Recalculate break-even with spend uplift assumptions
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
Extend the prior scenario, but now assume during the promo: (i) existing RH users increase RH spend by 20% (from $500 to $600); (ii) new customers who join because of the promo spend twice as much on RH as existing users during the promo period (i.e., $1,000). The discount remains 30% on RH spend and average first‑year net revenue per new cardholder remains $550. Let x be the new customers acquired due to the promo. a) Write and solve the break‑even equation: 550·x − 0.30·(1,000·x + 2,000,000·5%·600) = 0. b) Compare this x to the previous break‑even and explain intuitively why the required new‑customer count changes despite higher spend.
Quick Answer: This question evaluates proficiency in break-even analysis, algebraic modeling of promotional spend uplift, and unit-economics calculation for customer acquisition within a data science context.
