Question

Tanner Park is a small amusement park that provides a variety of rides and outdoor activities for children and teens. In a typical summer season, the number of adult and children’s tickets sold are 20,000 and 10,000, respectively. Adult ticket prices are $18 and the children’s price is $10. Revenue from food and beverage concessions is estimated to be $60,000, and souvenir revenue is expected to be $25,000. Variable costs per person (adult or child) are $3, and fixed costs amount to $150,000.

a. Determine the profitability of this business.

b.Now change the model based on the following information. In a typical summer season, the number of adult tickets sold has a normal distribution with a mean of 20,000 and a standard deviation of 2,000. The number of children’s tickets sold has a normal distribution with a mean of 10,000 and a standard deviation of 1,000. Adult ticket prices are $18 and the children’s price is $10.Revenue from food and beverage concessions is estimated to be between $50,000 and $100,000, with a most likely value of $60,000. Likewise, souvenir revenue has a minimum of $20,000, most likely value of $25,000, and a maximum value of $30,000. Variable costs per person are $3, and fixed costs amount to $150,000. Determine the profitability of this business. What is the probability that the park will incur a loss in any given season?

Answer 1

(a)

Selling price (adults) Selling price (children) Tickets sold (adults) Tickets sold (children Revenue from ticket Revenue from food and beverages Souvenir Revenue Total revenue Variable cost per customer Total variable cost Total fixed cost Profit 18 10 4 10000 60000 -SUM(C6:C8) 10 -C10* (C4+C5) 12 D9-D11-D12

Selling price (adults)	$18
Selling price (children)	$10
Tickets sold (adults)	20000
Tickets sold (children)	10000
Revenue from ticket	$460,000
Revenue from food and beverages	$60,000
Souvenir Revenue	$25,000
Total revenue		$545,000
Variable cost per customer	$3
Total variable cost		$90,000
Total fixed cost		$150,000
Profit		$305,000

(b)

We have used Monte-Carlo Simulation using the distributions specified in the question to the above model parameters. I have used @Risk^TM for this.

Selling price (adults) Selling price (children) Tickets sold (adults) Tickets sold (children Revenue from ticket Revenue from food and beverages -RiskTriang(50000,60000,100000, RiskStatic(60000)) Souvenir Revenue Total revenue Variable cost per customer Total variable cost Total fixed cost Profit 18 10 RiskNormal (20000,2000,RiskStatic(20000)) RiskNormal (10000,1000, RiskStatic(10000)) 4 RiskTriang(20000,25000,30000, RiskStatic(25000)) -SUM(C6:C8) -C10* (C4+C5) -RiskOutput()+D9-D11-D12 10 12

Il @RISK- Output: D13 Statistics Grid Profit Profit $0 $369,465 Cell Minimum Maximum Mean Sheet17!D13 S192,462.42 $426,162.41 S315,001.22 S757.81 S305,051.05 S314,643.55 S32,571.30 0.0169 3.0123 5000 95.0% 5.0% 1.4 1.2 90% Cl 1.0 Mode Mediarn Std Dev Skewness Kurtosis Values Errors Filtered Left X Left P Right X Right P Dif. X nif P @RISK Trial Version For Evaluation Purposes Only 0.6 0.2 S0 0.0 $369,465 95.0% S369,465.44 95 %. 1IiIClose

The probability of being in loss is close to zero.