Chapter 15
Debt and Taxes
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Chapter Outline
15.1 The Interest Tax Deduction
15.2 Valuing the Interest Tax Shield
15.3 Recapitalizing to Capture the Tax
Shield
15.4 Personal Taxes
15.5 Optimal Capital Structure with Taxes
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15-2
Learning Objectives
1. Explain the effect of interest payments on cash
flows to investors.
2. Calculate the interest tax shield, given the
corporate tax rate and interest payments.
3. Calculate the value of a levered firm.
4. Calculate the weighted average cost of capital
with corporate taxes.
5. Describe the effect of a leveraged
recapitalization on the value of equity.
6. Describe the effect of personal taxes on the
corporate tax benefits of leverage.
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15-3
Learning Objectives (cont'd)
7. Given corporate and personal tax rates on equity
and debt, calculate the tax benefit of debt with
personal taxes.
8. Discuss why the optimal level of leverage from a
tax-saving perspective is the level at which
interest equals EBIT.
9. Describe the relationship between the optimal
fraction of debt and the growth rate of the firm.
10. Assess the apparent under-leveraging of
corporations, both domestically and
internationally.
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15-4
15.1 The Interest Tax Deduction
• Corporations pay taxes on their profits
after interest payments are deducted.
Thus, interest expense reduces the
amount of corporate taxes. This creates an
incentive to use debt.
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15-5
15.1 The Interest Tax Deduction
(cont'd)
• Consider Safeway, Inc. which had earnings
before interest and taxes of approximately
$1.85 billion in 2008, and interest
expenses of about $350 million. Safeway’s
marginal corporate tax rate was 35%.
• As shown on the next slide, Safeway’s net
income in 2008 was lower with leverage
than it would have been without leverage.
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15-6
Table 15.1 Safeway’s Income with and
without Leverage, 2008 ($ millions)
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15-7
15.1 The Interest Tax Deduction
(cont'd)
• Safeway’s debt obligations reduced the
value of its equity. But the total amount
available to all investors was higher with
leverage.
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15-8
15.1 The Interest Tax Deduction
(cont'd)
• Without leverage, Safeway was able to pay
out $1,202 million in total to its investors.
• With leverage, Safeway was able to pay
out $1,325 million in total to its investors.
• Where does the additional $123 million
come from?
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15-9
15.1 The Interest Tax Deduction
(cont'd)
• Interest Tax Shield
– The reduction in taxes paid due to the tax
deductibility of interest
Interest Tax Shield  Corporate Tax Rate  Interest Payments
• In Safeway’s case, the gain is equal to the reduction
in taxes with leverage: $648 million − $525 million =
$123 million. The interest payments provided a tax
savings of 35% × $350 million = $123 million.
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15-10
Textbook Example 15.1
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15-11
Textbook Example 15.1 (cont'd)
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15-12
15.2 Valuing the Interest Tax Shield
• When a firm uses debt, the interest tax
shield provides a corporate tax benefit
each year.
• This benefit is the computed as the
present value of the stream of future
interest tax shields the firm will receive.
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15-13
The Interest Tax Shield and Firm
Value
• The cash flows a levered firm pays to
investors will be higher than they would be
without leverage by the amount of the
interest tax shield.
 Cash Flows to Investors 
 Cash Flows to Investors 




