Determine Revenue and Cost Components for Credit-Card Issuer
Overview
This question evaluates unit-economics and break-even analysis skills, focusing on revenue and cost component identification and algebraic reasoning applied to credit-card product economics for Analytics & Experimentation roles in data science.
Credit-Card Issuer Unit Economics and Break-even Analysis
Scenario
A card issuer is considering launching a new 1% cashback card alongside its existing no-cashback card. Both cards:
- Earn x% interchange on purchase transactions
- Charge the same interest rate y% on carried balances (APR)
For the existing no-cashback card, users carry an average balance of $1,000.
Assumption (to close the math cleanly): For a typical revolver, purchase volume over the period is roughly comparable to the average carried balance for that period (i.e., spend ≈ balance), so interchange and rewards can be modeled per dollar of average balance. Time bases (e.g., annual) are consistent across rates.
Tasks
- List the main revenue and cost components for a credit-card issuer.
- Using the setup above, compute how large the average balance on the 1% cashback card must be for the product to break even with the no-cashback card.
Optional generalization: If spend-to-balance ratio r = (spend)/(average balance) is known rather than assuming r ≈ 1, express the break-even in terms of r.
Solution
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