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New Approach
1. List alternatives
2. For each alternativea) List possible scenarios and their probabilities
I. Describe cashflow stream
II. Calculate NPV
b) Calculate E[NPV]
3. Choose alternative with largest E[NPV]
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• Decision nodes(we choose)
• Chance nodes(stuff happens)
• Outcome nodes
Decision Treesalternative 1
alternative 2
alternative 3
NPV= x
scenario A
scenario B
scenario C
papb
pc
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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?
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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) = pa V(a) + pb V(b) + pc 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
papb
pc
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Oil Example Cont.
Old ProblemAn 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?