How is the Zakat calculated for shares that were granted at a nominal price, then their price multiplied, and is the Zakat calculated based on their value at the time their hawl is completed, or on their current value, given the intention to sell them to repay debts?

If you bought shares with the intention of selling them when their price rises, then they are trade goods subject to Zakat on their value once they reach the Nisab and a full year has passed over them. The amount of Zakat is a quarter of a tenth (2.5%) of the value of the shares and their profits. Zakat does not lapse with statute of limitations but remains a debt payable.

As for the debts you owe, if you possess other non-Zakat-bearing assets that cover them, do not deduct them. If you do not possess such assets, then you may deduct the debts from the value of the shares and then pay Zakat on the remainder if it reaches the Nisab.

If you bought the shares without the intention of selling them (in industrial companies), Zakat is only due on the profits generated (if they reach the Nisab of gold or silver and a full year has passed over them), and not on the value of the shares themselves; this is because the shares represent a part of the factory, and Zakat is not obligatory on its tools. If the shares are sold and their price reaches the Nisab, a full year must pass before Zakat is paid on it.