Posted: December 8th, 2013
Choosing the Right Fork of a Decision Tree
Most decisions in the petroleum industry involve elements of risk and uncertainty, particularly in the area of oil exploration. When a decision is made to drill an exploratory oil well, company geologists and engineers are not able to measure or define specific values of factors contributing to overall profit (or loss) at the time of the decision. In addition, future events that could affect timing and/or size of projected cash flows from the prospective well (e.g., government price controls, cessation of oil imports from Iraq) cannot be reliably predicted. These risks and uncertainties have decision-makers in the oil industry relying more and more on decision analysis techniques. Chi U. Ikoku, Associate Professor and Associate Director of Drilling Research at the University of Tulsa, writes: “Decision analysis methods provide new and much more comprehensive ways to evaluate and compare the degree of risk and uncertainty associated with each [oil] investment choice. The net result is that the decision-maker is given a clearer insight of potential profitability and the likelihoods of achieving various levels of profitability than older, less formal methods of investment analysis. Because of rising drilling costs, the need to search for petroleum in deeper horizons or in remote areas of the world, increasing government control, etc., most petroleum exploration decision-makers are no longer satisfied to base decisions on experience, intuition, rules of thumb, or similar approaches. Instead, they recognize that better ways to evaluate and compare drilling investment strategies are needed. Decision analysis is fulfilling this need.” Ikoku lists several distinct advantages that decision analysis has over the less formal oil drilling decision-making techniques used in the past:
1. Decision analysis forces the decision-maker to consider all possible alternatives and their corresponding outcomes. 2. Decision analysis provides an excellent way to evaluate the sensitivity of various oil-drilling factors to overall profitability.
3. Decision analysis provides a means to compare the relative desirability of drilling prospects having varying degrees of risk and uncertainty.
4. Decision analysis is a convenient and unambiguous way to communicate judgements about risk and uncertainty.
5. Exceedingly complex oil investment options can be analyzed using decision analysis.
The decision-making technique discussed in his World Oilarticle is the expected value criterion. This procedure requires the decision-maker to assess the probability of occurrence of each possible state of nature. “Assigning probabilities of occurrence to various outcomes of a petroleum venture,” says Ikoku, “requires the cooperative judgement and skills of geologists, engineers, and geophysicists.” Some of the types of risks that oil investors commonly encounter and consequently need to assess are: risk of an exploratory or development dry well; political risk; economic risk; risk relating to future oil and gas prices; risk of storm damage to offshore installation; risk that an oil discovery will not be large enough to recover initial exploratory costs; risk of at least a given number of oil discoveries in a multi-well drilling program; environmental risk; and risk of a gambler’s ruin. Because of certain characteristics that are unique to a petroleum exploration, these state-of-nature probabilities cannot be determined exactly, and furthermore, their estimates often must be made on the basis of very little or no statistical data or experience. (Additional data can be obtained from additional wells, but, says Ikoku, ” normally, delaying decisions until there is sufficient data upon which to base probability estimates cannot be afforded.” Thus, the decision-maker usually must rely on his or her subjective judgment or past success ratios in order to assess the state-of-nature probabilities. As an illustration of how decision analysis may be applied to the petroleum industry, Ikoku presented the following example: A company is considering the purchase of 320 net acres in a proposed 640-acre oil unit.
Three decision alternatives or actions are available to the company:
a1: Participate in the unit (i.e., drill) with non-operating 50% working interest.
a2: Farm out, but retain 1/8 of 7/8 overriding royalty interest.
a3: Be carried under penalty with a back-in privilege after recovery of 150% of investment by participating parties. The possible outcomes or states of nature and their corresponding probabilities, based on detailed geological and engineering analyses of the prospect and surrounding wells, are given in Table 19.17. Since the company will base its decision on the objective variable Net Profit, the projected net profits for the action/state-of-nature combinations were determined as shown in Table 19.18
(a) Construct a payoff table for the oil-investment decision problem.
(b) Using the expected payoff criterion, which of the three alternative actions should the company accept?
(c) What is the maximin decision? The maximin dicision?
(d) Construct an opportunity loss table for the oil investment decision problem and find the minimax regret decision.
