I spent the hour or so to run through all of the numbers for capital ship production. Sadly, the Thanatos is the most profitable to produce. If you assume Jita pricing for minerals and the lowest contract pricing for capitals and capital component BPCs:

• Everything -- Rorqual, Carrier, Dreads, and Freighters can be had via forum shops for less than we could build them for without BPOs
• Not everyone checks the forum shops, and I did not contact the shop owners to make sure pricing was up to date 
• Freighters are a loss if you don't own the BPOs
• Dreads are break-even at market prices, and around 50M below break-even at contract prices
• Carriers are roughly break-even at market and contract prices. Thanatos, Chimera are above the line, Archon and Nid are below the line.

We could build everything but the freighters are a slight profit if you factor in the price the corp pays for minerals, but we could make more money building battleships and selling them for the lowest price in Derelik b/c we'll always make better than 10% that way. 

If the corp were to buy minerals via large market orders, we could turn a significantly larger profit. This ends up being more work for the people running the program. A freighter would be required to gather and move the minerals in question.

BPCs make up a large part of the price of capital ships. If the corp were able to invest in BPOs for the most common capital components and for some of the capital ships, we could make a significant profit. However, we would need to produce significantly more capital ships than we are now in order to justify this investment.