Well, it seems to have several times more than everything current gen consoles have, so it seems expecting it to roughly cost 2-3 times made sense; then on top of it is the added technology to the controller and also the camera.
But of course, if I knew what I was doing I wouldn't ask -_-
I didn't mean to be snappy, I'm sorry.
The PS3 and X360 are at this stage of their lives being sold for a profit. The hardware is cheaper now than it has ever been for them.
The new chips being used are an all in one design, so instead of having two separate lumps of silicone for CPU and GPU, you have one which comprises both called an APU.
Costs of chips are determined by how large that chip is (in so doing determining how many you get from one wafer) and how many usable chips you get from each wafer.
EG, the APU for PS4 might be small enough to get 20 chips on one wafer, but only 15 of them work properly. So the cost per chip is cost of wafer divided by 15, not 20.
As chips get made on smaller and smaller manufacturing processes, you can get more on to one wafer. As that process matures you also get more usable chips from that wafer.
IIRC the PS3 chips are still being made on 40nm and 45nm processes and are separate. The PS3 could potentially be being manufactured on the same size process or something considerably smaller like 22nm. I'm sure someone here knows where AMD are at on manufacturing sizes at the present time.
Also as that process size gets smaller you need less power, and so you generate less heat, so you need a smaller PSU and cooling solutions, saving you money on parts and weight when shipping.
As a result, a BOM is a little difficult to calculate, while soe might know the manufactuing size and I'm sure have already calculated the size of each chip, with no idea of yields each chip could be £60 or it could be £120 or more.
The memory is another one. If they are using stacking to get the GDDR5 on the board then it should be cheaper than putting 32/16 chips of RAM on the board. I think several people said stacking isn't ready yet though so maybe they'll do it the hard way for a year and then use stacking at a late date to save money and shrink the board down.
Nothing else in the box itself should be that expensive though I don't think.