  (Interest Tax Shield)
with Leverage


 without Leverage 
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15-14
Figure 15.1 The Cash Flows of the
Unlevered and Levered Firm
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15-15
The Interest Tax Shield
and Firm Value (cont'd)
• MM Proposition I with Taxes
– The total value of the levered firm exceeds the
value of the firm without leverage due to the
present value of the tax savings from debt.
V
L
 V
U
 PV (Interest Tax Shield)
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15-16
Textbook Example 15.2
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15-17
Textbook Example 15.2 (cont'd)
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15-18
Alternative Example 15.2
• Problem
– Suppose ALCO plans to pay $60 million in interest
each year for the next 8 years, and then repay the
principal of $1 billion in year 8.
– These payments are risk free, and ALCO’s marginal
tax rate will remain 39% throughout this period.
– If the risk-free interest rate is 6%, by how much
does the interest tax shield increase the value of
ALCO?
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15-19
Alternative Example 15.2
• Solution
– The annual interest tax shield is:
• $1 billion × 6% × 39% = $23.4 million for 8 years.
1
1
PV (Interest Tax Shield)  $23.4 million 
(1 
)
8
6%
1.06
 $145.31 million
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15-20
The Interest Tax Shield
with Permanent Debt
• Typically, the level of future interest payments is
uncertain due to changes in the marginal tax
rate, the amount of debt outstanding, the interest
rate on that debt, and the risk of the firm.
– For simplicity, we will consider the special case in
which the above variables are kept constant.
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15-21
The Interest Tax Shield
with Permanent Debt (cont'd)
• Suppose a firm borrows debt D and keeps the
debt permanently. If the firm’s marginal tax rate is
c , and if the debt is riskless with a risk-free
interest rate rf , then the interest tax shield each
year is c × rf × D, and the tax shield can be
valued as a perpetuity.
PV (Interest Tax Shield) 
 c  Interest
rf

 c  (rf  D)
rf
 c  D
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15-22
The Interest Tax Shield
with Permanent Debt (cont'd)
• If the debt is fairly priced, no arbitrage implies
that its market value must equal the present
value of the future interest payments.
Market Value of Debt  D  PV (Future Interest Payments)
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15-23
The Interest Tax Shield
with Permanent Debt (cont'd)
• If the firm’s marginal tax rate is constant, then:
PV (Interest Tax Shield)  PV ( c  Future Interest Payments)
  c  PV (Future Interest Payments)
 c  D
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15-24
The Weighted Average Cost
of Capital with Taxes
• With tax-deductible interest, the effective
after-tax borrowing rate is r(1 − c) and
the weighted average cost of capital
becomes
E
D
rwacc 
rE 
rD (1   c )
E  D
E  D
rwacc
E
D
D

