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

$$$$38\mathrm{.}9$

million to build. The second is for a$$ "custom" plant which will cost

$$$$52\mathrm{.}9$

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

$$$$16\mathrm{.}7$

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

$17\mathrm{.}5\%.$

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

b$.$Find the breakeven 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

Range of cash inflow$($$ millions$)$

Standard Plant

Custom Plant

$$$$0$ to$$ $$5$

$0\%$

$5\%$

$$$$5$ to$$ $$8$

$10$

$10$

$$$$8$ to$$ $$11$

$60$

$15$

$$$$11$ to$$ $$14$

$25$

$25$

$$$$14$ to$$ $$17$

$5$

$20$

$$$$17$ to$$ $$20$

$0$

$15$

Above$$ $$20$

$0$

$.$ What is the probability that each project will achieve the breakeven 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$?$