/usr/lib/linux-tools/3.16.0-31-generic/perf is in linux-tools-3.16.0-31-generic 3.16.0-31.43~14.04.1.
This file is owned by root:root, with mode 0o777.
It is a symlink to /usr/lib/linux-tools/3.16.0-31-generic/../../linux-lts-utopic-tools-3.16.0-31/perf