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.

Answer 1

Option 1 (start project now):

Option 1:
Initial investment (II)	(80,00,000.00)
Annual cash flow (CF)	4,000,0000.00
PV of CF	1,26,79,461.79
NPV (II + PV of CF)	46,79,461.79

Option 2 (start project 2 years from now):

Formula	Option 2:
	Initial investment (II)	(90,00,000.00)
	Annual cash flow (with 90% prob.)	42,00,000.00
	PV of annual cash flow (pv1)	1,33,13,434.87
90%*pv1	Prob. Weight PV (PV1)	1,19,82,091.39
	Annual cash flow (with 10% prob.)	22,00,000.00
	PV of annual cash flow (pv2)	69,73,703.98
10%*pv2	Prob. Weight PV (PV2)	6,97,370.40
(II+PV1+PV2)	NPV	36,79,461.785

For the Black-Scholes Model:

Spot price = NPV of choice 1 = 4,679,461.785

Strike price = NPV of choice 2 = 3,679,461.785

Time to expiry = 2 years (the time between the two options)

Variance = 0.111 or 11.1%, so volatility (or standard deviation) = 0.111^0.5 = 33.32%

Risk-free rate = 8%

Using a Black-Scholes calculator, the value of the option to wait is: $1,739,328.91 or  $1.739 million.