I have a DVD for upgrading Windows Vista to Windows 7 Pro; Can I use it to downgrade from Windows 8 (normal version)?
EDIT:
If it is not possible, is there any way to downgrade without having to pay for another entire copy of Windows 7?
I have a DVD for upgrading Windows Vista to Windows 7 Pro; Can I use it to downgrade from Windows 8 (normal version)?
EDIT:
If it is not possible, is there any way to downgrade without having to pay for another entire copy of Windows 7?
Windows 8 downgrade conditions are as followed:

AFAIK, you need a OEM or RTM media, update versions will not work.
edit: if you are elegible for a downgrade, you can do it without paying a cent. if you are not, you will have to purchase a new licence, according to the table.
quoting:
Downgrade rights -- which let customers replace a newer version of Windows with an older edition without paying for two copies -- are available only in Windows 8 Pro. That fits with previous practice: Only Windows 7 Professional, for instance, was allocated downgrade rights.Traditionally, downgrade rights are available only from OEM copies of Windows, those that are pre-installed by computer manufacturers. It looks to be the same with Windows 8: The software license for the retail version of Windows 8 Pro omitted the section on downgrades.
Unfortunately this won't work. When you try to "upgrade" you windows 8 installation, the Windows 7 Installer will identify that you are running a newer version of the OS than the one being installed, and will just quit.
EDIT: Your new question is answered by @Znau. Microsoft licensing agreement only permit downgrade of OEM or VLSC (Volume Licenses).
And, as for the "pay for another entire copy of Windows 7", unless you find it on your supply shop, you won't be able to buy Windows 7, as Microsoft usually stops selling older versions of the products, as soon as the newer is released.
What I understand is that you can re-use a product key that is already in use. Online activation will fail, at which point you must call Microsoft support. At that point, you can tell them you are exercising your downgrade rights from Windows 8, and they will sort it out for you.
However I found this out too late, and ended up buying a copy of Windows 7 in order to downgrade (it was for a work PC, so at least this way someone else can just use my copy of Windows 8).