Compute gala vs online break-even donors
Company: Capital One
Role: Data Scientist
Category: Statistics & Math
Difficulty: Medium
Interview Round: Onsite
A nonprofit must choose one of two fundraising options.
Option A (Gala): capacity 100 attendees; fixed cost $20,000; variable cost $100 per attendee. Donor segments: High (H) donate $1,000 each; Low (L) donate $250 each. Among the general donor pool, 80% are L and 20% are H. If k of the 100 gala attendees are H, the rest are L.
Option B (Online campaign): reach 1,000 people; fixed cost $8,000; variable cost $1 per person reached. Of the 1,000 reached, 80% are L and 20% are H. Conversion rates and average gifts: L convert at 8% and donate $50 on average; H convert at 15% and donate $500 on average.
Questions:
1) Compute the expected net revenue of Option B.
2) Express Option A's net revenue as a function of k. Find the minimum integer k such that Option A's net revenue is at least Option B's expected net revenue.
3) If gala invitations are random draws from the pool (80% L / 20% H), compute the expected net revenue of Option A and the expected advantage vs Option B.
4) By how much would the gala's fixed cost need to increase (holding all else constant) to raise the break-even k you found in (2) by 10 additional H attendees?
Quick Answer: This question evaluates a candidate's skill in expected-value computation, probability-weighted revenue modeling, break-even analysis, and sensitivity analysis of cost parameters within a donor-segmentation context.
