Choosing a Threshold From Business Costs

A subscription business builds a churn model that outputs a well calibrated probability of cancellation in the next 30 days. A retention call costs $8 to place (agent time). If a churner is called and retained, the business keeps a customer worth $150 in expected future revenue; if a non-churner is called, the $8 is wasted (no benefit, no harm otherwise). If a churner is not called, the business loses the $150.

1. Frame this as a cost matrix and derive the probability threshold at which calling becomes worthwhile.
2. The model's validation set shows only 4% of customers exceed that threshold. The VP asks whether that means "churn is rare, only 4% of customers are at risk." What's wrong with that reading?
3. Marketing wants to lower the threshold to call more people "to be safe." What operational trade-off are they making, and how would you quantify it before agreeing?