OpenSeas, Inc. is evaluating the purchase of a new cruise ship. The ship would cost $$505$ million now, and would operate for $20$ years. OpenSeas expects annual cash flows from operating the ship to be $$71\mathrm{.}5$ million $($at the end of each year, starting at the end of the $1$st year$)$ and its cost of capital is $12\mathrm{.}1\%.$

a$.$ Prepare an NPV profile of the purchase using discount rates of $2\%.$