How far can Cedar Hedge be cut back?

[cammer]

The house that I purchased last fall has an overgrown cedar hedge on one side of the back yard. It is approximately 15' high and 8-9' through. I would like to re-claim the 5 or so feet of my yard that are currently occupied by the hedge.

What I figure would be ideal is if I could cut the hedge back to the trunk, up the trunk about 6 feet and then shape the top section that remains. This way I would still have the privacy afforded by the upper section and could plant smaller plants underneath. I understand that new growth will not happen from the old wood on the bottom. My only concern is that this aggressive cut back will harm the hedge.

Any thoughts?