# NOTE: untested pseudo-code below!
package Base;

sub new {
	...
	$self->{'requiredValue'} = getRequiredValue();
	...
}

# ensure that my child classes do things properly
sub getRequiredValue { die "Subclasses must implement 'getRequiredValue'" }

...

package Child1;

sub getRequiredValue { 42 } # you know it's the answer :-)

...

package Child2;

sub getRequiredValue { 360 }

...

package main;

my ($c1, $c2);
$c1 = Child1->new(); # Call trace looks like:
                     # 1. Base::new
                     # 2. Child1::getRequiredValue
$c2 = Child2->new(); # This call trace is different:
                     # 1. Base::new
                     # 2. Child2::getRequiredValue !!!