Your code works, but there's no reason to create (and pop from) the separate @letters array. Additionally, by doing the multiplication first, we can get rid of the $pwr variable, and get to the much simpler (to my mind, at least),

sub v {
    my $sum = 0;
    for (split //, $_[0]) {
        $sum *= 26;
        $sum += ord($_) - ord("A") + 1;
    }
    return $sum;
}
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You could also factor out the ord("A") + 1 part into a separate variable, but I think it's a little easier to read this way (and the cost of the extra calls to ord is probably negligible).