Problem 13-17 (Algorithmic) Hemmingway, Inc., is considering a $7 million resear

ID: 466175 • Letter: P

Question

Problem 13-17 (Algorithmic)

Hemmingway, Inc., is considering a $7 million research and development (R&D) project. Profit projections appear promising, but Hemmingway's president is concerned because the probability that the R&D project will be successful is only 0.50. Furthermore, the president knows that even if the project is successful, it will require that the company build a new production facility at a cost of $20 million in order to manufacture the product. If the facility is built, uncertainty remains about the demand and thus uncertainty about the profit that will be realized. Another option is that if the R&D project is successful, the company could sell the rights to the product for an estimated $26 million. Under this option, the company would not build the $20 million production facility.

The decision tree is shown in Figure 13.18. The profit projection for each outcome is shown at the end of the branches. For example, the revenue projection for the high demand outcome is $65 million. However, the cost of the R&D project ($7 million) and the cost of the production facility ($20 million) show the profit of this outcome to be $65 $7 $20 = $38 million. Branch probabilities are also shown for the chance events.

A) Analyze the decision tree to determine whether the company should undertake the R&D project. If it does, and if the R&D project is successful, what should the company do?

What is the expected value of your strategy? If required, round your answer to 2 decimal places.

Expected value = $ ? M

B) Develop a risk profile for the optimal strategy. If required, round your answers to two decimal places.

(please fill in all question marks)

Possible Profit Associated Probability $38M ? $21M ? $10M ? -$7M ? ?

Explanation / Answer

A) Analyze the decision tree to determine whether the company should undertake the R&D project. If it does, and if the R&D project is successful, what should the company do?

Work backwards from right branch of the tree towards left side to calculate expected value for each chance or state of nature node.

EV at node 4 = 0.5 x $38 + 0.4 x $21 + 0.1 x $10 = $28.4
Maximum EV at decision node 3 = max ($28.4, $19) = $28.4

Thus, if the R&D project is successful then select to build new facility.

EV at node 2 = 0.5 x $28.4 + 0.5 x $(-7) = $10.7
Maximum EV at decision node 1 = max ($10.7, $0) = $10.7

Thus, start R&D project as its EMV value is higher than that of not starting project.

What is the expected value of your strategy? If required, round your answer to 2 decimal places.

Expected value = $ 10.7 M

B) Develop a risk profile for the optimal strategy. If required, round your answers to two decimal places.

To develop the risk profile for the optimal strategy, multiple the branch probabilities on all paths to the first decision node of the decision tree

Possible Profit

Associated Probability

$38M

0.5 x 0.5 = 0.25

$21M

0.4 x 0.5 = 0.20

$10M

0.1 x 0.5 = 0.05

-$7M

0.5

Total

1.00