$(25$ 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 are as

follows :

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 th at the cost of capital is $3\mathrm{.}4\%$ but there is uncertainty associated to the annual cash

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

summ xize 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 altern ative experiment al process that could yield the following projected cash flow

increases :

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 $a5\%$ Use the Monte Calo tool to

generate the profit for $5000$ scenarios and summarize the measures of dispersion. Knowing that

management at Sooner Industrial Solutions Co$.$ is risk$-$averse, would you advise to invest in this

experiment al alternative? Explain your answer. $($Note: in dude a snapshot of the output from

the Monte Carlo simulations.$)$