An oil well will produce 100,000 barrels of oil next year and 250,000 barrels in two years

(assume for simplicity that the oil will be available at the end of the year). After that, the oil

well will be closed forever. Suppose that: (i) the operating expenses are $48/barrel, (ii) the

forward price of oil delivered one year from now is $100/barrel and (iii) no forward market is

available in two years. Suppose that the risk-free rate is 5%, and that the project beta of oil-wells

is 0.9, and that the market expected risk premium is 6%. Suppose that, in the second year,

the oil price fluctuates so it can be: $130/barrel, $100/barrel, or $90/barrel with equal

probabilities.

a) Find the value of the oil well.

b) Suppose that the oil well would be only operative for one year (i.e., ignore any

information about year two). Form a perfect tracking portfolio for the oil well and value the

oil well in such a case.

c) Suppose that the oil well is only operative for one year (again, please ignore any

information about year two) and that the one-year oil forward price is $40/barrel. What is the

value of the oil well? Explain.

d) Suppose that in the second year, the operating expenses are not a constant $48/barrel

but they are $48/barrel on average and exhibit some variability. In particular, they are higher

when the oil price is higher and lower when the oil price is lower. Is the value of the oil well

higher, lower or equal to the value obtained in a)? Explain. (Hint: You don't need to make

calculations to answer this part of the question.)