Compute Groupon unit economics and break-even
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: Technical Screen
##### Question
You run a restaurant with the following daily economics:
- Baseline demand: 20 tables/day (assume one party per table)
- Average pre-discount spend: $30/table
- Variable cost (VC): 40% of pre-discount spend
- Fixed cost (FC): $100/day
- Ignore tips and taxes
A Groupon-style daily-deal site proposes the following voucher: a customer buys a voucher worth $30 of food for $15, and the deal site retains a 40% commission on the $15 the customer pays. At most one voucher can be applied per table. Let `n` be a table's total pre-discount spend when a voucher is used.
Show your formulas and your final numbers for each part.
1. **Baseline profit.** What is your daily profit before joining the deal site?
2. **Break-even on a voucher table.** Using the unit-economics model `Revenue = n` and `Costs = 0.4n + $15 (face value the customer redeems) + 0.4 x $15 (the site's commission)`, solve for the break-even `n` at which a voucher table contributes zero profit.
3. **All tables on vouchers.** If all 20 tables used a voucher and the table count stayed at 20/day, what average pre-discount spend per table would keep daily profit equal to baseline?
4. **Mixed day.** After joining you observe 25 tables/day; 10 of them present a voucher; the average pre-discount spend across all 25 tables is $36; VC and FC are unchanged. What is the new daily profit?
5. **Decomposition.** Decompose the profit change versus baseline into three labeled components: (i) change in table count, (ii) change in average spend per table, (iii) voucher cost on the coupon tables (face value plus commission). Is profit up or down versus baseline, by how much, and what is the primary driver?
6. **Sensitivity.** Holding regular tables at $36 and both counts unchanged, what is the minimum average pre-discount spend per coupon table that makes daily profit equal to the baseline in part 1?
Overview: A Capital One data science technical screen case on restaurant unit economics with a Groupon-style voucher. You compute baseline daily profit from a 20-table day, derive the break-even check for a voucher table under a $30-for-$15 offer with a 40% commission, profit a mixed 25-table day, and decompose the profit change into traffic, check size and voucher cost. Full worked arithmetic, a sensitivity solve, and the incrementality follow-ups an interviewer expects.
