24 May, 2017

# How can Decision Trees help you make Productive Decisions?

*The following is an excerpt from Economics of Worldwide Petroleum Production, Third Edition.*

In many decision-making situations, future choices in a train of events are inevitably affected by the actions taken in the immediate present. For cases in which consideration of the consequences of a series of decisions is important, and the likelihood, or probability of the subsequent events is known, the use of decision trees for risk analysis can be very helpful.

Decision trees are an excellent way of breaking down a highly complex decision problem into a series of simpler ones. They are constructed by diagramming all the decision options and subsequent chance events associated with the particular alternatives. This allows the user to react to a series of “what if” questions as well as to envision the range of possible outcomes of the project under study. Decision Trees also provide a useful vehicle for examining the value of additional information to the decision process.

Each decision tree is built for only one decision even though it may forecast other subsequent decisions. In exploration, for example, a typical sequence of operations and related decisions might involve taking a lease, undertaking geophysical work, deciding to drill a well, deciding to drop the acreage, whether to farm-out or drill a confirmation well, and so forth. At each of these branching points, several possible outcomes are indicated. Starting at the left of the tree with the initial decision alternatives each branch depicts a possible outcome which is given a value or “payoff.”

Two types of node symbols are normally employed:

The nodes of the tree from which the branches spread are all either decision nodes or chance nodes. The branches from a decision node represent alternative courses of action. The branches leaving the chance nodes represent chance events, or outcomes over which the decision maker has no control. The probability associated with each possible outcome from a chance node is written on the branch. Chance events are usually the work of nature such as weather, or geology, or possible political outcomes.

**Decision Tree Analy****sis**

Consider an exploratory drilling venture as depicted in Figure 6-16. If we assume a 65 percent probability of finding no production, the probabilities may be added to the decision tree as shown in Figure 6-17:

**Figure 6-16** SIMPLE DECISION TREE

**Figure 6-17** DECISION TREE WITH PROBABILITIES OF OCCURRENCE

The analysis is further complicated, as is shown in Figure 6-18, by the realization that not all successful wildcats are equally profitable. For this example, there is a 75% chance of the well being commercial, with a 25% chance that it will be marginal. A commercial well would have a conditional value (NPV) of $3M, a marginal well $0.5M, and the dry hole cost of $0.2M.

**Figure 6-18** DECISION TREE WITH ECONOMIC CONSEQUENCES

Thus, the drilling of the prospect can have only one of three possible outcomes. Any one excludes the others (mutually exclusive), and one of the events must happen. The outcomes at this stage comprise a collectively exhaustive, mutually exclusive set.

If the decision maker relied only on the most likely outcome, he would have to reject the project outright. On the other hand, a business decision would be made easier if excellent producing wells had a higher relative weighting, in economic terms, than marginal producers and dry holes. Expected value is clearly the preferred approach to decision making in these circumstances if it can be properly utilized.

The decision tree is evaluated using what is known as the “Rollback” procedure. This procedure calls for starting at the tips of the branches and working back toward the starting, or initial node of the tree, employing these two rules:

As each node is evaluated, working downstream from the right, the Expected Value calculated for Rules 1 and 2 can be determined and posted on the main tree. By working backward down the tree, many of the alternatives may be eliminated quite quickly from further consideration.

The resulting assessment of uncertainty can be shown diagrammatically in Figure 6-18.

The risk-weighted economic value of the drilling decision can also be posted on the diagram. These would be derived from the following value assessment:

Under the outlined conditions of uncertainty and expected value assignment, the risk-weighted or mean expected value of the particular decision to drill can be calculated as follows:

Now the question arises as to the value and meaning of the expected NPV of $702,000 calculated for this example. Using set criteria, this investment opportunity is acceptable because it is positive, indicating that the rate of return exceeds the hurdle rate, and all risks have been considered. The resulting value, however, is no better than the assumptions that went into its derivation. The successful use of the Expected Value technique as an index of investment quality depends upon the validity of both the probability figures and the expenditure estimates for each of the alternative investments. Risk adjustment does not eliminate uncertainty. It merely expresses its effect in a useful fashion which oftentimes proves helpful in decision making. To further enhance the utility of decision tree diagrams, values can be posted at each node, as has been done in Figure 6-19.

