We are concerned with a multiple replenishment contract with a purchase price discount in a supply chain. The chain is composed of one supplier, one buyer and consumers for a product. The replenishment contract is based upon the well-known (s,Q) policy but allows contracting several firmed orders at a time with a price discount. Due to a larger forecast error of the future demand, the buyer should keep a higher level of safety stock to provide the same level of service of the usual (s,Q) policy but can reduce his purchase cost by placing larger quantity. Thus there exists a trade-off between the price discount and inventory holding cost. We present a model for the contract and an algorithm to find the optimum number of the firmed orders. Computer experiments show that the algorithm finds the global optimum solution very fast.