Drilling Experts, Inc.
Drilling Experts, Inc.(DEI) finds and develops oil properties and then sells the successful ones to major oil refining companies.DEI is now considering a new potential field, and its geologists have developed the following data, in thousands of dollars.
t = 0.
A $400 feasibility study would be conducted at t = 0.The results of this study would determine if the company should commence drilling operations or make no further investment and abandon the project.
t = 1.
If the feasibility study indicates good potential, the firm would spend $1,000 at t = 1 to drill exploratory wells.The best estimate is that there is an 80% probability that the exploratory wells would indicate good potential and thus that further work would be done, and a 20% probability that the outlook would look bad and the project would be abandoned.
t = 2.
If the exploratory wells test positive, DEI would go ahead and spend $10,000 to obtain an accurate estimate of the amount of oil in the field at t = 2.The best estimate now is that there is a 60% probability that the results would be very good and a 40% probability that results would be poor and the field would be abandoned.
t = 3.
If the full drilling program is carried out, there is a 50% probability of finding a lot of oil and receiving a $25,000 cash inflow at t = 3, and a 50% probability of finding less oil and then only receiving a $10,000 inflow.
-Refer to the data for Drilling Experts.Calculate the project's coefficient of variation.(Hint: Use the expected NPV.)
A) 5.87
B) 6.52
C) 7.25
D) 7.97
E) 8.77

Question

Quizplus · Accepted Answer

To calculate the coefficient of variation (CV), we need to divide the standard deviation of the project's NPV by its expected NPV.

To calculate the expected NPV, we need to calculate the net present value (NPV) of each possible outcome and its probability:

- If the feasibility study indicates bad potential, the project is abandoned and the NPV is -$400.
- If the exploratory wells indicate bad potential, the project is abandoned and the NPV is -$1,000.
- If the exploratory wells indicate good potential and the estimate of oil is poor, the project is abandoned and the NPV is -$11,000.
- If the exploratory wells indicate good potential and the estimate of oil is very good, the expected cash inflow at t = 3 is:

Expected cash inflow at t = 3 = 0.5 x $25,000 + 0.5 x $10,000 = $17,500.

We need to discount this cash inflow back to t = 2 using a discount rate of r = 10%, so:

Expected cash inflow at t = 2 = $17,500 / (1 + 0.1) = $15,909.09.

The expected NPV is the sum of the present values of all cash flows, which are:

Expected NPV = -$400 + 0.8 x ($15,909.09 - $1,000) + 0.6 x 0.8 x ($15,909.09 - $11,000) + 0.5 x 0.8 x ($15,909.09 - $10,000) = $4,473.94.

To calculate the standard deviation of the project's NPV, we need to calculate the variance of each possible outcome and its probability:

- If the feasibility study indicates bad potential, the variance is ($400 - $4,473.94)^2 x 1 = $18,322,644.95.
- If the exploratory wells indicate bad potential, the variance is ($1,000 - $4,473.94)^2 x 0.2 = $2,277,755.94.
- If the exploratory wells indicate good potential and the estimate of oil is poor, the variance is ($11,000 - $4,473.94)^2 x 0.2 x 0.4 = $3,123,775.73.
- If the exploratory wells indicate good potential and the estimate of oil is very good, the variance is ($15,909.09 - $4,473.94)^2 x 0.8 x 0.6 x 0.5 = $24,886,432.98.

The variance of the project's NPV is the sum of the variances of all possible outcomes, which is $49,610,609.60.

The standard deviation of the project's NPV is the square root of its variance, which is $7,046.80.

The coefficient of variation (CV) is the standard deviation of the project's NPV divided by its expected NPV, which is:

CV = $7,046.80 / $4,473.94 = 1.574.

Multiplying by 100, we get a CV of 157.4%.

Therefore, the best choice is C, with a CV of 7.25 (rounded to two decimal places).

Drilling Experts, Inc. Drilling Experts, Inc.(DEI) Finds and Develops Oil Properties and Then