1. Decision Tree Analysis Introduction to DPL Prof. Luiz Brandão brandao@iag.puc-rio.br 2009

2. 2 DTA Analysis  Decision Tree Analysis is one of the tools available to aid in the decision making process.  It is a graphical method that chronologically displays all the decisions and uncertainties that a specific business problem involves.  It also provides a probability based solution, and its main appeal is its intuitive approach and ease of use.  There are many software programs that automate the model building and solving process.  In this course we will be using DPL IAG PUC – Rio Brandão

3. 3 Decision Trees  Decision trees are composed of nodes that are connected by branches.  The nodes represent points in time. A decision node is a time when a decision is made. A chance node is a time when the result of an uncertain event becomes known. An end node indicates that the problem is completed - all decisions have been made, all uncertainty have been resolved and all payoffs received IAG PUC – Rio Brandão

4. 4 Decision Trees  Time proceeds from left to right This means that branches leading into a node (from the left) have already occurred. Any branches leading out of a node (to the right) have not yet occurred.  Branches leading out of a decision node represent the possible decisions.  Branches leading out of probability nodes represent the possible outcomes of uncertain events.  Probabilities are listed in the chance nodes and must add to 1.  Cash flows are shown below the branches where they occur, and cumulative values are shown to above the branches. IAG PUC – Rio Brandão

5. 5 Decision Trees  Probabilities are listed in the chance nodes.  These probabilities are conditional on the events that have already been observed (those to the left).  The probabilities on branches leading out of any particular probability node must add to 1.  Cash flows are shown below the branches where they occur, and cumulative values are shown to above the branches. IAG PUC – Rio Brandão

6. IAG PUC – Rio Brandão 6 Oilfield Valuation (A)  Assume that a new oilfield will have a production of 500,000 barrel per year during for two year  Operational cost is $30/bbl  Exploration cost is $25,000,000  Expected oil price in the next two years is $60.  Should the firm invest in this project? Yes -25.000+2*500*(50-30) No 0 Invest?

7. IAG PUC – Rio Brandão 7 Oilfield Valuation(B)  Let´s now assume there is a price uncertainty in the second year  In the second year there will be a 0.30 probability that the price will be $75.  There is a 0.40 probability the price will be $60.  There will be a 0.30 probability the price will be $40. High 500*(Price2-30) Nominal 500*(Price2-30) Low 500*(Price2-30) Yes -25.000+500*(60 - 30) Price2 No Invest?

8. IAG PUC – Rio Brandão 8  We now assume uncertainty in both years  The price in year 1 will be $40, $60 or $75.  We assume there is price correlation, which implies that the price in year 2 is influenced by the price in year 1.  In year 2 the price will increase by $5, remain the same, or decrease by $10 relative to year 1 levels.  Probabilities are respectively 0.25, 0.50 e 0.25. High 500*(Price2-30) Nominal 500*(Price2-30) Low 500*(Price2-30) High 500*(Price1-30) Nominal 500*(Price1-30) Low 500*(Price1-30) Price2 Yes -20.000 Price1 No Invest? Oilfield Valuation (C)

9. IAG PUC – Rio Brandão 9 Oilfield Valuation (D)  Use of Variable Nodes  Difference between Cash Flows and Node Values  Extending the model to more periods  Reducing processing time  Sensitivity Analysis  Different Projects within a single DPL File

10. Decision Tree Analysis Introduction to DPL Prof. Luiz Brandão brandao@iag.puc-rio.br 2009