A company manufactures specialty pollution-sensing devices for the offshore oil industry. One particular device has reached maturity, and the company is considering whether to replace it with a newer model. Technologies have not changed dramatically, so the new device would have similar functionality to the existing one, but would be smaller and lighter in weight. The firm's three choices are: (1) keep the old model, (2) design a replacement device with internal resources, (3) and purchase a new design from a firm that is one of its suppliers. The market for these devices will be either "receptive" or "neutral" of the replacement model. The financial estimates are as follows: Keeping the old design will yield a profit of $6 million dollars. Designing the replacement internally will yield $10 million if the market is "receptive," but a $3 million loss if the market is "neutral." Acquiring the new design from the supplier will profit $4 million under "receptive," $1 million under "neutral." The company feels that the market has a 70 percent chance of being "receptive" and a 30 percent chance of being "neutral." Draw the appropriate decision tree. Calculate expected value for all courses of action. What action yields the highest expected value?

designing a replacement with internal resources yields the highest expected value = $6,100,000

Explanation:

expected values:

keep the old model

expected profits = $6,000,000

design a replacement with internal resources

receptive market = $10,000,000 x 0.7 = $7,000,000

neutral market = -$3,000,000 x 0.3 = -$900,000

total expected value = $6,100,000

purchase new design

receptive market = $4,000,000 x 0.7 = $2,800,000

neutral market = $1,000,000 x 0.3 = $300,000

total expected value = $3,100,000

there is no room here to draw a proper decision tree, but it would be something like this:

                                     ⇒ keep old model ⇒ $6,000,000 in profits

sensing device             ⇒ design a replacement ⇒ receptive market

                                                                                   $7,000,000

                                                                               ⇒ neutral market

                                                                                   -$900,000

                                         continuing from above ⇒ expected value

                                                                                       $6,100,000              

                                      ⇒ outside supplier ⇒ receptive market

                                                                              $2,800,000

                                                                       ⇒ neutral market

                                                                               $300,000

                                          continuing from above ⇒ expected value

                                                                                       $3,100,000