This problem concerns some extensions of the M-M theory. The M-M theorem assumes that the firm has only two classes of securities, perpetual debt and equity. Suppose that the firm has issued a third class of securities - preferred stock - and that y% of preferred dividends may be written off as an expense (0≤y≤1). Assume that the firm has preferred stock of face value FP, with a preferred dividend rate of rp. Preferred dividends and debt are riskless (use the risk free rate, rf). Assume that only corporate tax, τC, exists. No personal taxes. Also other assumptions of M-M hold. Rate of return of an unlevered company in risk-class k is ρU.

a) What is the appropriate expression for the value of the levered firm?

b) What is the appropriate expression for the after-tax cost of capital?