Free or cheap automatic shutdown utility for XP?

It is already in your XP computer.

Open a command prompt (c:\windows\system32\cmd.exe)

type in shutdown /? and you will get a complete overview of what you and do with shutdown

From your description you will want to use shutdown /f /p

You need to make this command with its options into a batch script or executable file. Open notepad, put your command in (c:\windows\system32\"shutdown /f /p") and save it with file extension .bat

Schedule this bat file to run at the times you want. Let it run under localsystem credentials or under the administrator account.

This will not work if the user sleeps or hibernates the computer, for that you need Wake on Lan

seek for oem copys of homestead windows xp ,the oem homestead windows xp disk is shoud be plenty much less or call ms to confirm in case you ought to purchase a purely a win xp disk .or try ubuntu linux on the pc

You could schedule shutdown.exe to run as a scheduled task. Try the follow through provided in the link below.