Luden's Echo is underpowered compared to Statikk Shiv (Analysis)

I love the new AP item, and it's a lot of fun to use. However, it seems a bit underwhelming compared to it's AD counterpart. Granted, the two items are not perfectly analogous, but I think comparing and contrasting them reveals some interesting facts.

Luden's Echo is only 93% gold efficient without the passive effect. Shiv is 102% gold efficient without its passive. They both do the same amount of base damage, but Shiv does 200 damage when it crits (250 with IE, which is almost always built first). In order for Luden's to do that much damage, it's bearer would have to have 667 AP, or 1000 AP to compare with IE crit Shiv. That will almost never happen in a normal game. Granted, additional magic damage from an item generally goes better with AP champs than AD, but still think Luden's is underpowered for its cost.

Potential solutions: Decrease cost of Luden's by ~100g, increase AP ratio on passive proc, increase base damage on passive proc, or add a small amount of a third caster stat to the item. (Such as spell vamp, CDR, flat magic pen, etc)

Thanks for you time.