Real Options: Decision$-$Tree Analysis

Utah Enterprises is considering buying a vacant lot that sells for $$1\mathrm{.}2$ million. If the property is purchased, the company's plan is to spend another $$5$ million today $($t $=0)$ to build a hotel on the property. The after$-$tax cash flows from the hotel will depend critically on whether the state imposes a tourism tax in this year's legislative session. If the tax is imposed, the hotel is expected to produce after$-$tax cash inflows of $$600,000$ at the end of each of the next $15$ years, versus $$1,200,000$ if the tax is not imposed. The project has a $14\%$ cost of capital. Assume at the outset that the company does not have the option to delay the project. Use decision$-$tree analysis to answer the following questions.

What is the project's expected NPV if the tax is imposed? 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. Negative value, if any, should be indicated by a minus sign.

$

million

What is the project's expected NPV if the tax is not imposed? 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. Negative value, if any, should be indicated by a minus sign.

$

million

Given that there is a $50\%$ chance that the tax will be imposed, what is the project's expected NPV if the company proceed with it today? 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. Negative value, if any, should be indicated by a minus sign.

$

million

Although the company does not have an option to delay construction, it does have the option to abandon the project if the tax is imposed. If it abandons the project, it would complete the sale of the property $1$ year from now at an expected price of $$6$ million. If the company decides to abandon the project, it won't receive any cash inflows from it except for the selling price. If all cash flows are discounted at $14\%,$ would the existence of this abandonment option affect the company's decision to proceed with the project today?

$-$Select$-$ Yes or No

Assume there is no option to abandon or delay the project but that the company has an option to purchase an adjacent property in $1$ year at a price of $$1\mathrm{.}6$ million. If the tourism tax is imposed, then the present value of future development opportunities for this property $($as of t $=1)$ is only $$500,000($so it wouldn't make sense to purchase the property for $$1\mathrm{.}6$ million$).$ However, if the tax is not imposed, then the present value of the future opportunities from developing the property would be $$4$ million $($as of t $=1).$ Thus, under this scenario it would make sense to purchase the property for $$1\mathrm{.}6$ million. Given that cash flows are discounted at $14\%$ and that there's a $50-50$ chance the tax will be imposed, how much would the company pay today for the option to purchase this property $1$ year from now for $$1\mathrm{.}6$ million? 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. Negative value, if any, should be indicated by a minus sign.

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Million