. 29
( 39)


But you shall now use the appropriate tax-adjusted cost of capital for discounting. There is
one tricky issue now: what is the ¬rm™s debt ratio? That is, WACC requires wDT = (1 ’ wEQ )
as an input. In the real world, you could just look up the current ¬rm values, so trust me (and
the Digging-Deeper box below) that the debt is about 35 percent of the ¬rm™s value today. You
know the other two remaining inputs that you need to compute WACC, which are the overall
corporate cost of capital at 30%, and the debt cost of capital at 20%.
You can now compute the ¬rm™s weighted average cost of capital as Return to the main task:
WACC valuation
tax debt c.o.c.

WACC ≈ ’ 40% · 35% · 20% ≈ 27.2%
WACC ≈ E (˜FM ) ’ „ · wDT · E (˜DT )
r r .

’$29 ’$19 +$56 +$46
NPV0 = + + +
(1 + 27.2%) (1 + 27.2%) (1 + 27.2%) (1 + 27.2%)4
2 3
+$36 +$36
+ + ≈ ,
(1 + 27.2%) (1 + 27.2%)6

which is a small 60 cents o¬ the value of the APV formula. Most of the di¬erence comes from
the fact that the fraction of debt in the capital structure is 35% in the ¬rst year, but a di¬erent
proportion of the value in subsequent years. Thus, as we noted on Page 558, WACC cannot
really apply in this case. In our case, this error is modest”and dwarved by errors in what you
have assumed about the tax code and by the uncertainty that such projects would carry in the
real world. Here you are 60 cents o¬”only modest harm done.

Your equity will have payments of $53, $43, $33, and $8 in the ¬nal four years. Let™s
Digging Deeper:
assume for a moment a 35% cost of capital on equity. (We will verify this later.) With a 35% cost-of-equity-capital
assumption, the market value of the equity in year 1 (not year 0!) will be

$53 $43 $33 $8
PVEquity,t=1 ≈ + + + ≈ $58.28 . (22.28)
(1 + 35%) (1 + 35%) (1 + 35%) (1 + 35%)5
2 3 4

The market value of the equity in year 1 will not be the $26 that the equity holders have to put in! The equity can
be sold for more and is therefore worth the higher $58.28. The debt however is priced right: when discounted
appropriately, it is worth $25. So, as a fraction of ¬nancing in the capital structure, equity will constitute

wEQ = ≈ 69% .
$58.28 + $25.00
Now, you know that the debt™s cost of capital is 20%. To have a consistent example in which the ¬rm™s cost of
capital is 30% requires an appropriate rate of return on the equity of around 35% without a tax subsidy:

69% · x + (1 ’ 69%) · 20% ≈ ’ x ≈ 35% .
wEQ · E (˜EQ ) + (1 ’ wDT ) · E (˜DT ) = E (˜FM ) .
r r r

so your assumption of a 35% cost-of-equity capital above was correct. Unfortunately, this 35% is correct only in
the ¬rst year.
¬le=capctaxes.tex: LP
564 Chapter 22. Corporate Taxes and A Tax Advantage of Debt.

Solve Now!
Q 22.9 Construct a pro forma for the following ¬rm: A 3-year project costs $150 (year 1), and
produces $70 in year 1, $60 in year 2, and $55 in year 3. Depreciation, both real and ¬nancial,
is 3 years. Projects of this riskiness (and with this term structure of project payo¬s) have an 18%
cost of capital. The marginal corporate income tax rate is 40%.

(a) Assume that the ¬rm is 100% equity ¬nanced. Construct the pro forma, and compute
expected project cash ¬‚ows.

(b) Compute the Project IRR.

(c) Compute the project NPV.

(d) Assume that this ¬rm expects to receive an extra bonus of $2 in years 2 and 3 from a
benevolent donor. What would be the project™s cash ¬‚ows and IRR now?

For the remaining questions, assume that the ¬rm instead has a capital structure ¬nancing $50
in debt raised in year 1 at a 10% (expected) interest rate. There is no interest paid in year 1, just
in years 2 and 3. The principal is repaid in year 3.

(e) Construct the pro forma now. What is the IRR of this project?

(f) From the pro forma, what is the NPV of the debt-¬nanced project?

(g) Compute the NPV via the APV method.

(h) Via the APV method, how much would ¬rm value be if the ¬rm would have taken on not
$50 but $40 in debt (assuming the same interest rate of 10%)?

(i) How much money must the equity provide in year 1? What is the debt ratio of the ¬rm?
Does it stay constant over time? Is this a good candidate ¬rm for the WACC method?
¬le=capctaxes.tex: RP
Section 22·6. The Tax Subsidy on PepsiCo™s Financial Statement.

22·6. The Tax Subsidy on PepsiCo™s Financial Statement

Table 22.4. PepsiCo™s Income Statement (Revisited).

Income Statement December
= Revenue 25,479
COGS 10,226
+ SG&A 11,104
+ Depreciation and Amortization 147
+ Unusual Expenses 184
= Total Operating Expenses
“ 21,661
Operating Income
= 3,818
+ Net Interest Income “57
Income Before Tax
= 3,761
“ Income Tax 1,218
Income After Tax
= 2,543
“ Extraordinary Items 0
Net Income
= 2,543

We now want to apply our theoretical knowledge to a practical example”in fact, the example One can infer the tax
subsidy from corporate
that you used in Chapter 9 to illustrate how ¬nancial statements work. Can you infer the tax
¬nancial statements.
subsidy from PepsiCo™s Income Statement? The answer is yes. For convenience, Table 22.4
reproduces PepsiCo™s Income Statement. In 2000, PepsiCo had $3.818 billion in operating
income, but only had to pay income taxes on $3.761 billion. With income taxes of $1.218 billion,
PepsiCo™s average corporate income tax rate was about 32.4%. If PepsiCo had been purely equity
¬nanced, it would have had to pay taxes on its operating income of $3.818 billion, or about
$1.237 billion. Thus, by having $57 million in interest, relative to a hypothetical dividend
payout of $57 million, PepsiCo enjoyed a tax shield in 2000 from its interest payments of

Debt Tax Shield = „ · [Interest Payments]
= 32.4% · $57 million = $19 million .

Note that you did not need to compute E(˜)·DT, because you could read the interest payments
directly o¬ the ¬nancials. Note also that for companies like PepsiCo with high income, the
marginal and the average tax rates are practically the same, so you can assume that PepsiCo
would have had to pay its average tax rate of 32.4% if it had paid out the $57 million interest
in dividends instead. (Finally note that you are also ignoring more complex tax issues, such as
deferred taxes, here.)
Solve Now!
Q 22.10 Compute the tax shield for a company of your choice (or Coca Cola if you have no
¬le=capctaxes.tex: LP
566 Chapter 22. Corporate Taxes and A Tax Advantage of Debt.

22·7. Odds and Ends

You now understand all there is to know about how managers can adjust to the presence of
corporate income taxes. But there are a number of issues that are worth discussing, if only
because you may wonder about them in the future.

22·7.A. Which Valuation Method is Best?

