How to allow someone to turn off my device
Easier, but sacrifices security

Create an admin account for him on the system.  

Have him type 

sudo -u his_short_user_name shutdown -h now


He then answers a password challenge with his password, and the system does a "somewhat hard" shutdown.  This means apps will not be asked about saving application data, so your half finished Illustrator drawing is gone.  

Better security

At Terminal, you write a bit of perl to wait for his shutdown request.  You launch it after every reboot with sudo perl program_name.  When you do, it'll challenge you for your password, and then run as superuser.  When it comes time to shutdown, it's already authenticated so it just does it. 

  my $signal_file = "/Users/(you)/Public/Drop Box/shutdown";
  unlink ($signal_file); 

  while (1) { 
    sleep(10);
    next if not -f $signal_file;
    system ”shutdown -h now";
  }


And your guest needs to simply touch '/Users/(you)/Public/Drop Box/shutdown' to trigger a shutdown.  He doesn't need any special rights to do this.  For instance you could publish your Public directory as a network share point, a perfectly reasonable thing to do from a security POV.  

If you want to temporarily prevent a user from doing this, either kill the process (ctrl-C) or create a directory there called shutdown.   Note that perl is testing for -f (presence of file).