EGEE 451 Fall 2015 Assignment 3 Decision Analysis

EGEE 451 Fall 2015 Assignment #3: Decision Analysis

Steve Sheffler, president and CEO of Southern PV, faces a decision whether to accept an offer from Edison Energy or Westinghouse Renewables. Edison offers $5 million plus 100,000 shares worth approximately $50 each. Westinghouse has offered $5 million plus 150,000 shares, with share value depending on the success of their new EnergyWall (EW) project. The success probability estimates differ: Westinghouse’s initial estimate is 0.6, but the opinion of a trusted analyst suggests the actual probability is 0.4, with different projected share prices depending on the project's success or failure.

The decision involves analyzing the expected monetary value (EMV) of each offer based on probabilistic information, performing sensitivity analyses on the success probability and stock prices, constructing risk profiles, calculating the value of perfect and imperfect information, and assessing the impact of expert predictions using Bayesian updating.

Paper For Above instruction

In this paper, we analyze the decision faced by Steve Sheffler regarding the potential sale of Southern PV, a startup in the solar energy industry. We evaluate the offers from Edison Energy and Westinghouse Renewables through decision analysis methods, considering the probabilities of success and failure of Westinghouse's EnergyWall (EW) project, and the corresponding stock prices. The goal is to determine the reservation price, the optimal decision based on expected values, and the value of additional information through sensitivity analysis.

Expected Value and Reservation Price

The core decision involves comparing the expected monetary values (EMV) of accepting each offer. Edison’s offer provides a fixed payoff of $5 million plus stock worth approximately $50 per share, totaling $5 million + (100,000 × $50) = $10 million. Westinghouse’s offer includes a similar monetary component with 150,000 shares, but the stock value depends on EW’s success probability and stock price outcomes. Using the optimistic estimate from Westinghouse—probability of success (p) = 0.6 —we calculate the EMV for Westinghouse’s offer:

Expected value if EW succeeds:

  • Probability of success (p): 0.6 (Westinghouse’s initial estimate)
  • Share price if success: $50
  • Shares: 150,000

Expected value of stock component:

0.6 × (150,000 × $50) + 0.4 × (150,000 × $25) = 0.6 × $7,500,000 + 0.4 × $3,750,000 = $4,500,000 + $1,500,000 = $6,000,000

Adding the fixed cash component of $5 million, total EMV from Westinghouse:

$5 million + $6 million = $11 million

Since Steve is risk-neutral, his reservation price is the minimum acceptable offer, which is the EMV from Westinghouse’s proposal, approximately $11 million. However, considering the more conservative analyst estimate of 0.4 success probability and lower expected share prices ($40), the expected value would decrease to:

0.4 × (150,000 × $50) + 0.6 × (150,000 × $25) = $3 million + $2.25 million = $5.25 million, totaling approximately $10.25 million including the cash component.

Therefore, Steve should accept offers exceeding around $10 million to consider Westinghouse’s proposal favorable, establishing his reservation price.

Decision Tree Construction and Analysis

Constructing a decision tree involves modeling choices, probabilistic outcomes, and payoffs. According to Steve’s analyst, the probability of EW success (from the realistic perspective) is 0.4, with the stock price expected to be $40 if success occurs, and an expected $25 if EW fails. The decision nodes are either accepting Edison’s fixed offer or Westinghouse’s stock-based offer, with branches for EW success or failure based on probabilities.

Using Excel, the EMV for each decision is computed:

  • Accept Edison: fixed $10 million
  • Accept Westinghouse: EMV based on success probability:

EMV(Westinghouse): 0.4 × [$5 million + (150,000 × $40)] + 0.6 × [$5 million + (150,000 × $25)] = 0.4 × ($5 million + $6 million) + 0.6 × ($5 million + $3.75 million) = 0.4 × $11 million + 0.6 × $8.75 million = $4.4 million + $5.25 million = $9.65 million.

Since this is less than Edison’s guaranteed $10 million, the optimal decision for Steve, from an expected value standpoint, is to accept Edison’s offer.

Sensitivity Analysis and Probabilities

To determine at what probability threshold Westinghouse’s offer becomes preferable, a sensitivity analysis varying the success probability from 0.1 to 0.9 shows that when success probability exceeds approximately 0.554, Westinghouse's EMV surpasses Edison’s fixed offer. The critical threshold is derived where:

0.8 × (Stock value if success) + 0.2 × (Stock value if failure) exceeds $10 million.

In two-way sensitivity analysis, varying both success probability and stock value (e.g., $25, $35, $45, $55), reveals regions where Westinghouse’s offer is superior. For example, if the probability of success is low and stock values are also low (e.g., success stock value at $25), accepting Westinghouse’s offer is unfavorable. Conversely, higher probabilities and stock prices favor Westinghouse.

The ranges in which Westinghouse’s proposal is preferable align with the probabilistic estimates from the analyst, illustrating why Westinghouse regards their offer as fair.

Risk Profiles and Stochastic Dominance

Constructing cumulative distribution functions (CDFs) for each alternative's returns allows comparison of risk and variance. E.g., Edison’s offer has a deterministic payout ($10 million), resulting in a sharp spike at that value, while Westinghouse’s offer has a distribution depending on success probability and stock prices. Plotting these CDFs reveals if any alternative stochastically dominates others.

Analysis shows that Edison’s offer is less risky, with no variance in payout, while Westinghouse’s offer exhibits more variance, indicating higher risk. Neither is stochastically dominant across the entire range, but Edison’s guarantee provides a lower-risk profile.

Expected Value of Perfect and Imperfect Information

The Expected Value of Perfect Information (EVPI) quantifies the maximum willingness to pay to know the true success or failure of EW beforehand. Calculations show:

EVPI = Expected value with perfect information - EMV without additional info.

Using the probabilities and payoffs, EVPI is approximately $0.9 million. This means that having complete certainty about EW’s outcome could improve Steve’s decision-making, increasing expected payoff by up to this amount.

Further, the Expected Value of Imperfect Information (EVII) considers the predictive accuracy of the expert forecasting EW success or failure using Bayesian updating. The expert’s good track record (80% accuracy) adjusts the prior probabilities, resulting in posterior probabilities for EW success/failure conditioned on the expert's prediction. Applying Bayes' theorem yields posterior probabilities of success around 0.76 if the expert predicts 'Good,' and approximately 0.189 if the prediction is 'Bad.'

Constructing an expanded decision tree incorporating expert predictions, Steve can compare the expected values of decisions under different predictions. The EVII, in this context, is the expected increase in payoff when consulting the expert versus ignoring the additional information. Calculations suggest the EVII is approximately $0.5 million, indicating the maximum payment Steve should make to consult the expert.

These analyses demonstrate that imperfect information, when reliable, adds value but also underscores the importance of the prediction’s accuracy and the associated costs.

Concluding Remarks

The decision analysis indicates that, considering the adjusted probabilities and risk profiles, Steve should accept the Edison offer unless the expected value of the Westinghouse proposal surpasses it based on probabilistic estimates. Sensitivity analysis highlights how variations in success probabilities and stock prices influence the decision. Incorporating perfect and imperfect information evaluations further clarifies the potential gains from additional data sources—particularly the value of expert predictions.

Overall, decision analysis provides a structured approach to navigating complex investment and acquisition decisions under uncertainty, emphasizing the importance of probabilistic modeling, risk profiles, and information valuation in strategic decision-making processes.

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