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) Assume that: 1) the corporate tax rate is zero, 2) firms stop their business in one year, 3) earnings before interest and taxes in one year are expected to be worth EBIT, 4) the probability that the levered firm defaults in one year is p, 5) bankruptcy costs are worth BC, 6) face value of debt is F, and 7) coupon rate is also rB. Provide a formula for the cost of levered equity rS. The formula has to depend on: S, EBIT, p, BC, F, rB, and r0 only.