A company faces the following investment alternatives:

$\backslash$table$[[$Project$,$Capital Investment,Cash Flows from Investment$],[$I$,$$$7$ million,$$1\mathrm{.}2$ million per year in perpetuity$],[$II$,$$$12$ million,$$1\mathrm{.}5$ million per year in perpetuity$],[$III$,$$$16$ million,$$2\mathrm{.}2$ million per year in perpetuity$],[$IV$,$$$10$ million,$$1\mathrm{.}4$ million per year in perpetuity$],[$V$,$$$11$ million,$$1\mathrm{.}6$ million per year in perpetuity$]]$

If the company's budget is $$30$ million, use the profitability index to determine the best combination of investments, given a cost of capital of $5\%.(4$ marks$)$