/usr/lib/linux-tools/4.4.0-116-generic/perf is in linux-tools-4.4.0-116-generic 4.4.0-116.140~14.04.1.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/linux-tools/4.4.0-116-generic/../../linux-lts-xenial-tools-4.4.0-116/perf