A manufacturing company is considering the acquisition of a heavy press to be used for stamping and forming of sheet metal parts. The board of directors has determined that all capital investments should be evaluated with a $10$ year horizon and that the appropriate WACC to be used for this case is $8,75\%.$ The cost of the press is R$12560000.$ The head of the manufacturing plant has estimated that the income $($positive cash flow$)$ generated from the new press will be as follows $($in millions$)$:

Yr $1$ Yr $2$ Yr $3$ Yr $4$ Yr $5$ Yr $6$ Yr $7$ Yr $8$ Yr $9$ Yr $10$

R$0,750$ R$1,125$ R$1,500$ R$1,875$ R$2,220$ R$2,400$ R$2,700$ R$3,150$ R$3,300$ R$3,300$

$3\mathrm{.}1$ Determine the NPV and IRR. Does the investment seem viable?

$3\mathrm{.}2$ The CFO has looked at the numbers and suggests that the WACC should rather be treated as a normal random variable with mean $9,5\%$ and standard deviation of $1\%.$ Produce a histogram and CDF for the NPV with this new information and answer the following questions:

$3\mathrm{.}2\mathrm{.}1$ what is your conclusion about the viability of the capital investment now?

$3\mathrm{.}2\mathrm{.}2$ what is the probability that the NPV will be negative?

$3\mathrm{.}2\mathrm{.}3$ what is the probability that the NPV calculated in $3\mathrm{.}1$ will not be achieved?

$3\mathrm{.}2\mathrm{.}4$ what is the IRR?

$3\mathrm{.}3$ Explain how a real options approach can be applied to this decision.