06.01.2021
Chapter 15
Debt and Taxes
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
15-2
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06.01.2021
15.1 The Interest Tax Deduction
•
Consider Safeway, Inc. which had earnings before interest and taxes
(EBIT) of approximately $1.85 billion , and interest expenses of about $350
million. Safeway’s marginal corporate tax rate was 35%.
Safeway’s net income was lower with leverage than it would have been
without leverage.
Safeway’s debt obligations reduced the value of its equity. But the total
amount available to all investors was higher with leverage.
Where does the additional $123 million come from?
15-3
INCOME
EXPENSES
EARNINGS BEFORE
INTEREST AND TAXES
INTEREST PAYMENTS
INCOME BEFORE TAXES
TAX
DIVIDENDS
NET
INCOME
RETAINED PROFIT
15-4
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06.01.2021
15.1 The Interest Tax Deduction
(cont'd)
• In Safeway’s case, the gain is equal to the
reduction in taxes with leverage: $648
million − $525 million = $123 million.
• Note that the interest payments provided a
tax savings of 35% × $350 million = $123
million.
• Interest Tax Shield
– The reduction in taxes paid due to the tax
deductibility of interest
Interest Tax Shield  Corporate Tax Rate  Interest Payments
15-5
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.
15-6
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06.01.2021
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
15-7
The Interest Tax Shield and Firm
Value
• The cash flows a levered firm pays to ALL
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 
15-8
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06.01.2021
15.2 Valuing the Interest Tax Shield
• 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)
MM Proposition I without taxes:
In a perfect capital market, the total value of a
firm is equal to the market value of the total cash
flows generated by its assets and is not affected
by its choice of capital structure (levered or
unlevered equity)
15-9
Valuing the Interest Tax Shield
(cont'd)
• When a firm uses debt, the interest tax shield
provides a corporate tax benefit each year.
• This benefit is computed as the present value
of the stream of future interest tax shields
the firm will receive.
15-10
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06.01.2021
Textbook Example 15.2
Hint: find the annual interest tax shield and value it as a
annuity
15-11
Impact of taxes on WACC
• In the case of debt, the return paid to the
debt holders is not the same as the cost to
the firm. How could this be?
15-12
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06.01.2021
Impact of taxes on WACC
• Suppose a firm with a 35% tax rate borrows
$100,000 at 10% interest per year
• Then its net cost at the end of the year is calculated
as follows
• The effective cost of the debt—the firm’s net cost of
interest on the debt after taxes—is only
$6500/$100,000 = 6.50% of the loan amount,
rather than the full 10% interest
15-13
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
Reduction Due
to Interest Tax Shield
15-15
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06.01.2021
Problem 15.11
Rumolt Motors has 30 million shares outstanding with
a price of $15 per share. In addition, Rumolt has
issued bonds with a total current market value of
$150 million. Suppose Rumolt’s equity cost of capital
is 10%, and its debt cost of capital is 5%.
a. What is Rumolt’s pretax weighted average cost of
capital?
b. If Rumolt’s corporate tax rate is 35%, what is its
after-tax weighted average cost of capital?
rwacc 
E
D
D
rE 
rD 
rD c
E  D
E  D
E  D
Pretax WACC
Reduction Due
to Interest Tax Shield
15-16
Valuing the Interest Tax Shield
(cont'd)
• The value of interest tax shield depends on
how the firm’s debt and interest payments
will vary over time:
– Permanent debt
– Target (fixed) debt-equity-ratio
15-17
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06.01.2021
A. The Interest Tax Shield with
Permanent Debt
• Typically, the level of future interest
payments is uncertain due to
• the amount of debt outstanding
• the interest rate on that debt
• the risk of the firm.
– For simplicity, we will consider the special case
in which the above variables are kept constant.
15-18
The Interest Tax Shield
with Permanent Debt (cont'd)
• Suppose :
– a firm borrows debt D and keeps the debt permanent
– the firm’s marginal tax rate is c
– 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.
C
P
V
(
C
i
n
p
e
r
p
e
t
u
i
t
y
)

