$)$ Salvatore Inc. is a motion picture production company. At the end of its most recent financial year, the firm had $ $500$ million in interest bearing debt on its books $($with interest payments of $ $35$ million a year and an average maturity of $8$ years$).$ The firm has a rating of B$+$ and a pre$-$tax cost of debt of $8\%.$ There are $50$ million shares trading at $ $6$ per share and the levered beta for the firm is $2\mathrm{.}25.$ The tax rate is $40\%,$ the risk free rate is $4\%$ and the market risk premium is $4\mathrm{.}82\%.$

a$.$ Estimate the current cost of capital for the firm.

b$.$ Assume now that Salvatore Inc. is able to issue enough stock to retire half of its outstanding debt $($in market value terms$).$ If the stock price does not change after this transaction, estimate the pre$-$tax cost of debt after the transaction.