Petroleum Inc.(PI)controls off-shore oil leases.It is considering the construction of a deep-sea oil rig at a cost of $500 million.The price of oil is $100/bbl.and extraction costs are $50/bbl.PI expects costs to remain constant.The rig will produce an estimated 1,200,000 bbl.per year forever.The risk-free rate is 10% per year,which is also the cost of capital.(Ignore taxes).Suppose that oil prices are uncertain and are equally likely to be $120/bbl.or $80/bbl.next year.
Suppose that PI has the option to postpone the project by one year.Calculate the value of the real option to postpone the project for one year.
A)+$30 million
B)+$50 million
C)+$54 million
D)+$70 million

Question

Quizplus · Accepted Answer

To calculate the value of the real option to postpone the project for one year, we need to calculate the expected future cash flows in both scenarios (high oil price and low oil price) and discount them back to the present value using the risk-free rate, and then compare them to the cash flows if we exercise the option to proceed with the project next year.

If we postpone the project for one year, we will lose the cash flows for this year (1,200,000 bbl. x ($100 - $50) = $60 million) but we will have the option to decide whether to proceed next year or not. If the oil price is $120/bbl. next year, the cash flows will be 1,200,000 bbl. x ($120 - $50) = $840 million. If the oil price is $80/bbl. next year, the cash flows will be 1,200,000 bbl. x ($80 - $50) = $360 million. The expected future cash flows if we postpone the project for one year are therefore:

Expected future cash flows = 0.5 x $840 million + 0.5 x $360 million = $600 million

Discounting these cash flows back to the present value using the risk-free rate of 10%, we get:

Present value of expected future cash flows = $600 million / (1 + 0.1) = $545.45 million

If we exercise the option to proceed with the project this year, the cash flows will be $60 million + 1,200,000 bbl. x ($100 - $50) = $120 million. Discounting these cash flows back to the present value using the risk-free rate of 10%, we get:

Present value of cash flows if we proceed this year = $120 million / (1 + 0.1) = $109.09 million

The value of the real option to postpone the project for one year is therefore:

Value of the real option = Present value of expected future cash flows - Present value of cash flows if we proceed this year
= $545.45 million - $109.09 million
= $436.36 million

Therefore, the best choice is C.