Question: 1. Use the minimum regret criterion to decide whether to drill or not to drill.

Petro-Co Project Minimax Regret

          The first question is about mini-max regret analysis of the oil discovery project carried out by the Petro-Co. According to the information presented in the question statement Petro-company wants to take a decision about oil discovery project. The company has two options: drill an exploratory for oil well (spending cost on drilling or other activities) or not to drill a well because chances are very limited for oil discovery (Kochenderfer). According to estimation, in case of oil discovery Petro-company will get a net profit of 800000 and in case of failure 800000 will be considered a loss. Considering this information following calculations are made for minimax regret criterion analysis. 

           Above mentioned min-max regret creation explain that drilling an exploratory well is not favorable for Petro-Co. Min-max regret criterion explains that the minimum amount is 600000 for this project that the company may suffer. In Min-max regret creation at the first information about possible payoffs for both options are discussed. In the second box maximum value is selected from each column to subtract all values of this column (Preuschoff, Mohr and Hsu). After that maximum values are selected from the third box. The final decision is taken by checking the minimum value of the third box. According to this criterion, the minimum value is 600000 for an oil discovery project.    

Question 2. What is the best choice Petro-Co should go for using the expected value of this major project?

Best Choice using Expected value

           Expected value calculations for the major project is the major source to select the appropriate decision for a project. In this Petro-Co project best choice is selected by using the expected value of this major project (Conejo, Carrión and Morales). Expected value is calculated through multiplying the oil discovery payoff and no oil discovery with the probabilities. The probability of oil discovery is 45% while the remaining 55% represents chances of failure in oil discovery. According to the expected value calculation formula (see presented below formula) expected value for drilling is -800000 that represents chances of loss rather than profit.  

Drill expected value calculation

Expected value for not-drilling the well

           Expected value calculation concludes that the company should not invest in this project. Because of the high probability of loss (as there is 55% probability that company will fail to discover oil after drilling an exploratory well) expected value is negative (Conejo, Carrión and Morales). If the company will drill oil well then they will face the loss of 800000. Somehow, the maximum expected value is 200000 that support the option of “not to drill”.

Question: 3 What is the best decision based on the EOL?

Best Decision based on EOL

           EOL refers to the expected opportunity loss for a project. In this Petro-Co project, EOL will explain how much loss the company can face in case they avail of this opportunity. Expected opportunity loss is calculated through the use of a simple EOL formula (Preuschoff, Mohr and Hsu). In EOL calculation maximum value is used to subtract the other loss related options (for instance in this case “not to drill” option was representing the loss). After the subtraction of these values, calculated “drill” value “0” and drilling loss “1000000” are multiplied by the probabilities 45% and 55% (converted to decimal as 0.45 and 0.55).  After that multiplication results are added up to get the calculated value of EOL.

            Thus in the light of EOL calculation and above-mentioned table, expected opportunity loss for Petro-Co is 550000. Calculated EOL value loss is almost double as compared to the initial cost of the project (Conejo, Carrión and Morales). Considering this information it is clear that the best decision for Petro-Co is to avoid investing in this project. The project is even not capable to meet breakeven point.  Therefore, instead of investing in this project they should search for a better opportunity (Kochenderfer).     

Question: 4 What is the expected value of perfect information?

The expected value of Perfect Information

          The expected value of perfect information for Petro-Co project elaborate increase in the overall possible or expected net profit that company or managers of the company (who is going to take decision for investment) will ensure through getting information about uncertainty and certainty of an event occurrence. The expected value of perfect information deals with the upper bound of the expected project value. The simple formula to calculate the expected value of perfect information is to subtract “A” value from “B” value.

If EVwPI (Expected value without perfect information) is 470000 then

Expected value with perfect information
STATES OF NATURE
DECISION	Oil	No oil	Expected Value
Drill	800000	-800000	-80000
Not to drill	200000	200000	200000
Probability	0.45	0.55
Evwpi	470000
Max. Expected value	200000
EVPI	270000

          The above-mentioned table provides an overview of the calculations and results of the expected value without and with perfect information. The total calculated value of EVPI is 270000 which means that Petro-Co has to spend this amount to get perfect information about the project. The expected value of perfect information and Expected value without perfect information cannot be all the same for a project. The margin between these values presents the requirements for market research, cost estimation, and other important information.  

Question: 5 Petro Co is considering conducting a seismic survey which costs $10,350, to see what the underground conditions are like. The survey history shows that

? There is a 96% chance of a favorable wave transmission, given that there is an oil discovery.

