Well, I'm not really qualified to talk about the BoM costs relative to the sale price because I don't do manufacturing, but the Beaglebone Black team claims they charge at margin based on the BoM: "Currently there is $0 margin on these boards [...]" [0]. I normally compare the BeagleBone Black to the Raspberry Pi in terms of cost: the initial Raspberry Pi cost $35, but came with no internal flash. So with 4GB of internal flash the BBB seemed like a reasonable deal at $50. If you're willing to go without HDMI, the Beaglebone Green is $39 [1]
The Allwinner CPUs are always extremely cheap, but I don't support the company because of what jerks they are to the open source community [2]
[0] http://elinux.org/Beagleboard:BeagleBoneBlack#Revision_C_.28...
[1] http://www.digikey.com/product-detail/en/seeed-technology-co...
[2] https://en.wikipedia.org/wiki/Allwinner#Linux_controversies