Compute expansion profits and expected value

A theme park currently sits on 2,000 acres, draws 1,000,000 entries per year, and sells 250,000 single-day tickets at $80, 100,000 five-day tickets at $300, and 10,000 annual passes at $1,000. Assume each annual-pass holder visits 25 days per year. Operating assumptions: variable operating cost is $22 per entry, fixed operating cost is $20,000,000 per year, and the land-owner fee is a percentage of revenue. Prices stay constant across all scenarios.

Tasks: (a) Compute current annual revenue, total variable cost, the land-owner fee at 5% of revenue, and profit. (b) Expansion Option A: acquire an adjacent 1,000 acres under terms that raise the land-owner fee from 5% to 10%. Assume entries and ticket sales scale proportionally with acreage, reaching 3,000 acres total. Fixed operating cost stays at $20,000,000, and variable cost per entry is unchanged. Compute profit under Option A. (c) Expansion Option B (bid): you may bid for the same 1,000 acres; if you win (80% probability), the land-owner fee remains 5% at 3,000 acres, while if you lose (20%), you remain at 2,000 acres with the current 5% fee. Compute the expected profit from bidding and compare it with (a) and (b). Recommend the best option. (d) Sensitivity: (i) What land-owner fee rate at 3,000 acres makes Option A’s profit equal to the current no-expansion profit? Solve for the break-even fee rate. (ii) Holding the fee at 10%, what variable cost per entry at 3,000 acres would make Option A tie the current profit? Show formulas and numeric results.

Overview: This question tests financial modeling, expected-value decision-making, probability reasoning, and sensitivity analysis applied to revenue, variable and fixed cost interactions, and contractual fee impacts, for a Data Scientist role.