Question II: Credit Scoring $(20$ points$)$ You decide that the most important factors in determining the probability of default for a potential borrower are its Deb$($t$)/($E$)$quity Ratio, Profit Margin, Current Ratio, and Pric$($e$)/($B$)$ook Ratio. Using this you estimate the following linear probability model of default: PD$\_($i$)=\mathrm{.}75+\mathrm{.}25(($D$)/($E$))+2($ Profit Margin $)+\mathrm{.}15($ Current Ratio $)-\mathrm{.}3(($P$)/($B$))$ a$.$ Calculate the probability of default using the estimated model, given a company with the following characteristics $(7$ points$)$: Liabilities $=250$ M $50$ M Current Liabilities Long$-$term debt $=200$M Assets $=400$M $100$ M current assets Profit Margin $=5\mathrm{.}75\%$ EBIT of $$17$ Million Sales of $$132$ Million The borrower's stock trades at $$15$ per share, and there are $13,333,333$ shares outstanding. Retained earnings of $$5$ Million b$.$ Calculate the non$-$linear estimate of the borrower's probability of default. $(5$ points$)$ c$.$ Given the same firm, calculate Altman's Z$.(5$ points$)$ d$.$ Should the bank lend to this borrower? Why or why not? $(3$ points$)$