and I could just take the tests with out sitting on the computer as long as you pass the test first time through they are good..

I'm beginning to wonder if I should continue with his lease or if I should consider issuing a notice of lease non-renewal and look for a new tenant.

@Jeff Peterson This is dictated in your states landlord tenant laws...here, we would call this is month-to-month tenancy...so, our requirement is to issue notice of non-renewal 30-days before the periodic rental due date...I'm sure your state has a similar law.There is a lot going on in this scenario...and sometimes it's not as simple as pushing someone out that has been there for a very long time...not saying its not the right call, but you may want to prepare for a fight.My first play is to always offer cash-for-keys....$500 cash on the day she is out...IU don't know what the right amount is in your market, but sometimes its the path of least resistanceGood luck

I was thinking to let them know I don't want to renew the lease in June?

Delaying close will trigger the inherited tenant’s unattractive lease to auto-renew for a year (I need to serve notice by end of February to prevent that).

We have also gotten some where we either non-renewed the tenant or claimed they were damaging the property (which they were).

It was headed as a Lease Renewal Request, originally we moved in June of 2017 and this is the 3rd owner.

., almost mandatory lease renewals), and making refusing to rent to Section 8 a fair housing violation.I'm told these proposals are "gaining momentum" for passing, which would be very bad for landlords IMO.

For a single family home, typical rates are below8-10% monthly management fee85-100% leasing fee (percentage of first month's rent) flate fee or up to 6.5% renewal feeLet me know if you have any questions, happy to help