From Brian MacPherson at the Providence Journal's Red Sox blog, published before the Ortiz deal. For the then 37 current players, he had an approximate* total payroll of $85.32M for the 2013 season. With Ortiz, that's about $98.32M.
* Utilizing arbitration projections from MLBTraderumors, which are generally reliable.
But the multiyear contracts for Lackey, Lester, Pedroia, Buchholz, and Iglesias collectively count for less when calculated by average annual value -- $10.23M less, if my math is right. That makes the current payroll (with Ortiz) an approximate $88.09M, as calculated for luxury tax purposes.
The threshold for the luxury tax will be $178M next year, taking into account total payroll, performance bonuses, and medical benefits. Last winter, when Alex Speier did all this, he estimated medical benefits to count for $10.5M, and performance bonuses for $2M, adding another $1.5M for extra 40-man roster salaries (describing this more explicitly here). Let's add all that together, rounding up to about $103M.
It would be lunacy for the Red Sox to have come this far in trimming down their payroll not to reap the benefits of coming under the $178M threshold and resetting their tax rate. And it would be irresponsible if they did not utilize their ample budget to improve the team.
So that gives the Red Sox very roughly $75M more to build the 2013 roster -- and likely more than that once you remove current players to make room for the newer, better ones. Let the offseason begin.