The document summarizes three studies on customer lifetime value and profitability relationships. Study 1 finds the relationship between lifetime and profits is not always positive, and both short-term and long-term customers can be profitable. Study 2 develops a model to estimate individual customer profitable lifetime durations based on projected revenues and costs. Study 3 analyzes factors that impact profitable lifetime durations, finding purchase amount, cross-buying, and mailings increase duration while returns and buying in a single department decrease it.