rE 
rD 
rD c
E  D
E  D
E  D
Pretax WACC
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Reduction Due
to Interest Tax Shield
15-25
Figure 15.2 The WACC with and
without Corporate Taxes
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15-26
The Interest Tax Shield
with a Target Debt-Equity Ratio
• When a firm adjusts its leverage to
maintain a target debt-equity ratio, we can
compute its value with leverage, VL, by
discounting its free cash flow using the
weighted average cost of capital.
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15-27
The Interest Tax Shield with a Target
Debt-Equity Ratio (cont'd)
• The value of the interest tax shield can be found
by comparing the value of the levered firm, VL, to
the unlevered value, VU, of the free cash flow
discounted at the firm’s unlevered cost of capital,
the pretax WACC.
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15-28
Textbook Example 15.3
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15-29
Textbook Example 15.3 (cont'd)
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15-30
15.3 Recapitalizing to Capture
the Tax Shield
• Assume that Midco Industries wants to
boost its stock price. The company
currently has 20 million shares outstanding
with a market price of $15 per share and
no debt. Midco has had consistently stable
earnings, and pays a 35% tax rate.
Management plans to borrow $100 million
on a permanent basis and they will use the
borrowed funds to repurchase outstanding
shares.
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15-31
The Tax Benefit
• Without leverage
– VU = (20 million shares) × ($15/share) = $300
million
• If Midco borrows $100 million using
permanent debt, the present value of the
firm’s future tax savings is
– PV(interest tax shield) = cD = 35% × $100
million = $35 million
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15-32
The Tax Benefit (cont'd)
• Thus the total value of the levered firm will
be
– VL = VU + cD = $300 million + $35 million =
$335 million
• Because the value of the debt is $100
million, the value of the equity is
– E = VL − D = $335 million − $100 million =
$235 million
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15-33
The Tax Benefit (cont'd)
• Although the value of the shares
outstanding drops to $235 million,
shareholders will also receive the $100
million that Midco will pay out through the
share repurchase.
• In total, they will receive the full $335
million, a gain of $35 million over the
value of their shares without leverage.
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15-34
The Share Repurchase
• Assume Midco repurchases its shares at
the current price of $15/share. The firm
will repurchase 6.67 million shares.
– $100 million ÷ $15/share = 6.67 million shares
• It will then have 13.33 million shares
outstanding.
– 20 million − 6.67 million = 13.33 million
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15-35
The Share Repurchase (cont'd)
• The total value of equity is $235 million;
therefore the new share price is
$17.625/share.
– $235 million ÷ 13.33 million shares = $17.625
• Shareholders that keep their shares earn a
capital gain of $2.625 per share.
– $17.625 − $15 = $2.625
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15-36
The Share Repurchase (cont'd)
• The total gain to shareholders is $35
million.
– $2.625/share × 13.33 million shares = $35
million
• If the shares are worth $17.625/share
after the repurchase, why would
shareholders tender their shares to Midco
at $15/share?
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15-37
No Arbitrage Pricing
• If investors could buy shares for $15
immediately before the repurchase, and
they could sell these shares immediately
afterward at a higher price, this would
represent an arbitrage opportunity.
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15-38
No Arbitrage Pricing (cont'd)
• Realistically, the value of the Midco’s
equity will rise immediately from $300
million to $335 million after the repurchase
announcement. With 20 million shares
outstanding, the share price will rise to
$16.75 per share.
– $335 million ÷ 20 million shares = $16.75 per
share
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15-39
No Arbitrage Pricing (cont'd)
• With a repurchase price of $16.75, the
shareholders who tender their shares and
the shareholders who hold their shares
both gain $1.75 per share as a result of
the transaction.
– $16.75 − $15 = $1.75
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15-40
No Arbitrage Pricing (cont'd)
• The benefit of the interest tax shield goes
to all 20 million of the original shares
outstanding for a total benefit of $35
million.
– $1.75/share × 20 million shares = $35 million
• When securities are fairly priced, the
original shareholders of a firm capture the
full benefit of the interest tax shield from
an increase in leverage.
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15-41
Textbook Example 15.4
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15-42
Textbook Example 15.4 (cont'd)
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15-43
Alternative Example 15.4
• Problem
– Suppose Midco still chooses to borrow $100
million, but only wishes to repurchase $75
million worth of its shares. What is the lowest
price it could offer and expect shareholders to
tender their shares?
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15-44
Alternative Example 15.4 (cont’d)
• Solution
Shares
Shares
Repurchase
New Share
Repurchased Remaining
Price
Price
(millions) (millions)
PR
$13.50
$13.75
$14.00
$14.25
$14.50
$14.75
$15.00
$15.25
$15.50
$15.75
$16.00
$16.25
$16.50
$16.75
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R = 125/PR N = 20 - R Pn = 235/N
5.56
14.44
$16.27
5.45
14.55
$16.16
5.36
14.64
$16.05
5.26
14.74
$15.95
5.17
14.83
$15.85
5.08
14.92
$15.76
5.00
15.00
$15.67
4.92
15.08
$15.58
$4.84
$15.16
$15.50
4.76
15.24
$15.42
4.69
15.31
$15.35
4.62
15.38
$15.28
4.55
15.45
$15.21
4.48
15.52
$15.14
15-45
Analyzing the Recap:
The Market Value Balance Sheet
• In the presence of corporate taxes, we
must include the interest tax shield as one
of the firm’s assets.
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15-46
Table 15.2 Market Value Balance Sheet for
the Steps in Midco’s Leveraged
Recapitalization
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15-47
15.4 Personal Taxes
• The cash flows to investors are typically
taxed twice. Once at the corporate level
and then investors are taxed again when
they receive their interest or divided
payment.
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15-48
15.4 Personal Taxes (cont'd)
• For individuals:
– Interest payments received from debt are
taxed as income.
– Equity investors also must pay taxes on
dividends and capital gains.
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15-49
Including Personal Taxes
in the Interest Tax Shield
• The amount of money an investor will pay
for a security depends on the the cash
flows the investor will receive after all
taxes have been paid.
• Personal taxes reduce the cash flows to
investors and can offset some of the
corporate tax benefits of leverage.
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15-50
Including Personal Taxes
in the Interest Tax Shield (cont'd)
• The actual interest tax shield depends on
both corporate and personal taxes that are
paid.
• To determine the true tax benefit of
leverage, the combined effect of both
corporate and personal taxes needs to be
evaluated.
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15-51
Figure 15.3 After-Tax Investor Cash
Flows Resulting from $1 in EBIT
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15-52
Table 15.3 Top Federal Tax Rates in
the United States, 1971–2009
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15-53
Including Personal Taxes
in the Interest Tax Shield (cont'd)
• In general, every $1 received after taxes
by debt holders from interest payments
costs equity holders $(1 − *) on an aftertax basis, where:

