I would forget what they paid for it. It's really irrelevant. And, really, so is what they are asking.
Rather than guesstimate how much it SHOULD have appreciated, are there reliable recent (I mean, within the last 3-6 months) comps in the same building that can be your guide in formulating an offer? Because condo buildings house many identical units, In the end, it will be your best defense to back up an offer. After all, how could they possibly expect to get $400,000 when unit 305 sold for $350,000 last month?
If there has been no activity in the building on which to base an offer, it becomes a little more difficult -- for both the seller and the buyer -- because it becomes a matter of perceived value.
In the end, it's only worth what you're willing to pay for it, and what they are willing to accept. Hopefully a little solid research and some flexibility on both parts will equal a win-win in the end.
While many units all appear the same, it is important to understand what features the current property may have versus CLOSED sales. What I find in this market is the motivation of the seller plays heavily into the price negotiation. The more motivated the seller, the more likely you will see movement in price. Some sellers want to step up, but don't have a time pressure - some sellers are in financial distress and need a quick sale - it is important to know that you have a truly motivated seller.
Regardless of what sellers may think, the ultimate price of a property is determined by what a motivated, well qualified buyer(s) will pay - it must be put it in writing. Price may not always be the key factor in negotiating as well - often times it is important for sellers to understand what they will net after the transaction. Closing costs include transfer taxes, title fees, attorney fees etc - all are negotiable in terms of who can/should pay. Sometimes assuming some closing fees - which are tax deductible - may allow the seller to net more, therefore allowing them to be less focused on price and more focused on net proceeds.
Interestingly enough, when the National Association of Realtors surveyed sellers as to what sellers want out of their real estate transaction, sellers stated that they wanted confidence that their sale was going to close ON TIME - getting THEIR price wasn't even in the top three.
I was only stating their purchase price as a touchpoint for THEM, since I figure they would probably not even want to entertain an offer for a price below what they paid for it (they're not super-desperate yet). I'm trying to dig into their psyche and make an offer I can feel comfortable with and that they can live with at the same time.
It's the same thing out here in the suburbs. I moved from Berwyn to Brookfield to LaGrange to Western Springs. I might have only move 1 to 2 miles away but for the exact same brick bungalow, the prices went up by $50K. Then after Hinsdale, the prices start going down by $50k.
LOCATION, LOCATION, LOCATION.
In re-reading your questions, and agreeing with Patti that what they paid is irrelevant, how do you know that the property appreciated 20% in the past 2-3 years? The property may have depreciated 20% but the buyers bought it at a 40% discount? Does that make sense to you?
Let's say there were a "Blue Book" for property values just like there is for cars. Ten people might have the exact same property and the average price at a given point in time is $100,000. If someone sold that same property at the same time for $60,000 and then the buyer turned around the next day and sold if $100,000, is that appreciation? Then 3 years later, the Blue Book says the property is worth $80,000. Does it matter if the person you are buying it from bought it at $60,000 3 years ago or yesterday? What matters is that you don't pay over $80,000.
Your goal as a buyer should be to not overpay. Some buyers have a goal of buying at a discount, others their goal is to buy a home that they want. You have to decide which is your motivation. If it is to buy at a discount, then you need to find sellers who are motivated to sell because of duress. In that case, you don't need credibility that your offer is inline with the comps, because it won't be, it will be low. But the comps are vital to know if the seller's price is credible.
I hope this helps.
But it all comes down to motivation. How motivated are the sellers to sell and how motivated are you to buy. Offer what it is worth to you.
What you think is unreasonable once again has no basis...this is why people hire buyers agents...so they have factual information to help them make decisions based on real numbers, not just how they feel.
So find yourself a buyers agent, look at the ACTUAL comps, and base your decision on that.
There are alot of really good deals downtown Chicago, in a market that does not have wide mood swings like Miami or Vegas, etc. Also consider your lifestyle...the proximity to work, running along the lakefront...and then the amenities that are offered...will you use them all? Mesh all that info together with the COMPS, and make an offer. The worst they could say is "no"....so go for it...for once you have the knowledge base, one can argue that your basis for an offer is justified, how ever it falls out...5% or 50% below asking...however the numbers fall through the hourglass have a basis from which to work from.