The Lion$$s Firm is considering buying a vacant lot that is selling for $$1\mathrm{.}5$ million. It will take them two years to permit and construct a large retail center and will cost an additional $$1$ million in permitting and $$2\mathrm{.}5$ million in construction. They anticipate an overall hold of $10$ years including the permitting and construction time. Permitting will occur in year $1$ at which time if the market has shifted, they can abandon the project without incurring the cost to construct but also not gaining any future cash flows. If they do abandon the project, they anticipate being able to sell the land with permits for $$4\mathrm{.}5$ million at the end of year $1.$ Construction will occur in and placed into service by the end of year $2.$ If there is a shift in the market for retail space between purchase and start of operations $($but after permitting$)$ the after$-$tax cash flows would be $$1,980,000$ rather than the strong market of $$3,300,000$ for the remainder of the $10$ years. They anticipate being able to sell the property at the end of the $10-$year hold for an after$-$tax value of $$60,000,000$ if the market is good and $$26,400,000$ if the market is bad. There is $50\%$ chance of a change in market $($at any decision point, aka after permitting, at expansion option and at sale$).$ Finally, assume if there is no option to abandon or delay the project, but that the company has the option to expand the facility at a cost of $$2$ million in year $3.$ If the market is good the net present value of developing this additional property $($as of t$=3)$ is $$4$ million, but if the market is bad then the net present value of development would be $$1$ million $($so it wouldn$$t make sense to expand$).$ The Lion$$s Firm has a discount rate of $12\%.$

Find the value of the real option for both market conditions and state if the project should be accepted.

Find the value of the abandonment option under both market conditions and if they should choose to abandon the project rather than proceed with construction. $($Assume you will only abandon is the market has already shifted at end of permitting$).$

Find the value of the expansion option and the state if the expansion should occur.