The Karns Oil Company is deciding whether to drill for oil on a tract of land the company owns. The

company estimates the project would cost $$8$ million today. Karns estimates that, once drilled, the oil

will generate positive 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 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 $$4\mathrm{.}2$ million a year for $4$ years and a $10\%$ chance that they would be $$2\mathrm{.}2$ million a year for $4$ years.

Assume all cash flows are discounted at $10\%.$

a$.$ If the company chooses to drill today, what is the project's net present value?

b$.$ Use the Black$-$Scholes model to estimate the value of the investment timing option. Use the

indirect approach to calculate the project's variance of the rate of return. Assume the risk$-$free

rate is $6\%.$

c$.$ Should Karns implement the project today or should it wait $2$ years?

$C=P**N(d_1)-x{e}^{-r_f^T}T**N(d_2)$

$d_1=\frac{ln(\frac{P}{x})+(r_f+\frac{{}^2}{2})(T)}{\sqrt[\phantom{2}]{{}^2}\sqrt[\phantom{2}]{T}}$

$d_2=d_1-\sqrt[\phantom{2}]{{}^2}\sqrt[\phantom{2}]{T}$

Check answers:

a$.4\mathrm{.}68$

b$.P=10\mathrm{.}48,{}^2=0\mathrm{.}0111,d_1=1\mathrm{.}90,d_2=1\mathrm{.}75,C=2\mathrm{.}52$

The answers must match exactly. And please show handwritten math in how to achieve the correct answers.