VIPSolutionsGive step-by-step solution with explanation and final answer: 2-19 An amusement park faces large fixed costs of $500,000 per month and low average variable costs of $10 per visitor. It charges all visitors a flat entry fee of $50 for unlimited rides. a. What is the breakeven point for this park? b. The park currently has 42,000 visitors a month and proposes to raise its entry fee to $60 per person in order to cover the cost of a new Harry Potter–themed ride. What is the new breakeven point if the variable cost increases to $15 per visitor? c. If the park now receives 25,000 visitors a month because of the increase in entrance fee in Part (b), will the park still be profitable? (2.2)
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Give step-by-step solution with explanation and final answer: 2-19 An amusement park faces large fixed costs of $500,000 per month and low average variable costs of $10 per visitor. It charges all visitors a flat entry fee of $50 for unlimited rides. a. What is the breakeven point for this park? b. The park currently has 42,000 visitors a month and proposes to raise its entry fee to $60 per person in order to cover the cost of a new Harry Potter–themed ride. What is the new breakeven point if the variable cost increases to $15 per visitor? c. If the park now receives 25,000 visitors a month because of the increase in entrance fee in Part (b), will the park still be profitable? (2.2)
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Asked by: Shadab
Created at: 2025-09-17 22:33:49
Asked by: Shadab
Created at: 2025-09-17 22:33:49
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Let's solve each part step by step.
---
## Part (a): Breakeven Point (Original Situation)
**Given:**
- Fixed costs (\(FC\)) = \$500,000/month
- Average variable cost (\(AVC\)) = \$10/visitor
- Entry fee (Price, \(P\)) = \$50/visitor
**Breakeven Point Formula:**
\[
\text{Breakeven quantity} = \frac{\text{Fixed Cost}}{\text{Price per unit} - \text{Variable Cost per unit}}
\]
Plug in the values:
\[
\text{Breakeven quantity} = \frac{500{,}000}{50 - 10} = \frac{500{,}000}{40} = 12{,}500
\]
**Explanation:**
The breakeven point is where total revenue equals total costs (fixed + variable). Each visitor generates a contribution margin of \$40 (\$50 - \$10) toward covering fixed costs.
**Final Answer:**
> The breakeven point is **12,500 visitors per month**.
---
## Part (b): New Breakeven Point (After Changes)
**Changes:**
- Entry fee (\(P\)) = \$60/visitor
- Variable cost (\(AVC\)) = \$15/visitor
- Fixed costs remain = \$500,000/month
Apply the breakeven formula:
\[
\text{Breakeven quantity} = \frac{500{,}000}{60 - 15} = \frac{500{,}000}{45} \approx 11{,}111
\]
**Interpretation:**
The new contribution margin is \$45 per visitor (\$60 - \$15). Fewer visitors are needed to break even due to the higher fee and higher variable cost.
**Final Answer:**
> The new breakeven point is **11,111 visitors per month** (rounded to the nearest whole visitor).
---
## Part (c): Profitability at 25,000 Visitors (After Fee Increase)
**Given:**
- Visitors per month = 25,000
- Entry fee = \$60
- Variable cost = \$15
- Fixed cost = \$500,000
**Calculate:**
1. **Total Revenue:**
\[
\text{Total Revenue} = 25,000 \times 60 = \$1,500,000
\]
2. **Total Variable Cost:**
\[
\text{Total Variable Cost} = 25,000 \times 15 = \$375,000
\]
3. **Total Cost:**
\[
\text{Total Cost} = \text{Fixed Cost} + \text{Total Variable Cost} = 500,000 + 375,000 = \$875,000
\]
4. **Profit:**
\[
\text{Profit} = \text{Total Revenue} - \text{Total Cost} = 1,500,000 - 875,000 = \$625,000
\]
**Final Answer:**
> **Yes, the park will be profitable**, with a monthly profit of **\$625,000** at 25,000 visitors.
---
### Summary Table
| Part | Breakeven Point (Visitors) | Profit at 25,000 Visitors |
|------|---------------------------|---------------------------|
| (a) | 12,500 | N/A |
| (b) | 11,111 | N/A |
| (c) | N/A | \$625,000 |
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