We have seen that MM1 with taxes and bankruptcy costs is written

S + B = S0 + T S P VBC ,

where S is the levered firms value of equity, B is the levered firms value of debt, S0 is the unlevered firms value, T S is the levered firms tax shields, and P VBC is the levered firms present value of expected bankruptcy costs.

The cost of levered equity is rS, the cost of debt is rB, and the cost of unlevered equity is r0. Assume that expected bankruptcy costs are discounted at the unlevered cost of equity. Cash-flows are not necessarily perpetual!

(5 points) Assuming that firms never default, provide a formula for the cost of levered equity rS. The formula has to depend on: S0, S, B, TS, rB, and r0 only. Hint: Use the fact that the expected return on a portfolio P invested in J securities is: rP = x1r1 + x2r2+,...,+xJrJ, where r1,r2,r3,... are the expected returns of each security and x1, x2, x3, . . . the weights/fractions of the portfolio invested in each security.