Kim Hotels is interested in developing a new hotel in Seoul. The company estimates that the hotel would require an initial investment of $$20$ million. Kim expects that the hotel will produce positive cash flows of $$3$ million a year at the end of each of the next $20$ years. The project's cost of capital is $13\%.$

While Kim expects the cash flows to be $$3$ million a year, it recognizes that the cash flows could, in fact, be much higher or lower, depending on whether the Korean government imposes a large hotel tax. One year from now, Kim will know whether the tax will be imposed. There is a $50\%$ chance that the tax will be imposed, in which case the yearly cash flows will be only $$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 $$3\mathrm{.}8$ million. Kim is deciding whether to proceed with the hotel today or to wait $1$ year to find out whether the tax will be imposed. If Kim waits a year, the initial investment will remain at $$20$ million. Assume that all cash flows are discounted at $13\%.$

The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

Open spreadsheet

Use the Black$-$Scholes model to estimate the value of the option. Assume the variance of the project's rate of return is $5\mathrm{.}85\%$ and the risk$-$free rate is $7\%.$ Enter your answer in millions. For example, an answer of $$1\mathrm{.}22$ million should be entered as $1\mathrm{.}22,$ not $1,220,000.$ Do not round intermediate calculations. Round your answer to two decimal places.