Capital Structure. Effect of Corporate Capital Structure. Effect of Corporate TaxesTaxes

So far capital structure was irrelevant. What if So far capital structure was irrelevant. What if we introduces corporate taxes?we introduces corporate taxes?

Corporate taxes are paid Corporate taxes are paid afterafter interest interest

Hence, under corporate taxes debt financing has Hence, under corporate taxes debt financing has an advantage (the more debt the firm has the an advantage (the more debt the firm has the greater unterest it pays greater unterest it pays the lower taxable part the lower taxable part of income (EBT) isof income (EBT) is

The Interest Tax DeductionThe Interest Tax Deduction

Safeway’s Income with and without Leverage, 2005 ($ million)

Net income is lower in the levered firm, however total Net income is lower in the levered firm, however total amount available to all investors is higher!amount available to all investors is higher! Without leverage it is 812Without leverage it is 812 With leverage it is 552 + 400 = 952 > 812With leverage it is 552 + 400 = 952 > 812

Interest Tax ShieldInterest Tax Shield

Hence, the gain from leverage is 952-812 = 140 Hence, the gain from leverage is 952-812 = 140 = = C C Interest Interest

C C Interest is called Interest is called interest tax shield. interest tax shield. This is This is the difference in cash available for all investorsthe difference in cash available for all investorsThe following is true:The following is true:CF to investors with leverage = Cash flow to CF to investors with leverage = Cash flow to investors without leverage + interest tax shieldinvestors without leverage + interest tax shieldHence:Hence:PV (CF to investors with leverage) =PV (CF to investors with leverage) =PV (Cash flow to investors without leverage) + PV (Cash flow to investors without leverage) + PV (interest tax shield), that is…PV (interest tax shield), that is…

Modigliani-Miller Proposition I with Modigliani-Miller Proposition I with corporate taxescorporate taxes

The total value of the levered firm = the value of The total value of the levered firm = the value of the firm without leverage + the present value of the firm without leverage + the present value of the interest tax shield:the interest tax shield:

VVLL=V=VUU+PV+PV(Interest tax shield)(Interest tax shield)

Cash flows of levered and unlevered firmCash flows of levered and unlevered firm

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

How to compute PV(interest tax shield)?How to compute PV(interest tax shield)?

Example: valuing interest tax shield without riskExample: valuing interest tax shield without risk

The interest tax shield with The interest tax shield with permanent debtpermanent debt

Suppose a firm borrows D and keeps it Suppose a firm borrows D and keeps it permanently, paying the same annual interest permanently, paying the same annual interest each year, i.e. perpetual consol bond (you may each year, i.e. perpetual consol bond (you may also think of a short debt which is rolled over). also think of a short debt which is rolled over). Interest is rf (assume risk-free debt)Interest is rf (assume risk-free debt)

PV(Interest tax shield) = PV(Interest tax shield) = C C ((rrf f DD) / ) / rrff = = C C DD

Note: the same is true if debt is risky and is fairly Note: the same is true if debt is risky and is fairly priced.priced.

Modigliani-Miller Proposition II with Modigliani-Miller Proposition II with taxestaxes

rrE E = = rrU U + (+ (rrU U - - rrDD)(1 - )(1 - CC)()(DD//EE))

Proof:Proof: From MM Proposition I with taxes: From MM Proposition I with taxes: VVLL

≡ ≡ E E + + D D = = VVUU + + CCDD

The expected per period cash flow can be written both as The expected per period cash flow can be written both as DDrrDD + + EErrEE and and VVUUrrUU

+ + CCDDrrDD

Thus, Thus, DDrrDD + + EErrEE = = VVUUrrUU + + CCDDrrDD

And, hence,And, hence, r rEE = = ((VVUU//EE))rrUU -- (1 - (1 - CC)()(DD//EE))rrDD

Using that Using that VVU U = = E E + + D - D - CCDD, we obtain the result, we obtain the result

The same is true for beta:The same is true for beta:

ββE E = = ββU U + (+ (ββU U - - ββDD)(1 - )(1 - CC)()(DD//EE))

Weighted Average Cost of Capital Weighted Average Cost of Capital With TaxesWith Taxes

Suppose a firm with tax rate Suppose a firm with tax rate CC borrows D borrows D

at interest rate at interest rate rr per year. Then its net per year. Then its net annual cost of debt service is:annual cost of debt service is:

rD - rD - CCrD = rrD = r(1(1 - - CC))DD

Hence, the effective after-tax borrowing Hence, the effective after-tax borrowing rate is rate is rr(1(1 - - CC))

WACC:WACC:

Weighted Average Cost of Capital Weighted Average Cost of Capital With TaxesWith Taxes

WACCWACC

Remember: WACC is the cost of capital Remember: WACC is the cost of capital for FCF generated by assets, calculated for FCF generated by assets, calculated for for unleveredunlevered firm. All effect of leverage is firm. All effect of leverage is in WACC, not in FCFin WACC, not in FCF

