Design theme-park profit model and bid decision

You are assessing pricing and a land purchase decision for a Disney-style theme park. Baseline: 10,000,000 unique visitors per year. Each visitor buys exactly one of three products; the mix is 60% Day Pass, 30% 3-Day Pass, 10% Annual Pass. Ticket prices and average visits per buyer are: Day Pass $120 for 1 visit; 3-Day Pass $300 for 3 visits; Annual Pass $800 for 6 visits. Variable operating cost is $25 per visit (regardless of pass type). Ancillary gross margin (food/merchandise, after cost) is $12 per visit. Ignore existing fixed costs. A land auction opportunity would raise unique visitors by 15% starting next year for 10 years with the same mix and spending behavior. The one-time purchase price is $1.2B paid upfront; incremental fixed operating cost is $100M per year; discount rate is 10%; terminal value is $0 at the end of year 10. Tasks:

1. Compute current annual contribution profit (ticket revenue plus ancillary revenue minus per-visit variable costs).
2. Compute the 10-year NPV of the land project and state whether you would bid, and explain why.
3. Identify the three most critical assumptions to stress-test, and show a simple sensitivity (±10%) on each to see how the decision boundary shifts.
4. If capacity constraints cap total annual visits at 30,000,000, explain how you would adjust your analysis and what data you would need to validate the assumptions. Overview: This question assesses a candidate's skills in quantitative pricing analytics, contribution-margin and NPV financial modeling, sensitivity analysis, and capacity planning in the Analytics & Experimentation area for a data scientist position. This question came from a data scientist interview experience.