$(1.)$You are evaluating a $4-$year investment opportunity in a new ice$-$skating rink in the Bishop Arts neighborhood. The purchase price is $$8\mathrm{.}4$M$.$ Shipping & installation costs are $$600$K$.$ The capi$-$talized value of the asset $($i$.$e$.,$ its beginning book value$)$ will be depreciated down to an end$-$of$-$life book value of zero, which is the same as the anticipated selling price. The ice rink is ex$-$pected to provide cash sales of $$14\mathrm{.}1$M per year, and will require cash expenditures of $$9\mathrm{.}3$M each year. Also, at t$=0,$ working capital will rise by $$420$K; at termination, this change will all be reversed. The relevant marginal tax rate is $30\%.$ The appropriate discount rate is $8\%.$ Your task is to construct a worksheet, which shows the relevant cash flows, as well as the calculations of the cash flows for all relevant points of time in your investment horizon. Then, you should calculate NPV$.$

$(2.)$Re$-$do the above problem with an anticipated selling price of $$1\mathrm{.}63$M $($instead of $$0).$ The asset$$s net book value is still depreciated down to $$0.$

$(3.)$Re$-$do the Take$-2$ problem with a desired ending book value of $$1$M $($instead of zero$).$

$(4.)$Re$-$do the Take$-2$ problem with a desired ending book value of $$2$M $($instead of zero$).$