First, you might wonder which of the three valuation method is best: the pro forma, the APV,
None of the method
dominates. or the WACC method. If one were always best, we would not have bothered with the other two,
so each must have advantages and disadvantages.
Of course, the three methods should usually come out if not with the same, then at least with
They may provide
different answers, but very similar results”otherwise, something would be wrong. As the example in Section 22·5
the differences should
showed, if suitably applied, the di¬erences are usually due to “rounding error.” This is espe-
be modest.
cially true if you compare them to the errors that you will inevitably introduce in your simpli-
¬cation of the tax code and your assessment of expected cash ¬‚ows and appropriate costs of
Here is how I see the three methods:

Pro Forma (Flow to Equity) The advantage of the pro forma is that it is lucid and makes it
less likely that you will use an incorrect expected cash ¬‚ow. The disadvantage of the pro
forma is that it requires a lot more e¬ort (you have to construct full ¬nancials!), and that
it does not break out the tax advantage of debt explicitly. This makes it more di¬cult to
think about the role of changes in contemplated capital structure changes.

APV The APV formula makes it relatively easier to determine how an extra dollar of debt in-
creases ¬rm value. When thinking of a speci¬c addition or project with a speci¬c cost,
this may be the easiest formula to use.

WACC The WACC formula makes it relatively easier to determine how an extra percentage in
debt increases ¬rm value. When thinking of a target ratio change in capital structure
policy, this may be the easiest formula to use.

Still, in many cases, APV is easier to work with than WACC. For example, APV makes it much
Personal Author Advice:
APV is often simplest. easier to think about projects that add debt capacity only at some stage in their life. What drives
project debt capacity? The simple answer is that more tangible (collateralizable) projects tend
to add more debt capacity, because your bank will ¬nd it easier to repossess and resell tangible
assets. A research and development (R&D) project may require equity investment upfront,
followed by the construction of a laboratory that can be debt-¬nanced. The laboratory adds
debt capacity, the R&D does not. APV makes it easy to add in the debt capacity only in later
stages. APV also makes it easier to assign di¬erent discount factors to the ¬rm™s projects and
to the ¬rm™s tax shields (Section a).
WACC may be the most di¬cult method. It requires assumptions about the capital structure
WACC is often most
complex!. policy in future years that are not immediately obvious. An assumption of “corporate neglect”
won™t work, because if the ¬rm does nothing, the value of the ¬rm and thus the value of equity
next year will almost certainly be di¬erent. To keep a constant debt ratio, a corporation would
have to issue more debt when its equity value increases, and repurchase more debt when its
equity value decreases. Even if everything turns out as expected, the equity would likely be
expected to increase in value more than the debt each year. This means that without corporate
action, the debt ratio can go down over time. If the debt ratio is not constant over time, you
cannot use WACC, because you do not know how to do multi-year compounding with WACC.
(There is indeed some evidence that many publicly traded ¬rms tend not to follow constant
debt ratio strategies”but of course you do not care about other ¬rms, you care about your own
¬rm.) If your ¬rm plans to stick to a constant market-based debt ratio, WACC can indeed be
the most convenient way to think about the added tax advantages of debt. On a more technical
note, WACC also leans more heavily on the assumptions that borrowing rates are competitive
¬le=capctaxes.tex: RP
Section 22·7. Odds and Ends.

and thus zero NPV. Therefore, WACC works only in “normal” situations in which creditors are
paid the appropriate cost of capital on the debt. WACC cannot deal with “below-market” or
“above-market” unfairly priced loans”much like the CAPM cannot. (We already know that the
CAPM rate of return needs to be replaced by the certainty equivalence in this case.)

22·7.B. A Quick-and-Dirty Heuristic Tax-Savings Rule

Do not confuse the question of whether tax savings are important with the question of whether Why bother with such
puny tax savings?
the right discount factor for the tax savings is important. The former is much bigger than
the latter. But aren™t even the tax savings too small to bother with? Before you draw this
conclusion, realize that the ¬rm need not invent anything new or work extra hard to obtain the
tax savings. And, tax savings materialize year after year after year. In fact, this provides a nice
back-of-the-envelope heuristic of what the ¬rm can gain in value from one dollar extra in debt.
Start with the APV formula. If a large ¬rm today takes on and maintains an extra $1 billion in A rule of thumb: Each
perpetual dollar of debt
debt rather than an extra $1 billion in equity, the interest is on the order of about 6%, or $60
increases ¬rm value by
million per year. The tax rate for many corporation is about 40%, leading to a savings of $24 the corporate income
million per year”this can pay for a nice executive bonus. But this is only the ¬rst year. The tax-rate.
$24 million per year saving is a perpetuity. If the cost of capital on the tax shelter is the cost
of capital on the debt (6%), then we can compute the total value increase to the ¬rm today to
be $24/6% = $400 million.
40% · 6% · $1 billion
Value Increase = = $400 million
„ · E (˜DT ) · DT
Value Increase = = „ · DT .
E (˜DT )

This is a nice shortcut: for every dollar extra in eternal debt, the value of the ¬rm increases by
the tax rate of the ¬rm. And Formula 22.32 is so easy, you can often compute it in your head.
For example, compare ¬nancing a $1 million project with 50% debt (rather than all-equity), in
which a ¬rm in the 40% marginal tax bracket plans not to repay any of the debt principal or to
take on new debt. The tax savings would be 40% · $500, 000 = $200, 000.
It is important that you recognize that the „ · D formula for the tax savings is not a perfect Problems with the
heuristics are the
calculation, but only a heuristic”that is, a rule that gives you a good but not perfect number very
discount rate and the
quickly. For example, it has made at least two assumptions that are never perfectly satis¬ed. perpetual assumption.
The ¬rst is that the appropriate discount rate on the debt shelter is exactly the same as the
cost of capital on debt. The second is that the debt and its tax shelter are truly perpetual, with
constant cash ¬‚ows and discount rates. Nevertheless, the formula is very useful to quickly get
a handle on the long-term bene¬ts of additional debt.

22·7.C. Can Investment and Financing Decisions Be Separate?

In the perfect M&M world, investment and ¬nancing decisions can be made independently: If the world is not
perfect, projects with
Managers can focus on production choices and leave the ¬nancing to the nerds in the ¬nance
different ¬nancing
department. Unfortunately, if debt is tax advantaged, this will not be the case outside the M&M options can offer
world. different values. Thus,
¬nancing and
For example, consider two projects with equal costs, equal payo¬s, and equal costs of capitals. investment decisions
must be considered
(Alternatively, just consider their NPVs to be the same.) The ¬rst project is a research and together, not separately.
development project; the second is a building. In the real world, it is di¬cult to ¬nd a bank
An example.
to lend money for R&D: after all, if the ¬rm fails to pay its interest payments, there is often
little that the bank can collect and resell. Buildings, on the other hand, are easy to repossess.
Therefore, the building o¬ers more debt capacity than the R&D project. This can make it more
valuable than the otherwise equally promising R&D project. Managers cannot choose among
projects without taking into consideration how each project aids the debt capacity of the ¬rm.
¬le=capctaxes.tex: LP
568 Chapter 22. Corporate Taxes and A Tax Advantage of Debt.

Important: In an imperfect world, unlike the M&M world, managers cannot
ignore or delay ¬nancing decisions when making real investment decisions. The
two decisions are intertwined.

A second complication derives from the fact that the value of the debt capacity can depend
on who the owner is. Although most pro¬table and older ¬rms are in the same highest tax
bracket, some younger, growing, and unpro¬table ¬rms are in lower tax brackets. To these
younger ¬rms, the debt capacity is worth a lot less than it is to a large ¬rm like PepsiCo (which
can immediately use the tax deduction).

