Petroleum Inc. owns a lease to extract crude oil from sea. It is considering the construction of a deep-sea oil rig at a cost of $50 million (I0) and is expected to remain constant. The price of oil is $50/bbl and the extraction costs are $20/bbl. The quantity of oil Q = 200,000 bbl per year forever. The risk-free rate is 10% per year which is also the cost of capital (Ignore taxes). Suppose the oil price is uncertain and can be $70/bbl or $40/bbl next year. If the project if postponed by one year, calculate the value of the option to wait for one year: (approximately)
A) +15,000,000
B) +40,000,000
C) +10,000,000
D) none of the above

Question

Quizplus · Accepted Answer

Without delay, the present value of the project is:
PV = -50,000,000 + (200,000 bbl*$30/bbl)/(1+10%) = $56,000,000
where $30/bbl is the net profit of each barrel of oil sold.

If the project is postponed by one year, the option to wait can be exercised if the oil price next year is $70/bbl, and the present value of the new project is:
PV = -(50,000,000-$56,000,000) + (200,000 bbl*$50/bbl)/(1+10%) = $54,000,000
where $50/bbl is the net profit when the oil price is $70/bbl.

If the oil price next year is $40/bbl, the project is abandoned, and the present value of the new project is zero.

The value of the option to wait is the difference between the present value of the new project if the option is exercised and the present value of the project without waiting:
Option = $54,000,000 - $56,000,000 = +$2,000,000

Therefore, the best choice is to postpone the project by one year and exercise the option to wait if the oil price next year is $70/bbl. The expected present value of the new project is higher than the present value of the project without waiting, by approximately $2,000,000.