Changing facing doesn’t take up movement “points.” When you get to your destination hex, you can face whichever hex side you wish. And instead of moving to another hex, you can change facing within the same hex.
However, if you are face-up disrupted, you cannot change facing, because you cannot move. And if defensive fire or a failed movement roll stops your movement, you must stop facing the hex you tried to enter.
For the exact rules wording, go to the Avalon Hill webpage and download the rules.