Where in Park City can one find a four bedroom home for 400K (or, as the OP specified, "under 400K") these days? Real estate bottomed out in about 2010 and even then family homes in areas like Ranch Place, Sunpeaks, etc. were moving in the 650-850 range. Prospector a bit lower, 550-700. Now those places are 1 mill plus. Don't know about Pinebrook or Jeremy Ranch, maybe there, although I doubt it.
It's possible. $400k is about the very bottom of the market for a detached 4 bedroom home but they do exist. There are some 4 bd places in Summit Park, Silver Creek and Park City proper going for just under $400k. Generally though you will have to venture out to Heber, or one of the eastern valley communities (Oakley, Kamas, etc.) to get a 4 bd place for that kind of money.