A theme park currently operates on 2,000 acres with annual entries of 1,000,000 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 an annual-pass holder visits 25 days/year. Operating assumptions: variable operating cost is $22 per entry; fixed operating cost is $20,000,000 per year; the land-owner fee is a percentage of revenue. Prices remain constant under all 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 under terms that increase the land-owner fee from 5% to 10%. Assume entries and ticket sales scale proportionally with acreage (to 3,000 acres total). Fixed operating cost remains $20,000,000; 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 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 (a) and (b). Recommend the best option. (d) Sensitivity: (i) What land-owner fee rate under 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.

This question evaluates financial modeling, expected-value decision-making, probability reasoning, and sensitivity analysis skills applied to revenue, variable and fixed cost interactions and contractual fee impacts, aimed at a Data Scientist role.

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Compute expansion profits and expected value | Capital One Interview Question

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.

Context

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.

20,000,000 and variable cost per entry remains

22. Compute the profit under Option A.

(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.

Compute expansion profits and expected value

Quick Overview

Theme Park Expansion Profit Analysis

Context

Tasks

Solution

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Compute expansion profits and expected value

Quick Overview

Theme Park Expansion Profit Analysis

Context

Tasks

Solution

Submit Your Answer