If a team is below the cap, then their Disabled Player, Bi-Annual, Mid-Level and/or Traded Player exceptions are added to their team salary, and the league treats the team as though they are over the cap. This is to prevent a loophole, in a manner similar to free agent amounts (see question numbers 30, 31, 32, 33). A team can't act like they're under the cap and sign free agents using cap room, and then use their Disabled Player, Bi-Annual, Mid-Level and/or Traded Player exceptions. Consequently, the exceptions are added to their team salary (putting the team over the cap) if the team is under the cap and adding the exceptions puts them over the cap. If a team is already over the cap, then the exceptions are not added to their team salary. There would be no point in doing so, since there is no cap room for signing free agents.
So being under the cap does not necessarily mean a team has room to sign free agents. For example, assume the cap is $49.5 million, and a team has $43 million committed to salaries. They also have a Mid-Level exception for $5 million and a Traded Player exception for $5.5 million. Even though their salaries put them $6.5 million under the cap, their exceptions are added to their salaries, putting them at $53.5 million, or $4 million over the cap. So they actually have no cap room to sign free agents, and instead must use their exceptions.
Teams have the option of renouncing their exceptions in order to claim the cap room. So in the example above, if the team renounced their Traded Player and Mid-Level exceptions, then the $10.5 million is taken off their team salary, which then totals $43 million, leaving them with $6.5 million of cap room which can then be used to sign free agent(s).
