Question

Investment Timing Option: Option 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 10%. Use the Black-Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is 0.111 and that the risk-free rate is 8%. Do not round intermediate calculations. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55. Round your answer to three decimal places.

$ ???  million

Answer 1

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Answer:

Black-Scholes Model:

Spot Price = Option 1 = $4.68

Strike Price = Option 2 = $3.04

Time to Expiration = 2 years between Option 1 and Option 2

Variance of the project's rate of return = 11.10% (Volatility)

Risk-free Rate of Interest = 8%

Value of the Option = $2.09 million (From Black-Scholes calculator)