22·7.D. Using Our Tax Formulas

Let us tie up three loose ends.

The One Important Mistake To Avoid
The one big mistake you should never commit is to use the wrong expected cash ¬‚ows for APV
or WACC. Using the wrong discount rate on the tax shelter or tax liability is forgivable (within
bounds)”using the wrong expected cash ¬‚ow is not. So, let™s reemphasize what you must do.
In the pro forma method, you already have both the projected debt cash ¬‚ows and the projected
equity cash ¬‚ows, so your life is simple. You can just use these pro forma cash ¬‚ows which
already take the debt tax shield into account. In contrast, in both the APV and WACC methods,
you must not use the expected cash ¬‚ows of the ¬rm under the current capital structure (much
less the expected cash ¬‚ows to the current equity), but the cash ¬‚ows that would accrue if the
¬rm was fully equity ¬nanced.

What About Personal Income Taxes or Other Issues?!
From Section 6·5.C, you know that your owners want you to work only with expected after-
Do we need more
formulas, one for each tax cash ¬‚ows and expected after-tax costs of capital. As manager, do you need to adjust the
M&M distortion?
corporate expected debt cost of capital and expected equity cost of capital (from the CAPM)
for your investors™ income taxes? From your perspective, if you use the CAPM or if you ask
your investment banker what the appropriate expected cost of capital is at which you can ¬nd
¬nancing, are these estimates the costs of capital you need in our WACC or APV formulas, or
will you need to make further adjustments to these formulas?
It turns out that the WACC and APV are the last formulas that you shall need. The reason is
For us as corporate
managers, the expected that all other e¬ects will be transparent to you. As managers, the costs of capital (E(˜EQ ) and
costs of capital already
E(˜DT )) demanded by your investors will take into account any other “issues” they may have
re¬‚ect investors™ other
with your ¬rm. For example, if your investors su¬er higher taxes by investing with you, this will
be re¬‚ected in your seeing higher costs of capital. If your investors believe you will go bankrupt,
it will be re¬‚ected in your seeing higher costs of capital. If your investors love you, it will be
re¬‚ected in your seeing lower costs of capital. And so on. But then why were corporate income
taxes so special in needing their own formula? Why did they not ¬‚ow through the costs of
capital, too? The reason is that the corporate income taxes already sat fully budgeted as a line
item in your own corporate ¬nancials. You had already subtracted them o¬, and just needed
to add them back in when you as corporate managers could avoid them. Any other concerns
that your investors may have with your ¬rm have not been re¬‚ected in your ¬nancials, and
therefore do not need their own formulas.
¬le=capctaxes.tex: RP
Section 22·7. Odds and Ends.

The fact that you will not need another formula does not excuse you from thinking about what No formula does not
mean no thinking!
else your investors may care about. After all, you can create value for your investors if you can
reduce the necessary cost of capital. For example, if you can minimize your investors™ personal
tax obligations, you as a ¬rm will face a lower cost of capital, because you are creating more
value for our investors.

Combining WACC with the CAPM
Formally speaking, in the presence of taxes (or other imperfections), the CAPM does not hold Formally, it is wrong to
use the CAPM in a world
and should not be used. But this does not help you in the real world. What choice do you have
of taxes.
but the CAPM to provide you with an appropriate discount rate?
So, it has become common practice to combine the tax-adjusted WACC Formula with a cost Informally, no one has a
better alternative.
of capital derived from a CAPM model. Most often, the CAPM provides the cost of capital for
the equity (E(˜EQ )), while the borrowing interest rate provides the cost of capital for the debt
(E(˜DT )).

E (˜FM ) = wEQ ·E (˜EQ ) + (1 ’ „)·wDT ·E (˜DT )
r r r
≈ wEQ · rF + [E (˜M ) ’ rF ] · βEQ + (1 ’ „)·wDT · rF + [E (˜M ) ’ rF ] · βDT
r r .

Of course, corporate debt also has a default premium, so you cannot use the bank™s quoted
interest rate. You must use the expected interest rate (cost of capital), which is the estimate
that the CAPM provides. Fortunately, for large companies with low default probabilities, the
two are often close.

22·7.E. Other Capital Structure Related Tax Avoidance Schemes

Wall Street and Main Street employ armies of tax experts to help their clients avoid taxes, but There are too many tax
schemes in existence to
this is really an arms race between the IRS (Congress) and investors. Investors keep looking
list in just one book.
for new tax avoidance schemes and the IRS tries to close these new loopholes. There are a They are also changing
large number of both past (now closed) and current tax avoidance schemes. Some of the more all the time. Here are
some examples.
noteworthy remaining tax reduction schemes are as follows:

• Sometimes, high-tax ¬rms may be able to purchase low-tax ¬rms, and thereby immediately
use the acquired ¬rm™s existing net operating losses NOLs.
For example, the Financial Times reported on February 10, 1994, that the £2.5B GKN
corporation made a hostile bid for the £300M Westland corporation, solely because GKN
needed Westland™s NOLs to reduce its own corporate taxes due.

• Compared to purchasing on credit, leasing can be a tax advantageous arrangement. If the
borrower does not have enough income to e¬ciently use the interest deduction, someone
else should be the o¬cial owner of the asset and “lease” it to the borrower, thereby cap-
turing the full bene¬t of the interest deductability.

• Multinational corporations can shift di¬cult-to-value assets producing income from a
high-tax country into a low-tax country. For example, corporate income taxes in Switzer-
land (federal and canton) can be as low as 7.8% (for holding companies) and as high as
25%. This contrasts with state and federal corporate income tax rates as high as 45% in
the United States.
For example, consider a company that has just developed a patent worth $10 million per
year. If the U.S. branch owned the patent, the ¬rm would retain only (1 ’ 45%)·$10 =
$5.5 million per year. If the Swiss branch owned the patent, the ¬rm would retain up to
(1 ’ 7.8%)·$10 = $9.2 million per year. Why stop at $10 million? If the Swiss branch
charged the U.S. branch $20 million per year, the ¬rm™s U.S. tax obligations (resulting
from pro¬ts from other businesses) would decline by $9 million per year (45% times $20
million), but Swiss tax obligations would increase by $1.56 million. Still, this is a healthy
$7.4 million net gain.
¬le=capctaxes.tex: LP
570 Chapter 22. Corporate Taxes and A Tax Advantage of Debt.

This tax-e¬cient capital transfer can also be accomplished with capital structure. For
example, if the Swiss branch lent funds to the U.S. branch at an interest rate of 36% per
year, rather than 6% per year, the e¬ect would be a reduction of the ¬rm™s tax liabilities.
For every $1,000 in excess interest paid (at the 36% instead of the 6% rate), the company
would retain an extra (45% ’ 7.8% = 37.2%) $372 in pro¬ts. Companies can play similar,
but less drastic, tax games by choosing the U.S. state and municipality in which they are
The IRS is very much aware of these issues. For example, the Wall Street Journal reported
on June 24, 2002 that the IRS is trying to prevent ¬rms from shifting intellectual property,
such as patents, to other countries in which corporations would have fewer taxes to pay.

