Not to nitpick, but it's closer to $13.7 mil than $13.9 mil. The NBA salary cap was only $58.044 mil IIRC, and the combined payroll without Barbosa but with Wright and Dorsey is a bit over $43.3 mil.
And if we strike Wright, don't forget to add back a rookie minimum salary (without Wright, we're at under 12 players, even with our draft pick added).
That puts my calculation at $14,283,287 cap space, but only if 1) Barbosa turns down the player option (unlikely), 2) we forfeit the TPE (likely), and 3) the cap stays the same (unlikely, as the owners are asking for a $45 mil hard cap to be implemented over a series of seasons).
Realistically, we have only $6,683,287 cap space, minus however much the salary cap is reduced by. In that event, we are unlikely to attract any desirable FAs.
The other question is, is he worth however much we would have to offer to keep him from the Clippers or any other team, based on his one decent season? The Yogi Stewart experience was a bit traumatizing, and Jordan was Bargnani bad on defense the two seasons before this one.