Gift card payment or cash payment: Which payment is suitable for trade-in rebate?

New trade-in services such as online trade-in, trade-in on e-commerce platforms and omni-channel trade-in, are emerging due to the development of e-commerce. To offer these new trade-in services, firms need to determine the optimal product price and rebate and decide whether to pay the rebate with a gift card (G) or cash (C). To address these challenges for firms, our paper considers a firm selling a new product to new consumers and offering a trade-in service to replacement consumers. In addition, we develop theoretical models to examine the optimal decisions in the cases of G and C and explore the optimal payment for the rebate. We reveal that G payment is a better choice for the firm only if the used product residual value is relatively low and the market size ratio between replacement and new consumers is relatively low; otherwise, the firm should choose C payment. Interestingly, replacement consumers preferred trade-in rebate payment (i.e., C payment) leads a lower trade-in demand than G payment and C payment may be harmful. In the extension, we consider a firm with online and offline sales channels and different types of replacement consumers who own different used products, and find that our main results regarding the optimal rebate payment still hold. Moreover, we find that in the context of a used product with a relatively medium residual value, firms with online and offline sales channels are more likely to choose G than firms with one sales channel; otherwise, firms are more likely to choose C.