Statistics

Chapter 12 Simulation and Risk Analysis

Instructions: Please submit your work in one single Excel file with one tab/worksheet for each problem.

1. (50 points) In class, we developed a simple spreadsheet model for computing profit in Excel. Use this profit model to implement a financial simulation model for a new product proposal and determine a distribution of profits using the discrete distribution below for the demand, unit cost, and fixed cost. Price is fixed at $1,000. Demand is unknown and follow the distribution:

Demand	Probability
120	0.25
140	0.50
160	0.25

Unit costs are also variable and follow the following distribution:

Unit Cost	Probability
$400	0.20
$600	0.40
$700	0.25
$800	0.15

Fixed costs are estimated to follow the distribution:

Fixed Costs	Probability
$45,000	0.20
$50,000	0.50
$55,000	0.30

Simulate this model for 50 trials and a production quantity of 140. What is the average profit?

2. (50 points) J&G Bank receives a large number of credit card applications each month, an average of 30,000 with a standard deviation of 4,000, normally distributed. Approximately 60% of them are approved, but this typically varies between 50% and 70%. Each customer charges a total of $2,000, normally distributed, with a standard deviation of $250, to his or her credit card each month. Approximately 85% pay off their balances in full, and the remaining incur finance charges. The average finance charge has recently been ranged from 3% to 4% per month. The bank also receives income from fees charged for late payments and annual fees associated with the credit cards. This is a percentage of totally monthly charges and has varied between 6.8% and 7.2%. It costs the bank $20 per application, whether it is approved or not. The monthly maintenance cost for credit card customers is normally distributed with a mean of $10 and standard deviation of $1.50. Finally, losses due to charge-offs of customers’ accounts are between 4.6% and 5.4% of total charges. Use Monte Carlo simulation with 500 trials to analyze the profitability of the credit card product.