Southern PV (Adapted from Clemen, 1996).

This assignment is designed to familiarize you with using tools of decision analysis to build decision trees, analyze alternatives under uncertainty, explore the value of information, and the value of flexibility.

Problem Description:

Steve Sheffler is president, CEO, and majority stockholder of Southern PV, a startup technology firm with a revolutionary new material for solar photovoltaic cells. Steve faces a major decision: Two firms, Edison Energy and Westinghouse Renewables, are bidding to purchase Southern PV.

Steve founded Southern 15 years ago, and the company has been extremely successful in developing advanced materials for solar cells. Steve is ready to sell the company (as long as the price is right!) so that he can pursue other interests. Last month, Edison Energy offered Steve $5 million and 100,000 shares of Edison Energy stock (currently trading at $50 per share and not expected to change substantially in the future). Until yesterday, Edison Energy's offer sounded good to Steve, and he had planned on accepting it this week. But a lawyer from Westinghouse Renewables called last week and indicated that Westinghouse was interested in acquiring Southern PV. In discussions this past week, Steve has learned that Westinghouse is developing a new solar-energy storage system, codenamed EnergyWall (EW) that, if successful, will revolutionize the industry. Southern PV could play an important role in the development of the energy system design.

In their discussions, several important points have surfaced. First, Westinghouse has said that it believes the probability that the EW will succeed is 0.6, and that if it does, the value of Westinghouse’s stock will increase from the current value of $30 per share. Although the future price is uncertain, Westinghouse judges that, conditional on the EW’s success, the anticipated price of the stock is $50 per share. If the EW is not successful, the price will probably decrease slightly. Westinghouse judges that if the EW fails, Westinghouse’s share price will be between $20 and $30, with an expected value of $25.

Yesterday Steve discussed this information with his financial analyst, who is an expert regarding the energy technology industry and whose counsel Steve trusts completely. The analyst pointed out that Westinghouse has an incentive to be very optimistic about the EW project. "Being realistic, though," said the analyst, "the probability that the EW succeeds is only 0.4, and if it does succeed, the expected price of the stock would be only $40 per share. On the other hand, I agree with Westinghouse’s assessment for the share price if the EW fails."

Negotiations today have proceeded to the point where Westinghouse has made a final offer to Steve of $5 million and 150,000 shares of Westinghouse stock. The company's representative has stated quite clearly that Westinghouse cannot pay any more than this in a straight transaction. Furthermore, the representative claims, it is not clear why Steve will not accept the offer because it appears to them to be more valuable than the Edison Energy offer.

Questions:

1. In terms of expected value, what is the least that Steve should accept from Westinghouse (This amount is called his reservation price)?

2. Create and solve the decision tree for Steve’s problem (use the probabilities and stock price estimates from Steve’s analyst , not Westinghouse’s estimates). Which offer should Steve accept and why (assume Steve is risk-neutral)? [Build and solve your decision tree in Excel to make the remaining questions easier].

3. (Sensitivity Analysis).

a. Conduct a sensitivity analysis on the probability that EW succeeds (the probability of failure is 1 minus this value). Using an Excel version of the decision tree, test these values for the probability of success: {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9} Above what probability of success is Westinghouse’s offer better than Edison Energy’s.

b. Perform a two-way sensitivity on Westinghouse’s stock price conditional on EW success and probability of success (the price if EW is a failure is still a mean of $25). Test all combinations of the following values: probability of success = {0.1, 0.3, 0.5, 0.7, 0.9} and stock price if success = {$25, $35, $45, $55}. For each combination, which is the best decision (Westinghouse or Edison)? For what ranges of values should Steve accept Westinghouse’s offer. Does this explain why Westinghouse thinks their offer is fair? You can show these results with a table or a contour plot in excel (e.g., where the third dimension is 0 for Westinghouse and 1 for Edison).

4. (Risk Profiles/Target Curves). Return to the original decision tree you built for Q2. Draw/plot the cumulative distributions for the alternatives (also known as the ‘Risk Profiles’ or the ‘Target Curves’). Are any alternatives stochastically dominant? Is one higher risk/variance than the other?

5. (Expected Value of Perfect Information). Return to the original decision tree you built for Q2, and calculate the Expected Value of Perfect Information. What is this number and what does it mean? Give an intuitive interpretation.

6. (Expected Value of Imperfect Information). For the original decision in Q2, Steve’s analyst now tells him he knows an expert in the specific technology type that EW is in. This expert has a good track record of predictions: 80% of the time that a technology succeeds, this expert has predicted “Good”, and 80% of the times that a technology has failed, this expert has predicted “bad”.

a. Using Bayes’ rule, calculate the posterior probabilities for EW success and failure for either prediction by the expert. (Assume that the prior probabilities of failure/success are the original values of 0.6/0.4).

b. In the above calculations, also indicate the marginal probabilities that the expert will predict “good” or “Bad”.

c. Create a new decision tree adding a third alternative to consult the expert, with a first chance node for what the expert predicts, a decision node for each prediction where Steve decides which offer to accept, and a second chance node for whether EW actually succeeds or not. Use this tree to calculate the Expected Value of Imperfect Information (EVII). What is the MOST Steve should be willing to pay the expert?

[HINT: use one uncertainty node for what the expert will predict followed by a second decision node where Steve decides which offer to accept, followed by another uncertainty node for what actually happens, using the four posterior probabilities you calculated in part a].

Assignment Submission

· Turn in the following template (complete with your answers).

· Submission should only consist of template along with your answers.

· Please do not re-type any parts of the questions (presented in pages 1 – 3 of this document); simply provide your answers as outlined below.

· Please hand in HARDCOPY printouts in class

· You must use footers with your name, assignment name and pagination (as on this document).

[Enter Name here]

EGEE 451 Homework #3

1. Calculate the reservation price. What is the value? (Show your work)

2. Paste/Draw Decision Tree below. Which offer should Steve accept and why?

3. (a) Paste 1-way Sensitivity curve below. Above what probability of success is Westinghouse’s offer better than Edison’s?

3. (b) Paste 2-way sensitivity curve below. Under what expectations should Steve accept Westinghouse’s offer. Does this explain why Westinghouse thinks their offer is fair?

4. Paste CDFs of alternatives below (in single graph). How do the returns of the alternatives compare?

5. Calculate the expected value of perfect information. What is this number and what does it mean? Give an intuitive interpretation.

6. (a) Calculate the posterior probabilities for EW success and failure for either prediction by the expert. (Show your work)

6. (b) Calculate the prior probabilities that the expert will predict success or failure.

Paste/draw your revised decision tree below.

What is the MOST Steve should be willing to pay the expert (EVII)?

Compare this number (the EVII) to your answer from Q5 above (the EVPI).

HW3 Decision Analysis 1