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 for Boardman$$s $$standard$$ plant, which will cost $$38\mathrm{.}5$ million to build. The second is for a $$custom$$ plant, which will cost $$53\mathrm{.}5$ million to build. The custom plant will allow Boardman to produce the highly specialized gases required for an emerging semiconductor manufacturing process. Boardman estimates that a standard plant will generate free cash flows of $$12\mathrm{.}5$ million per year, but if the custom design is put in place, Boardman expects to produce $$17\mathrm{.}5$ million in cash flow annually. 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 $16\mathrm{.}9\%.$

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

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

c$.$ The firm has estimated the probabilities of achieving various ranges of free cash flow for the two projects as shown in the following table. What is the probability that each project will achieve at least the break$-$even free cash flow found in part b$?$

Probability of achieving free cash flow in given range

Range of free cash flow $($$ millions$)$ Standard Plant Custom Plant

$$0$$$50\%5\%$

$$5$$$81010$

$$8$$$116015$

$$11$$$142525$

$$14$$$17520$

$$17$$$20015$

Above $$20010$

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

e$.$ If the firm wished to minimize losses $($i$.$e$.,$ NPV$<$$$0),$ which project would you recommend? Which would you recommend if the goal were to achieve a higher NPV$?$

Please show your work $($including excel formulas if applicable$).$