– Effective Tax Advantage of Debt
(1   i )  (1   c ) (1   e )
(1   c ) (1   e )

 1 
(1   i )
(1   i )
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15-54
Including Personal Taxes
in the Interest Tax Shield (cont'd)
 
(1   i )  (1   c ) (1   e )
(1   c ) (1   e )
 1 
(1   i )
(1   i )
– When there are no personal taxes on debt
income
(i = 0) or when the personal tax rates on debt
and equity income are the same (i = e ), the
formula reduces to * = c.
– When equity income is taxed less heavily (e is
less than i), then * is less than c.
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15-55
Textbook Example 15.5
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15-56
Textbook Example 15.5 (cont'd)
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15-57
Alternative Example 15.5
• Problem
– Given the following tax rates:
Corporate Tax
Rate
Average Personal Tax
Rate on Equity Income
Average Personal
Tax Rate on Interest
Income
1985
46%
35%
50%
1995
35%
34%
28%
2009
35%
15%
35%
Year
– What is the effective tax advantage of debt for
each of the years listed?
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15-58
Alternative Example 15.5
• Solution
(1   c ) (1   e )
  1
(1   i )

(1  .46 ) (1  .35)
 1985  1 
 29.8%
(1  .50 )

(1  .35) (1  .34 )
 1995  1 
 40.4%
(1  .28 )



2009
(1  .35 ) (1  .15 )
 1 
 15.0%
(1  .35 )
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15-59
Figure 15.4 The Effective Tax Advantage
of Debt with and without Personal Taxes,
1971–2009
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15-60
Valuing the Interest Tax Shield
with Personal Taxes
• With personal taxes and permanent debt,
the value of the firm with leverage
becomes
V
L
 V
U
  D

