This is possible, you just need to buy the right MDP to HDMI adapter. The best option would be one of the MDP+USB to HDMI adapters, which pull audio from your comp via the USB cable, and it is carried along like normal HDMI audio signal.
Options where audio is carried through the MDP itself do exist but they're much more expensive. the MDP to HDMI with USB audio adapters are usually only $20-40.