We open 200,000 new cards a quarter, and 50% of them make a first purchase within 30 days. Of those who do, 80% are still active after 12 months, versus only 30% of those who don't, and an active customer is worth 150 dollars a year. Product wants to give a 20 dollar reward to every customer who makes a first purchase, which they expect to lift the first-purchase rate to 60%. Is it worth it?

我们每季度新开20万张卡，现在30天内首刷率是50%。首刷的客户12个月后还活跃的有80%，没首刷的只有30%，一个活跃客户年利润150美元。产品想给每个首刷客户发20美元奖励，预计首刷率能提到60%。你觉得值不值？