The tenant has, in fact, not been paying this premium because previous landlord(s) have evidently not picked up on the discrepancy.

If you have a partner, make sure you are both on the same page as far as how much you'll need from them after closing; 5) When disclosing your purchase price to an underwriter, disclose it as "the lower of p & l" - this way if there's a discrepancy between your appraisal and your P&L statement or tax returns, lenders will prefer your lower number since that's closer to the actual value of the property.

I am worried that after the offer gets accepted, the appraisal value might come in significantly lower than the contract price.I understand that discrepancies happen, and I’m not concerned about a small gap (10-20k), however, if the appraised value would come in significantly lower (50-100k, or more), then I would simply not be able to afford this property (given my then lower down payment, and worse mortgage interest rates).I am wondering if anyone has any experience with what happens in such cases?

I am curious what the discrepancy here would be with the bottom line (your cash flow). 

I couldn't believe the discrepancy!

If I understand your response, you are saying the best way to ensure the LLC is fully realized and prevent a discrepancy (Mortgage in my name and title in LLC's name, is to refinance.

The standard printed exception as to discrepancies, conflicts, shortages in area orboundary lines, encroachments or protrusions, or overlapping improvements:(i) will not be amended or deleted from the title policy; or(ii) will be amended to read, "shortages in area" at the expense of Buyer Seller.Why would I choose (i)? 

Typically there's a pretty big discrepancy, but it's typically one that goes in the opposite direction (tax assessed is way under market value).

Although that does sound like a big discrepancy.

We had a fire and ended up with a huge discrepancy on a 4 plex.