Problem $4.($All cash flows in this problem are in thousands of dollars$)$ World Airways is considering

acquisition of an additional airplane for its short routes. An airplane costs $$40,000$ and can be sold for $

$S_2$ at the end of two years, where $S_2$ is an uniform random variable in the range $(15,000,17,000).$ The

annual fixed cost of having an airplane in service is $$6000.$ Annual revenue before deducting the fixed

cost in year $n$ is $$300**M_n,$ where $M_n$ is the number of passengers per flight in year $n$ and follows

IE$402$

Spring $2024$

normal distribution with a mean of $150$ and a standard deviation of $$25,$ for $n=1$ and $2.$ Assume that $M_1$

and $M_2$ are dependent on each other with a correlation coefficient of $0\mathrm{.}6.M_1$ and $M_2$ are independent of

the initial investment and $M_2$ and $S_2$ are independent of each other.

Find the expected value and the standard deviation of the NPV of this investment at MARR $=$

$10\%.$ Assume that the planning horizon is $2$ years.