Before such corporate tax avoidance schemes outrage you too much, you should realize that
Should we prevent
corporate tax avoidance? you may even be lucky if tax lawyers and Congress help many U.S. companies succeed in es-
caping some of their tax burdens. First, corporations are just vehicles owned by investors.
Corporate income taxes are really ultimately paid by the investors”often small dispersed in-
vestors, like yourself. Second, the United States has no monopoly on corporate locations. If U.S.
taxes are too high, some corporations may just leave the United States, others may never come.
Many ¬nancial services ¬rms have already done so. U.S. disclosure and tax laws and regulations
have built strong ¬nancial services centers in places like the Bermudas and Cayman Islands, and
Switzerland. Greenwich Connecticut is the ¬nancial services center that the New York tax code
has built. Many European countries have even stronger regulations than the United States and
are in fact experiencing dramatic capital ¬‚ight right now. Of course, this does not mean that
the U.S. system cannot be improved. The lawyer-and-accountant-and-legislative-pork method
does not seem like the most rational and e¬cient way to run an economy.
So, taking into account debt and other shelters, what tax rates do publicly traded companies
Many ¬rms pay almost
no taxes. ultimately pay? John Graham reports that a large number of ¬rms”but not all”are fully
cognizant of how to e¬ectively manage their taxes. In ¬scal year 2001, about 6,000 ¬rms had
e¬ective tax rates of 5% or less! Between 1,500 and 2,000 ¬rms had tax rates between 5% and
30%. And about 4,000 ¬rms had tax rates between 30% and 40%. These are of course average
tax rates, and not the marginal tax rates that would apply to one more dollar earned. But
the nature of the distribution of tax rates (at the two extremes) suggests that the marginal tax
rates are probably close to the average tax rates. That is, low-tax ¬rms could likely continue
to manage paying low taxes on any extra dollar earned, while high-tax rate ¬rms would likely
continue to pay high taxes.
Solve Now!
Q 22.11 A ¬rm has expected before-tax earnings of $20 per year forever, starting next year. It
is ¬nanced with half debt (risk-free, at 5% per year) and half equity (at 10% per year), and this
is eternally maintained. If the ¬rm is in the 25% tax bracket, then what is its NPV?

Q 22.12 (Continued.) If this ¬rm took on $50 in debt and maintained the debt load at $50 forever,
rather than maintain a 50/50 debt-equity ratio, then what would this ¬rm™s value be?

Anecdote: Stanley Toolworks and Foreign Domiciles
Stanley Toolworks, a hundred-year-old prominent Connecticut-based global manufacturer of tools, was in
the process of locating its headquarters to the Bermudas in mid-2002. This would allow Stanley™s foreign
subsidiaries to escape U.S. income taxes. In the end, only unusually strong media attention, public outcries, and
the threat of special legislation prevented this departure.
¬le=capctaxes.tex: RP
Section 22·8. Summary.

22·8. Summary

The chapter covered the following major points:

• In the imperfect real world, the U.S. tax code favors debt over equity. Managers should
take this corporate income tax advantage into account.

• The calculation of the income tax advantage can be done either through a full pro forma
(via a ¬nancing scenario that subtracts the interest and thereafter the tax burden), through
an adjusted WACC method, or through the APV method.

• Both the WACC and the APV method begin with cash ¬‚ows as if fully equity-¬nanced and
thus fully taxed, which is why they need to put back the tax advantage derived from the
presence of debt.

“ WACC does so by lowering the cost of debt capital:

E (CF)
= ,
1 + WACC
WACC = E (˜FM ) ’ „ · E (˜DT ) · wDT
r r

= wEQ · E (˜EQ ) + wDT · E (˜DT ) · (1 ’ „)
r r

“ APV does so by adding back the tax bene¬t:

E (CF) E („ · E (˜DT )·DT)
APV = + .
1 + E (˜FM ) 1 + E (˜)
r r

If the ¬rm™s debt ratio will shrink over time, use the ¬rm™s debt cost of capital to
discount the interest payments. If it will remain constant, use the ¬rm™s overall cost
of capital. If it will increase, use the equity™s cost of capital.

• These methods usually arrive at very similar but not exactly identical valuations. We often
are not sure about the appropriate discount rate that should be applied to the future tax
bene¬ts in the APV formula; and the WACC formula cannot really deal with changing costs
of capital or debt ratios over time. However, the errors that an incorrect discount rate on
the tax shield would cause are usually dwarved by other simpli¬cations and uncertainty
in expected cash ¬‚ows and discount rates.
The one error you should never commit is to use the wrong expected cash ¬‚ows in one of
our three methods.

• A constant extra dollar of debt forever increases the value of the ¬rm by the ¬rm™s
marginal income tax rate. A $100 eternal debt increase will create $30 in value for a
¬rm in the 30% marginal income tax bracket.

• In the imperfect real world, ¬nancing and investment decisions can no longer be separated:
projects that add more debt capacity may add value through the ¬nancing channel.

• It is common and reasonable to combine the WACC formula or APV formula with the CAPM
formula, even if this is not entirely correct.

• As a manager, you will not need a more complex formula than WACC, because other in-
vestor considerations are re¬‚ected in the cost of capital that the ¬rm faces on its securities.
However, not needing a formula does not mean that you do not need to think about how
you can address these other investor considerations”quite the opposite.
¬le=capctaxes.tex: LP
572 Chapter 22. Corporate Taxes and A Tax Advantage of Debt.

Solutions and Exercises

1. $500 if designated an interest payment. $750 if designated a dividend distribution, because only $500 is left
after corporate income taxes have been paid.

2. With an internal rate of return of 20%, Uncle Sam would see $90,000 if you pay cash. If you ¬nance with
80% debt, you will have $40,000 in interest to deduct from $200,000 in return, and thus pay taxes only on
$160,000. This lowers your tax bill to $72,000. (Side Advice: If you borrow $800,000, you may have to invest
your $800,000 elsewhere. If you do not choose tax-exempts, Uncle Sam may receive more taxes therefrom.)
3. The net subsidy is $90, 000 ’ $72, 000 = $18, 000 next year. At an appropriate cost of capital of 8%, this is
an PV of $16, 667.

4. The WACC valuation is

PV0 = = $229.80 .
1 + 12% ’ 25% · 30% · 8%
The ¬rm has $229.80 · 25% = $57.45 of debt and $172.35 in equity value today. Its APV is

E (CF1 ) „ · E (˜DT ) · DT
APV0 = +
1 + E (˜FM ) 1 + E (˜FM )
r r
30% · 8% · $57.45
= + = $229.80 .
1 + 12% 1 + 12%

5. The APV valuation is

E (CFFM,1 ) „ · E (˜DT ) · DT
APV0 = +
1 + E (˜FM ) 1 + E (˜FM )
r r
30% · 8.7% · $100
= + = $230.90 .
1 + 12% 1 + 12%
Therefore, the $100 debt is 43.3% of the ¬rm™s value today, and

