How is the zakat calculated for a restaurant that was purchased for a certain amount, then sold later with profits realized during its periods of operation?

If the restaurant was purchased with the intention of leasing it or operating it, then there is no Zakat on the restaurant itself or its machinery. Zakat is only due on the goods prepared for sale. There is no Zakat on the value of a sold restaurant until a full Hijri year has passed since its acquisition. As for the profits of the past three years, Zakat was obligatory on whatever portion of them came into your possession, provided a full year had passed on the principal amount with which you purchased the materials and equipment, and it reached the Nisab (minimum threshold). The money you spent is not subject to Zakat because it is no longer in your possession. If you ascertain that Zakat was obligatory upon you during this period, then you must pay Zakat for the past years because it is a debt owed by you, and Allah's debt is more deserving of being paid. However, if the restaurant was purchased with the intention of reselling it, then it is considered a trade commodity, and Zakat of a quarter of a tenth (2.5%) is obligatory on its purchase price each time a full year passes.