4kw is well over 300 amps, and approaching 400 amps when considering your amplifier's efficiency.
Its easy to say "Im running X number of watts on my stock alt", but as Ive said many times before, just because you have a certain sized amplifier hooked up is no guarantee you are pulling that much current. There are a lot of factors that go into figuring your average current draw over time, which is what should be considered here, not some arbitrary number that your amplifier is advertised as producing in ideal circumstances.