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
 With leverage it is 552 + 400 = 952 > 812
Interest Tax Shield
Hence, the gain from leverage is 952-812 = 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:
VL=VU+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  (rf  D) / rf = C  D
Note: the same is true if debt is risky and is fairly
priced.
Modigliani-Miller Proposition II with
taxes
rE = rU + (rU - rD)(1 - C)(D/E)
Proof:
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From MM Proposition I with taxes: VL ≡ E + D = VU + CD
The expected per period cash flow can be written both as DrD +
ErE and VUrU + CDrD
Thus, DrD + ErE = VUrU + CDrD
And, hence, rE = (VU/E)rU - (1 - C)(D/E)rD
Using that VU = E + D - CD, we obtain the result
The same is true for beta:
βE = βU + (βU - βD)(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 - CrD = 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 rE = rU + (rU - rD)(1 - C)(D/E),
rWACC = rU - CrU(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:
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VU = 20 mln  $15 = $300 mln
PV(interest tax shield) = CD = 35%  $100
mln = $35 mln
VL = VU + CD = $335 mln
E = VL – 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
The share repurchase:
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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 13.33 mln shares. Since E
= $235 mln, the stock price after the repurchase
would be 235/13.33 = $17.625 > $15  nobody
would sell for $15
No arbitrage pricing:
(20 mln – $100 mln/price)  price = $235 mln
 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).
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?
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Consider a firm with risk free debt D which generates
X (EBIT) in t=0,1,2,...
corporate tax rate: C
personal tax rate on debt: 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-rDD)] + (1-pD)rDD, which can be
rewritten as (1-pE)(1-C)X + [(1-pD) - (1-pE)(1-C)]rDD
Discounting now the stream of [(1-pD) - (1-pE)(1-C)]rDD
at (1-pD)rD (assuming perpetuity) we get the total tax
advantage (tax shield) of debt:
[1- (1-pE)(1-C)/(1-pD)]rDD
MM Proposition I becomes:
VL = VU + [1- (1-pE)(1-C)/(1-pD)]rDD
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