I'm not really sure what to look for in this output...

I think the main thing is that we can now see that we're not dealing with an old perl, that PERL5OPT (and/or other perl-specific environment variables) have not been set, and that everything looks sane.
The main thing is that you look for a "standout" difference between that output and the output that you get.
If there's nothing to be seen there, as is apparently the case, then at least we know to look elsewhere.

AFAICS, the issue should be reproducible on the problem machine by running this script:

use warnings;
#use Tk;

print "result:\n";
$_A = '16.25'; # string, not number
$_V = '12.99'; # string, not number
$formula = 'sprintf("%.0f", ($_V * $_A))';
$_W = eval($formula);

print "$_V\n";
print "$_A\n";
print "$_W\n";
[download]

If that doesn't reproduce the problem, then I would begin reinstating bits of the original script to it (starting by commenting in the "use Tk;" line) until you hit the point where the problem does kick in.

It's an interesting one ... even if that simplified test script successfully demonstrates the bug, then there's still the question of "why and how ??".
But let's not get too far ahead of ourselves ;-)

UPDATE: If the script I provided did not tickle the bug, then how about this one that fully reinstates the Tk stuff:

use warnings;
use Tk;

my $mw=MainWindow->new();
$mw->Button(-text=>"   Test   ", -command=>sub{test()}, -font=>'Helvet
+ica 18 bold', -pady=>20)->pack();
MainLoop;

sub test {
  print "result:\n";
  $_A = '16.25'; # string, not number
  $_V = '12.99'; # string, not number
  $formula = 'sprintf("%.0f", ($_V * $_A))';
  $_W = eval($formula);

  print "$_V\n";
  print "$_A\n";
  print "$_W\n";
}
[download]

Cheers,
Rob