PV0 = = $230.90 .
1 + 12% ’ 43.3% · 30% · 8.7%

6. WACC for ratio, APV for dollar amounts. Look at the previous two questions. You cannot ¬gure out the APV
in the ¬rst question before you determine the WACC, and the opposite in the second question.
7. • The ¬rm™s overall cost of capital today is 6% · 1/3 + 12% · 2/3 = 10%. (Because 4% + 3%·2 = 10%, the beta is
2.) • The easy way is to recognize that the ¬rm is sheltering $500 · 6% = $30 through interest payments. If it
re¬nanced with $1,000, it could now shelter $1, 000 · 8% = $80. Uncle Sam would get to see an additional $50
less in income, which means that the ¬rm would pay $50·20% = $10 less in income tax next year. • Now you
need to determine the appropriate discount rate for $10 in tax savings. For convenience, use the debt cost
of capital: 8%. This means that our recapitalization increases ¬rm value by $10/1.08 ≈ $9.26. (If you prefer
to use the overall ¬rm cost of capital, you would obtain $9.09.) • The question intentionally gave additional
irrelevant information.
8. Because you know that the cost of capital if all ¬nanced by debt has to be the cost of capital for the ¬rm,
you know that the ¬rm™s overall cost of capital is E (˜DT ) = 15% + 100% · 5% = 20%. Now, this project will
o¬er $200 pretax pro¬t in year 1. Discounted back at the ¬rm™s cost of capital, the NPV without taxes is
’$300 + $500/(1 + 20%) = $116.67. But, if equity ¬nanced, the IRS will declare taxes due on $200 of pro¬t,
or $80. So, the NPV with taxes and all equity ¬nanced is ’$300 + $420/(1 + 20%) = $50.

Now, right after the investment, the ¬rm has a value of $420/1.2 = $350. With debt of $50 ($100), the ¬rm
carries a debt load of around 15% (30%). The cost of debt capital formula given in the question suggests that
E (˜DT ) = 15% + 15% · 5% = 15.75% (16.5%). (Note: the question is a bit ambiguous in that it does not tell you
what to use as ¬rm value. The 15% and 30% debt ratios are reasonable values, though.)

Interest payments on $50 ($100) at a cost of capital of 15.75% (16.5%) are $7.88 ($16.50) next year. Facing a tax
rate of about 40%, Uncle Sam would thereby subsidize the project to the tune of 40% · $7.88 = $3.15 ($6.60),
which in today™s value would be worth around $3.15/(1 + 20%) ≈ $2.63 ($6.6/1.2 ≈ $5.50). Therefore, under
APV, if ¬nanced with $50 in debt ($100 in debt), the project is worth $50 + $2.63 = $52.63 ($50 + $5.50).
¬le=capctaxes.tex: RP
Section 22·8. Summary.

The cost of capital, if 15% of the ¬rm is ¬nanced by debt at an interest rate of 15.75% is the solution to
15% · 15.75 + 85% · E (˜EQ ) = 20% ’ E (˜EQ ) = 20.75%. So, the WACC is given by the formula, wEQ · E (˜EQ ) +
r r r
wDT · E (˜DT ) · (1 ’ „) = 85% · 20.75% + 15% · 15.75% · (1 ’ 40%) ≈ 19.06%. Similarly, if $100 is borrowed,
E (˜EQ ) = 21.5%, and WACC = wEQ ·E (˜EQ )+wDT ·E (˜DT )·(1’„) = 70%·21.5%+30%·16.5%·(1’40%) ≈ 18.02%.
r r r
The WACC based value is thus ’$300 + $420/(1 + 19.06%) ≈ $52.76. Note that you have made enough little
assumptions and approximations that it would make little sense to now worry about being o¬ by a little in
the APV and WACC computations ($52.76 and $52.63).

(a) The pro forma for a 100% equity ¬nanced ¬rm is

Income Statement
Year 1 Year 2 Year 3
EBITDA (=Net Sales) $70 $60 $55
“ Depreciation $50 $50 $50
= EBIT (=Operating Income) $20 $10 $5
“ Interest Expense $0 $0 $0
“ Corporate Income Tax $8 $4 $2
Net income
= $12 $6 $3
Cash Flow Statement
Net income $12 $6 $3
+ Depreciation $50 $50 $50
Operating Cash Flow $62 $56 $53
capital expenditures “$150 $0 $0
Investing Cash Flow “$150 0 0

Economic Project Cash Flows
(Operating CF+ Investing CF+ Interest)
“$88 +$56 +$53
Project Cash Flows

(b) The IRR of our project solves

’$88 +$56 +$53
+ + =0. (22.40)
1 + IRR (1 + IRR) (1 + IRR)3

Thus, the IRR of a purely equity ¬nanced project is 15.7%.
(c) The NPV of the purely equity ¬nanced project is

’$88 +$56 +$53
NPV = + + = ’$2.10 . (22.41)
1 + 18% (1 + 18%) (1 + 18%)3

This is in line with the fact that the project IRR of 15.7% is less than the 18% cost of capital.
(d) The cash ¬‚ows would increase to ’$88, +$58, and +$55. The IRR would increase to 18.6%.
¬le=capctaxes.tex: LP
574 Chapter 22. Corporate Taxes and A Tax Advantage of Debt.

(e) The debt-¬nanced pro forma would now be

Income Statement
Year 1 Year 2 Year 3
EBITDA (=Net Sales) $70 $60 $55
“ Depreciation $50 $50 $50
= EBIT(=operating income) $20 $10 $5
$0 $5 $5
“ Interest Expense
“ Corporate Income Tax $8 $2 $0
Net income
= $12 $3 $0
Cash Flow Statement
Net income $12 $3 $0
+ Depreciation $50 $50 $50
$62 $53 $50
= Operating Cash Flow
Capital Expenditures “$150 $0 $0
“$150 0 0
= Investing Cash Flow

Economic Project Cash Flows
(Operating CF + Investing CF + Interest)
Project Cash Flows “$150+$62 +$53+$5 +$50+$5
“$88 +$58 +$55
The Economics of Financing
Debt +$50 +$5 +$55
Equity +$38 +$53 +$0

Not surprisingly, these are the same as our aforementioned cash ¬‚ows, with a $2 income-tax subsidy in
years 2 and 3. So, the IRR is again 18.6%.
(f) The NPV of the debt-¬nanced ¬rm is

’$88 +$58 +$55
NPV = + + = +$0.55 . (22.42)
1 + 18% (1 + 18%) (1 + 18%)3

So, with the tax subsidy, this project becomes worthwhile.
(g) The APV of this project would be the value as-if-100%-equity-¬nanced, which is “$2.10 (Formula 22.41),
plus the discounted tax subsidies in years 2 and 3. These have a value of

$2 $2
Tax Subsidy = + = $1.44 + $1.22 = $2.66 . (22.43)
(1 + 18%) (1 + 18%)3

Therefore, the APV would be ’$2.10 + $2.66 = $0.56.
(h) By APV, the expected tax subsidy would shrink from „·E (IP ) = 40%·$5 = $2 per year to „·E (IP ) =
40%·$4 = $1.60 per year. The expected value of the tax subsidy would therefore be

$1.60 $1.60
Tax Subsidy = + = $2.12 . (22.44)
(1 + 18%) (1 + 18%)3

The net project value would be about $0.02.
(i) In year 0, the weight of the debt is wDT,0 = $50/$88 ≈ 57%. But after year 2 and before year 3, the
debt is expected to be 100% of the capital structure, so its weight in the capital structure is drastically
changing each year. So, this ¬rm is not at all a good candidate for WACC application.

Do not try to compute a weighted average cost of capital from the debt and
Digging Deeper:
equity internal rates of return (10% and 40%, respectively). If the debt would remain at 57% of the
¬rm™s capital structure, then the appropriate rate of return of equity would have to be around 30%
so that the weighted cost of capital would come out to E (˜FM ) = wDT ·E (˜DT ) + wEQ ·E (˜EQ ) = 18.6%.
r r r
This is much lower than the equity IRR of 40% (which is the same as its expected rate of return from
year 1 to year 2), because from year 2 to 3, the equity becomes a much smaller part of the ¬rm. What
bites you in this case is the fact that you have a strong term structure of investment weights.

