1. New Approach 1.List alternatives 2.For each alternative a)List possible scenarios and their probabilities I.Describe cashflow stream II.Calculate NPV b)Calculate E[NPV] 3.Choose alternative with largest E[NPV]

2. Decision nodes (we choose) Chance nodes (stuff happens) Outcome nodes Decision Trees alternative 1 alternative 2 alternative 3 NPV= x scenario A scenario B scenario C papa pbpb pcpc

3. Oil Well Example An oil field has a 50% probability of being rich, in which case it will produce cashflows of $5 million per year for 15 years, starting one year after an oil well is drilled. The field has a 50% probability of being poor, in which case it will produce cashflows of $1 million per year for 15 years, starting one year after an oil well is drilled. Drilling a well costs $15 million. The discount rate is 10%. What should you do?

4. Solving Decision Trees Calculate value V at each node At outcome node: do NPV calculation At chance node: take expectation of value of scenarios V(node) = p a V(a) + p b V(b) + p c V(c) At decision node: –Pick value of largest alternative V(node) = max { V(1), V(2), V(3) } –Prune sub-optimal branches (rejected alternatives) alternative 1 alternative 2 alternative 3 scenario A scenario B scenario C papa pbpb pcpc

5. Oil Example Cont. Old Problem An oil field has a 50% probability of being rich, in which case it will produce cashflows of $5 million per year for 15 years, starting one year after an oil well is drilled. The field has a 50% probability of being poor, in which case it will produce cashflows of $1 million per year for 15 years, starting one year after an oil well is drilled. Drilling a well costs $15 million. The discount rate is 10%. What should you do? Extension If you spend $1 million testing the oil field, then after 1 year you will learn whether the oil field is rich or poor, and you can decide then whether or not to drill. What should you do?