Many sellers allow consumers to pay with reward points instead of cash or credit card. While the revenue implications of cash purchases are transparent, the implication of reward sales is not trivial, when a firm that issues points is not a seller. In this case, a seller receives a compensation from the point issuer when a consumer purchases the good with points. We examine how reward sales influence a seller's pricing and inventory decisions. We consider a consumer who can choose to pay with cash or points based on reservation price, point balance, and the perceived value of a point. Then, we incorporate this into a pricing model where a seller earns revenues from both cash and reward sales. In contrast to an intuition that reward sales will increase sales and revenue, we show that the effect of reward sales on the seller's price is non-trivial as the seller could either add a premium or discount depending on the inventory level, time, and the reimbursement rate. Furthermore, such price adjustments can attenuate the optimal mark-up or mark-down level, and reduce the price fluctuation caused by inventory level and remaining time. We investigate settings where the seller has different operational controls over reward sales and find that allowing reward sales is still better even when the revenue from the reward sales is smaller than the cash sales. We also find that a seller with an ability to control availability (i.e., allow a reward sale or not) can achieve a revenue similar to the revenue of a seller with an ability to change point requirements and price
