A firm must decide whether to construct a small, medium, or large stamping plant. A consultant's report indicates a 0.40 probability that demand will be low and a 0.60 probability that demand will be high.If the firm builds a small facility and demand turns out to be low, the net present value will be $40 million. If demand turns out to be high, the firm can either subcontract and realize the net present value of $60 million or expand greatly for a net present value of $48 million.The firm could build a medium-size facility as a hedge: If demand turns out to be low, its net present value is estimated at $12 million; if demand turns out to be high, the firm could do nothing and realize a net present value of $45 million, or it could expand and realize a net present value of $50 million.If the firm builds a large facility and demand is low, the net present value will be -$30 million, whereas high demand will result in a net present value of $75 million.

a. Draw a decision tree for this problem.

b. Which size of facility the firm should construct? What is the expected payoff for this alternative?

a. Conclusion: Build a medium facility, with an expected payoff of $56.5 million.

b. Conclusion: Build a large facility, with an expected payoff of $48.6 million.

c. Conclusion: Build a small facility, with an expected payoff of $52.0 million.