Investment Timing Option: Option Analysis

Kim Hotels 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 $$3$ million a year, but it recognizes that the cash flows could actually be much higher or lower, depending on whether the Korean government imposes a large hotel tax. One year from now, Kim will know whether the tax will be imposed. There is a $50\%$ chance that the tax will be imposed, in which case the yearly cash flows will be only $$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 $0\mathrm{.}0687$ and that the risk$-$free rate is $8\%.$ Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $$1\mathrm{.}234$ million should be entered as $1\mathrm{.}234,$ not $1,234,000.$ Round your answer to three decimal places.

Use computer software packages, such as Minitab or Excel, to solve this problem.