Compute partnership profit and break-even population

You are evaluating a 12‑month co‑marketing partnership between issuer C1 and a single merchant. C1 earns 1% of cardholders’ total card spending (interchange-like revenue). Offer: 20% instant discount at the partner merchant for targeted cardholders, fully funded by C1, for the entire 12 months. The merchant expects the following average per-cardholder monthly behavior by segment. Assumptions: - If Total Spend After − Total Spend Before < (Merchant Spend After − Merchant Spend Before), the shortfall is cannibalization from other merchants on the same card (no incremental issuer revenue from cannibalized spend). Only increases in total card spend create incremental issuer revenue for C1. - All figures are monthly and stable for 12 months; ignore fixed fees, interest income, and credit losses. Segments and inputs (monthly per cardholder): Segment | Population | Merchant Spend Before | Merchant Spend After | Total Spend Before | Total Spend After 1 | 100,000 | 0 | 200 | 200 | 200 2 | 50,000 | 10 | 20 | 400 | 410 3 | 50,000 | 0 | 40 | 300 | 500 Tasks: (a) For each segment and in total, compute: - Incremental issuer revenue per month = 1% × (Total After − Total Before). - Discount cost per month to C1 = 20% × (Merchant Spend After). - Incremental profit per month = Revenue − Cost; then annualize (×12). State the total annual profit/loss and whether the partnership is profitable. (b) Provide at least three insights about customer behavior and economics (e.g., cannibalization vs. true lift, concentration of losses, segment prioritization). (c) What important factors have we not considered that could change the decision? List at least three, including acquisition of a new customer segment. (d) New customer segment (acquisition from the merchant’s audience): Segment 4 consists of new-to-C1 customers who sign up because of the partnership. For each such new cardholder, average monthly Total Spend = 800 and Merchant Spend at the partner = 20 (all incremental). What minimum Segment 4 population is required over the 12‑month partnership to exactly break even on the total profit/loss from part (a)? Show both the formula and the numeric answer. (e) Sensitivity: If the merchant funds 50% of the 20% discount (C1 pays the other half), recompute the annual total profit/loss in (a) and the break-even population in (d). (f) Decision: Based on your results and insights, would you recommend partnering with this merchant? If not, name the top three traits of a better-fit merchant that would flip the economics.