Compute Groupon unit economics and break-even
Overview
This question evaluates unit economics, break-even analysis, basic algebra, and sensitivity analysis skills within a Data Scientist context. It is commonly asked to measure applied statistical and mathematical reasoning in the Statistics & Math domain, testing practical application of quantitative modeling and profitability metrics rather than purely conceptual theory.
Capital One
Oct 13, 2025, 9:49 PM
Data Scientist
Technical Screen
Statistics & Math
0
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Restaurant Coupons and Unit Economics
Context: A restaurant's variable cost (VC) is 40% of pre-discount spend and fixed cost (FC) is $100/day. Assume one table per party. Ignore tips and taxes. Use the simplified unit-economics provided.
Given
- VC rate = 40% of pre-discount spend
- FC = $100/day
- One table per party
Tasks
- Baseline day (no coupons): 20 tables/day, average spend per table = $30. Compute daily profit.
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Groupon voucher mechanics: Customers buy a
15; Groupon retains a 40% commission on the $15; one voucher per table. Let n be the table’s total pre-discount spend when a voucher is used. Using the model
- Revenue = n
- Costs = 0.4n + 15 (commission on voucher payment) Solve for the break-even n where the table contributes zero profit.
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New day with mixed tables: 25 tables/day total, 10 tables use a voucher, and the average pre-discount spend for all tables (coupon and regular) = $36. Compute total daily profit using:
- Profit_regular_table = 0.6×36
- Profit_coupon_table = 36 − 0.4×36 − 15 − 0.4×15
- Daily profit = 15×Profit_regular_table + 10×Profit_coupon_table − 100
- Sensitivity: What minimum average pre-discount spend per coupon table makes daily profit equal to the baseline in part 1? Assume regular tables remain at $36 and counts unchanged (15 regular, 10 coupon).
Solution
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