Especially if the financials on the LLC are not really reflecting its use as a real company (just paper, but no or very little transactions).

It is a desirable area (and will continue to be so if they can manage to put a grocery store back in), and the price on that 4-plex seems to reflect it.

Most of the owners of the homes for sale indicated there homes were very dated but again the price did not reflect that.

I assume your research on comps reflects actual sold prices, not listed prices, that they are true comparables (sq. ft., number of bedrooms/ baths, garages, etc.), and that the lender (why does seller not know who that is?)

Yes that is a great deal for an investor, but for other people living in the area who want to sell their home that is also valued at $400K, that $50K price is not a true reflection of the value of the homes in the neighborhood. 

If you want to pool other people's money for this investment you need to let your offer and documentation reflect that. 

In my previous rental purchases the tax appraisal value always ended up reflecting at or near what I paid for the property when records were updated.

Calculating Effective Rental Income� Any net rental income from the subject property must be added to the borrower’s qualifying gross monthly income by applying 75% of the lesser of;o Fair Market Rent reported by the appraiser; oroThe rent reflected on the existing or proposed lease agreement.History of Rental Income.

To sum it up you can go exempt for a good while before you file for you loan and show you made more money that year and your recent paychecks the lender requires will also reflect that and im sure you will get approved. 

Generally a low cap rate market is because of anticipation of increasing rents and appreciation where high cap rates reflect little change in either rents of value.