For this exercise, I'm just looking at where the Bulls are if they decide to get under the cap (by using amnesty on Boozer and renouncing their NG contracts for Mike James, Lou Amundson, and Ronnie Brewer).
|4||M. Dunleavy||$ 3.33|
|6||D. McDermott||$ 1.90|
|7||T. Snell||$ 1.47|
|8||A. Randolph||$ 1.83|
|9||G. Smith||$ 0.95|
|11||C. Bairstow||$ 0.51|
|12||Cap Hold||$ 0.51|
Total team salary is $53.46M. which means if the cap falls at the expected $63.2M, the Bulls would have $9.74M in cap space.
A big wrinkle to consider is the status of Nikola Mirotic. Under the CBA, the Bulls and Mirotic could mutually agree for him to stay in Europe another year, at which point his $1.08M cap hold would be replaced by a $0.51M cap hold for a minimum salary player. However, the latest word is that Mirotic has parted from Real Madrid on poor terms and come to the US with the expectation to play in the NBA this year. Unbeknownst to the Bulls, who have still been waffling about it. If Mirotic is set on playing in the NBA this year, it's a bit of a challenge to the Bulls' cap space. Previous discussions have suggested he'll need more than the rookie scale amount to play, owing to his buyout with Real Madrid.
The upshot of this is that if Mirotic won't agree to stay in Europe another year, then the Bulls must either set aside enough cap space to sign him, or they will lose his rights and he will become a free agent (this is pretty much what happened with Luis Scola a few years ago, and ended with the Spurs, who originally drafted him, arranging a sign and trade to the Rockets because they couldn't pay him themselves).
The latest I've heard (check the BaB archives) is that Mirotic would maybe sign for about $3.5M. So, if your plans include Mirotic, let's assume you have to subtract another $2.42M from your cap space to sign him. Despite the weirdness of his departure from Real Madrid, Mirotic still seems like a player we should obviously want, and especially on a relatively friendly contract like that. So... unless he's like totally the deal-breaker in a sign and trade for Love or Melo, I'd say this is a no-brainer.
But... that brings our cap space down to $7.31M. Which is more than the MLE, but less than, say, Lance Stephenson has already been offered.
What that means is that to generate more cap space, the Bulls have to be able to pawn off players currently under contract to teams under the cap (or sign and trade partners). Each time the Bulls would pawn a guy off, he's be replaced on the "team salary" by an "incomplete roster charge cap hold" of $507,336. Hence, for each of the following players, trading them to a team under the cap would generate just over $500k less than their current salary/cap hold:
|T. Snell||$ 0.97|
|G. Smith||$ 0.44|
Obviously I think a trade of McDermott or Butler is unlikely, but I'm including these guys for completeness. If you can imagine the Bulls trading away those guys in any combination you like, you can add that much more salary to what the Bulls could offer a free agent. For example, trading MDJr, Butler, Snell, Randolph and Smith away would add $7.04M in cap space to the $7.31M I'm estimating above (net of Mirotic signing at $3.5M). That would let the Bulls make a $14.35M starting offer to a player. That's just under the max for a 0-6 year player.
Now, obviously this isn't a completely exhaustive list of possibilities, but I'm just laying out what I see as the practical limits of getting under the cap and signing players with cap space.
If I were going to speculate on a good use for this option, the only viable candidate I see is Gordon Hayward. As I lay out here, there really is a lot to like about him, and in many ways he's preferable to Eric Bledsoe and Lance Stephenson. I think he's a guy that people would, after watching him, be shocked at how good he is. The big problem is the Jazz have suggested they'd likely match any offer for him. My suggestion would be to use Butler (cheap for one more year) as the primary offer in sign and trade to the Jazz to induce them to let Hayward go to us.