The cap is projected to go up to 92.5 mil. We have $66,512,857 committed to 8 forwards (Panarin, Zib, Kreider, Laf, Trocheck, Chytil, Carrick and Brodzinski) and 4 defensemen (Fox, Trouba, Schneider and Mancini). That leaves us with roughly 26 mil.
Assuming we don't retain on Kreider or Trouba, and we don't take back any contracts, that raises our total to 40.5 mil. We need to leave ourselves some cap space for in-season transactions, so let's call it 40 mil, with 7 forwards and 3 dmen under contract.
Shesty 12 mil, Rantanen 12 mil, Miller 6 mil. That leaves us 10 mil, and we still need 5 forwards, 3 dmen and a backup goalie, because we aren't going into the season without at least 1 spare forward and 1 spare dman. But even if we do go with a 21-man roster, that's still 10 mil for 8 players, and you want to sign Cuylle (2.5 mil), Kakko (3 mil), and Pettersson, who makes 4 mil now and could get even more as a UFA.
So, no, we can't afford Rantanen. It's basic math.