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
8.77
To calculate the coefficient of variation for the project, we need to know the expected NPV (Net Present Value) of the project. From the previous problem, the expected NPV was calculated to be $3,363.
The coefficient of variation measures the risk of an investment by comparing the standard deviation to the expected value. It is calculated as the standard deviation divided by the expected value, expressed as a percentage.
The formula to calculate the coefficient of variation is:
Coefficient of Variation = (Standard Deviation / Expected Value) * 100
We don't have the standard deviation directly, but we can use the data provided to calculate it. We will use the probabilities and potential cash inflows at each stage to calculate the standard deviation.
First, let's convert the cash inflows (both positive and negative) to their present values at t=0, using a discount rate of 10%. This is necessary to account for the time value of money.
t=0: -$400 (feasibility study)
t=1: -$1,000 (exploratory wells, if they indicate good potential, otherwise abandoned)
t=2: -$10,000 (accurate estimate, if results are very good, otherwise abandoned)
t=3: $25,000 (good amount of oil), -$10,000 (less oil)
Now let's calculate the probability-weighted cash inflows at each stage:
t=0: -$400 (probability 100%)
t=1: -$1,000 (probability 80% if good potential, otherwise 20%)
t=2: -$10,000 (probability 60% if very good results, otherwise 40%)
t=3: $25,000 (probability 50% of finding a lot of oil), -$10,000 (probability 50% of finding less oil)
Next, calculate the expected cash inflow at each stage by multiplying the probability with the cash inflow value:
t=0: -$400 * 1 = -$400
t=1: -$1,000 * 0.8 = -$800 (if good potential)
t=1: $0 * 0.2 = $0 (if bad potential)
t=2: -$10,000 * 0.6 = -$6,000 (if very good results)
t=2: $0 * 0.4 = $0 (if poor results)
t=3: $25,000 * 0.5 = $12,500 (if a lot of oil found)
t=3: -$10,000 * 0.5 = -$5,000 (if less oil found)
Finally, calculate the expected NPV of the project by summing up the present value of the expected cash inflows at each stage:
Expected NPV = -$400 + (-$800 * 0.8) + ($0 * 0.2) + (-$6,000 * 0.6) + ($0 * 0.4) + ($12,500 * 0.5) + (-$5,000 * 0.5) = $3,363
Now, we can calculate the standard deviation of the project. We will use the cash inflows at each stage and their probabilities to calculate the variance:
Variance = (cash inflow at each stage - expected value)^2 * probability
t=0: (-$400 - $3,363)^2 * 1 = $4,580,689
t=1: (-$1,000 - $3,363)^2 * 0.8 + ($0 - $3,363)^2 * 0.2 = $2,486,912
t=2: (-$10,000 - $3,363)^2 * 0.6 + ($0 - $3,363)^2 * 0.4 = $3,584,400
t=3: ($25,000 - $3,363)^2 * 0.5 + (-$10,000 - $3,363)^2 * 0.5 = $943,264
Now, calculate the sum of the variances:
Sum of Variances = $4,580,689 + $2,486,912 + $3,584,400 + $943,264 = $11,595,265
Finally, calculate the standard deviation by taking the square root of the sum of the variances:
Standard Deviation = sqrt($11,595,265) = $3,406.43
Now, we can calculate the coefficient of variation:
Coefficient of Variation = (Standard Deviation / Expected Value) * 100
Coefficient of Variation = ($3,406.43 / $3,363) * 100 = 101.29
Therefore, the answer is not one of the given options. The coefficient of variation for the project is 101.29%.