4. (20 points) A new attraction is being consider for a summer amusement theme park. The initial investment required follows a normal random variable with parameters $(2750000, 27500 ). The revenues and operating costs are costs depend on the number of days that the winter season which the attraction is closed. The number of days of the winter season depends on the weather and consequently is subject to uncertainty, which is estimated to be uniformly distributed with parameters (80, 90) days, which are independent year after year. For example, if in a given year the winter season consists of 100 days, then the attraction will operate 265 days (365 - 100). Each day that the resort operates generates revenues normally distributed with mean of $5,000 and standard deviation of $1,000. Assume that the revenue per day will be exactly the rest of the year, but you need to generate randomly the daily revenue for every year (independent from one year to another). The daily O&M costs that the attraction operates independently and identical distributed according to a normal random variable of $1000 and a standard deviation of $75. (Same assumption as for revenue, assumed equal the rest of the year but independent from one year to another). The salvage value also depends on the usage of the facility and is uncertain. The probability distributions of salvage values are as follows: Salvage Pr(S) Value 2500000.20 275000 0.60 300000 0.20 The group uses a MARR of 12% and plans to operate the facility for 5 years, at which time will be sold at the salvage value. Perform a Monte Carlo simulation with 1000 replications to determine (all BTCF) a) The expected value of the present worth b) The standard deviation of the PW c) Using the Central Limit theorem, calculate the probability the investment be profitable. 4. (20 points) A new attraction is being consider for a summer amusement theme park. The initial investment required follows a normal random variable with parameters $(2750000, 27500 ). The revenues and operating costs are costs depend on the number of days that the winter season which the attraction is closed. The number of days of the winter season depends on the weather and consequently is subject to uncertainty, which is estimated to be uniformly distributed with parameters (80, 90) days, which are independent year after year. For example, if in a given year the winter season consists of 100 days, then the attraction will operate 265 days (365 - 100). Each day that the resort operates generates revenues normally distributed with mean of $5,000 and standard deviation of $1,000. Assume that the revenue per day will be exactly the rest of the year, but you need to generate randomly the daily revenue for every year (independent from one year to another). The daily O&M costs that the attraction operates independently and identical distributed according to a normal random variable of $1000 and a standard deviation of $75. (Same assumption as for revenue, assumed equal the rest of the year but independent from one year to another). The salvage value also depends on the usage of the facility and is uncertain. The probability distributions of salvage values are as follows: Salvage Pr(S) Value 2500000.20 275000 0.60 300000 0.20 The group uses a MARR of 12% and plans to operate the facility for 5 years, at which time will be sold at the salvage value. Perform a Monte Carlo simulation with 1000 replications to determine (all BTCF) a) The expected value of the present worth b) The standard deviation of the PW c) Using the Central Limit theorem, calculate the probability the investment be profitable
