$(25$ points$)$ Sooner Industrial Solutions Co$.$ is trying to determine whether to spend $8500000$ in process improvements. The projected cash flow increases based on the process improvements are as follows :

Annu al increased

$\backslash$table$[[$Year$,$cash flow $(8$ thous and$)],[1,25],[2,75],[3,100],[4,125],[5,250]]$

The alternative is to do nothing and leave the $8500000$ in the investment portfolio earning interest.

$($a$)$ What cost of capital $($interest rate$)$ is required in the investment portfolio for the better choice to be to do nothing?

$($b$)$ Suppose that the cost of capit al is $3\mathrm{.}4\%$ but there is uncertainty associated to the annual carh flow increases, which can be $7\%$ below and $5\%$ above the annual most likely values given by the figures in the table above. Use the Monte $C$ arlo tool to gener ate the profit for $5000$ scenarios and summaize the measures of dispersion. What is the probability of the process being profitable? $($Note: include a snapshot of the output from the Monte Carlo simulations.$)$

$($c$)$ There is an alternative experiment al process that could yield the following projected cash flow increases:

$\backslash$table$[[$Year$,\backslash$table$[[$Annual increased$],[$c ahh flow $(8$ thousand$)]]],[1,40],[2,80],[3,130],[4,220],[5,360]]$

Sooner Industrial Solutions Co$.$ can implement it at the same cost as the other process. However, since this is experiment al technology, the cost of capital is $12\mathrm{.}5\%.$ Moreover, the uncertainty in annua cash flows can be as low as $15\%$ and as high as $5\%.$ Use the Monte Calo tool to generate the profit for $5000$ scenarios and summarize the measures of dispersion. Knowing that m anagement at Sooner Industrial Solutions Co$.$ is risk$-$averse, would you advise to invest in this experiment a alternative? Explain your answer. $($Note: in clude a snapshot of the output from the Monte Carlo simulations.$)$