4. (20 points) A snow resort group is considering investing in a ski resort at the Pocono's Mountains. The initial investment required is $3 millions but the revenues and operating costs depends on the number of days of the winter season. The number of days of the winter season depends on the weather and consequently is subject to uncertainty, which is estimated to be normally distributed with a mean of 210 days and a standard deviation of 15 days, which are independent year after year. Each day that the resort operates generates revenues of $6000. The operating and maintenance costs of the first year are estimated to be $500,000 but they increase each year (independently) based on usage of the facility, which is a random variable. The salvage value also depends on the usage of the facility and is uncertain. The probability distributions of the incremental cost per year in the O&M costs and the salvage values are as follows: Incremental Pr(G) Salvage Value Pr(S) Cost per year 18000 0.20 750000 22000 0.30 1000000 0.60 24000 0.25 1200000 0.20 26000 0.15 30000 0.10 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 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.