Use the following information pertaining to Totem #$16-$#$20.$

You are assessing the optimal capital structure for Totem Holdings, a large publicly traded chemical company with $100$ million shares trading at $$30$ per share and $$1$ billion in debt outstanding. The firm currently has a pre$-$tax cost of debt of $6\%$ and you have correctly estimated the current cost of capital to be $9\%.$ The firm is planning to borrow an additional $$2$ billion $($which will push up the pre$-$tax cost of debt to $7\%)$ and

use the proceeds to buy back $$1$ billion in stock and invest $$1$ billion in its existing business. For simplicity, assume that the debt beta remains to be zero. The firm's tax rate is $40\%,$ the current riskfree rate is $5\%,$ and the market risk premium is $4\%.$Current coat of equity is $10\mathrm{.}8\%($before capital raising$)$

$1.$ Find the unlevered asset beta

$2.$Find the new levered equity beta after the transaction

$3.$ Find the new cost of equity after the transaction

$4$ Find the new WACC after the transaction