$(25$ points$)$ Sooner Industrial Solutions Co$.$ is trying to determine whether to spend $$500000$ in process improvements. The projected cash flow increases based on the process improvements ae as follows:

$\backslash$table$[[$Year$,\backslash$table$[[$Annual increased$],[$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 capital is $3\mathrm{.}4\%$ but there is uncertainty associated to the annual cah 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 Carlo tool to gener ate the profit for $5000$ scenarios and summ xize the measures of dispersion. What is the probability of the process being profitable? $($Note: include a sn apshot of the output from the Monte Carlo simulations.$)$

$($c$)$ There is an altern ative experimental process that could yield the following projected cash flow increases:

$\backslash$table$[[$Year$,\backslash$table$[[$Annual increased$],[$cah flow $(8$ thousand