A beverage preparation device, in particular for preparing coffee, tea or milk beverages, having a milk system for dispensing milk and/or milk froth, and having a control unit for controlling the beverage preparation device to dispense beverages portion by portion. The milk system here has a connectable conveying line to a milk container, and a milk pump which is attached to the conveying line. A first mechanical flow meter is arranged in the conveying line, this flow meter meters the volume of milk conveyed by the milk pump and is connected in terms of signaling to the control unit.