Texas Wildcatters Inc. (TWI) is in the business of finding and developing oil properties, and then selling the successful ones to major oil refining companies. TWI 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, TWI 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 Scenario 14-1. In the previous problem you were asked to find the expected NPV of a project TWI is considering. Use the same data to calculate the project's coefficient of variation. (Hint: Use the expected NPV as found in the previous problem.)
Answer

5.87

6.52

7.25

7.97

8.77

6.52

To calculate the project's coefficient of variation, we need to know the expected NPV (Net Present Value) of the project. The expected NPV can be calculated by multiplying each outcome by its corresponding probability, and then summing them up.

Let's calculate the expected NPV using the given data:

1. Feasibility Study at t = 0: Cost = -$400 (negative cash outflow)
Probability of good potential: 100% (no chance of abandonment)
Expected NPV at t = 0: $400 * 1 = $400

2. Exploratory Wells at t = 1: Cost = -$1,000 (negative cash outflow)
Probability of good potential: 80% (further work will be done)
Probability of abandonment: 20% (project will be abandoned)
Expected NPV at t = 1: (-$1,000 * 0.8) + ($0 * 0.2) = -$800

3. Accurate Estimate at t = 2: Cost = -$10,000 (negative cash outflow)
Probability of very good results: 60%
Probability of abandonment: 40%
Expected NPV at t = 2: (-$10,000 * 0.6) + ($0 * 0.4) = -$6,000

4. Full Drilling Program at t = 3:
Probability of finding a lot of oil: 50%, Cash inflow = $25,000
Probability of finding less oil: 50%, Cash inflow = $10,000
Expected NPV at t = 3: ($25,000 * 0.5) + ($10,000 * 0.5) = $17,500

Now, let's calculate the expected NPV of the project by summing up the values at each time period:

Expected NPV = $400 + -$800 + -$6,000 + $17,500 = $11,100

To calculate the coefficient of variation, we need to know the standard deviation of the project's cash flows. We can calculate it using the formula:

Standard Deviation = √[∑(Probability * (Value - Expected Value)^2)]

Let's calculate the standard deviation:

1. Feasibility Study at t = 0:
Probability: 100%
Value: $400
Standard Deviation = √[(1 * ($400 - $11,100)^2)] = $10,700

2. Exploratory Wells at t = 1:
Probability of good potential: 80%
Probability of abandonment: 20%
Values: -$800 (for good potential) and $0 (for abandonment)
Standard Deviation = √[(0.8 * (-$800 - $11,100)^2) + (0.2 * ($0 - $11,100)^2)] = $10,427

3. Accurate Estimate at t = 2:
Probability of very good results: 60%
Probability of abandonment: 40%
Values: -$6,000 (for very good results) and $0 (for abandonment)
Standard Deviation = √[(0.6 * (-$6,000 - $11,100)^2) + (0.4 * ($0 - $11,100)^2)] = $9,161

4. Full Drilling Program at t = 3:
Probability of finding a lot of oil: 50%
Probability of finding less oil: 50%
Values: $17,500 (for a lot of oil) and $17,500 (for less oil)
Standard Deviation = √[(0.5 * ($17,500 - $11,100)^2) + (0.5 * ($17,500 - $11,100)^2)] = $3,718

Now, we can calculate the coefficient of variation using the formula:

Coefficient of Variation = (Standard Deviation / Expected NPV) * 100

Coefficient of Variation = ($3,718 / $11,100) * 100 = 33.51

Therefore, the coefficient of variation of the project is approximately 33.51.