Decide and test a 20% discount strategy

Context: Marketing proposes a 20% discount to boost purchases. Questions: 1) Should we offer the discount? Formulate the business case and decision rule using incremental profit and payback period. Explicitly include coupon cost, cannibalization, and processing fees. 2) Design an experiment to measure causal impact. Address self-selection and leakage (users sharing codes) via randomized code eligibility, geo or user-level randomization, and holdout cells. Define primary metrics (incremental gross profit per user, LTV over a 90-day window) and guardrails (refunds, fraud, customer support contacts). 3) Targeting: describe a two-stage approach—first estimate heterogeneous treatment effects, then deploy targeted eligibility. Compare simple rules (cohorts, recency/frequency/monetary) vs uplift modeling; specify how you would validate targeting without bias (e.g., nested experiments or interleaved randomized eligibility). 4) Outline sample size, duration, and data quality needs (exposure logging, redemption attribution, multiple redemptions). Include a pre-registered analysis plan with CUPED and cluster-robust SEs if randomized by geo. 5) Define rollout, monitoring, and kill-switch thresholds. Provide an example of a breakeven calculation for a segment with AOV, margin, and expected lift that justifies or rejects the discount.