Compute partnership profit and break-even population

You are assessing a 12-month co-marketing arrangement between card issuer C1 and a single merchant. C1 receives 1% of cardholders' overall card spend as interchange-like revenue. The offer is a 20% immediate discount at the partner merchant for selected cardholders, paid entirely by C1, for all 12 months. The merchant projects the following average monthly per-cardholder behavior by segment.

Assumptions:

• If $\text{Total Spend After} - \text{Total Spend Before} < \text{Merchant Spend After} - \text{Merchant Spend Before}$, the shortfall is cannibalization from other merchants on the same card, so cannibalized spend produces no incremental issuer revenue. Only growth in total card spend generates incremental issuer revenue for C1.
• All figures are monthly and constant over the 12 months; ignore fixed fees, interest income, and credit losses.

Segments and inputs (monthly per cardholder):

Tasks: (a) For each segment and overall, calculate:

• Incremental issuer revenue per month = $1\% \times (\text{Total After} - \text{Total Before})$.
• Discount cost per month to C1 = $20\% \times \text{Merchant Spend After}$.
• Incremental profit per month = revenue minus cost; then multiply by 12 to annualize. State the total annual profit or loss and whether the partnership is profitable.

(b) Give at least three insights about customer behavior and economics, such as cannibalization versus true lift, where losses are concentrated, and how to prioritize segments.

(c) What important factors have we left out that could change the decision? List at least three, one of which should be acquiring a new customer segment.

(d) New customer segment (acquisition from the merchant's audience): Segment 4 is made up of customers new to C1 who sign up because of the partnership. For each such new cardholder, average monthly Total Spend is $800$ and Merchant Spend at the partner is $20$, all incremental. What minimum Segment 4 population is needed over the 12-month partnership to exactly break even on the total profit or loss from part (a)? Show both the formula and the numeric answer.

(e) Sensitivity: If the merchant covers 50% of the 20% discount and C1 pays the other half, recompute the annual total profit or loss from (a) and the break-even population from (d).

(f) Decision: Based on your results and insights, would you recommend partnering with this merchant? If not, identify the top three traits of a better-fit merchant that would reverse the economics.

Overview: This question tests analytics and experiment-driven financial modeling skills, including unit economics, cannibalization versus true lift, break-even and sensitivity analysis, and interpreting segment-level effects on partnership profitability.