You have been asked to value Oneida Steel, a midsize steel company. The firm reported $$80$ million in net income, $$50$ million in capital expenditures, and $$20$ million in depreciation in the just$-$completed financial year. The firm reported that its noncash working capital increased by $$20$ million during the year and the total debt outstanding increased by $$10$ million during the year. The book value of equity at Oneida Steel at the beginning of the last financial year was $$400$ million. The cost of equity is $10\%.$

a$.$ Estimate the equity reinvestment rate, return on equity, and expected growth rate for Oneida Steel. $($You can assume that the firm will continue to maintain the same debt ratio that it used last year to finance its reinvestment needs.$)$

b$.$ If this growth rate is expected to last five years and then drop to a $4\%$ stable growth rate after that and the return on equity after year $5$ is expected to be $12\%,$ estimate the value of equity today, using projected free cash flows to equity.

a$.NI=80,$CapEx$=50,$Dep$=20,$ Change in $WC=20,$ Debt increase by $10,$ Book Value of Equity $=400,$COE$=10\%$

b$.$ Equity Reinvestment Rate after year $5=\frac{g}{R}OE=4\frac{\%}{12}\%=33\mathrm{.}33\%$

$NI$ in year $6={128\mathrm{.}84}^{**}(1+4\%)=133\mathrm{.}99$

Terminal value in year $5=\frac{89\mathrm{.}33}{10\%-4\%}=1488\mathrm{.}83$

Value $=40+40+40+40+40+\frac{1488\mathrm{.}83}{(1+10\%{)}^{{?}^{{?}^{?}}}}5=1124\mathrm{.}45$

In the answers above, how were the NI$,$ FCFE, and PV calculated in b$?$

In the answers above, how was $$1124\mathrm{.}45$ reached from the formula in for "Value" of b$?$