# Question: A firm must decide whether to construct a small medium

A firm must decide whether to construct a small, medium, or large stamping plant. A consultant’s report indicates a .20 probability that demand will be low and an .80 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 $ 42 million. If demand turns out to be high, the firm can either subcontract and realize the net present value of $ 42 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 $ 22 million; if demand turns out to be high, the firm could do nothing and realize a net present value of $ 46 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 $ 20 million, whereas high demand will result in a net present value of $ 72 million.

a. Analyze this problem using a decision tree.

b. What is the maximin alternative?

c. Compute the EVPI and interpret it.

d. Perform sensitivity analysis on P (high).

If the firm builds a small facility and demand turns out to be low, the net present value will be $ 42 million. If demand turns out to be high, the firm can either subcontract and realize the net present value of $ 42 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 $ 22 million; if demand turns out to be high, the firm could do nothing and realize a net present value of $ 46 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 $ 20 million, whereas high demand will result in a net present value of $ 72 million.

a. Analyze this problem using a decision tree.

b. What is the maximin alternative?

c. Compute the EVPI and interpret it.

d. Perform sensitivity analysis on P (high).

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