6. Widget, Inc., has just developed a new product. Since all available production capacity is being utilized and the introduction of this product will not affect sales of the current product line, a new manufacturing facility is needed. Widget has three choices: a small, medium, or large facility. If a large facility is built and sales are good, the PW of after-tax revenues is $25 mil- lion. If sales are moderate, the PW will be $15 million. A PW of $5 million is expected if sales are poor. Two additional options exist when sales are poor. They can sell the fa- cility for an after-tax price of $8 million, or they can subcontract the extra capacity to another company for an after-tax PW of $10 million.. Alternatively, the construction of the medium facility would result in the following PW of revenues: good sales, $20 million; moderate sales, $18 million; and poor sales, $12 million. A small facility is estimated to generate the following PW of after-tax revenues: good sales, $15 million; moderate sales, $14 million; and poor sales, $12 million. This facility can be expanded for an additional cost of $7 million if sales are good. The new PW of revenue would be $20 million.

Alternatively, the construction costs (in PW) are: large, $10 million; medium, $8 million; and small, $5 million. The probability of good sales is 0.3, moderate sales 0.3, and poor sales 0.4.

a. Draw the decision tree for this decision.

b. What decision should Widget make in view of the above information?