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 $13 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $6.11 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 $14 million. Moreover, if it waits 2 years, then there is a 90% chance that the net cash flows would be $6.89 million a year for 4 years and a 10% chance that they would be $3.9 million a year for 4 years. Assume all cash flows are discounted at 11%.

If the company chooses to drill today, what is the project's net present value? A negative value should be entered with a negative sign. Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. 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?

Answer 1

To solve this problem, we will make use of the following formula:

NPV=−CF₀+CF₁ / (1+r) +CF₂ / (1+r)^2....CF_n(1+r)ⁿ

Project cost $13 million, Discount rate =11%

NPV=−13,000,000+6,110,000/ (1+0.11)+6,110,000(1+0.11)²+6,110,000(1+0.11)³+6,110,000/ (1+0.11)⁴

= 5,955,943.16

To calculate the NPV of Option 2, two steps are required. First, calculate the NPV of the project. This provides the NPV in 2 years' time. Then, discount the NPV an additional 2 years to today's date in order to provide a direct comparison with the NPV calculated above.

Cashflow=(0.9)*($6,890,000)+(0.1)*($3,900,000) =6,591,000

NPV= =−$14,000,000+6,591,000/ (1+0.11)+ 6,591,000 (1+0.11)²+6,591,000 (1+0.11)³+6,591,000/ (1+0.11)⁴    = 6,448,219.54

Further discounting 2 years, the NPV of Option 2 today is:

NPV= 6,448,219.54 / (1+0.11)²

= 5,233,519.63

Option 1 has the higher NPV and Karns Oil should drill today.