Question

Investment Timing Option: Decision-Tree Analysis

The Karns Oil Company is deciding whether to drill for oil on a tract of land that the company owns. The company estimates the project would cost $8 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $4 million a year at the end of each of the next 4 years. Although the company is fairly confident about its cash flow forecast, in 2 years it will have more information about the local geology and about the price of oil. Karns estimates that if it waits 2 years then the project would cost $9 million. Moreover, if it waits 2 years, then there is a 90% chance that the net cash flows would be $4.2 million a year for 4 years and a 10% chance that they would be $2.2 million a year for 4 years. Assume all cash flows are discounted at 9%.

If the company chooses to drill today, what is the project's net present value? Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $1.23 million should be entered as 1.23, not 1,230,000. Round your answer to two decimal places.
$ million

Using decision-tree analysis, does it make sense to wait 2 years before deciding whether to drill?
-Select-Yes, it makes sense to wait two years to drill.No, it makes sense to drill today.Item 2

Answer 1

The net present value (NPV) of drilling today is $12.877 million. Waiting 2 years would result in an expected NPV of $8.39 million. Comparing the two, drilling today has a higher NPV, indicating it is the better financial option. Therefore, it does not make sense to wait 2 years before deciding whether to drill.

Step-by-step explanation:

In order to determine whether it makes sense to wait 2 years before deciding whether to drill, we need to calculate the net present value (NPV) of the project both if it is drilled today and if the company waits 2 years. To calculate the NPV for drilling today, we discount the cash flows of $4 million a year for 4 years at a 9% interest rate. This can be done using the formula: NPV = CF1 / (1 + r)1 + CF2 / (1 + r)2 + CF3 / (1 + r)3 + CF4 / (1 + r)4 - Initial Cost, where CFi is the cash flow in year i and r is the discount rate. Plugging in the values, we get NPV = 4 / (1 + 0.09)1 + 4 / (1 + 0.09)2 + 4 / (1 + 0.09)3 + 4 / (1 + 0.09)4 - 8 = 12.877. Therefore, the NPV of drilling today is $12.877 million.

To calculate the NPV for waiting 2 years, we need to take into account the different cash flow scenarios. There is a 90% chance of having cash flows of $4.2 million a year for 4 years, and a 10% chance of having cash flows of $2.2 million a year for 4 years. We can calculate the NPV for both scenarios and then take the expected value.

For the 90% probability scenario, the NPV can be calculated similarly to the drilling today scenario, with the only difference being that the initial cost is $9 million instead of $8 million. So, NPV = 4.2 / (1 + 0.09)1 + 4.2 / (1 + 0.09)2 + 4.2 / (1 + 0.09)3 + 4.2 / (1 + 0.09)4 - 9 = 9.189.

For the 10% probability scenario, the NPV is calculated the same way but with cash flows of $2.2 million and an initial cost of $9 million. So, NPV = 2.2 / (1 + 0.09)1 + 2.2 / (1 + 0.09)2 + 2.2 / (1 + 0.09)3 + 2.2 / (1 + 0.09)4 - 9 = 0.197.

To calculate the expected NPV, we multiply the NPV of each scenario by their respective probabilities and sum them up. Expected NPV = 0.9 * 9.189 + 0.1 * 0.197 = 8.39. Therefore, the expected NPV of waiting 2 years is $8.39 million.

Comparing the NPV of drilling today (12.877) with the expected NPV of waiting 2 years (8.39), we can see that drilling today has a higher NPV. This suggests that drilling today is the better option from a financial perspective. Therefore, it does not make sense to wait 2 years before deciding whether to drill.