Question

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

Answer 1

Complete problem was modelled in Excel and snapshots are attached below with formulas.

Formulas are shown below:

A. Expression for PW is shown below:

where, C = Yearly cash flow (simulated)

R = 18% (interest rate)

I = Initial investment (Simulated)

B. After performing 1000 Monte simulation runs (Monte Carlo), we found expected value of PW =

¥1,347.47

C. Std deviation of PW =

¥316.30

E. 200 simulations were performed and result of simulation is shown below:

Due to limitation of image size, I cannot show all 200 rows. So, I am showing only 30 rows for clarity of calculations and formulas. It can be easily copied and simulated at any computer with Excel.

Formulas:

D. Probability of PW>0 cannot be found out with 100% confidence, since there is not single distribution of PW as it is composed of various different probability distributions of investment, sales units and cash flows.

However, assuming it to be a normal distribution the required probability is close to ~ 100%