Take a bus for 3€ a head to the Palma intermodal station and then take line 351 to Alcúdia. Appears to be another 2.57€ per person.
I'll assume that's significantly cheaper.
http://www.tib.org/portal/web/ctm/autobus/linia/351
The interurban transport on Mallorca is included in the transport directions on google maps as well.