I did some math to find out which AP items were the best if you wanted as much damage as possible. I only did the math for Void staff, Horizon Focus, Shadowflame and Rabadon (considering you already have Luden and sorcerer boots).
In the end Horizon Focus is always higher if you can proc its effect. So I’m wondering why every Lux player for example aren’t buying it second item.
I updated the post to show the math. Shadowflame outdamage Horizon focus if you cannot recast spells (because ability haste would be useless) so SF is better on assassin but HF is better otherwise even on champ with no magic resist from items.