Global Z Inc. reported net income of $$770$ million in $2023$ after interest expenses of $$320$ million. $($The corporate tax rate was $36\%.)$ It reported depreciation of $$960$ million in that year, and capital spending was $$1\mathrm{.}2$ billion. The firm also had $$4$ billion in debt outstanding on the books, rated AA $($carrying a yield to maturity of $8\%)$ and trading at par $($up from $$3\mathrm{.}8$ billion at the end of $2022).$ The beta of the stock was $1\mathrm{.}05,$ and there were $200$ million shares outstanding $($trading at $$60$ per share$),$ with a book value of $$5$ billion. Company's working capital requirements were negligible. $($The Treasury bond rate was $6\%,$ and the risk premium was $5\%.)$

a$.$ Estimate the free cash flow to the firm in $2023.$

b$.$ Estimate the value of the firm

c$.$ Estimate the value of equity