I like core module Time::Local's timelocal_nocheck / timegm_nocheck for doing time and date arithmetic.

use strict;
use warnings;

use POSIX       qw( strftime       );
use Time::Local qw( timegm_nocheck );


# Supplied definitions.

my $base_year  = 2004;
my $base_month = 1; # 0-based
my $base_day   = 1; # 1-based

my @weeks_in_month = (
   4, # Feb
   5, # Mar
   4, # Apr
   4, # May
   5, # Jun
   4, # Jul
   4, # Aug
   5, # Sep
   4, # Oct
   4, # Nov
   5, # Dec
   4, # Jan
);


# Derived constants.

my @days_before_month = (0);
for (0..11) {
   $days_before_month[$_+1] = $days_before_month[$_]
                            + $weeks_in_month[$_] * 7;
}

my $days_in_year = $days_before_month[12];


# The guts.

sub first_day_of_accounting_month {
   my ($year, $month) = @_;

   my $day = $base_day
           + ($year - $base_year) * $days_in_year
           + $days_before_month[$month];

   my $time = timegm_nocheck(0,0,0, $day, $base_month, $base_year);
}


sub first_day_of_accounting_year {
   push(@_, 0);
   goto &first_day_of_accounting_month;
}


# Generate a bunch of data for demo purposes.

# The output format can easily be changed.
my $date_format = '%b %d, %Y';

for my $year (2004 .. 2015) {
   my $time;

   $time = first_day_of_accounting_year($year);
   print("Accounting year $year\n");
   print(strftime($date_format, gmtime($time)) . "\n");
   print("\n");

   for my $month (0..11) { # Feb..Jan
      $time = first_day_of_accounting_month($year, $month);
      print(strftime($date_format, gmtime($time)) . "\n");
   }

   print("\n");
   print("\n");
}
[download]

The above prints:

Accounting year 2004
Feb 01, 2004

Feb 01, 2004
Feb 29, 2004
Apr 04, 2004
May 02, 2004
May 30, 2004
Jul 04, 2004
Aug 01, 2004
Aug 29, 2004
Oct 03, 2004
Oct 31, 2004
Nov 28, 2004
Jan 02, 2005


Accounting year 2005
Jan 30, 2005

Jan 30, 2005
Feb 27, 2005
...


Accounting year 2006
Jan 29, 2006

Jan 29, 2006
Feb 26, 2006
...


Accounting year 2007
Jan 28, 2007

Jan 28, 2007
Feb 25, 2007
...
[download]

Update: I moved the guts into functions, and I added a few more comments.