We have 8 players under contract, assuming we opt in with Gafford and opt out with Gil:
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PG Westbrook 44.2M
SG Beal 34.5M
SF Hutchinson 4.0M
SF Avdija 4.7M
PF Hachimura 4.9M
PF Bertans 16.0M
C Bryant 8.7M
C Gafford 1.8M
Optimistically, we can sign Mathews with Early Bird Rights for $1.5M. We can match any expected offer, so if someone offers more, we can still retain him. If Neto can be retained for the vet minimum ($1.6M) or the non-Bird exception ($1.7M), I'd keep him too, or another equivalent backup PG for that cost. That gives us 10 guys, 2 at each position, for 120.7M.
Our first round pick will cost between 7 and 10M if it's top 4, or about $5.5M if it's 7th or so. That's 11 guys. Additional vets will cost about $1.5M each. (Maybe one of those guys will be Bonga.) First year players will cost $900K. The luxtax threshold is $136.6.
So it looks like, at best, we will have $7M to spend on a decent free agent if we want to stay under the tax, less if we land a top 4 pick.
I suspect the team will be willing to exceed the tax if they retain Beal. It will be their last opportunity to appear to be committed to winning. If that's the case, then they could use Early Bird rights to retain Bonga and non-Bird rights to retain Lopez if they want, and thereby preserve the entire MLE to go after a $10M free agent.