Catalysis of the reaction: histone H4 N6-acetyl-L-lysine (position 16) + NAD+ + H2O = histone H4 L-lysine (position 16) + 2''-O-acetyl-ADP-D-ribose + nicotinamide. This reaction transfers an acetyl group attached to a lysine residue in H4K16 to NAD, producing nicotinamide.
NAD-dependent histone deacetylase activity (H4-K16 specific)