In 2013,2014, the maximum salary is $13,701,250 for a player with six or fewer years in the NBA, $16,441,500 for a player with 7 to 9 years, and $19,181,750 for a player with 10 or more years. Let's assume that the NBA sees a growth in revenue so that those amounts are close enough to $14, $17, and $20 million so that we can use those as easy estimates.
Assuming there are no roster changes, the Celtics have guaranteed money for Rajon Rondo, Jeff Green, Gerald Wallace, Brandon Bass, Courtney Lee, and Kelly Olynyk in the overall amount of 45,931,160. If they exercise their team options on Jared Sullinger(no-brainer), MarShon Brooks(likely), Fab Melo(less likely but I think probable), that's another 4,971,514 for a total of $50,902,674 committed to 9 players. Keith Bogans, Victor Faverani and Phil Pressey will have unguaranteed contracts. Jordan Crawford and Avery Bradley will be restricted free agents if they are tendered a qualifying offer.
If the Celtics don't have 12 players, a roster charge of $507,336 will be counted against the cap to bring them up to a combination of 12 players or roster charges.
The Celtics will have cap holds for their 2014 first-round picks. In 2013-2014, the rookie scale first-year salary will be $4,436,900 for the first pick, $2,910,600 for the 5th pick, $1,930,600 for the 10th pick, $1,493,800 for the 15th pick, $1,174,200 for the 20th pick, and $957,500 for the 25th pick.
There are several scenarios for how the Celtics can sign a max free agent next season.
SCENARIO ONE - KEEP AVERY BRADLEY
Tony Allen signed a four-year, $20 million dollar contract with the Grizzlies. It would be fair to estimate that Avery Bradley could be re-signed for a contract that begins at $4-5 million. Let's say that Bradley plays well enough that Ainge wants to lock him down for a contract starting at $4.5m.
If the Celtics were to salary dump Brandon Bass, Courtney Lee, and Fab Melo to a team with cap space, also sending out their lesser 2014 first-round pick and another pick (something significantly less than the two firsts, three second, and cash that Utah got for taking on the higher-paid and more worthless Andris Biedrins and Richard Jefferson this summer) and getting back a scrub on an unguaranteed contract, the Celtics would have 41,685,034 committed to 7 players, plus a cap hold for a draft pick, and roster charges for three more players. (Actually roster charges for four, but signing a big free agent would reduce the roster charges by one.) If the Celtics end up with the 8th pick, they would have a cap hold of $2,210,900 and the Celtics would have $45,417,942 in salary if they renounced all free agents and waived all unguaranteed contracts. If the salary cap rose from $58.679 million this season to $60 million in 2014-2015, the Celtics would be able to offer a free agent a contract beginning at approximately $14.6 million, or more than the max salary for a 0-6 year player.
This means that the Celtics could theoretically give a max-contract offer sheet to some of those young centers who are likely to be restricted free agents in 2014: DeMarcus Cousins, Greg Monroe, and (my personal choice) Larry Sanders. Sanders is especially attractive to me because, looking at the history of the Bucks and how they are dealing with Brandon Jennings, they may be reluctant to match and could be willing to work out a sign-and-trade (see below).
The Celtics have even more room to maneuver if they can sign Bradley for less or have a lower draft pick with a smaller cap hold. That could allow the team to hold on to players with unguaranteed contracts, such as Faverani or Pressey.
SCENARIO TWO - RENOUNCE AVERY BRADLEY
While I love Rondo-Bradley as the starting backcourt, the Celtics don't have to keep Bradley. Ainge can renounce Bradley, removing his cap hold. This would mean the Celtics can now offer a starting salary of around $18.6 million to a free agent or make it easier to keep Faverani and/or Pressey. I don't think Carmelo Anthony is opting out so he can sign for that much with the Celtics, but if that's your fantasy, it's possible to make the money work out.
SCENARIO THREE - SIGN AND TRADE
The Celtics could threaten to clear cap space as incentive for another team to work out a sign-and-trade deal. This would be good for the Celtics because they can use the full MLE and (if Ainge works fast) the trade exception from the Pierce/Garnett deal to improve the team.
If the Celtics make a trade while over the cap and do not end up as a tax-paying team after the trade, they have to send out $9.27 million in salary to acquire a $14 million max-contract guy, $12 million for someone who will make $17 million, and $15.92 million for someone who is set to make $20 million.
A trade of the expiring contract of Brandon Bass and the unguaranteed contract of Keith Bogans provides enough trade ballast to do a deal for a $14 million or $17 million guy. You would have to add $3.735 million to do a deal. That could be Courtney Lee. That could be including Jordan Crawford in a sign-and-trade. That could be MarShon Brooks, Fab Melo, and Phil Pressey. In an ideal world, maybe another team is willing to take Gerald Wallace and Bogans as the salary-matching contracts.
SCENARIO FOUR - JUST PLAIN TRADE
Some people believe that the free agent class of 2014 isn't that strong, since Carmelo, Lebron, D-Wade, and Bosh seem unlikely to opt out and test the waters. The Celtics can offer cap relief in the form of expiring and unguaranteed contracts, some young players on rookie scale contracts, and draft picks if an All-Star caliber player (like LaMarcus Aldridge) is being shopped around.
That doesn't fit the title of signing a max free agent, but I am throwing it out there. It would make sense for Ainge to throw some assets at a star on an expiring contract in the hopes that he can convince the player to re-sign with Boston.
It's not at all certain that a big free agent will be willing to come to Boston, but if there is one who wants to be a Celtic, Danny Ainge can make it happen and he might be able to do it without touching the Rondo/Bradley/Green/Sullinger/Olynyk core. That group plus a max-contract player worth his salary and a solid 2014 draft pick could be the foundation for a contender.