On some PCs the hibernation option is already installed on the shutdown menu. If it isn't installed in your shutdown menu and you want it displayed there then proceed as follows.
You should be aware that this method 'does' disable the hybrid sleep option.
1/ Click Start button
2/ On the Start Menu, Click the Control panel icon
3/ In the Control Panel Window, Click the Power Options icon
4/ In the Power Options window look in the 'preferred plan' section in the Right hand pane
5/ Below your preferred plan, i.e., Balanced, you will see a link marked 'Change plan settings', Click on this
6/ In the 'Change Settings For Plan' window, Click the 'Change advanced power settings link'
7/ The Advanced power settings window now opens
8/ Look down the list that appears in this window and Click the Plus (+) sign next to the Sleep option
9/ Now Click the Plus (+) sign next to the 'Allow hybrid sleep' option. The setting should currently be 'On'
10/ Click on the Allow hybrid sleep setting an a dialogue box will appear with an arrow to the Right
11/ Click the Arrow and from the drop down Menu select OFF
12/ Now Click the OK button
13/ Finally Close the change settings for the plan window
14/ If you now look at your Shutdown menu on the Start button menu you should see the hibernate option.