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.