Powerbalance

The mana value of a split card not on the stack or a fused split spell on the stack is determined by the combined mana cost of its two halves. Otherwise, while a split card is on the stack, its mana value is determined by the mana cost of the half that was chosen to be cast.

If you cast a spell "without paying its mana cost," you can't choose to cast it for any alternative costs. You can, however, pay additional costs, such as kicker costs. If the spell has any mandatory additional costs, those must be paid to cast it.

A spell's mana value is determined only by its mana cost. Ignore any alternative costs, additional costs, cost increases, or cost reductions.

You choose whether or not to cast the exiled card as Powerbalance's triggered ability resolves. If you do, you do so as part of the resolution of that ability. You can't wait to cast it later in the turn. Timing restrictions based on the card's type are ignored.