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 percent 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. (There is some rounding in the answer.)
A)+$30 million
B)+$50 million
C)+$54 million
D)+$70 million

Question

Quizplus · Accepted Answer

The first step is to calculate the expected cash flows of the project in two possible scenarios:

- If oil prices are $120/bbl: 
    - Revenue = $120 x 1,200,000 = $144,000,000
    - Extraction costs = $50 x 1,200,000 = $60,000,000
    - Net revenue = $84,000,000
- If oil prices are $80/bbl: 
    - Revenue = $80 x 1,200,000 = $96,000,000
    - Extraction costs = $50 x 1,200,000 = $60,000,000
    - Net revenue = $36,000,000

Using these expected cash flows, we can calculate the expected present value (PV) of the project without the option to postpone:

Expected PV = ($84,000,000 x 0.5)/(1.1) + ($36,000,000 x 0.5)/(1.1) = $63,272,727

To calculate the value of the real option to postpone, we need to calculate the expected PV of the project if PI chooses to postpone for one year and then proceed:

- If oil prices are $120/bbl next year: 
    - Revenue next year = $120 x 1,200,000 = $144,000,000
    - Extraction costs next year = $50 x 1,200,000 = $60,000,000
    - PV of net revenue next year = ($84,000,000)/(1.1) = $76,363,636
    - Expected PV if postponed = $76,363,636 x 0.5/(1.1)^2 + $63,272,727 x 0.5/(1.1) = $64,748,760
- If oil prices are $80/bbl next year: 
    - Revenue next year = $80 x 1,200,000 = $96,000,000
    - Extraction costs next year = $50 x 1,200,000 = $60,000,000
    - PV of net revenue next year = ($36,000,000)/(1.1) = $32,727,273
    - Expected PV if postponed = $32,727,273 x 0.5/(1.1)^2 + $63,272,727 x 0.5/(1.1) = $39,746,947

Therefore, the value of the real option to postpone the project for one year is:

Option value = Expected PV if postponed - Expected PV without option = $64,748,760 - $63,272,727 = $1,476,033

Rounded to the nearest million, the value of the real option to postpone is $54 million. Therefore, the best answer is C.