OpenSeas, Inc. is evaluating the purchase of a new cruise ship. The ship will cost $$503\mathrm{.}7$ million, and will operate for $20$ years. OpenSeas expects annual cash flows from operating the ship to be $$68\mathrm{.}5$ million and its cost of capital is $11\mathrm{.}49\%.$

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

b$.$ Identify the IRR on the graph.

c$.$ Should OpenSeas proceed with the purchase?

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