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I wasn't expecting a full unit economics case in a DS interview.
Start by clearly defining the revenue and cost components per cardholder, then set up the break-even equation where total revenue equals total costs. Solve for the number of active cardholders (N) algebraically, plug in the given numbers, and interpret the result. Finally, discuss how changes in cashback rate or annual fee affect the break-even point by analyzing their impact on the equation.
Pro tip: Always state your assumptions explicitly (e.g., average interchange fee per cardholder, average spend) and mention that in reality, these variables may vary by customer segment. This shows you understand the business context and can communicate uncertainty.
Identify all revenue and cost components per cardholder: annual fee (A), interchange fee per cardholder (I), cashback rate (c) as a percentage of spend, and average spend per cardholder (S). Assume fixed costs (F) if any, and variable costs per cardholder.
Set total revenue equal to total costs: N*(A + I) = N*(c*S) + F. If no fixed costs, simplify to N*(A + I - c*S) = 0, but since N>0, break-even occurs when A + I = c*S. If fixed costs exist, solve for N = F / (A + I - c*S).
Substitute the provided values for A, I, c, S, and F (if any) into the equation. Calculate the break-even number of cardholders (N). If the denominator is negative, the product never breaks even; if positive, N is the required number.
Explain that increasing cashback rate (c) increases costs, raising the break-even point (or making it unattainable if c*S > A+I). Increasing annual fee (A) increases revenue, lowering the break-even point. Quantify the impact if possible.
State the break-even number in business terms (e.g., 'We need X active cardholders to cover costs'). Discuss implications for pricing strategy and product design, and note any limitations of the model.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.