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]

• 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

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?

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

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?