This might be a bit dry, but here's what I got.
Here's the calculations about our current salary total and capspace we have and what we can and what we cannot offer to Hill and/or Favors:
Current Salary Total for the Jazz is: $80,498,192
The Salary cap is: $94,143,000
This means we have 13,644,808 to spend on renegotiate and extend with either Hill or Favors... or both.
We also have about 1M tied in Withey's non-guaranteed contract. Meaning we can get to about 14.65M if we want to by waiving Withey.
The question is... what do we want to do with this 13.6M? Is it enough to extend both Favors and Hill? Or should we choose one? Favors' max is about 22M. This means that if we max him, We will be left with only 2.5M for Hill. In order to see what a reasonable contract for Favors would be I think it would be beneficial to calculate what's the absolute max he can get over the next 4 years if he doesn't renegotiate and extend his current contract - this would be 23M from his current contract and max for the first two years of his new contract(~63M). The total would be around 86M over the next 4 years. I think for the Jazz to have a chance to extend him, they need to make him whole for those 4 years. They need to offer him a renegotiate and extend contract that's at least at that 86M value(or very close). How can we do that? We can front load it or we can back load it. The max we can give him is about 22M in the first year(this year). If want to do both Hill and Favors we probably need to back load Favors' contract. So he would start at say 19M -> 20.5 -> 22 -> 23.5. That gets him to about 85. Lets say that's enough to make him sign it.
This leaves about 5.6M to give to Hill.
The real question here is what do you think he will get as an offer in the summer? Would he get 4/80? 4/64? Maybe 4/100? I don't know. This is the hardest part in this calculation really - I have no idea what he will be looking to get. He will be going into his mid-30s for the duration of this contract - keep this in mind. I think 4/64 is fair, but he might be looking for more. I don't know. Lets say he is OK with getting 16M/year. We are doing the same calculation as above with Favors - what would he get for the first 4 years if he doesn't renegotiate - 8M(this year's salary) + 3x16M =~56M. So the Jazz need to make him whole for those 4 years(we need to give him 56M for those 4 years). We bump his salary for this current year from 8 to 13.6M -> 14.6 -> 15.6 -> 16.6 = ~60.5M This is probably not enough, but lets say he loves it so much that he makes us that discount.
Where would we be after this with salary cap and luxury tax next year?
Here's all players we will have under contract next summer(after renegotiating and extending Hill and Favors to the amounts listed above):
Gobert: 23M
Favors: 20.5M
Hill: 14.6M
Burks: 10.8M
Joe Johnson: 10.5M
Exum:5M
Lyles: 2.5M
Hood: 2.4M
----------------------------
That's 89.3M
The projected salary cap is 103M. The projected luxury tax is 123M.
Before July 1st Hayward will opt out of his 16.7M and his cap hold will jump to ~25M. If we resign Hayward for the max, this would cost us ~28.5M in the first year.
So, best case scenario he stays and we add his 28.5M to the salary sheet and we get 117.8M salary sheet. And we only have 9 players under contract at this point.
Lets say we keep Neto and Bolomboy at 1M each. We have 2 first round picks that would probably be in the 20s, thus they will cost us about 1M each(although the rookie scale might jump so, we don't know yet). That gets us to 13 roster spots and ~121.8M of salaries. We will have MLE so we can sign some minimum level guy or we can sign the second rounders to min contracts, but in general we are dangerously close to the luxury tax. We might need to unload Burks at this point. But for the time being, lets say Gordon gives us a very slight discount so we wouldn't go into the tax.
Here's our roster:
George Hill, Dante Exum, Raul Neto
Rodney Hood, Alec Burks, ???first round pick???
Gordon Hayward, Joe Johnson, ???min vet or second round pick???
Derrick Favors, Trey Lyles, Joel Bolomboy
Rudy Gobert, ??? first round pick???, ???min vet or second round pick???
The year after things might get really dicey with Hood and Exum up for extensions. In general at some point we will need to start making decisions... It pains me to say it because I absolutely love Alec, but he seems like the first potential casualty if we want to keep this core together past the summer of 2018. And even with him gone, it's very possible that we will need to make yet another tough decision about who to keep going past 2018.
(there is another very obvious and easier option, but I'm not sure the Jazz would like it - give all the money to Hill this year in a front-loaded contract that drops significantly later to facilitate keeping the core until 2018. The problem with this option is that Favors will be FA in 2018 and the all decisions will need to be made that summer(Favors, Hood, Exum)).
tl;dr it's probably possible to give both Favors and Hill renegotiate and extend. This however might mean the Jazz would need to find a way to dump Burks' contract sooner or later if they want to avoid luxury tax. Things get even more dicey past 2018, when Exum and Hood would require extensions.