– If * is less than c, the benefit of leverage is
reduced in the presence of personal taxes.
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15-61
Valuing the Interest Tax Shield
with Personal Taxes (cont'd)
• Personal taxes have a similar effect on the
firm’s weighted average cost of capital.
• While we still compute the WACC as
E
D
rwacc 
rE 
rD (1   c )
E  D
E  D
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15-62
Valuing the Interest Tax Shield
with Personal Taxes (cont'd)
• With personal taxes the firm’s equity and
debt costs of capital will adjust to
compensate investors for their respective
tax burdens.
• The net result is that a personal tax
disadvantage for debt causes the WACC to
decline more slowly with leverage than it
otherwise would.
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15-63
Textbook Example 15.6
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15-64
Textbook Example 15.6 (cont'd)
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15-65
Alternative Example 15.6
• Problem
– Estimate the value of Midco if it goes through
with the $100 million recapitalization,
accounting for personal taxes at their 1980
levels.
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15-66
Alternative Example 15.6 (cont’d)
• Solution
– From example 15.5, we know  in 1980 was
8.2%. Given Midco’s current value of VU =$300
millon, VL is estimated as VU +  D = $300
million + 8.2%($100 million) = $308.20. With
20 million original shares outstanding, the
stock price would increase by $8.2 million ÷20
million shares = $0.41 per share.
– In contrast, as shown in Example 15.6 in the
text, at 2009 personal and corporate tax levels,
the stock price would increase by $0.75 per
share.
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15-67
Determining the Actual Tax
Advantage of Debt
• Several assumptions were made in
estimating the effective tax advantage of
debt after taking personal taxes into
account that may need adjustment when
determining the actual tax benefit for a
particular firm or investor.
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15-68
Determining the Actual Tax
Advantage of Debt (cont'd)
• It was assumed that investors paid capital
gains taxes every year.
• However, capital gains taxes are paid only
when the investor sells the stock and
realizes the gain. Deferring the payment of
capital gains taxes lowers the present
value of the taxes, which can be
interpreted as a lower effective capital
gains tax rate.
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15-69
Determining the Actual Tax
Advantage of Debt (cont'd)
• Investors with accrued losses that they
can use to offset gains face a zero
effective capital gains tax rate.
• Thus, investors with longer holding periods
or with accrued losses face a lower tax
rate on equity income, decreasing the
effective tax advantage of debt.
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15-70
Determining the Actual Tax
Advantage of Debt (cont'd)
• It was also assumed that that shareholder
gains from additional earnings were evenly
split between dividends and capital gains.
• For firms with much higher or much lower
payout ratios, however, this average would
not be accurate.
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15-71
Determining the Actual Tax
Advantage of Debt (cont'd)
• In addition, it was assumed that investors
pay the top marginal federal income tax
rates.
• In reality, rates vary for individual
investors, and many investors face lower
rates.
– At lower rates, the effects of personal taxes are
less substantial.
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15-72
Determining the Actual Tax
Advantage of Debt (cont'd)
• Many investors face no personal taxes.
– For example, investments held in retirement
savings accounts or pension funds that are not
subject to taxes.
– For these investors, the effective tax advantage
of debt is the full corporate tax rate.
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15-73
Determining the Actual Tax
Advantage of Debt (cont'd)
• The bottom line:
– Calculating the effective tax advantage of debt
accurately is extremely difficult.
• A firm must consider the tax bracket of its typical
debt holders, and the tax bracket and holding period
of its typical equity holders.
– The tax advantage of debt will vary across
firms and from investor to investor.
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15-74
15.5 Optimal Capital Structure with
Taxes
• Do Firms Prefer Debt?
– When firms raise new capital from investors,
they do so primarily by issuing debt.
– In most years aggregate equity issues are
negative, meaning that on average, firms are
reducing the amount of equity outstanding by
buying shares.
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15-75
Figure 15.5 Net External Financing and Capital
Expenditures by U.S. Corporations, 1975–2008
Source: Federal Reserve, Flow of Funds Accounts of the United States, 2009.
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15-76
15.5 Optimal Capital Structure
with Taxes (cont'd)
• Do Firms Prefer Debt?
– While firms seem to prefer debt when raising
external funds, not all investment is externally
funded.
– Most investment and growth is supported by
internally generated funds.
• Even though firms have not issued new equity, the
market value of equity has risen over time as firms
have grown. For the average firm, the result is that
debt as a fraction of firm value has varied in a range
from 30–45%.
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15-77
Figure 15.6 Debt-to-Value Ratio
[D / (E + D)] of U.S. Firms, 1975–2008
Source: Compustat and Federal Reserve, Flow of Funds Accounts of the
United States, 2009.
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15-78
15.5 Optimal Capital Structure
with Taxes (cont'd)
• Do Firms Prefer Debt?
– The use of debt varies greatly by industry.
– Firms in growth industries like biotechnology or
high technology carry very little debt, while
airlines, automakers, utilities, and financial
firms have high leverage ratios.
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15-79
Figure 15.7
Debt-toValue Ratio
[D / (E +
D)] for
Select
Industries
Source: Capital IQ, 2009.
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15-80
Limits to the Tax Benefit of Debt
• To receive the full tax benefits of leverage,
a firm need not use 100% debt financing,
but the firm does need to have taxable
earnings.
– This constraint may limit the amount of debt
needed as a tax shield.
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15-81
Table 15.4 Tax Savings with Different
Amounts of Leverage
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15-82
Limits to the Tax Benefit of Debt
(cont'd)
• From the previous slide:
– With no leverage, the firm receives no tax
benefit.
– With high leverage, the firm saves $350 in
taxes.
– With excess leverage, the firm has a net
operating loss and there is no increase in the
tax savings.
• Because the firm is already not paying taxes, there
is no immediate tax shield from the excess leverage
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Limits to the Tax Benefit of Debt
(cont'd)
• No corporate tax benefit arises from
incurring interest payments that exceed
EBIT.
• Because interest payments constitute a
tax disadvantage at the investor level,
investors will pay higher personal taxes
with excess leverage, making them worse
off.
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Limits to the Tax Benefit of Debt
(cont'd)
• If the firm is not paying taxes, where c =
0, then the tax disadvantage of excess
leverage is:


