mine went out at 80K. Red battery showed on the dash.
I have a 10 dollar voltmeter that I plug in the cigarette lighter plug.
when normal: Before I start the car it shows 12 volts, which is battery voltage.
then I start it and voltage slowly rises to 14 volts, meaning that alternator kicked in.
If you start the car and voltage does not show 14 volts it means your alternator is not working.

Those BMW alternators are weird. They sometimes have voltage and sometimes they go out. So you have to monitor them by changing your engine rev speed. My alternator would sometimes kick in and work ok, but then it would cut out. That's usually a sign of a voltage regulator going bad. on my older X5 alternator would start working after 10 minutes of driving. showing, 4x4, abs and all kinds of lights.