Capital Structure. Effect of Corporate Taxes So far capital structure was irrelevant. What if we introduces corporate taxes? Corporate taxes are paid after interest Hence, under corporate taxes debt financing has an advantage (the more debt the firm has the greater unterest it pays  the lower taxable part of income (EBT) is

The Interest Tax Deduction Safeway’s Income with and without Leverage, 2005 ($ million) Net income is lower in the levered firm, however total amount available to all investors is higher! Without leverage it is 812 Without leverage it is 812 With leverage it is = 952 > 812 With leverage it is = 952 > 812

Interest Tax Shield Hence, the gain from leverage is = 140 =  C  Interest  C  Interest is called interest tax shield. This is the difference in cash available for all investors The following is true: CF to investors with leverage = Cash flow to investors without leverage + interest tax shield Hence: PV (CF to investors with leverage) = PV (Cash flow to investors without leverage) + PV (interest tax shield), that is…

Modigliani-Miller Proposition I with corporate taxes The total value of the levered firm = the value of the firm without leverage + the present value of the interest tax shield: V L =V U +PV(Interest tax shield)

Cash flows of levered and unlevered firm By increasing the cash flows paid to debt holders through interest payments, a firm reduces the amount paid in taxes. The increase in total cash flows paid to investors is the interest tax shield. (Figure assumes a 40% marginal corporate tax rate.)

How to compute PV(interest tax shield)? Example: valuing interest tax shield without risk

The interest tax shield with permanent debt Suppose a firm borrows D and keeps it permanently, paying the same annual interest each year, i.e. perpetual consol bond (you may also think of a short debt which is rolled over). Interest is rf (assume risk-free debt) PV(Interest tax shield) =  C  (r f  D) / r f =  C  D Note: the same is true if debt is risky and is fairly priced.

Modigliani-Miller Proposition II with taxes r E = r U + (r U - r D )(1 -  C )(D/E) Proof: From MM Proposition I with taxes: V L ≡ E + D = V U +  C D From MM Proposition I with taxes: V L ≡ E + D = V U +  C D The expected per period cash flow can be written both as Dr D + Er E and V U r U +  C Dr D The expected per period cash flow can be written both as Dr D + Er E and V U r U +  C Dr D Thus, Dr D + Er E = V U r U +  C Dr D Thus, Dr D + Er E = V U r U +  C Dr D And, hence, r E = (V U /E)r U - (1 -  C )(D/E)r D And, hence, r E = (V U /E)r U - (1 -  C )(D/E)r D Using that V U = E + D -  C D, we obtain the result Using that V U = E + D -  C D, we obtain the result The same is true for beta: β E = β U + (β U - β D )(1 -  C )(D/E)

Weighted Average Cost of Capital With Taxes Suppose a firm with tax rate  C borrows D at interest rate r per year. Then its net annual cost of debt service is: rD -  C rD = r(1 -  C )D Hence, the effective after-tax borrowing rate is r(1 -  C ) WACC:

Weighted Average Cost of Capital With Taxes WACC Remember: WACC is the cost of capital for FCF generated by assets, calculated for unlevered firm. All effect of leverage is in WACC, not in FCF

In contrast to the no taxes case, leverage reduces WACC now: Using r E = r U + (r U - r D )(1 -  C )(D/E), r WACC = r U -  C r U (D/E)/(1+(D/E)) – decreases in D/E

Using WACC to value the Interest Tax Shield with a Target Debt-Equity Ratio

Recapitalizing to Capture the Benefits of the Tax Shield Midco industries has 20 mln shares outstanding traded at $15 per share and no debt Consistently stable earnings tax rate = 35% Recap plan: borrow $100 mln and use the money to repurchase shares What’s going to happen with the stock price?

Tax consequences: V U = 20 mln  $15 = $300 mln V U = 20 mln  $15 = $300 mln PV(interest tax shield) =  C D = 35%  $100 mln = $35 mln PV(interest tax shield) =  C D = 35%  $100 mln = $35 mln V L = V U +  C D = $335 mln V L = V U +  C D = $335 mln E = V L – D = $235 mln E = V L – D = $235 mln In total shareholders will receive full $335 mln = E + $100 mln in cash for sold shares. Hence, they will receive a gain of $35 mln – the full value of the interest tax shield In total shareholders will receive full $335 mln = E + $100 mln in cash for sold shares. Hence, they will receive a gain of $35 mln – the full value of the interest tax shield

The share repurchase: The price before announcement is $15, but the firm won’t be able to repurchase for such price. Why? The price before announcement is $15, but the firm won’t be able to repurchase for such price. Why? Because if it does it will buy 100 mln / 15 = 6.67 mln shares, and the rest will be mln shares. Since E = $235 mln, the stock price after the repurchase would be 235/13.33 = $ > $15  nobody would sell for $15 Because if it does it will buy 100 mln / 15 = 6.67 mln shares, and the rest will be mln shares. Since E = $235 mln, the stock price after the repurchase would be 235/13.33 = $ > $15  nobody would sell for $15 No arbitrage pricing: No arbitrage pricing: (20 mln – $100 mln/price)  price = $235 mln  price = $16.75  price = $16.75 The company can offer more than $16.75, but then everybody wants to sell and rationing is needed (to avoid discrimination shares can be bough from everybody on a pro rata basis). The company can offer more than $16.75, but then everybody wants to sell and rationing is needed (to avoid discrimination shares can be bough from everybody on a pro rata basis).

Market Value Balance Sheet for the Steps in Midco’s Leveraged Recapitalization

Introducing personal taxes So far, with only corporate taxes debt has clear advantage over equity How are previous results affected by tax advantage of equity at personal level? Consider a firm with risk free debt D which generates X (EBIT) in t=0,1,2,... Consider a firm with risk free debt D which generates X (EBIT) in t=0,1,2,... corporate tax rate:  C corporate tax rate:  C personal tax rate on debt:  pD personal tax rate on debt:  pD personal tax rate on equity (dividend + capital gains):  pE <  pD personal tax rate on equity (dividend + capital gains):  pE <  pD

Each period, the cash flow after corporate and personal taxes is [(1-  pE )(1-  C )(X-r D D)] + (1-  pD )r D D, which can be rewritten as (1-  pE )(1-  C )X + [(1-  pD ) - (1-  pE )(1-  C )]r D D Discounting now the stream of [(1-  pD ) - (1-  pE )(1-  C )]r D D at (1-  pD )r D (assuming perpetuity) we get the total tax advantage (tax shield) of debt: [1- (1-  pE )(1-  C )/(1-  pD )]r D D MM Proposition I becomes: V L = V U + [1- (1-  pE )(1-  C )/(1-  pD )]r D D Depending on the relationship between (1-  pE )(1-  C ) and (1-  pD ), either debt or equity will be the preferred sourse of financing. Hence, introducing personal taxes can explain why equity is used