(Hypothetical) What if Nashor's and Lich Bane were combined into one item?

On a whim, I wanted to see what a combination of Nashor's Tooth and Lich Bane would look like and be worth (roughly).

Nashor's Bane

Recipe: Sheen (1050) + Stinger (1100) + Aether Wisp (850) + 600 = 3600

+80 Ability Power +40% Attack Speed +7% Movement Speed +250 Mana

Unique Passive: +20% Cooldown Reduction

Unique Passive: Basic attacks deal 15 + (15% AP) bonus Magic Damage on-hit.

Unique Passive - Spellblade: After using an ability, this item's bonus Magic Damage on-hit for your next basic attack is increased to (75% Base AD) + (50% AP).

This item is about 129% gold efficient in terms of raw stats. Sounds like a lot, huh? Well, as a fun fact, Nashor's Tooth as it is now is 142.17% efficient.

Again, this wasn't a serious suggestion so much as me wanting to see what the two items would look like mashed together and adjusted a bit. Mainly because Nashor's as it is now is only consistently built on two champions that I'm aware of, and one of those two only builds it for its stats and not the passive.

As for why I posted it if it was just me having dumb ideas? I dunno.