In case it helps, here is the procedure I followed on Ubuntu 14.04. I have not tried it on 16.04 yet but it worked like a charm on my hardware with 14.04:
Save your work and use the command line to test if hibernate works on your computer: open the Terminal by pressing Ctrl+Alt+T or by searching for terminal in the Dash. Type
into the terminal and press Enter. Enter your password when prompted, and press Enter again. After your computer turns off, switch it back on. Are the applications that were running before hibernate still running? If hibernate doesn't work, check if your swap partition is at least as large as your available RAM.
If the hibernate test works, you can continue to use the
sudo pm-hibernate command when you want to hibernate.
You can also enable the hibernate option in the user menus. To do that, use your favorite text editor to create
/etc/polkit-1/localauthority/50-local.d/com.ubuntu.enable-hibernate.pkla. Add the following to the file and save:
[Re-enable hibernate by default in upower]
[Re-enable hibernate by default in logind]