Question

(Note: show your work, do not use excel) Real Options and Option to Abandon Problem: An integrated oil company is evaluating the exploration and development of an oil field. Initial investment of $100 mil is needed for start-up costs. After a year of start-up, three levels of oil are expected to be uncovered. There is a 20% chance of getting a high level with expected annual FCFF of $25 mil for 20 years; a 60% chance that annual FCFF will be $15 mil for 20 years; and a 20% chance that the operation will be unsuccessful and produce $-6 mil annual FCFF for 20 years. (Note all the expected FCFFs start from year 2.) Assume the cost of capital is 10%.

A. What is the NPV of the project ignoring any option?

B. If project can be abandoned at the end of the start-up phase after the outcome is revealed, what is the NPV with this abandon option? Assuming the cost of shutting down the operation is $5 million.

C. What is the value of the option?

Answer 1

Case 1:

There is a 20% chance of getting a high level with expected annual FCFF of $25 mil for 20 years;

p1 = 20%; FCFF from year 2 onwards = C = 25; n = 20; r = 10%

PV of FCFF at the end of year 1 = C/r x [1 - (1 + r)-n] = 25/10% x [1 - (1 + 10%)-20] = 212.84

Hence, PV of FCFF today = 212.84 / (1 + r) = 212.84 / (1 + 10%) = 193.49

Hence, NPV1 = - C0 + PV of FCFF today = -100 + 193.49 = $ 93.49 million

Case 2:

A 60% chance that annual FCFF will be $15 mil for 20 years;

p2 = 60%; FCFF from year 2 onwards = C = 15; n = 20; r = 10%

PV of FCFF at the end of year 1 = C/r x [1 - (1 + r)-n] = 15/10% x [1 - (1 + 10%)-20] = 127.70

Hence, PV of FCFF today = 127.70 / (1 + r) = 127.70 / (1 + 10%) = 116.09

Hence, NPV2 = - C0 + PV of FCFF today = -100 + 116.09 = $ 16.09 million

Case 3:

A 20% chance that the operation will be unsuccessful and produce $-6 mil annual FCFF for 20 years.

p3 = 20%; FCFF from year 2 onwards = C = -6; n = 20; r = 10%

PV of FCFF at the end of year 1 = C/r x [1 - (1 + r)-n] = -6/10% x [1 - (1 + 10%)-20] = -51.08

Hence, PV of FCFF today = -51.08 / (1 + r) = -51.08 / (1 + 10%) = -46.44

Hence, NPV2 = - C0 + PV of FCFF today = -100 + (-46.44) = - $ 146.44 million

A. What is the NPV of the project ignoring any option?

NPV = p1 x NPV1 + p2 x NPV2 + p3 x NPV3 = 20% x 93.49 + 60% x 16.09 + 20% x (-146.44) = - $ 0.9331 million (Please note that NPV is negative, there is a negative sign before the figure)

B. If project can be abandoned at the end of the start-up phase after the outcome is revealed, what is the NPV with this abandon option? Assuming the cost of shutting down the operation is $5 million.

NPV in case 3 = NPV3 will now be = -C0 + C/(1 + r) = -100 - 5/(1 + 10%) = - $ 104.55 million

Hence, NPV = p1 x NPV1 + p2 x NPV2 + p3 x NPV3 = 20% x 93.49 + 60% x 16.09 + 20% x (-104.55) = $ 7.4454 million

C. What is the value of the option?

The value of the option = NPV in part B - NPV in part A = 7.4454 - (-0.9331) = $ 8.3784 million