Synthesizes the second messengers cyclic ADP-ribose and nicotinate-adenine dinucleotide phosphate, the former a second messenger for glucose-induced insulin secretion. Also has cADPr hydrolase activity (By similarity). H2O + NAD(+) = ADP-D-ribose + H(+) + nicotinamide NADP(+) + nicotinate = nicotinamide + nicotinate-adenine dinucleotide phosphate Belongs to the ADP-ribosyl cyclase family.