Taxes and bankruptcy costs is written: S + B = S0 + TS - PVBC

S = levered firm's value of equity

B = levered firm's value of debt

S0 = unlevered firm's value

TS = levered firm's tax shields

PVBC = levered firm's present value of expected bankruptcy costs

rS = cost of levered equity

rB = cost of debt

r0 = cost of unlevered equity

F = face value of debt

*Assume that expected bankruptcy costs are discounted at the unlevered cost of equity

*Cash-flows are not necessarily perpetual

Question: Assume that:

Firms stop their business in one year

Earnings before interest and taxes in one year are expected to be worth EBIT

The corporate tax rate is Tc

The cash-flow to debt holders in one year is expected to be IP + F, where IP is the expected interest payment

The probability that the levered firm defaults in one year is p

Bankruptcy costs are worth BC

Provide a formula for the cost of levered equity rS. The formula has to depend on: S, EBIT, Tc, IP, F, p, BC, rB, and r0 only.