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 $4 million today. Karns estimates that, once drilled, the oil will generate positive net cash flows of $2 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 $5 million. Moreover, if it waits 2 years, then there is a 90% chance that the net cash flows would be $2.1 million a year for 4 years and a 10% chance that they would be $1.1 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 5.12% and that the risk-free rate is 7%.

Investing today is a better option because it has a better NPV of $2.3398 million

Explanation:

Given data :

For Today's Investment

Initial capital investment = $4 million

positive cash flow = $2 million

period of cash flow = 4 years

project cost of capital = 10%

To get the value of This option we have to determine the NPV of this option

NPV = PMT *   ----------- (1)

PMT = $2 million

r = 10%

initial cash flow = $4 million

Equation 1 becomes

NPV = (2 * 3.1699 ) - 4

        = $6.3398 - $4 =  $2.3398 million

For later investment ( 2 years )

initial capital investment = $5 million

90% chance of positive cash flow = $2.1 million

10% chance of positive cash flow = $1.1 million

project cost of capital = 10%

NPV value for a cash flow of $1.1 million

NPV = PMT *

PMT = $1.1 million

initial cash flow = $5 million

r = 10%

Hence NPV = ($1.1 * 3.1699 ) - $5 million

                    = $3.48689 - $5 million

                    = - $1.51311  

therefore the present NPV =   - $1.51311 / 1.21 =  -$1.25 million  ( therefore no investment will be made )

NPV value for a cash flow of $2.1 million

NPV = PMT *

PMT = $2.1 million

initial cash flow = $5 million

r = 10%

hence NPV = ($2.1 * 3.1699 ) - $5 million

                   = $6.65679 - $5

                   = $1.65679

therefore the present NPV = $ 1.65679 / 1.21 = $1.369 million

The Expected NPV value of later investment ( after 2 years )

= $0 * 10% + $1.369 * 90%

= $1.2321 million