$$OpenSeas$,$ Inc. is evaluating the purchase of a new cruise ship. The ship will cost $$503$ million and will operate for $2020$ years. OpenSeas expects annual cash flows from operating the ship to be $$68\mathrm{.}8$ million and its cost of capital is $11\mathrm{.}7\%11\mathrm{.}7\%.$

a$.$ Prepare an NPV profile of the purchase.

b$.$ Identify the IRR on the graph.

c$.$ Should OpenSeas go ahead with the$$ purchase?

d$.$ How far off could$$ OpenSeas's cost of capital estimate be before your purchase decision would$$ change?