Assuming you don't actually need any of the intermediate stuff, this calculates it directly:

#!/usr/bin/perl -slw
use strict;
use warnings;
use Time::Local;
use Test::More "no_plan";

sub lastBusinessDayPrevQ {
    my( $y, $m, $d ) = unpack 'A4A2A2', shift;
    my $t = timelocal( 0,0,12, $d, $m-1, $y );
    $t -= 43200 until localtime( $t ) !~ m[Mar|Jun|Sep|Dec];
    $t -= 43200 until localtime( $t ) =~ m[Mar|Jun|Sep|Dec];
    $t -= 43200 until localtime( $t ) =~ m[Mon|Tue|Wed|Thu|Fri];
    ( $y, $m, $d ) = unpack 'x20a4 X20a3 xa2', scalar localtime( $t );
    $m = { Mar=>'03', Jun=>'06', Sep=>'09', Dec=>'12' }->{ $m };
    return join '', $y, $m, $d;
}


test();

sub test {
    ok ( lastBusinessDayPrevQ("20110901") eq "20110630");
    ok ( lastBusinessDayPrevQ("20120101") eq "20111230");
}
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