$(15$ Percent$)$ Suppose you have developed the following information for a potential investment: current market value is $$1,200,000$; anticipated loan to value ratio is $\mathrm{.}80$ with $2$ points; and predicated cash flows of ATCF$1=$ $$38,560,$ ATCF$2=$$$41,780,$ ATCF$3=$ $$37,210,$ ATCF$4=$$$39,127,$ and ATER$4=$ $$191,730.$ Further, assume the investor's minimum required after$-$tax rate of return on equity is $12\%.$

a$.$ What is the internal rate of return on this potential investment?

b$.$ What is the profitability index on this investment?