Singh Development Co$.$ is deciding whether to proceed with Project $x.$ The after$-$tax cost would be $$8$ million in Year $0.$ There is a $50\%$ chance that $x$ would be hugely successful and would generate annual after$-$tax cash flows of $$6$ million per year during Years $1,2,$ and $3.$ However, there is a $50\%$ chance that $x$ would be less successful and would generate aftertax cash flows of only $$1$ million per year for the $3$ years. If Project $x$ is hugely successful, it would open the door to another investment, Project $Y,$ which would require an after$-$tax outlay of $$9$ million at the end of Year $2.$ Project $Y$ would then be sold to another company netting $$18$ million after taxes at the end of Year $3.$ Singh's WACC is $10\%.$

a$.$ If the company does not consider real options, what is Project X$\text{'}$s expected NPV$?$ Enter your answers in millions. For example, an answer of $$10,550,000$ should be entered as $10\mathrm{.}55.$ Negative value, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to three decimal places.

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b$.$ What is X$\text{'}$s expected NPV with the growth option? Enter your answers in millions. For example, an answer of $$10,550,000$ should be entered as $10\mathrm{.}55.$ Negative value, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to three decimal places.

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c$.$ What is the value of the growth option? Enter your answers in millions. For example, an answer of $$10,550,000$ should be entered as $10\mathrm{.}55.$ Negative value, if any, should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to three decimal places.

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