Continuing our discussion of decision tree diagrams, let’s next consider adding a farmout option to the drilling decision, in which the decision maker could come back in for a quarter working interest after payout of the drilling and completion cost. This is diagramed in Figure 6-19:

**Figure 6-19** DECISION TREE WITH FARMOUT OPTION

Conclusion: The drilling option is better (EMV + $702,000) vs. the farmout (EMV + $208,000) although both are positive in this case.

**Interpretation of Decision Trees**

The Decision Tree method of analysis can be further enhanced by scaling the branches in terms of time. For example, in the case of a secondary recovery project, discounting all values back to a common time point for comparison can be helpful.

Several other analytical techniques based on decision trees are documented. One is Nature’s Tree in which only the chance nodes from the basic tree are included and are replotted separately. From this tree it is relatively simple to ascertain what the maximum, or minimum outcomes due to chance alone will be. This method facilitates the computation of any series of chance events that may be dispersed through the basic tree.

The decision tree can also be used to test decision alternatives for the sensitivity of the probability of occurrence and conditional value of any or all of the outcomes anticipated by the tree. This requires the resolving of the decision tree for a range of values or selected discrete values for the parameters being investigated.

Another interesting variation of Decision Tree analyses involves the inclusion of the effects of expenditures for additional information, such as additional seismic surveys, or special laboratory work for an enhanced oil recovery project. The added costs, project delays, and changes in Expected Values, either positive or negative, can be incorporated in the diagram employing the same techniques already described. These costs are carried to the end of all branches to the right of such expenditures and are included in the conditional value of each subsequent outcome.

Decision trees do not eliminate risk, they merely aid in assessing it. One drawback to the decision tree methodology is the implicit assumption that maximizing expected NPV is the ideal decision criterion. This ignores the fact that most companies are to a greater or lesser extent, risk averse. The fact that a decision problem is formalized as a diagram helps, of itself, to clarify the important issues and to demonstrate the interrelationship of the decision process.

The decision tree examples presented up to this point have only included a single decision node. However as noted at the beginning of this section, decision trees are not limited to a single decision node. A tree may include as many decision nodes as the user wishes, representing all future decisions expected to be made. Although each tree is prepared to assist in making only a single decision, which is the decision represented by the decision node at the extreme left side of the diagram, all decision nodes to the right of the prime decision node represent future anticipated decisions. They are dependent upon the prime decision and/or the outcome at certain chance nodes and will not be made until something else occurs. For example, it may be anticipated that a decision to drill a well will be made only after obtaining additional seismic data. The decision will be highly dependent upon that information. A single dry hole may not completely condemn a prospect. It may be desirable to delay making the decision to drill a second wildcat well until the data provided by the first dry hole can be fully analyzed.

Not only can the decision tree be used to evaluate alternatives by including and weighing the various outcomes which may result from those alternatives, but once it has been prepared it does provide a plan for carrying out the decision. The decision tree is also an excellent surveillance tool for monitoring the results of outcomes represented by the chance nodes and for making the future decisions that were anticipated when the tree was initially drawn. As new information is obtained the tree should be updated and altered when dictated by the new information. As subsequent decisions are made and outcomes become known, the nodes to the left of these points become moot and those branches emanating from them which were not followed should be eliminated. It may also be necessary to add more branches and nodes to the diagram as the result of additional information obtained.

We can observe that any sequence of decisions, no matter how complicated, can be analyzed by the decision tree method. Contingencies and various alternatives are defined and analyzed in a consistent manner. Almost any number of assumptions can be incorporated. However, the more assumptions, the larger the number of cases, and the laws of diminishing returns limits the practicality of making the tree too extensive. How extensive to make the tree is, of course, a matter of judgment on the part of the analyst.

**Decision Tree Process Summary**

For more information, see our Expanded Basic Petroleum Economics course, or take a look at our other Petroleum Business courses.

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