Part - 1:
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. 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 onWestinghouse'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 thatthe priorprobabilities 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 whetherEW 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?
Part -2:
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?
(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).