Answer the problem based on the framework of Modigliani and Miller Propositions. Assume that a company has earnings before interest and taxes $($EBIT$)$ of $$50,000,000$ every year forever. The firm also has perpetual bonds with the market value of $$100,000,000.$ The before$-$tax cost of debt is $8$ percent. The firm's unlevered cost of capital is $15$ percent. The tax rate is $25$ percent.

a$)$ Find the value of the levered firm $($value of the firm with debt$).$

b$)$ Find the value of equity.

c$)$ Find the firm's cost of equity $($i$.$e$.,$ required return on equity$).$

d$)$ Find the firm's weighted average cost of capital.