So basically you are saying the person wants a 6% commission to sell your house to them plus $5k to go towards closing costs.
Yeah, I think the person is trying to buy the house for a quick flip while you pay the cash out of hand costs of doing so. I am guessing the realtor values your house at something above what you have asked and if he/she can get you to sign it over to them, then they can make a tidy little profit.
Regardless of the above, your goal is to get out of the house with $XXX,XXX dollars in hand. If they are offering you something that allows you to get what you want/need, do you really care what they do with it later?
Basically, if they intend to flip it, they are taking a bit of a risk in that they could get stuck with owning it for a long time if your estimate of what it's worth is more realistic than theirs. In order for them to make money on it they have to flip it pretty quickly because each month they "own" it costs them money in the form of interest to whoever the lender ends up being. I figure with today's interest rates it would cost them about $400 a month in interest/taxes/insurance per $100k of the value of the place. It doesn't take long to kill any profit they may envision.
Of course, I am neither a banker or real estate expert, nor do I have any insight to the housing market of your area.
One thing I WOULD absolutely recommend is to contact a different realtor and have them do a market assessment for you. Some will do this for free in hoping to get your business, but you may be able to come clean with them and just let them know you are planning on selling by owner and are willing to pay a few bucks for their time. $300-500 in this sense can be money well spent.
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Note: My experience with "appraisals" is that unless you are way out of line, their motto tends to be one of "the appraisal will come in as needed". And yes, I don't see why this wouldn't be legal. Perhaps a little on the fringe of what banks want though as the buyer doesn't really have much skin in the game.