Table 19.17 state of nature= probability
Dry hole=.30
Unit produces 20000 barrels=.25
unit produces 40000 barrels=.25
unit produces 80000 barrels=.10
unit produces 100000 barrels=.10
Table 19.18
Drill/dryhole=-40000 Drill/20000=50000
Drill/40000 bbls=300000
Drill/80000 bbls=700000
drill/100000=800000
farm out/dry hole=0
farm out/20000 bbls=12000
farm out/40000=60000
farm out/80000=120000
farm out/100000=130000
backinoption/dry hole=0
backinoption/2000
0=12000
0=12000
backinoption/40000=145000
backinoption/80000=400000
backinoption/100000=500000
Case Study 19.2Chi U. Ikoku continues his World Oil article on decision analysis in the petroleum industry (see Case Study 19.1 attached) with a discussion of decision trees and their importance in solving decision problems much more complex than the examples and exercises of chapter 19. Nontrivial decision problems consist of not one but a sequence of major choices or decisions that must be made. Writes Ikoku quotIn a complex decision problem involving a long sequence of alternatives, a formal procedure for decision analysis is necessary to array the alternatives so that economic ramifications of each are clearly delineated. This formal array also promotes effective internal communication. The decision tree analysis fits this criterion.quot To illustrate, Ikoku presented the following example of a drilling venture evaluation.
XYZ Enterprises has a nontransferable short-term option to drill on a certain plot of land. Two recent dry holes elsewhere have reduced XYZs liquid assets to $130,000 and John Doe, president and principal stockholder, must decide whether XYZ should exercise its option (i.e., drill) or allow it to expire. Complicating the decision problem is the fact that Doe may pay to have a seismic test run in the next few days, and then, depending on the results, decide whether to drill. Thu, Doe has three possible alternatives or actions from which to choose:
a1:Drill immediately.
a2:Pay to haave a seismic test run. then decide whether to drill.
a3:Let the opinion expire (1.e., do not run the seismic test and do not drill).
XYZ can have the seismic test performed for a fee of $30,000 and the well can be drilled for $100,000. XYZ usually sells the rights of any oil discovered. A major oil company has promised to purchase all of the oil rights for $400,000.
What is the oil company’s decision, using the expected payoff criterion?
This decision problem is structered in the form of a decsion tree, as shown in Figure 19.4. As before, the square denotes a decision fork and the circle denotes a chance fork. Notice the probabilities assigned to the states of nature, Strike Oil, Do not strike oil (given in parentheses under the appropiate fork), vary according to whether the seismic test is run, and if run, whether the test is favorable. Also note that the objective variable in this decision problem is Net liquid as sets (in dollars).
The expected payoff strategy as applied to decision trees that involve a sequence of choices to be made requires the decision maker to work through the decision tree “backward” (i.e., from right to left), computing at each chance fork (circle) the corresponding expected payoff. The at each decision fork (square), choose the action with the maximum expected payoff (thereby eliminating from further consideration all other alternatives at that particular fork). Repeat the procedure until only a single action or branch remains. This is the optimal expected payoff strategy.
(a) From Figure 19.4, compute the expected payoff for action a1: Drill immediately.
(b) From Figure 19.4(attached), compute the expected payoff for the action a3: Do not run seismic test, do not drill.
(c) The expected payoff for the action, a2: Run seismic test, then decide whether to drill, is not computed as easily as for action a1 and a3 because action a2 involves two different chance forks-the fork corresponding to the result of the seismic test Favorable or Unfavorable) and the fork corresponding to the result of drilling (Oil or No oil). The first step in computing the expected payoff for a2 is to compute the expected payoff at each of the two rightmost chance forks in the Run seismic test branch of the tree. Place these expected values above the corresponding chance fork symbol (circle) in Figure 19.4. [For example, the expected payoff for the top, rightmost is ($400,000)(.85) + ($0) (1.5) = $340,000.]
(d) The second step is to determine the optimal action at each decision fork (square) in the Run seismic test branch by comparing the expected payoffs of the two actions Drill and Do not drill. Choose the action with the largest expected payoff and eliminate the alternative branch from further consideration. [For example, the optimal action corresponding to the top, rightmost decision fork (square) os Drill, because the expected payoff for this action, namely $340,000, is larger than the expected payoff ($100,000) corresponding to the action Do not drill. Thus, we can eliminate the action Test favorable, Do not drill from further consideration.]
(e) If you have performer the second step in part d correctly, there should remain only two “clear” paths or options available to the decision maker in the upper portion of the tree: the Test favorable, Drill option and the test unfavorable, Do not drill option. To compute the expected payoff for action a2: Run seismic test, multiply the expected payoffs of these optimal actions by their corresponding state of nature (Favorable or Unfavorable) probabilities and sum these two values. [Hint: The correct expected payoff is ($340,000) (.6) + ($100,000) (.4) = $244,000.]
(f) Now that you have computed the expected payoffs for each of the three actions, apply the expected payoff criterion in the usual manner, that is choose the action with the maximum expected payoff. What is the oil company’s decision?Click here for more on this paper…….
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