Plastix, Inc. is considering adding a new line to its current product mix and the capital budgeting analysis is being managed by Chris Washington. $$The production facilities would be set up in an unused section of Plastixs main plant. $$New machinery with an estimated cost of $$10$ million would be purchased, but shipping costs to move the machinery to Plastix, Inc.s plant would total $$250,000,$ and installation charges would add another $$300,000$ to the total equipment cost. $$Additional initial expenses would run $$250,000$ to train employees to operate the new machinery. $$Furthermore$,$ Plastix, Inc.s inital working capital investment is estimated to be $5\%$ of the first years sales revenue with no additional net working capital investments made thereafter. The machinery has an economic life of $4$ years, and the company has obtained a special tax ruling that allows it to depreciate the equipment, under the MACRS $3-$year class $(0\mathrm{.}33,0\mathrm{.}45,0\mathrm{.}15$ and $0\mathrm{.}07$ in Years $1$ through $4,$ respectively$).$The machinery is expected to have a salvage value of $$750,000$ after $4$ years of use and is expected to be sold.The section of the plant in which production would occur had not been used for several years and, consequently, had suffered some deterioration. An investment of $$300,000$ will have to be spent to get it completely ready as a production facility. $($For simplicity sake, assume this expenditure is not depreciable.$)$Plastix$,$ Inc.s management expects to sell $300,000$ units in year $1$ and anticipates that sales in units to remain constant. $$Todaysselling price would be $$25$ per unit but due to inflation the selling price is expected to increase by $5\%$ each year, so year $1$ selling price is expected to be $$26\mathrm{.}25.$Cash operating costs today would be $$10$ per unit but are expected to increase by only $3\%$ annually $($so year $1$ operating cost is expected to be $$10\mathrm{.}30)$ from the initial cost estimate because over half of the costs are fixed by long$-$term contracts. $$For simplicity, assume no other cash flows are affected by inflation $($externalities$,$ etc.$).$ Plastix, Inc.s federal$-$plus$-$state tax rate is $40$ percent, and its overall cost of capital is $16$ percent. $$Due to obsolescence of inventory, it is assumed only half of the NWC investment can be recaptured at the end of the life of the project.It was also determined that the executive committee would want to see a thorough risk analysis on the project. $$As the meeting was winding down, Washington was asked to develop a base case set of cash flows and then to perform a sensitivity analysis of plus and minus $30\%,20\%$ and $10\%$ from the base cash flow estimates for $2$ risk factors. $$The risk factors are $1)$ number of units sold $2)$ price per unit $($note: Begin the sensitivity analysis by changing the price in year $1$ by each of the percentages rather than changing the base price. $$For example, the problem states that the base price today is $$25$ and so year $1$ price will be $$26\mathrm{.}50$ due to inflation. $$Begin your sensitivity by changing the $$26\mathrm{.}50$ price by plus and minus $30\%,20\%$ and $10\%$ and assume the same $5\%$ inflation rate thereafter.$)$ Washington met with the marketing and production managers to get a feel for the uncertainties involved in the cash flow estimates. $$After several sessions, they concluded that unit sales and sales price provided the most uncertainty. $$Costs estimates were fairly well defined. As estimated by the marketing staff, if product acceptance were normal, then sales quantity during Year $1$ would be $300,000$ units $($and constant$)$ with a year $1$ selling price of $$26\mathrm{.}25$; if acceptance were poor, then only $200,000$ units would be sold the first year $($and constant$)$ with a year $1$ selling price of $$20\mathrm{.}00$; and if acceptance were strong, then sales volume for Year $1$ would be $350,000$ units $($and constant$)$ with a year $1$ selling price of $$30\mathrm{.}00.$In all cases, the price would increase at the inflation rate of $5\%$ per year as in the original base case and costs would be expected to increase at a $3\%$ rate and NWC would still be $5\%$ of revenues.Washington also discussed the scenarios probabilities with the marketing staff. $$After considerable debate, they finally agreed on a guesstimate of a $20\%$ probability of poor acceptance, a $60\%$ probability of average acceptance, and a $20\%$ probability of excellent acceptance.Washington also researched the risk inherent in Plastix, Inc.saverage project and how the company typically adjusts for risk. $$Based on historical data, Plastix, Inc.s average project has a coefficient of variation of NPV in the range of $2$ to $2\mathrm{.}50.$You have been asked to assist in the project and are responsible for answering the following questions.$$Compute the base case cash flow estimates for the project $($Net investment, Operating CFAT and Terminal Cash Flow$).(30$pts$.)2)$ Compute the NPV$,$ IRR, MIRR and PI for the base cash flows. $(16$ pts$.)$ Do any of these techniques indicate that the project is worthwhile? $$Explain$.3)$ Perform a sensitivity analysis of NPV assuming the $2$ risk variables given in the case. $$Assume that each of these variables can deviate from its base case by plus or minus $10\%,20\%$ and $30\%.$Create an NPV matrix and explain your results. $(10$points$)4)$ Look over the sensitivity results and note that the MIRR is different than the IRR. $$Why is this the case? $$Explain$.($Please put the answer to this question on the page where you NPV matrix is shown so I can find it easily.$)(5$ points$)5)$ Complete a scenario analysis assuming a worst case, base case, and best case using the data presented in the case. Explain your results. $(9$ points$)6)$ Based on the scenario results, what is the expected NPV$,$ standard deviation, and coefficient of variation? $$How does the risk of this project compare to other projects the firm is invested? $(10$ points$)7)$ Would you recommend investing? $$Why or why not? $$ Explain your results. $(5$ points$)8)$ Please answer the following questions: $($A$)$ Explain how the cost of capital is an integral part of the capital budgeting process and why firms seek to minimize their cost of capital. $$In other words, how does a lower cost of capital impact NPV$?(5$ points$)($B$)$ Why can the NPV and IRR give you conflicting rankings for mutually exclusive projects? $(5$ points$)($C$)$ Which capital budgeting techniques yields the value maximizing project every time and why is that