You need to run the following command:
/sbin/shutdown -r now
with root pirviliges. The way to do it is to use root's crontab, not your user crontab. A
sudo before the usual crontab command does that:
sudo crontab -e
Tip: You can switch the shell's standard editor for things like
sudo update-alternatives --config editor (and than selecting the editor of your choice.
Editing the crontab you should add the following line to you file:
# For more information see the manual pages of crontab(5) and cron(8)
# m h dom mon dow command
@daily root /sbin/shutdown -r now
The "@daily" here is a shortcut for every day at midnight (equivalent to "0 0 * * *"). By the way - why do you want a daily reboot?
EDIT - see https://help.ubuntu.com/community/CronHowto for the following: "Crontab commands are generally stored in the crontab file belonging to your user account (and executed with your user's level of permissions). If you want to regularly run a command requiring administrative permissions, edit the root crontab file: sudo crontab -e"
EDIT - thanks to @charlesbridge for his comment - edited answer to include the full path