Question

"An oil producer is trying to decide if and when it should abandon an oil field. For simplicity, assume the producer will abandon immediately (year 0), at the end of year 1, at the end of year 2, or stay at least through the next two years. The major uncertainty is the price of oil, which can go up or down in any year. In each year, there is a 0.33 probability the oil price will go up and a 0.67 probability the oil price will go down. The oil producer decides whether or not to abandon the oil field and then observes whether the price of oil increases or decreases in the following year. The NPV includes all the relevant costs of abandoning the oil field and producing oil and the revenue gained from producing oil. It also already incorporates the producer's MARR. After the producer makes a decision at the end of year 2, we assume there is no more uncertainty. If the producer abandons the oil field at the end of a year, the price of oil in the following years does not impact the producer's NPV.
Solve a decision tree to calculate what the oil producer should do immediately, at the end of year 1, and at the end of year 2. You should assume an expected-value decision maker.
Enter the expected NPV of the best alternative. The best alternative may have a negative expected NPV.
- If the producer decides to abandon the oil field immediately, the NPV is -$43,000
- If the producer decides to abandon at the end of year 1 and the oil price goes up, the NPV is $0
- If the producer decides to abandon at the end of year 1 and the oil price goes down, the NPV is -$60,000
- If the producer decides to abandon at the end of year 2 and the oil price goes up in years 1 and 2, the NPV is $72,000
- If the producer decides to abandon at the end of year 2 and the oil price goes up in year 1 and goes down in year 2, the NPV is $37,000
- If the producer decides to abandon at the end of year 2 and the oil price goes down in year 1 and goes up in year 2, the NPV is -$4,000
- If the producer decides to abandon at the end of year 2 and the oil price goes down in years 1 and 2, the NPV is -$120,000
- If the producer decides to not abandon the oil field and the oil price goes up in years 1 and 2, the NPV is $41,000
- If the producer decides to not abandon and the oil price goes up in year 1 and goes down in year 2, the NPV is $21,000
- If the producer decides not to abandon and the oil price goes down in year 1 and goes up in year 2, the NPV is -$37,000
- If the producer decides not to abandon and the oil price goes down in years 1 and 2, the NPV is -$86,000"

Answer 1

The producer has 4 choices :

i) to abondon immediately

ii) To abandon at the end of year 1

iii)To abandon at the end of year 2 and

iv) To not abandon ,

The producer should choose the one where the NPV is most positive or least negative

1.Abandon the oil field immediately, the NPV is -$43,000

2.  Abandon at the end of year 1

Expected NPV = 0.33* Expected NPV in case the price goes up + 0.67* Expected NPV in case the price goes down

= 0.33*0+0.67*(-$60000)

= -$40200

3. Abandon at the end of year 2

Expected NPV= 0.33*0.33*Expected NPV in case the price goes up in year 1 and year 2+0.33* 0.67* Expected NPV in case the price goes up in year 1 and down in year 2 + 0.67* 0.33* Expected NPV in case the price goes down in year 1 and up in year 2 +0.67* 0.67* Expected NPV in case the price goes down in year 1 and down in year 2

= 0.33*0.33*72000 +0.33*0.67*37000+0.67*0.33*(-40000)+0.67*0.67*(-120000)

= -$46690.50

4) Not abandon

Expected NPV= 0.33*0.33*Expected NPV in case the price goes up in year 1 and year 2+0.33* 0.67* Expected NPV in case the price goes up in year 1 and down in year 2 + 0.67* 0.33* Expected NPV in case the price goes down in year 1 and up in year 2 +0.67* 0.67* Expected NPV in case the price goes down in year 1 and down in year 2

= 0.33*0.33*41000 +0.33*0.67*21000+0.67*0.33*(-37000)+0.67*0.67*(-86000)

= -$37678.10

As the NPV is least negative in the case when the producer does not abandon the project

The producer should not abandon the project