Pair programming doesn't double the cost - it just halves the amount of typing. Typing isn't programming. Completing the functionality in the software is programming. It's problem solving. You can't just measure it in lines of code typed. Some programmers will use a better algorithm so they end up typing less.
How would you define value for money? Possibly total time elapsed between start of coding and completed, working feature in live?
The cost of not pairing isn't often counted correctly: The problem is that most people don't measure the number of defects or the amount of extra time taken to fix work that wasn't completed properly in the first place - they just measure the time taken to "throw the work over the fence" in the first place.
There are a few attempts at measuring productivity when paring, but unfortunately it gets a bit tied up with "number of lines of code delivered" - which is a bogus metric.
You might find this study relevant: http://collaboration.csc.ncsu.edu/laurie/Papers/XPSardinia.PDF
