Investment Timing Option: Decision$-$Tree Analysis

Kim Hotels is interested in developing a new hotel in Seoul. The company estimates that the hotel would require an initial investment of $$18$ million. Kim expects the hotel will produce positive cash flows of $$3$ million a year at the end of each of the next $20$ years. The project's cost of capital is $13\%.$

a$.$ What is the project's net present value? Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $$1\mathrm{.}23$ million should be entered as $1\mathrm{.}23,$ not $1,230,000.$ Round your answer to two decimal places.

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b$.$ 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{.}1$ 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 $$3\mathrm{.}9$ million. Kim is deciding whether to proceed with the hotel today or to wait a year to find out whether the tax will be imposed. If Kim waits a year, the initial investment will remain at $$18$ million. Assume that all cash flows are discounted at $13\%.$ Use decision$-$tree analysis to determine whether Kim should proceed with the project today or wait a yeat before deciding.

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