Check out this node on how to parse the timestamps coming back from Net::FTP's dir() method.

With this tool under your belt, you'll probably come up with something like this:

use warnings;
use strict;

use Net::FTP;
use File::Listing;
use List::Util qw(reduce);

my $ftp = Net::FTP->new('ftp.host.com');
$ftp->login('username', 'password');

my $latest = reduce { $b->[3] < $a->[3] ? $a : $b }
                    File::Listing::parse_dir($ftp->dir());

print "Last modified file is: '$latest->[0]'\n";
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