China's Galanz built a new complex at the expected cost of 2 billion yuan in order to produce 12 million air-conditioning units annually. The site was completed in 2004.
1. Make the following assumptions:
• The actual investment cost is either 1.9, 2.0, or 2.1 billion yuan, with respective probabilities of 0.25,0.50, and 0.25.
• The plant operates for 15 years, with the salvage value being either 50 million, 0, or-100 million(remediation costs) yuan at that time, with probabilities of 0.20,0.50, and 0.30, respectively.
• Finally, the net cash flow resulting from operations and sales is 60 yuan per unit. The number of units sold in each year is either 9 (0.1), 10 (0.2), 11 (0.3), or 12 (0.4) million. The figures in parentheses represent the probabilities of the given level of production.
Assume that these are the only relevant cash flows and the interest rate is 18% per year.
a) Find an expression for the present worth (PW).
b) Find the expected value of the PW(if possible).
c) Find the standard deviation of the PW(if possible).
d) Find Pr(PW >0) (if possible).
e) Perform 200 simulations, and find the sample mean, standard deviation, as well as the probability that the investment will have a positive PW (point & interval estimates). Finally, summarize your process (which will naturally include all the appropriate steps) and results.