10. Do it!
¬le=capctaxes.tex: RP
Section 22·8. Summary.

11. The weighted average cost of capital (WACC) is

WACC = wDT ·E (˜DT )·(1 ’ „) + wEQ ·E (˜EQ )
r r
= 50%·5%·(1 ’ 25%) + = 6.875% .

The numerator has to be post corporate income tax; therefore, it is (1 ’ „)·CF = $15. This is an annuity,
therefore the NPV is
PV = = $218.18 .

12. The cost of capital for a fully equity ¬nanced ¬rm without a tax subsidy would be 7.5%, because it had 50%
debt at 5% and 50% debt at 10%. Therefore, the “as if fully equity ¬nanced” value is

PV = = $200.00 .
Now, we need to add back the tax subsidy. With $50 in debt, risk-free and therefore with an interest rate of 5%,
the interest payments would be E (˜DT ) · DT = $2.50 per year. The taxes saved would be „ · $2.50 = $0.625,
which is an eternal cash ¬‚ow. At the interest rate of 5%, the value of the tax subsidy today is $12.50. Therefore,
the value of this ¬rm is $200+$12.50= $212.50.

(All answers should be treated as suspect. They have only been sketched, and not been checked.)
¬le=capctaxes.tex: LP
576 Chapter 22. Corporate Taxes and A Tax Advantage of Debt.

a. Advanced Appendix: The Discount Factor on Tax Obliga-
tions and Tax Shelters

On Page 553, I stated that it is common (but not unique) to use the ¬rm™s cost of capital in
discounting the tax shelter. Let™s ¬nd out why. Start with the ¬rm in Table 22.2. To gain
intuition about proper discount rates for tax payments and tax shelters, we must work an
example in which claims can be risky, so that they can carry di¬erent costs of capital. The
example will be easiest if the debt is risk-free, so that only the equity is risky. For convenience,
assume that the ¬rm™s beta is positive, so the ¬rm™s equity cost of capital exceeds its debt cost
of capital. Our revised scenario is in Table 22.5.

Table 22.5. Two Financing Scenarios for a Risky 1-Year Firm

Scenario EF: All Equity Financing.

E(Value) Bad Good
Before-Tax Return Next Year $280.00 $250.00 $310.00

Taxable Pro¬ts Next Year $80.00 $50.00 $110.00
Corporate Income Taxes („ = 30%) Next Year $24.00 $15.00 $33.00
Owners Will Keep Next Year $56.00 $35.00 $77.00

Scenario DF: $200 Debt Today at 11% for Promised Repayment of $222. Rest is Levered Equity.

E(Value) Bad Good
Before-Tax Return Next Year $280.00 $250.00 $310.00

Interest Payments $22.00 $22.00 $22.00
Taxable Pro¬ts Next Year $58.00 $28.00 $88.00
Corporate Income Taxes („ = 30%) Next Year $17.40 $8.40 $26.40
Equity Owners Will Keep Next Year $40.60 $19.60 $61.60
Equity+Debt Owners Will Keep Next Year $62.60 $41.60 $83.60

Tax Savings (Scenario EF vs. Scenario DF)

E(Value) Bad Good
” risky
Before-Tax Return Next Year $280.00 $250.00 $310.00

Scenario 1 corporate income taxes $24.00 $15.00 $33.00 ” risky

Scenario 2 corporate income taxes $17.40 $8.40 $26.40 ” risky

Relative Net Tax Savings Next Year $6.60 $6.60 $6.60 ” safe

What should you use as the appropriate discount rate (cost of capital) for the future tax obliga-
We know the future
tax-related cash ¬‚ows. tion ($24 in EF, $17.40 in DF) or for the relative tax shelter (the di¬erence of $6.60)? To answer
How do you discount
this, we make the ¬rm risky. Assume that the value of the ¬rm with $280 in expected pro¬ts
them? Let™s work a
will be either $250 (bad) or $310 (good) with equal probability. Therefore, the $200 debt at 11%
simple example with
risky payoffs.
interest is risk-free. Because we have constructed it this way, you know that you can use the
debt™s (risk-free) cost of capital of 11% for any cash ¬‚ow that does not covary with the ¬rm™s
¬le=capctaxes.tex: RP
Section a. Advanced Appendix: The Discount Factor on Tax Obligations and Tax Shelters.

outcome. And you would use a higher discount rate for any cash ¬‚ow that covaries positively
with the ¬rm™s outcome.
The bottom panel in Table 22.5 shows that the income tax obligation is risky and covaries with The tax payment is as
the ¬rm™s return under either ¬nancing scenario. Uncle Sam is basically a co-owner, partaking risky as the ¬rm, and
thus warrants a higher
in the good and the bad times. So, you now know that you need to use a discount rate on the cost of capital.
tax obligation that is higher than the risk-free rate.
But what is the cost of capital for the tax shelter ? Table 22.5 shows that the tax savings For our 1-year,
non-growing ¬rm, the
(because of the debt) remain the same $6.60, regardless of the ¬rm™s performance. Indeed, we
tax shelter is safer than
have constructed the example so that it would be easy to see that the debt payment and with the ¬rm, and thus
it tax shelter that the owners get from the presence of debt does not depend on the ¬rm™s warrants a lower cost of
fortunes. The tax shelter is as safe as the ¬rm™s debt. Thus, you should use a discount rate on
the tax savings that is the same as the one you use on the ¬rm™s debt.
Nevertheless, it is common practice to apply the ¬rm™s cost of capital and not the debt™s cost Alas, we often use the
¬rm™s cost of capital also
of capital to the ¬rm™s tax obligation. Is this an invitation to deliberately use incorrect discount
on the tax shelter. Why?
factors in general? No, but it is a good and convenient working assumption in this particular
context of discounting the tax shelter. Let me explain why.

1. In general, it is more important to get the discount rate right on larger amounts. If you Worry more about the
correct discount factor
wanted to get discount rates on individual component cash ¬‚ows 100% right, why stop
on big amounts.
with the corporate tax shelter? Why not also determine individual discount rates for ev-
ery other component of the company (taxes, depreciation, SG&A, marketing, advertising,
furniture, paper clips, etc.)? This is not only impractical, but also beyond anyone™s capabil-
ities. More importantly, if you want to allow yourself to use a possibly incorrect discount
factor, you have to convince yourself that any added valuation precision would be very
How big is the tax shelter relative to the cash ¬‚ows? The cash ¬‚ows are $280, the debt is
$200. (This is unusually large. More typically, ¬rms have debt ratios around 30%.) The
interest paid is 11% thereof, or $22. You need to multiply this further by your corporate
income tax rate of 30% to obtain the tax shelter $6.60. And now your “big” question is
whether to discount this by the ¬rm™s cost of capital (say, 15%) or by the ¬rm™s debt cost
of capital (say, 11%). This makes the di¬erence between $5.95 and $5.74, which is 21
cents today on cash ¬‚ows of $280 next year.
Yes, you should de¬nitely worry about the correct discount rate for the project™s cash
¬‚ows of $280. Yes, the presence and amount of the tax shelter is important. Yes, it would
be nice to use the correct discount factor on the tax shelter, too. But, no, it will not make
much di¬erence whether you apply the ¬rm™s cost of capital or the debt cost of capital to
the tax shelter.

