Investment Timing Option: Option Analysis

AIII nuters is interested in developing a new hotel in Seoul. The company estimates that the hotel would require an

initial investment of $$20$ million. Kim expects the hotel will produce positive cash flows of $$3$ million a year at the end

of each of the next $20$ years. The project's cost of capital is $13\%.$

Kim expects the cash flows to be $$3$ million a year, but it recognizes that the cash flows could actually be much

or lower, depending on whether the Korean government imposes a large hotel tax. One year from now, Kim will know

whether the tax will be imposed. There is a $50\%$ chance that the tax will be imposed, in which case the yearly cash

flows will be only $$2\mathrm{.}2$ million. At the same time, there is a $50\%$ chance that the tax will not be imposed, in which

case the yearly cash flows will be $$3\mathrm{.}8$ million. Kim is deciding whether to proceed with the hotel today or to wait a

year to find out whether the tax will be imposed. If Kim waits a year, the initial investment will remain at $$20$ million.

Assume that all cash flows are discounted at $13\%.$ Use the Black$-$Scholes model to estimate the value of the option.

Assume that the variance of the project's rate of return is $0\mathrm{.}0585$ and that the risk$-$free rate is $7\%.$ Do not round

intermediate calculations. Enter your answer in millions.

$

million