Amazing company Ltd$.$ has $8\mathrm{.}2$ million shares of common stock outstanding and $195,000$ semi$-$annual bonds outstanding with a face value of $$1,000$ and a $9\mathrm{.}5\%$ coupon rate. The common stock currently sells for $$208$ per share and has a beta of $1\mathrm{.}02,$ and the bonds have $18$ years to maturity and sell for $91\%$ of face value. The market risk premium is $5\mathrm{.}3\%,$ T$-$bills $($risk$-$free$)$ yield $5\%,$ and the company's tax rate is $38\%.$

a$)$ What is the firm's market value capital structure?

b$)$ Estimate the firm's cost of equity, and after tax cost of debt.

$($c$)$ Estimate the company's total cost of capital.