Theme Park Expansion Profit Analysis

Context

You are evaluating the financial impact of capacity expansion for a theme park. Current operations and pricing are stable. The land-owner fee is a percentage of gross revenue. Ticket prices do not change under any scenario.

• Current size: 2,000 acres
• Ticket sales and prices per year:
  • 250,000 single-day tickets at $80
  • 100,000 five-day tickets at $300
  • 10,000 annual passes at $1,000 (each pass holder visits 25 days/year)
• Current annual entries: 1,000,000 (consistent with the above ticket mix)
• Costs:
  • Variable operating cost: $22 per entry
  • Fixed operating cost: $20,000,000 per year
  • Land-owner fee: a percentage of revenue (rate varies by scenario)
• Prices remain constant across scenarios.

Tasks

(a) Compute current annual revenue, total variable cost, land-owner fee at 5% of revenue, and profit.

(b) Expansion Option A: Acquire an adjacent 1,000 acres (total becomes 3,000 acres). Under the acquisition terms, the land-owner fee rate increases from 5% to 10%. Assume entries and ticket sales scale proportionally with acreage (i.e., by a factor of 3,000/2,000 = 1.5). Fixed operating cost remains $20,000,000 and variable cost per entry remains$22. Compute the profit under Option A.

(c) Expansion Option B (bid): You may bid for the same 1,000 acres such that, if you win (80% probability), the land-owner fee remains 5% at 3,000 acres; if you lose (20%), you stay at 2,000 acres with the current 5% fee. Compute the expected profit of bidding and compare to parts (a) and (b). Recommend the best option.

(d) Sensitivity under 3,000 acres:

• (i) What land-owner fee rate 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 would make Option A tie the current profit? Show formulas and numeric results.