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A firm that plans to expand its product line must decide whether to build a small or a large facility to produce the new products. If it builds a small facility and demand is low, the net present value after deducting for building costs will be \$400,000. If demand is high, the firm can either maintain the small facility or expand it. Expansion would have a net present value of \$450,000, and maintaining the small facility would have a net present value is \$50,000.
If a large facility is built and demand is high, the estimated net present value is \$800,000. If demand turns out to be low, the net present value will be -\$10,000.
The probability that demand will be high is estimated to be .60, and the probability of low demand is estimated to be .40.

a. Analyze using a tree diagram.
b. Compute the EVPI. How could this information be used ?
c. Determine the range over which each alternative would be best in terms of the value of P(demand low).

#### Solution Preview

I have included a tree diagram in the attached spreadsheet.
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<br>If the firm builds a small facility and demand is high it can either expand or maintain the facility. Since there is no more risk involved (the firm already knows that demand is high) the firm will take the more profitable option of expanding and thus the outcome for that scenario will have an NPV of \$450,000.
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<br>If the firm builds a small facility the NPV is 0.40 * \$400,000 + 0.60 * \$450,000 = \$430,000
<br>If the firm builds a large facility the NPV is 0.40 * - \$10,000 + 0.60 * \$800,000 = \$476,000
<br>The ...

#### Solution Summary

This problem uses a decision tree to come up with an optimal solution given the probabilities of different demands.

\$2.49