I'm looking for a projector that is going to light up a 240" screen at night. A friend of mine is using one of those $280 projectors to light up a 190" screen. Its pretty decent but I am sure a better projector can do better. I am not new to projectors because I have a home theater with one but the shear size of 200+ inches is incredible. The problem with the inexpensive projector was the picture wasnt sharp and the colors were off. It claimed it had 7000 lumens, I need some that can produce a good picture on the screen I mentioned. 4k is a must, there doesn't appear to be any native 4k under $3000 but 4k pixel shift is good enough. 3d is good but not necessary. What would foot my bill?