2. The ¬rm™s overall cost of capital may in fact be more correct than the debt cost of capital, In a normal ¬rm
context, corporate debt
because the risk-free tax-shelter intuition does not easily generalize from the simple one-
policy will induce the tax
period scenario to many periods. The reason is that if your ¬rm value doubles by next shelter to vary with ¬rm
year, you can probably borrow twice as much then, and thus enjoy higher tax savings scale.
henceforth. If your ¬rm follows such an intelligent dynamic borrowing strategy, the tax
shelter obtained by debt ¬nancing will not remain constant, but will increase with the
¬rm value, too. To compute the lifetime tax shelter a¬orded to your ¬rm by its ability to
take on more debt, you must therefore realize that intelligent capital structure policies
will induce the dollar amount of debt (and thus the tax shelter) to also covary positively
with ¬rm value. This is why it is often sensible to discount the tax shelter not with the
debt™s cost of capital, but with the ¬rm™s cost of capital (or a discount rate somewhere in
¬le=capctaxes.tex: LP
578 Chapter 22. Corporate Taxes and A Tax Advantage of Debt.

Because this is a nerd appendix, we may as well go through the argument with a numerical
This is a nerdnote within
a nerd appendix”how it example. Think of a ¬rm that operates for one year, and either doubles or disappears in
the following year. It follows a dynamic debt policy so that its one-year debt and one-year-
ahead tax shelter is always risk-free. Assume the risk-free rate on the debt is 10%. Further
assume the ¬rm™s expected tax shelter is $22 next year. If it doubles, both its risk-free
debt and tax shelter will double, too. If it disappears, it will have no tax shelters.
How does the dynamic aspect in¬‚uence the two-year ahead discount rate for the tax shel-
ter? It would be wrong to discount the stream at the risk-free rate of 11% as $22/1.11 +
$22/1.112 ≈ $37.68. Instead, the ¬rm™s stream of tax shelter value today is

$22 $44 $0
1/2 · + 1/2 ·
+ (22.48)
(1 + 11%) [1 + E (˜)] · (1 + 11%) [1 + E (˜)] · (1 + 11%)
r r

What is E(˜)? Because the shelter cash ¬‚ow $0 or $44 depends on the ¬rm™s performance
in the ¬rst period, it cannot be the risk-free rate. Instead, E(˜) is related to the ¬rm™s
cost of capital.
You can also think of collapsing our example into the combined PV of all future tax shelters
that you will own as of next year. Depending on ¬rm performance this year, next year you
will either sit on shelter cash ¬‚ows totaling of $44/1.11 + $5 ≈ $44.64. or $22. Therefore,
if you use the expected $22 as a representative standin for the tax shelter in both future
years, you cannot assume that the right interest rate is the risk-free interest rate. Again,
because it depends on ¬rm performance in the ¬rst year, a discount rate between the debt
and the ¬rm™s cost of capital would be more appropriate.

Figure 22.1 should help you to think about reasonable choices for the discount rate on the
Reasonable costs of
capital for the tax tax shelter. We assume that we are dealing with a typical ¬rm, which tends to grow over time
shelter depend on the
(upper left).
dynamic debt policy.

A Decreasing Debt Target The upper right graph shows a ¬rm that plans to reduce its debt
ratio over time. This is the case if a growing ¬rm wants to retain the same absolute dollar
interest payments. Such a ¬rm would expect to save about the same dollar amount in
taxes each year, regardless of ¬rm performance. In this case, you should use some rate
close to the debt cost of capital (E(˜DT )).

A Constant Debt Target The lower left graph shows a ¬rm that plans to keep a constant debt
target. (Many CFOs pay lip service to targeting constant debt ratios.) Firm growth will
translate into more and more debt and thus into higher and higher dollar interest pay-
ments. Consequently, the tax shelter will grow and shrink with the value of the ¬rm,
which means that it will be exposed to about the same risk as the ¬rm overall. In turn,
this means that you should use some rate close to the ¬rm™s overall cost of capital (E(˜FM ))
to discount the tax shelter.

An Increasing Debt Target The lower right graph shows two ¬rms with increasing debt targets.
(This kind of debt policy is rare.) The ¬rm with the discontinuous debt target might be
a typical R&D project, which will initially provide no debt capacity and thus no debt tax
shelter. Thereafter, if the R&D pays o¬, the ¬rm has positive cash ¬‚ows and can take on
debt ¬nancing. The blue continuous line is a ¬rm that wants to become smoothly more
aggressive in its debt policy over time. The values of these tax shelters is even more
highly correlated with the value of the ¬rm than if the target is constant. Therefore, the
tax shelter should be discounted even more aggressively. You should use some rate above
the ¬rm™s overall cost of capital, perhaps something close to the equity cost of capital,
E(˜EQ ).
¬le=capctaxes.tex: RP
Section a. Advanced Appendix: The Discount Factor on Tax Obligations and Tax Shelters.

Figure 22.1. Thinking About Proper Discount Rates For The Tax Shelter

E (V) D/V

b Target
  && rr
 & ¨
¨¨ rr
¨ r
 && ¨¨ rr
 & ¨ r
 &¨¨¨ rr
$$$ j
 &¨ $

¨ E

Time Time

The background of the other three graphs: This ¬rm plans to reduce its debt ratio over
The typical ¬rm value grows over time. time, perhaps to keep its dollar debt and its
interest payments constant.
’ Use E (˜DT ) to discount the tax shelter.

Target Target

Firm R&D

$$ X
$$$Firm Inc

Time Time

This ¬rm plans to keep its debt ratio con- These two ¬rms, called “R&D” and “Inc” plan
stant. to raise their debt ratios over time. Firm
R&D wants to sharply increase its debt ratio
only after it will have higher tax-deductible
’ Use E (˜FM ) to discount the tax shelter. ’ Use E (˜EQ ) to discount the tax shelter.
r r

V is the ¬rm™s value. D is the ¬rm™s debt. D/V is the ¬rm™s debt ratio.
These scenarios illustrate cases in which the ¬rm™s leverage changes over time, which in turn in¬‚uences the discount
rate that should be applied to the tax shelter. For example, if the ¬rm wants to keep a constant debt ratio over the
years, then it will have more debt and therefore a higher debt tax shelter if the ¬rm experiences good times in the
¬rst year. This means that the value of the future tax shelter covaries positively with the ¬rm value in the ¬rst year.
It is therefore not almost risk-free (as it was in our example in which the ¬rm existed only for one year), but more
risky (in fact, almost as risky as the ¬rm is in its ¬rst year).
Fortunately, although it would be a ¬rst-order error to compute the wrong tax shelter, it is often a second-order
error to use the wrong discount factor on the tax shelter. Yes, you should try to get it right anyway, but realize that
getting other quantities right is often more important than agonizing whether you should use E (˜FM ) or E (˜DT ).
r r
¬le=capctaxes.tex: LP
580 Chapter 22. Corporate Taxes and A Tax Advantage of Debt.

