Trade-Off Theory

EXERCISE 01

Yoda is an all-equity firm worth €80,000. It raises permanent debt of €60,000. Corporate tax is 35%; the transaction creates a 20% probability of distress costing €10,000. Treat the stated expected distress cost as a present value.

A.Calculate levered firm value.

A.

V_L=V_U+T_cD-PV(E[\mathrm{distress\ costs}])

V_L=80{,}000+0.35(60{,}000)-0.20(10{,}000)

€99,000.

Trade-Off Theory

EXERCISE 02

Dempsey’s equity market value is €18,500 and debt €52,500. Debt cost is 6%. Expected distress probability is 25% and distress cost €20,000. Use the 35% corporate tax rate specified in the accompanying source calculation and treat expected distress costs as present values.

A.Calculate the value of the firm without debt.

A.

V_U=E+D-T_cD+PV(E[\mathrm{distress\ costs}])

V_U=18500+52500-0.35(52500)+0.25(20000)

€57,625.

Trade-Off Theory

EXERCISE 03

A.What determines the optimal level of debt under the trade-off theory? Should a firm with low distress risk necessarily borrow less?

A.

V_L=V_U+PV(TS)-PV(\mathrm{distress\ costs})

The optimum balances the marginal tax benefit of additional debt against the marginal expected distress and other financing costs. Holding operating cash flows and valuation assumptions fixed, firm value is highest and WACC is lowest at that optimum. Lower expected distress costs normally permit more debt, not less. Beyond the optimum, additional borrowing destroys value; a tax shield is not an unconditional reason to increase leverage.