This paper analyses a multi-period single-item repairable inventory system with stochastic new and warranty demands. We assume that newly-procured items are indistinguishable from items repaired from repairable warranty returns and new demand has higher priority than warranty demand within a period. Our model also captures the “repair loss” in repairing returns in each period. We formulate the problem by a dynamic programme, and prove that the optimal policy is completely defined by three period-dependent thresholds: the purchase-up-to level, the repair-up-to level, and the scrap-down-to level. Numerical results demonstrate the effectiveness of the optimal policy and show that our optimal strategy outperforms the repair-all strategy and no-repair strategy. Managerial insights are also generated.