The Pinkerton Publishing Company is considering two mutually exclusive expansion plans. Plan A calls for the expenditure of $$50$ million on a large$-$scale, integrated plant that will provide an expected cash flow stream of $$8$ million per year for $20$ years. Plan B calls for the expenditure of $$15$ million to build a somewhat less efficient, more labor$-$intensive plant that has an expected cash flow stream of $$3\mathrm{.}4$ million per year for $20$ years. The firm's cost of capital is $10\%.$

a$.$ Calculate each projects NPV and IRR.

B$.$ Graph NPV profiles for plan A$,$ Plan B

C$.$ Find the cross$-$over rate

Show your work