Question

A. ArmaCo must determine whether or not to drill for oil at the Northern part of Jubail. It costs $100,000 to drill, and if oil is found, the value is estimated to be $600,000. At present, ArmaCo believes there is a 45% chance that the field contains oil with the profit payoffs give in the table below. Alternatives State of Nature Oil Dry Drill 500 –100 No Drill 0 0 a. [0.5 Mark] Show the decision tree for the situation. b. Which alternative should the Armaco choose using: i. [1 Mark] the optimistic approach ii. [1 Mark] the conservative approach iii. [1 Mark] the minimax regret approach. c. [1 Mark] Determine which alternative should be chosen based on expected value. d. [1 Mark] Determine the expected value with perfect information. e. [1 Mark] Determine the expected value of the perfect information. B. Before drilling, ArmaCo can hire (for $10,000) a geologist to obtain more information about the likelihood that the field will contain oil. There is a 50% chance that the geologist will issue a favorable report and a 50% chance of an unfavorable report. Given a favorable report, there is an 80% chance that the field contains oil. Given an unfavorable report, there is a 10% chance that the field contains oil. f. [1 Mark] Show the decision tree for the situation. g. [1 Mark] Determine ArmaCo’s optimal course of action. h. [0.5 Mark] How much is the expected profit? i. [1 Mark] Determine the Expected Value of Sample Information.

Answer 1

Here the object is to determine the optimal course of action to follow by the company "O" and determine EVSI and EVPI.

The following is the information provided.

The Cost of drilling : $100,000;

If oil found then value is :$600,000;

Present, the chance of field contains oil is 45%;

Hiring cost of a Geologist is : $10,000;

The chance of favorable report by Geologist is 50%;

The chance of failure report by Geologist is 50%;

If the report is favorable then chance that the field contains oil is 80%;

If the report is failure then chance that the field contains oil is 10%;

Using the above information first draw a decision tree which covers all of the above points.

The Decision tree has to be drawn using excel ( Use excel Add ins-Precision tree/Decision tree )

Then find the value of the assets at each node ( decision fork is represented in the diagram with symbol 'Square' and event fork is represented with 'circle') starting from the final node.

The following is the decision tree with the expected value of assets

The value of assets at final nodes and at forks is calculated as follows :

The value of the asset at final node of the event Oil found followed by Geologist is not hired is

.

The value of the asset at final node of the event Oil not found followed by Geologist is not hired is

The value of the asset at final node of the event Not drill followed by Geologist is not hired is .

The value of the asset at final node of the event Oil found followed by Geologist favor report is

The value of the asset at final node of the event Oil not found followed by Geologist favor report is

The value of the asset at final node of the event Not drill followed by Geologist favor report is

.

The value of the asset at final node of the event Oil found followed by Geologist not favor report is

The value of the asset at final node of the event Oil not found followed by Geologist not favor report is

The value of the asset at final node of the event Not drill followed by Geologist not favor report is

.

The following are the expected final asset positions at event forks:

Oil found when Geologist not hired is

The following are the expected final asset positions at event forks:

Oil found when Geologist hired followed by favor report is

The following are the expected final asset positions at event forks:

Oil found when Geologist hired followed by not favor report is

The expected final asset positions at decision forks are :

Decision after not hiring is the larger asset value of when drilled and not drilled which is $170,000

Similarly Decision after hiring geologist with favor report is the largest asset of drilled and not drilled which is maximum of {$370,000, -$10,000}

Therefore Decision after hiring geologist with favor report is $370,000

Similarly Decision after hiring geologist with not favor report is -$10,000

Now, the final asset value when geologist hired is

Now the final asset value when geologist is not hired is $170,000

The value at Decision node Hire or not is the larger value of {$170,000, $180,000}

Therefore the value decision node Hire or not is $180,000.

Therefore the expected profit is $180,000

Therefore the optimal course of action is "Hire Geologist". If the Geologist gives favorable report then Hire Geologist, if not then don't hire Geologist.

Expected value of sample Information is the value of information that would be obtained from sample Information.

First find the Expected Value with sample Information. This is the sum of expected value when geologist takes the survey plus cost of hiring geologist.

Next, obtain Expected Value with Original Information. That is the expected value without any test. Here, .

Therefore,

EVPI Calculation:

Expected Value of Perfect Information is obtained by drawing a decision tree i.e geologist is not hired.

The following is the Decision tree with asset values at each nodes

Expected Value with Perfect Information is

Expected Value with Original Information is 170,000.

Now the Expected Value of Perfect Information is :