ex
(1   e )
e  i
 1 

 0
(1   i )
(1   i )
– Note: *ex is negative because (*e < i).
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Limits to the Tax Benefit of Debt
(cont'd)
• The optimal level of leverage from a tax
saving perspective is the level such that
interest equals EBIT.
– At the optimal level of leverage, the firm
shields all of its taxable income and it does
not have any tax-disadvantaged excess
interest.
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Limits to the Tax Benefit of Debt
(cont'd)
• However, it is unlikely that a firm can
predict its future EBIT (and the optimal
level of debt) precisely.
– If there is uncertainty regarding EBIT, then
there is a risk that interest will exceed EBIT.
As a result, the tax savings for high levels of
interest falls, possibly reducing the optimal
level of the interest payment.
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Figure 15.8 Tax Savings for Different
Levels of Interest
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Limits to the Tax Benefit of Debt
(cont'd)
• In general, as a firm’s interest expense
approaches its expected taxable
earnings, the marginal tax advantage of
debt declines, limiting the amount of debt
the firm should use.
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Growth and Debt
• Growth will affect the optimal leverage
ratio.
– To avoid excess interest, a firm with positive
earnings should have a level of debt such that
interest payments are below its expected
taxable earnings.
Interest  rD  Debt  EBIT or Debt  EBIT / rD
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Growth and Debt (cont'd)
• From a tax perspective, the firm’s optimal
level of debt is proportional to its current
earnings. However, the value of the firm’s
equity will depend on the growth rate of
earnings:
– The higher the growth rate, the higher the
value of equity. As a result, the optimal
proportion of debt in the firm’s capital structure
[D / (E + D)] will be lower, the higher the
firm’s growth rate.
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Other Tax Shields
• There are numerous provisions in the tax
laws for deductions and tax credits, such
as depreciation, investment tax credits,
carryforwards of past operating losses,
etc.
• To the extent that a firm has other tax
shields, its taxable earnings will be
reduced and it will rely less heavily on the
interest tax shield.
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The Low Leverage Puzzle
• The figure on the following slide reveals
two important patterns.
– Firms have used debt to shield a greater
percentage of their earnings from taxes in
more recent years (mirroring the increase in
the effective tax advantage of debt).
– Firms have far less leverage than our analysis
of the interest tax shield would predict.
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Figure 15.9 Interest Payments as a
Percentage of EBIT for S&P 500 Firms, 1975–
2008
Source: Compustat.
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The Low Leverage Puzzle (cont'd)
• Firms worldwide have similar low
proportions of debt financing.
– Although the corporate tax codes are similar
across all countries in terms of the tax
advantage of debt, personal tax rates vary
more significantly, leading to greater variation
in *.
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Table 15.5 International Leverage and
Tax Rates (1990)
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The Low Leverage Puzzle (cont'd)
• It would appear that firms, on average,
are under-leveraged. However, it is hard to
accept that most firms are acting
suboptimally.
– In reality, there is more to the capital structure
story than discussed so far.
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The Low Leverage Puzzle (cont'd)
• A key item missing from the analysis thus
far is that increasing the level of debt
increases the probability of bankruptcy.
• If bankruptcy is costly, these costs might
offset the tax advantages of debt
financing.
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Discussion of Data Case Key Topic
• By how much did Home Depot’s debt/equity ratio
actually change over the last year?
• With the benefit of hindsight, based on what
really happened to the D/E ratio over the last
year, should you have recommended that Home
Depot issue additional debt and repurchase stock?
• Ir.HomeDepot.com
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Chapter Quiz
1. How do corporate taxes impact a firm’s value as
leverage changes?
2. How does leverage affect a firm’s weighted
average cost of capital?
3. How can shareholders benefit form a leveraged
recapitalization when it reduces the total value
of equity?
4. Under current tax law, why is there a personal
tax disadvantage of debt?
5. How does the growth rate of a firm affect the
optimal fraction of debt in the capital structure?
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