Because you are posting this in the Flipping forum, I am going to assume you are not buying this for your personal residence. In that case, I will first advise you to remove the "I REALLY want this house" emotion from your decision. That kind of thinking can cost you a lot of money.
Second, completely forget what the house previously sold for. That is entirely irrelevant. All that matters is what you can resell the house for once it is fixed up in this current market. You say that the houses in the neighborhood range from $265k to $485k, but then you give a specific example of a recent sale for a turnkey house that sold for only $229k. So, you really need to figure out what you can actually sell for right now. If the $229k is your best real comp for the house you are considering, you have to figure that you will only be able to sell for around that amount. This is crucial. Don't look at what the market was two or three years ago, or even sales from last year. You must look for sales that are similar to your subject property that occurred in the last 3 months, or at most back to the beginning of the year. And by similar to the subject property, I mean things like the number of rooms, size of the home, neighborhood, school, street type (major street vs. quiet side street), and special features (pool, large lot size, view, etc.).
Also, forget what you think the bank will accept. You need to make an offer that will allow you to make a decent profit on the deal. I would suggest that if you are not relatively confident that you will profit at least $20k on this deal offering $202k, then don't make that offer. Or, if you are comfortable with your initial $199k offer and don't feel comfortable going higher than that, then don't. It's better to miss out on a purchase than get burned on a purchase. I like the quote, "sometimes the best deal is the one you didn't do."
Another thought: the first REO we purchased, the bank said submit your highest and best. We resubmitted the exact same offer, and it was accepted. And I've heard similar stories from others here on BP, so don't feel pushed into making an offer that you aren't comfortable with. If the numbers don't work, don't make the offer.
Also, remember that when you go to sell the property, you have good odds of getting an FHA buyer, which means you will likely have to cover a good chunk of their closing costs, so don't forget to figure that into your calculations. Actually, there are a good number of things you need to figure into your calculations, but I'm going to assume that you have already learned about those things from this site or elsewhere, or if you haven't that you will do a search here on BP after reading this.
Okay, I'm not trying to sound all doom and gloom and scare you away, but I would rather you skip out on a deal than get into something that hurts you. If you have solid info on your property and are confident with your numbers, I say make the best offer you are comfortable with and good luck!
