$5.$ FIN$222$ Ltd carries $$20$ million in debt. The market value of debt matches its book value of $20$ million. The firm expects to generate $15$ million per year in free cash flows after corporate taxes, into perpetuity, with no growth expected. The expected dividend payable to shareholders is $$13\mathrm{.}6$ million per year, into perpetuity. The cost of debt is $10\%$ before tax and the cost of equity to the firm is $12\%.$ Corporate tax rate is $30\%.$ Assume that all of its shareholders can fully utilise the franking credits.

a$.$ Assume a classical tax system and calculate the market value of equity.

b$.$ Assume a classical tax system and calculate the value of the firm.

c$.$ Assume an imputation tax system and calculate the market value of equity.

d$.$ Assume an imputation tax system and calculate the WACC.