@Brad E.
Let me give you an insight into a similar situation of yours that I recently dealt with.
Although it might be slightly different, I'm sure you can relate to my story.
I had to learn it the hard way- lost roughly $1000 on Due diligence, credit check, flood cert, and Appraisal partially on my part but you can't predict everything.
So here goes:
I went through the whole process, placing an offer, getting a counter, accepting, depositing due diligence deposit and earnest money. I had 2 weeks to do the due diligence process= get my home inspection, start my loan paperwork with the local lender, get an appraisal. I wanted to do it within the 2 weeks of due diligence process because I knew if I went over that and I still haven't finalized my research on the property, I could lose big.
Based on my home inspection I found out that there were a lot of repairs to be done, already with a thin margin of ~$50/month cash flow (if you take out all expenses including PM), I would be at a loss for quite some time because of repairs being factored into it. Going in, when I did the walk through, I didn't see anything that would be a major concern (I wish I had more knowledge and/or had a home inspector come out with me on another time after I walk the property initially). Big ticket items such as: toilet leak leading to replace the whole bathroom floor, faucet leaks on under sinks, etc etc (something I hadn't noticed during my initial inspection). Long story short, I was looking at around $1000 repairs and HVAC needed replacement in roughly 3-4 years. With $50/month cash flow, that is way too thin of a margin for me to factor in the repair cost and items such as HVAC (even if I added in the CapEX expense per month-which I did).
All in all, I asked the seller to repair everything based on my home inspection. They only agreed on fixing minor things and I could not do it because of the big ticket items that would eat into my cash flow. So I terminated my contract and took my loss.
I learned a lot, but it hurt to lose $1K into thin air. My advice is this: you have to look at your numbers: for your case, even if you're paying 11K over, if you have $100 cash flow (like you said) a month, that is a pretty good margin- not too thin- you have a decent amount of cushion if things go wrong- assuming you did your analysis correctly. If you're a buy and hold (long-term) investor like me, I would still do it even if it appraised lower than your purchase price. Also, if your market is on the rise, that property can appreciate and make-up for the $11K difference and you're still making money with the cash flow! It really depends on your goal, if you want cash flow, and it works, go for it. If you're trying to flip, that is a different story.
Good luck and hope to hear how it went!