$($Real options and capital budgeting$)$ You have come up with a great idea for a Tex$-$Mex$-$Thai fusion restaurant. After doing a financial analysis of this venture, you estimate that the initial outlay will be $$5\mathrm{.}8$ million. You also estimate that there is a $50$ percent chance that this new restaurant will be well received and will produce annual cash flows of $$760,000$ per year forever $($a perpetuity$),$ while there is a $50$ percent chance of it producing a cash flow of only $$220,000$ per year forever $($a perpetuity$)$ if it isn't received well.

a$.$ What is the NPV of the restaurant if the required rate of return you use to discount the project cash flows is $12$ percent?

b$.$ What are the real options that this analysis may be ignoring?

c$.$ Explain why the project may be worthwhile even though you have just estimated that its NPV is negative?

a$.$ Assume the required rate of return you use to discount the project cash flows is $12\%.$ What is the NPV of the restaurant if things go well?

& $($Round to the nearest dollar.$)$