? There is a 84% chance of an unfavorable wave transmission, given that there is a dry well.

According to the given data, find the posterior probabilities.

Posterior Probabilities

             Posterior probabilities have significant importance in the decision-making process. Posterior Probabilities put light on the possible outcomes of an event. Bayes Theorem is the basis of Posterior Probabilities analysis (Conejo, Carrión and Morales). In statistics and business decision analysis related courses, posterior probabilities are also known as branch probabilities for decision trees (Preuschoff, Mohr and Hsu). With the help of these Posterior Probabilities, managers can understand possible outcomes of their decisions. In this case, information related to the Petro-Co oil discovering project is used to search out Posterior Probabilities of events. 

           In the analysis chances of favorable wave transmission (oil discovery) is 96% while 84% chances stand for unfavorable wave transmission. According to the unfavorable wave transmission well are dry therefore the company can not extract oil from these well. Posterior Probabilities calculation is used as a technique to evaluate available alternative options to select the best one for Petro-Co. In the presented below tables information about Posterior Probabilities are projected.      

Posterior Probabilities
STATES OF NATURE
DECISION	Oil	No oil	Expected Value
Drill	800000	-800000	96000
Not to drill	10350	10350	18630
Probability	0.96	0.84

 

Posterior Probabilities of favorable wave transmission
State	Prior	Likelihoods	Joint	Posterior
Oil	0.96	0.960	0.9216	0.964824121
No oil	0.84	0.04	0.0336	0.035175879
			0.9552	1
Posterior Probabilities of Un-favorable wave transmission
State	Prior	Likelihoods	Joint	Posterior
Oil	0.96	0.840	0.8064	0.857142857
No oil	0.84	0.16	0.1344	0.142857143
			0.9408	1

        In the above-mentioned table, two states are used for events. Prior probabilities are simple probability given in the question statement (Preuschoff, Mohr and Hsu). While likelihoods, joint, and posterior are calculated. Joint is calculated by multiply the prior values with the likelihoods of the states. Posterior value is calculated by dividing the joint value from total joint values (Conejo, Carrión and Morales). In the above-presented tables of two events, favorable wave transmission and un-favorable wave transmission total posterior is equal to 1. Somehow, total posterior value 1 represents the accuracy of Posterior Probabilities calculation.

           Following image represents the posterior probabilities for both options (drill the well or not to drill a well for oil). Red color values represent not to drill options while purpose color is for Drill option.

 

Figure 1 Posterior Probabilities

Question: 6 What is the value of sample information?

Value of Sample Information

           The expected value of sample information and the expected value of perfect information both are relatively the same. Both values relate to the additional expected profit caused by the detailed information about the project. Somehow, both cannot be interpreted as the same value because of the difference. EVSI concerns with the sample while EVPI relates to perfect information. Survey results and knowledge gained from the samples is not perfect information, therefore, values of EVSI and EVPI cannot be the same. In this case, EVIS is calculated through the use of the presented below formula.  

18630

According to the calculations expected value for sample information is -8280. 

Question: 7 Examine how your decision might change with different oil discovery probabilities. Let p denote the probability of a dry well and 1-p denote the probability of well discovery. What are the ranges of p that affect your decision? Solve this part as a risk neutral decision maker without any perfect or sample information.

Risk Neutral

             Decision making is not as easy as usual, we take it. Organizational success and business profitability high depend on effective and appropriate decision making. Managers taking the wrong decision because of limited available information contributes to the failure of the organization in the market. As competition and need for profitability are growing it's becoming essential for the project manager and business managers to take the right decision at right time after evaluating all available alternative options. In the case of Petro-Co risk factor is really high for the company.

           The company is going to invest a huge amount of money with less 45% probability of getting net profit ($800000). Changes in the probability of oil discovery can change decision also. Even then the low probability is not the indicator of loss (Mittelhammer). It does not mean that the company should not invest in their project there are many other factors also that need to be taken into consideration while making the investment. For instance, in this case, we cannot ignore the expected return on this investment and possible loss. If the loss is not really high then the company can take the risk.

          There are a number of ways and methods supported by academic theories that can be used for risk analysis. Ranges of p that can influence or change my decision are between the ranges 65-100%. Risk factor shows how much company will suffer in case they invest in drilling project and get dried well in discovery (Kochenderfer).  Of course, dry well cannot provide oil, therefore, dry well discovery is a direct loss for the company. The risk-neutral person always guesses 1 as the sum of whole probability should be equal to one. Less than one indicate that outcomes are not 100 %, therefore, there is a possibility of failure.