r
PV (Interest Tax Shield) 
 c  Interest
rf
 c  D

 c  (rf  D)
rf
15-19
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06.01.2021
The Interest Tax Shield
with Permanent Debt (cont'd)
• What if debt is risky and interest rate is not fixed ?
• 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)
• 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
15-20
B. The Interest Tax Shield
with a Target Debt-Equity Ratio
• 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.
• 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.
15-21
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06.01.2021
Unlevered cost of capital
– Even though the company may actually have debt, the
company’s unlevered cost of capital still matters
- If the unlevered cost of capital is found to be 10% and a
company has debt at a cost of just 5% then its actual cost of
capital (WACC) will be lower than the 10% unlevered cost.
Remember that the after-tax cost of debt is lower than the
pre-tax cost of debt, and the WACC is lower than the
unlevered cost of capital
- This unlevered cost is still informative, but if the company fails
to achieve the 10% unlevered returns that investors in this
market require, then investor capital may move to alternative
investments. This will lead to a fall in the company’s stock
price.
- The firm’s unlevered cost of capital equals its pretax WACC
because it represents investors’ required return for holding the
15-22
entire firm (equity and debt)
Textbook Example 15.3
Hint: Compute the value of Western Lumber as a
constant growth perpetuity
- for unlevered value use pretax WACC as r
- for levered value use WACC as r
- Interest tax shield = VL-VU
15-23
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06.01.2021
Summary Point
• 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
With Permanent Debt :
• Interest tax shield c × D
With a Target Debt-Equity Ratio :
• Interest tax shield = VL-VU
15-24
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
15-25
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06.01.2021
15.3 Recapitalizing to Capture
the Tax Shield
• when a firm uses debt to repurchase
outstanding shares and captures the
benefit of tax shield
15-26
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 to use the
borrowed funds to repurchase outstanding
shares.
15-27
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06.01.2021
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) = c∙D = 35% × $100
million = $35 million
15-28
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
– 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.
15-29
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06.01.2021
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
• 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
• The total gain to shareholders is $35 million.
– $2.625/share × 13.33 million shares = $35 million
15-30
The Share Repurchase
If the shares are worth $17.625/share after
the repurchase,
why would
• Assume Midco repurchases
its shares
atshareholders
the current price of
their shares to Midco at $15/share?
$15/share. The firm willtender
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
• 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
• The total gain to shareholders is $35 million.
– $2.625/share × 13.33 million shares = $35 million
15-31
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06.01.2021
The Share Repurchase (cont'd)
• 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
• 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 immediately to $16.75 per share.
– $335 million ÷ 20 million shares = $16.75 per share
• 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.
15-32
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 = $35 million
• When securities are fairly priced, the
original shareholders of a firm capture the
full benefit of the interest tax shield from
an increase in leverage.
15-33
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06.01.2021
Analyzing the Recap:
The Market Value Balance Sheet
• In the presence of corporate taxes, we
must include the interest tax shield as one
of the firm’s assets.
15-34
Table 15.2 Market Value Balance Sheet for
the Steps in Midco’s Leveraged
Recapitalization
Original MVBS
After Debt issuance
Assets
Assets
Cash
Cash
100
Original Assets
300
Original Assets
300
Total Assets
300
Total Assets
400
Liabilities
Liabilities
Debt
Debt
100
Equity
300
Equity
300
Total Liab.
300
Total Liab.
400
Shares outstanding
(M)
20
Shares outstanding
(M)
20
Price per share ($)
15.00
Price per share ($)
15.00
it is true
only in a
perfect
capital
market
15-35
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06.01.2021
Table 15.2 Market Value Balance Sheet for the Steps
in Midco’s Leveraged Recapitalization
Original MVBS
Recap Announced
Debt issuance
Share repurchase
Assets
Assets
Assets
Assets
Cash
Cash
100
Cash
Original Assets
300
Original Assets
300
Original Assets
300
Interest tax
shield
35
Int. tax shield
35
Int. tax shield
35
Total Assets
335
Total Assets
435
Total Assets
335
Cash
Original Assets
Total Assets
300
300
Liabilities
Liabilities
Debt
Debt
Liabilities
Liabilities
Debt
100
Debt
100
Equity
300
Equity
335
Equity
335
Equity
235
Total Liab.
300
Total Liab.
335
Total Liab.
435
Total Liab.
335
Shares
outstanding (M)
20
Shares
outstanding (M)
20
Shares
outstanding (M)
20
Shares
outstanding (M)
14.03
Price per share
($)
15.00
Price per share
($)
16.75
Price per share
($)
16.75
Price per share
($)
16.75
15-36
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
15-37
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06.01.2021
15.4 Personal Taxes
• The cash flows to investors are typically
taxed twice:
– first at the corporate level
– investors are taxed again when they receive
their interest or dividend payment.
 Equity investors also must pay taxes on
dividends and capital gains.
15-38
Including Personal Taxes
in the Interest Tax Shield
• The amount of money an investor will pay
for a security depends on 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.
15-39
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06.01.2021
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.
15-40
Figure 15.3 After-Tax Investor Cash
Flows Resulting from $1 in EBIT
15-41
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06.01.2021
Table 15.3 Top Federal Tax Rates in
the United States, 1971–2012
15-42
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 after-tax basis,
where:
– Effective Tax Advantage of Debt
(1   i )  (1   c ) (1   e )
(1   c ) (1   e )
 
 1 
(1   i )
(1   i )
– 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
15-43
than i), then * is less than c.
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06.01.2021
Valuing the Interest Tax Shield
with Personal Taxes
• Without personal taxes and with permanent debt the value of the
firm with leverage is
VL = VU + cD
• 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.
15-44
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.
15-45
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06.01.2021
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.
15-46
Determining the Actual Tax
Advantage of Debt (cont'd)
A. 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.
15-47
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06.01.2021
Determining the Actual Tax
Advantage of Debt (cont'd)
B. 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.
15-48
Determining the Actual Tax
Advantage of Debt (cont'd)
C. It was also assumed 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.
15-49
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06.01.2021
Determining the Actual Tax
Advantage of Debt (cont'd)
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.
15-50
Determining the Actual Tax
Advantage of Debt (cont'd)
E. 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.
15-51
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06.01.2021
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.
15-52
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
15-53
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06.01.2021
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.
– 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%.
15-54
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.
15-55
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06.01.2021
Figure 15.7
Debt-toValue Ratio
[D / (E +
D)] for
Select
Industries
Source: Capital IQ, 2012
15-56
Limits to the Tax Benefit of Debt
• Level of earnings
• Growth rate
15-57
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06.01.2021
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.
15-58
Table 15.4 Tax Savings with Different
Amounts of Leverage
?
?
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
15-59
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06.01.2021
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.
15-62
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.
– 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.
15-63
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06.01.2021
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
15-64
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.
15-65
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06.01.2021
Other Tax Shields
• There are numerous provisions in the tax
laws for deductions and tax credits, such
as depreciation, investment tax credits,
carry-forwards 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.
15-66
• 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 that our analysis of the interest tax shield would
predict.
15-67
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06.01.2021
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 *.
15-68
Table 15.5 International Leverage and
Tax Rates (1990)
15-69
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06.01.2021
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.
15-70
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.
15-71
34