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 $10\%.$

i$.$ Calculate each project$$s NPV and IRR.

ii$.$ Set up a Project $\backslash$Delta by showing the cash flows $($in a table$)$ that will exist if the firm goes with the large plant rather than the smaller plant. What are the NPV and the IRR for this Project $\backslash$Delta $?$

iii. Graph the NPV profiles for Plan A$,$ Plan B$,$ and Project $\backslash$Delta $.$

iv$.$ Give a logical explanation, based on reinvestment rates and opportunity costs, as to why the NPV method is better than the IRR method when the firm$$s cost of capital is constant at some value such as $10\%$