Not a bad idea at all.

The problem is that you are calling the subroutine as a normal function rather than as an object method. Try changing to:

my $method = $this->{ACTIVITIES}->{$this->{ACT}}->{'func'};
$this->$method($arg);
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Also, it would be easier to assign to ACTIVITIES without the de-reference:

$this->{ACTIVITIES} = {
    Sale => {},
    ....
};
[download]

Within an object, you don't need to take a reference to the subroutine, so you could just have:

$this->{ACTIVITIES} = {
    Sale => {
        func      => 'total_sold',
        datefield => 'date_sold',
    },
    Purchase => {
        func      => 'total_bought',
        datefield => 'date_bought',
    },
};
[download]