Breakeven cash inflows and risk Boardman Gases and Chemicals is a supplier of highly purified gases to semiconductor manufacturers. A large chip producer has asked Boardman to build a new gas production facility close to an existing semiconductor plant. Once the new gas plant is in place, Boardman will be the exclusive supplier for that semiconductor fabrication plant for the subsequent $10$ years. Boardman is considering one of two plant designs. The first is Boardman's "standard" plant which will cost $$37\mathrm{.}8$ million to build. The second is for a "custom" plant which will cost $$53\mathrm{.}8$ million to build. The custom plant will allow Boardman to produce the highly specialized gases required for an emergency semiconductor manufacturing process. Boardman estimates that its client will order $$12\mathrm{.}7$ million of product per year if the standard plant is constructed, but if the custom design is put in place, Boardman expects to sell $$17\mathrm{.}5$ million worth of product annually to its client. Boardman has enough money to build either type of plant, and, in the absence of risk differences, accepts the project with the highest NPV$.$ The cost of capital is $17\mathrm{.}2\%.$

a$.$ Find the NPV for each project. Are the projects acceptable?

b$.$ Find the break$-$even cash inflow for each project.

c$.$ The firm has estimated the probabilities of achieving various ranges of cash inflows for the two projects, as shown in the table $.$ What is the probability that each project will achieve the break$-$even cash inflow found in part $($b$)?$

d$.$ Which project is more risky? Which project has the potentially higher NPV$?$ Discuss the risk$-$return trade$-$offs of the two projects.

e$.$ If the firm wished to minimize losses $($that is$,$ NPV $$$$0),$ which project would you recommend? Which would you recommend if the goal was achieving a higher NPV$?$

Data table

$\backslash$table$[[,$Probability of achieving cash inflow in given range$],[$Range of cash inflow millions$),$Standard Plant,Custom Plant$],[$$$0$ to $$5,0\%,5\%$