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### Presentation 7

1. 1. Petroleum Project Economics Econ210D Presentation 7 Risk Analysis for Uncertain Variables Week 7
2. 2. Uncertain Variables and Risk Analysis <ul><li>Some variables used in the economic evaluation of a project may not be know with certainty. </li></ul><ul><li>The outcome of an investment decision depends on a wide range of uncertain variables. </li></ul><ul><li>Geological, economic uncertainties etc </li></ul>Risk Analysis for Uncertain Variables Week 7
3. 3. <ul><li>This means that there might be different possible outcomes. </li></ul><ul><li>Such uncertainty has to be taken into account in the analysis. </li></ul><ul><li>Uncertainties can be quantified in terms of probabilities. </li></ul>Uncertain Variables and Risk Analysis Risk Analysis for Uncertain Variables Week 7
4. 4. <ul><li>A geologist has estimated the probability of drilling a successful well is 60%. </li></ul><ul><li>This means P(Productive well) = 0.6 </li></ul><ul><li>And P(Dry hole) = 0.4 </li></ul>Example Risk Analysis for Uncertain Variables Week 7
5. 5. <ul><li>The expected value is calculated as the weighted average net present value given uncertainty and different possible outcomes. </li></ul><ul><li>Probability values are used as weights for the net present value of each possible outcome. </li></ul>EXPECTED VALUE Risk Analysis for Uncertain Variables Week 7
6. 6. <ul><li>Where : </li></ul><ul><li>x i = possible outcome of the project </li></ul><ul><li>P(x i )= probability of the outcome x i </li></ul>EXPECTED VALUE Risk Analysis for Uncertain Variables Week 7
7. 7. <ul><li>It is estimated that the probability of drilling a productive well is 35% and the probability of a dry hole is 65%. </li></ul><ul><li>Drilling a dry hole results in a net loss of \$100,000 (cost of drilling the well in present value). </li></ul><ul><li>If the well is successful, then the net revenues will be \$900,000 (Revenue minus cost of drilling the well in present value). </li></ul><ul><li>What is the expected value? </li></ul>Example – Expected Value Risk Analysis for Uncertain Variables Week 7
8. 8. Solution – Expected Value Risk Analysis for Uncertain Variables Week 7 Outcome Probability NPV in \$m Probability × NPV in \$m Dry hole 0.65 -100 -65 Strike Oil 0.35 900 315 Total Probability = 1 Expected Value = 250
9. 9. <ul><li>A diagrammatic representation of a decision situation with different outcomes. </li></ul><ul><li>The associated probabilities with each outcome is shown </li></ul><ul><li>Used to assist in the computation of Expected Value. </li></ul>Decision Tree Risk Analysis for Uncertain Variables Week 7
10. 10. Binomial Distribution <ul><li>The binomial distribution applies when the following conditions must be met. </li></ul><ul><li>Fixed number of trials </li></ul><ul><li>Two possible outcomes in each trial which are termed success and failure </li></ul><ul><li>Same probability of a success for each trial. </li></ul>Risk Analysis for Uncertain Variables Week 7
11. 11. Binomial Formula where X = number of successes n = number of trials p = probability of success q = probability of failure Risk Analysis for Uncertain Variables Week 7
12. 12. Binomial Decision Trees <ul><li>This applies when a choice has two outcomes as shown by each branch. </li></ul><ul><li>The same choice has to be repeated over many trials </li></ul><ul><li>This is applicable to a multiple well drilling programme. </li></ul>Risk Analysis for Uncertain Variables Week 7
13. 13. <ul><li>Drilling a well is expected to result in either a dry hole or a productive well . </li></ul><ul><li>If 3 wells are drilled, use a decision tree to demonstrate the possible outcomes. </li></ul><ul><li>Use the decision tree to determine the expected value </li></ul>Example - Multiple Well Drilling Programme Risk Analysis for Uncertain Variables Week 7
14. 14. Decision Trees Risk Analysis for Uncertain Variables Week 7 Productive Dry hole 0.6 0.4 Productive Dry hole 0.6 0.4 Productive Dry hole 0.6 0.4 Productive Dry hole 0.6 0.4 Productive Dry hole 0.6 0.4 Productive Dry hole 0.6 0.4 Productive Dry hole 0.6 0.4
15. 15. Solution – Expected Value Risk Analysis for Uncertain Variables Week 7 Number of Successful Wells Probability using Binomial Distribution NPV in \$m Probability × NPV in \$m 0 0.064 -300 -19.2 1 0.288 700 201.6 2 0.432 1700 734.4 3 0.216 2700 583.2 Total Probability = 1 Expected Value = 1500
16. 16. Question 1 <ul><li>You have mineral rights on a piece of land that you believe may have oil underground. There is only a 10% chance that you will strike oil if you drill, but the payoff is \$200,000. It costs \$10,000 to drill. The alternative is not to drill at all, in which case your profit is zero. Draw a decision tree to represent your problem. Using the decision tree calculate the expected value and state whether the well should be drilled. </li></ul>Risk Analysis for Uncertain Variables Week 7
17. 17. Question 2 <ul><li>An oil company has plans to drill ten wells. The probability of hitting oil in each well is 3% and it costs \$250M to drill a well. If the revenue from each well in present value for the company will be \$2B find the expected value of the drilling program. </li></ul>Risk Analysis for Uncertain Variables Week 7