Assess card rewards profitability and break-even spend
Overview
This question evaluates a data scientist's ability to perform unit-economics and break-even analysis, including modeling interchange revenue, rewards costs, interest income on revolving balances, credit losses, operating expenses, sensitivity/stress testing, and incremental impact assessment.
Capital One
Oct 13, 2025, 9:49 PM
Data Scientist
HR Screen
Analytics & Experimentation
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Credit Card Unit Economics and Break-even Spend
Context
A bank is evaluating launching a credit card that pays 1% rewards on all purchases. Consider per-customer annual unit economics. Let S denote average monthly purchase spend (in dollars). Assume S ≥ 0. Average revolving balance refers to the outstanding balance that accrues interest and loss.
Given parameters:
- Interchange revenue = 2% of purchase volume
- Rewards rate = 1% of purchase volume
- Average monthly spend S; baseline S = $500
- Average revolving balance (baseline) = $2,000
- Net interest margin (APR minus cost of funds) on revolving balance = 10% annually
- Credit loss rate = 3% annually on the average balance
- Operating expense (OPEX) = $50 per year
Tasks
- Compute annual unit economics (revenue, costs, profit) per customer with rewards at 1% when S = $500. Should the bank issue the card?
- Solve for the minimum monthly spend S* such that expected annual profit = 0 under: a) Average balance fixed at 2,000 baseline (i.e., avg balance B = 2{,}000 + 0.20 × 12 × S).
- Stress test: if interchange falls to 1.6% and the loss rate rises to 5%, recompute S* for cases (2a) and (2b).
- Incremental analysis: For a rewards change on an existing customer, when is it valid to ignore the outstanding balance term, and what shortcut does that imply for estimating break-even new spend?
Solution
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