Are you talking about shipping just the computer system, or will it be added to a general shipment? If the latter, then the extra cost will be much less than it would cost to ship the computer just by itself.
With regard to power, most PC power units are selectable for 120 or 240V input. Many of the latest monitors, including LCD and plasma displays are also designed to operate on either, although there are some exceptions (check the label on the rear). Power units for printers and other peripherals are often single-voltage only though.