In contrast to the no taxes case, leverage In contrast to the no taxes case, leverage reduces WACC now:reduces WACC now:

Using Using rrE E = = rrU U + (+ (rrU U - - rrDD)(1 - )(1 - CC)()(DD//EE),),

rrWACC WACC = r= rUU - - CCrrUU((DD//EE)/(1+()/(1+(DD//EE)) – )) –

decreases in decreases in DD//EE

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

Recapitalizing to Capture the Recapitalizing to Capture the Benefits of the Tax ShieldBenefits of the Tax Shield

Midco industries has 20 mln shares Midco industries has 20 mln shares outstanding traded at $15 per share and outstanding traded at $15 per share and no debtno debtConsistently stable earningsConsistently stable earningstax rate = 35%tax rate = 35%Recap plan: borrow $100 mln and use the Recap plan: borrow $100 mln and use the money to repurchase sharesmoney to repurchase sharesWhat’s going to happen with the stock What’s going to happen with the stock price?price?

Tax consequences:Tax consequences: VVUU = 20 mln = 20 mln $15 = $300 mln $15 = $300 mln PVPV(interest tax shield) = (interest tax shield) = CCD = D = 35% 35% $100 $100

mln = $35 mlnmln = $35 mln VVLL = = VVUU + + CCD = D = $335 mln$335 mln E = E = VVLL – D = $235 mln – D = $235 mln In total shareholders will receive full $335 mln In total shareholders will receive full $335 mln

= = EE + $100 mln in cash for sold shares. + $100 mln in cash for sold shares. Hence, they will receive a gain of $35 mln – Hence, they will receive a gain of $35 mln – the full value of the interest tax shieldthe full value of the interest tax shield

The share repurchase:The share repurchase: The price before announcement is $15, but the firm The price before announcement is $15, but the firm

won’t be able to repurchase for such price. Why?won’t be able to repurchase for such price. Why? Because if it does it will buy 100 mln / 15 = 6.67 mln Because if it does it will buy 100 mln / 15 = 6.67 mln

shares, and the rest will be 13.33 mln shares. Since shares, and the rest will be 13.33 mln shares. Since EE = $235 mln, the stock price after the repurchase = $235 mln, the stock price after the repurchase would be 235/13.33 = $17.625 > $15 would be 235/13.33 = $17.625 > $15 nobody would nobody would sell for $15sell for $15

No arbitrage pricing:No arbitrage pricing:(20 mln – $100 mln/price) (20 mln – $100 mln/price) price = $235 mln price = $235 mln price = $16.75price = $16.75

The company can offer more than $16.75, but then The company can offer more than $16.75, but then everybody wants to sell and rationing is needed (to everybody wants to sell and rationing is needed (to avoid discrimination shares can be bough from avoid discrimination shares can be bough from everybody on a pro rata basis).everybody on a pro rata basis).

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

RecapitalizationRecapitalization

Introducing personal taxesIntroducing personal taxes

So far, with only corporate taxes debt has clear So far, with only corporate taxes debt has clear advantage over equityadvantage over equity

How are previous results affected by tax How are previous results affected by tax advantage of equity at personal level?advantage of equity at personal level? Consider a firm with risk free debt Consider a firm with risk free debt DD which generates which generates

X X (EBIT) in t=0,1,2,...(EBIT) in t=0,1,2,... corporate tax rate: corporate tax rate: CC

personal tax rate on debt: personal tax rate on debt: pDpD

personal tax rate on equity (dividend + capital gains): personal tax rate on equity (dividend + capital gains): pEpE < < pDpD

Each period, the cash flow after corporate and personal Each period, the cash flow after corporate and personal taxes is [(1-taxes is [(1-pEpE)(1-)(1-CC)()(XX--rrDDDD)] + (1-)] + (1-pDpD))rrDDDD, which can be , which can be rewritten as (1-rewritten as (1-pEpE)(1-)(1-CC))XX + [(1- + [(1-pDpD) - (1-) - (1-pEpE)(1-)(1-CC)])]rrDDDD

Discounting now the stream of [(1-Discounting now the stream of [(1-pDpD) - (1-) - (1-pEpE)(1-)(1-CC)])]rrDDDD at at (1-(1-pDpD))rrDD (assuming perpetuity) we get the total tax (assuming perpetuity) we get the total tax advantage (tax shield) of debt:advantage (tax shield) of debt:

[1- (1-[1- (1-pEpE)(1-)(1-CC)/(1-)/(1-pDpD)])]rrDDDD

MM Proposition I becomes:MM Proposition I becomes:

VVLL = = VVUU + [1- (1- + [1- (1-pEpE)(1-)(1-CC)/(1-)/(1-pDpD)])]rrDDDD

Depending on the relationship between (1-Depending on the relationship between (1-pEpE)(1-)(1-CC) ) andand (1-(1-pDpD)), , either debt or equity will be the preferred sourse of either debt or equity will be the preferred sourse of financing. Hence, introducing personal taxes can explain financing. Hence, introducing personal taxes can explain why equity is usedwhy equity is used