Your voltage is too low with and without the alternator running.
A properly charged battery should show a voltage of about 13.8V. The alternator should give a voltage of 14.5 to 15V when running.
Several things come to mind as possibilities.
1) Both the alternator and battery may be shot
2) The battery is OK but the alternator is not putting out enough
3) There is a common cause for such a low reading, eg a bad ground
4) The drive belt for the alternator is slipping
5) The battery is shot and is loading up the alternator badly
6) The idiot light in the dash has blown and is causing a malfunction in the alternator
When I last supected my alternator, my local Bosch agent bench checked it for free. Last time I bought a rebuilt alternator from my 190E I paid 38 GBP, say $55, from my Bosch agent.
The voltage regulator is a unit held into the back of the alternator with two screws. It included the brush assembly which is just as likely to give trouble as the VR.