30.
What does renouncing a player mean?
As detailed in question number 27, free agents continue to count toward team salary.
By renouncing a player, a team gives up its right until the following June 30 to use the Larry Bird, Early Bird, or Non-Bird exceptions (see question number 16) to re-sign that player. A renounced player no longer counts toward team salary, so teams use renouncement to gain additional cap room. After renouncing a player, the team is still permitted to re-sign that player (the previous CBA prevented teams from re-signing a renounced player until 55 days into the regular season), but they must either have enough cap room to fit the salary, or sign the player without using one of the three "Bird" exceptions.
For example, in August 1999 Charles Oakley was renounced by the Toronto Raptors. Had they not renounced him, the Raptors could have re-signed Oakley for any amount up to the maximum $14 million using the Larry Bird exception. Following the renouncement, they were only allowed to give him up to the $6 million they had available under the cap.
After renouncing a player, a team can still trade the player in a sign-and-trade agreement (see question number 69).