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This is the foundation question and I actually felt okay on it.
Start by clearly defining the revenue streams (interchange and net interest income) and cost components (rewards, operating expense, and credit losses). Calculate each item using the given assumptions, then sum to find annual profit per customer. Finally, assess whether the profit is positive and consider qualitative factors like customer lifetime value and risk.
Pro tip: Always annualize monthly figures and double-check units; a common mistake is mixing monthly and annual numbers. Also, mention that profitability should be evaluated over the customer lifetime, not just one year.
Compute annual interchange revenue from spend and net interest income from revolving balance. Interchange = 2% * monthly spend * 12; Net interest = 10% * average revolving balance.
Calculate annual rewards cost (1% * monthly spend * 12), operating expense ($50), and credit losses (3% * average revolving balance).
Subtract total costs from total revenue to get annual profit. Ensure all figures are annualized.
If profit is positive, the card is profitable on a per-customer basis; consider if it meets the bank's profitability threshold. Also discuss qualitative factors like risk, competition, and customer retention.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Case (a) was fine once I set up profit as a function of S.
Start by clearly defining the profit equation: Profit = Revenue - Costs, where Revenue includes interest income from revolving balances and interchange fees from purchase volume, and Costs include fixed and variable expenses. Then set Profit = 0 and solve for the monthly spend S, first with a fixed revolving balance of $2,000, and then with an additional revolving balance equal to 20% of annual purchase volume. Be explicit about all assumptions and units (monthly vs annual).
Pro tip: Clarify whether the $2,000 baseline revolving balance is per customer or total, and whether the 20% of annual purchase volume becomes revolving immediately or over time; stating these assumptions upfront shows analytical rigor and prevents misinterpretation.
Write Profit = (Interest income from revolving balances + Interchange income from purchase volume) - (Fixed costs + Variable costs). Specify all components and their units (e.g., monthly vs annual).
Assume revolving balance is fixed at $2,000. Express interest income as a function of the APR, and interchange income as a percentage of monthly spend S. Set Profit = 0 and solve for S*.
Assume 20% of annual purchase volume becomes revolving balance on top of the $2,000 baseline. Express the new revolving balance in terms of S (e.g., if S is monthly spend, annual volume = 12S, so additional revolving = 0.2 * 12S = 2.4S). Update interest income accordingly and solve for S*.
Solve the equations for S* in both scenarios. Compare the results and discuss the sensitivity of S* to the revolving balance assumption.
Check that the solution makes business sense (e.g., S* is positive and realistic). Discuss how changes in APR, interchange rate, or cost structure would affect S*.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
First, define the break-even spend S* as the spend level where revenue from interchange equals losses from fraud/default. Then, recalculate S* under the new assumptions (interchange 1.6%, loss rate 5%) for both scenarios: fixed balance (balance independent of spend) and balance scaling with spend (balance proportional to spend). Compare the new S* to the original to assess sensitivity.
Pro tip: Clearly state your assumptions about the relationship between spend and balance, and note that in reality, higher spend might correlate with higher balances but also potentially higher risk. This shows you understand the business context beyond the math.
Set up the equation: interchange revenue = loss amount. For fixed-balance, revenue = interchange rate * balance, loss = loss rate * balance. For balance-scales-with-spend, revenue = interchange rate * (k * spend), loss = loss rate * (k * spend), where k is the scaling factor.
Plug in the new interchange rate (1.6%) and loss rate (5%). Note that if loss rate exceeds interchange rate, the break-even may be unattainable (i.e., losses always exceed revenue) unless there are other revenue sources.
In fixed-balance, revenue and loss are independent of spend, so break-even depends only on balance. If interchange rate < loss rate, there is no break-even spend; the product loses money regardless of spend. If equal, any spend breaks even.
Here, revenue and loss both scale with spend, so the break-even condition reduces to interchange rate = loss rate. With 1.6% < 5%, losses always exceed revenue, so no finite S* achieves break-even; S* is undefined or infinite.
Conclude that under both scenarios, with loss rate > interchange rate, the break-even spend does not exist (or is infinite). Discuss implications: the product is unprofitable at any spend level, so other mitigations (e.g., reducing loss rate, increasing interchange) are needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by defining the incremental analysis framework for a rewards change, explicitly writing out the profit equation including the outstanding balance term. Then identify the conditions under which that term becomes negligible or cancels out, and explain how the break-even new spend simplifies as a result. Use a clear mathematical derivation and tie it back to business intuition.
Pro tip: Emphasize that ignoring the outstanding balance term is only valid when the rewards change does not alter the customer's existing balance behavior—e.g., if the change applies only to new spend and the balance is either zero or unaffected. This shows you understand the subtle behavioral assumptions behind the math.
Write the change in profit as the difference between incremental revenue from new spend and incremental rewards cost, including any effect on the outstanding balance (e.g., interest income or rewards on balance).
The outstanding balance term can be ignored if the rewards change does not affect the balance (e.g., balance is zero, or the change applies only to new transactions and the customer's balance behavior is unchanged).
With the balance term removed, break-even new spend is simply the incremental rewards cost divided by the incremental margin on new spend (or the point where incremental revenue equals incremental cost).
Discuss whether the simplification is realistic: consider customer segments, potential balance cannibalization, and whether the rewards change might indirectly alter balance behavior.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.