(Simulation) Model the new investment, whose value is determined by the following random variables: Annual revenues from reclaimed waste in Year 1 follow a triangular distribution with a minimum value of $100,000, a most likely value of $200,000, and a maximum value of $300,000.

In Year 2 (and each year thereafter), the distribution is still triangular; however, the most likely value is now equal to the value observed in the previous year. The minimum value is equal to 50% of the observed value in the previous year, and the maximum is equal to 150% of the observed value in the previous year. Furthermore, the revenues from reclaimed waste exhibit a correlation coef?cient from year to year of .90. Labor cost savings can be forecast with a high degree of certainty, because they represent the savings from one hourly worker that will no longer be needed once the new waste-handling system has been put into place. The reductions in waste disposal costs come from a uniform distribution, with minimum value of $15,000 and maximum value of $21,000.The waste disposal costs are assumed to be uncorrelated over time. i. What is the probability of a cash ?ow less than $150,000 in Year 1? In Year 5?
(Hint: De?ne the annual Project FCFs for Years 1 through 5 as forecast variables. You will use only the Years 1 and 5 cash ?ow distributions for this question but will use all of them to answer part iii.)

ii. What are the expected NPV and IRR for the project?
iii. (Optional) What are the means and standard deviations of the simulated distribution of cash ?ows for Years 1 through 5? What is the effect of the positive correlation in the underlying determinants of the project's cash ?ows?
(Hint: Look at the standard deviations in annual cash ?ows through time.)