The Treasury has published a letter which confirms that cancelling one of two aircraft carriers would have cost hundreds of millions of pounds more than building both ships.
It would also have led to the closure of the last two shipyards on the Clyde with thousands of job losses.
The letter, from BAE Systems to David Cameron, was written during negotiations over the defence review.
Both carriers will cost £5.2bn but just one would have cost almost £5.5bn.
The letter outlines cancellation costs and penalty clauses.
BAE also warned the prime minister that cancellation would have led to the closure of three shipyards - including the last two on the Upper Clyde - by 2013, with the loss of more than 5,000 jobs.
MPs have criticised the original deal.
The SNP said Labour ministers allowed the UK to "sleepwalk" into a contract.