How is the zakat on money calculated for sheep raised in a partnership under a profit-sharing system, given that the breeding cycle is four months?

If the intention behind raising sheep is to confine them and provide them with fodder, then these are fed sheep, and there is no zakat due on them according to the majority of scholars, unless they are for trade. In that case, they are subject to zakat as trade goods. You must consider your share in the trade; if it reaches the nisab (approximately equivalent to 85 grams of gold) either by itself or by combining it with your money or other trade goods, and a full year has passed over it, then zakat of one-quarter of one-tenth (2.5%) is obligatory.