In sum, I hope you are convinced that your overall project valuation will be robust with respect
Think about the
appropriate discount to moderate variations or errors in the choice of discount rate on the tax shelter. (I typically use
rate on the tax shelter,
whatever is most convenient, although I try to keep track of whether I think my assumptions
but don™t torture
overestimate or underestimate the true ¬rm value.) You should worry primarily about the
yourself to get it perfect.
amount of the tax shelter, and only secondarily about whether the precise discount factor is
the ¬rm™s cost of capital or the debt cost of capital. So, please, give yourself a break here!


• The discount rates on the tax obligations and on the tax shelter are usually
not exact, but just reasonable and convenient approximations. The value
consequences of reasonable errors are minor.

• It is common and usually reasonable to value tax liabilities at a discount rate
equal to the ¬rm™s overall cost of capital (E(˜FM )).

• For the tax shelter due to interest payments, assuming that the ¬rm will grow
over time, it is common and usually reasonable to

“ use the debt cost of capital (E(˜DT )) if the ¬rm plans on a decreasing
debt ratio;
“ use the ¬rm cost of capital (E(˜FM )) if the ¬rm plans on a constant debt
“ use the equity cost of capital (E(˜EQ )) if the ¬rm plans on an increasing
debt ratio.

Be aware that our entire discussion that we can allow ourselves some latitude was only about the
Taxes are important; we
are only fudging the discount factor. Importantly, the (expected) amount of the tax shelter itself is not unimportant.
divisor, not the
This also applies to the idiosyncratic risk in the expected tax shelter, a quantity that ¬gures
into the present value numerator of the tax shelter, not the denominator (the discount rate).
For example, an R&D project may not generate any tax shelter half the time”in which case, the
expected tax shelter (in the PV numerator) to be discounted would be something like
Tax Shelter If R&D is Successful
Expected Tax Shelter = 50% · + 50% · $0 . (22.49)
= Tax-Rate Times Interest Paid
Other Capital Structure Considerations

Personal Taxes, Bankruptcy Costs, Inside Information, Behavior
last ¬le change: Mar 2, 2006 (10:59h)

last major edit: Apr 2005

Managers should consider corporate income taxes to be important determinants of capital
structure”but not the only one. Personal income taxes, ¬nancial distress, agency considera-
tions, and others can all play important roles. They are the subject of this chapter.
Corporate income taxes turn out to be unique in one respect: corporate income taxes distort
the debt cost of capital. For example, with a corporate income tax rate of 40%, our corporation
would not face the 10% interest rate that it would have to pay creditors, but instead consider
the debt cost of capital to be only 6%. In contrast, the capital structure considerations that we
shall cover in this chapter work through di¬erent conduits”they change the appropriate cost
of capital that our corporation has to pay. In other words, they can in¬‚uence our cost of equity
capital E(˜EQ ), our cost of debt capital E(˜DT ), or both. Moreover, their importance is often
r r
not easy to quantify”but this does not make them any less important than corporate income

¬le=caprest.tex: LP
582 Chapter 23. Other Capital Structure Considerations.

23·1. The Role of Personal Income Taxes and Clientele Ef-

We focus only on the U.S. system, although many other countries have similar tax codes. The
Firms can reduce their
cost of capital if they can corporate income taxes that we discussed in the previous chapter are just one side of what Uncle
reduce their investors™
Sam receives: he also wants his share from investors™ income. Should corporate managers think
taxable income.
about their investors™ personal taxes? Yes! It would not be smart to economize on corporate
income tax through debt ¬nancing on behalf of our investors if Uncle Sam then were to take
away 99% of any interest payments the instant they exit the corporation and our investors
receive them. Our owners would be left with very little. Therefore, this section will show
how investors™ personal income taxes can in¬‚uence the optimal corporate capital structure.
The interplay between personal and corporate taxes creates both investor clienteles and ¬rm
clienteles: small growth ¬rms should have more equity in their capital structure than large cash-
rich ¬rms; and highly-taxed individual investors should invest more in equity-¬nanced ¬rms
than tax-exempt investors, while tax-exempt investors should hold more corporate bonds.

23·1.A. Background: The Tax Code For Security Owners

When investors receive cash from the company, the form in which this cash arrives matters:
The type of income
matters: capital gains
income is better for
Ordinary Income is taxed at relatively high ordinary income tax rates (up to 35%), and is very
taxable investors than
interest income. di¬cult to shelter from taxes.

Interest Income is basically taxed like ordinary income.

Dividend Income is taxed at a lower rate. As of 2005, if the corporation has already paid taxes
on its earnings, its dividends are considered “quali¬ed,” which reduces the personal tax
rate required to be paid by the dividend recipients. Individuals in the 10% and 15% ordi-
nary income tax brackets pay a 5% dividend tax, while individuals in higher tax brackets
pay a 15% dividend tax. Giving investors credit for dividends paid from already taxed
earnings is similar to how the United Kingdom and many other countries have taxed div-
idends for a long time. However, in the United States, this is not a stable situation. The
current dividend taxation scheme was put in place by the Bush tax cuts of 2003”but
dividends are scheduled to revert to being taxed at ordinary income tax rates after 2008,
just as they were before 2003.

Capital Gains are generally the most tax-advantaged form of income. In 2005, short-term
capital gains (on ¬nancial assets that you hold for less than 1 year and real assets that
you hold for less than 3 years) are federally taxed at 28% (again in 2005), while long-term
capital gains are taxed at the same statutory rate as qualifying dividends (i.e., 15% for
high-income tax investors). One exception is if the investor is a corporation”it is then
taxed at a higher capital gains rate of 25%.
Check the 25% rate.
It may be higher.
The advantage of capital gains is not only the relatively low statutory tax rate, but also the
tax applicability. Unlike interest or dividend income, capital gains can be o¬set by capital
losses. Moreover, capital gains are not incurred on an annual basis, but only when they
are realized. Therefore, the best form of income for investors is long-term capital gains.

The tax treatment of ¬nancial securities”and especially bonds”is an ongoing cat-and-mouse
Details, details, details...
game between the IRS and corporate tax lawyers. For example, there are some very intricate
tax rules on how capital gain income and interest income on bonds must be computed. Such
regulations prevent ¬rms from paying out interest income in a form that makes them capital
gains for their investors. (The speci¬c loophole that these regulations originally closed were
discount bonds.) In addition, there are hundreds of special clauses”some pure corporate
subsidies in the tax codes (and some targeted at one qualifying company only!), and others
penalizing particular situations for no obvious reason. We just noted that even the dividend
tax treatment is “sunset” in 2008”plus, the tax code may change every other year before and
¬le=caprest.tex: RP
Section 23·1. The Role of Personal Income Taxes and Clientele E¬ects.

after 2008, too! So, it is more important for you to learn how to think about taxes than it is for
you to know the detailed tax clauses and rates. Any details will likely be outdated within 10
years”if not sooner.

23·1.B. The Principle Should Be “Joint Tax Avoidance”

The main point of this section is that managers, who want to best represent corporate owners, The owners care not
about where taxes are
should consider not only their own corporate income taxes, but also their investors™ personal
paid (corporation or
income taxes. To see this, pretend that you are the owner of a corner shop (“the corporation”) personal), just that as
and you are also its manager. Do you care whether the IRS taxes you right at the cash register of little as possible is paid
in total.
your corporate business, or taxes you personally when you move the cash from the corporate
register into your personal pocket? Or do you care how much you can ultimately put into your
pocket? The ¬nance premise is that you care only about the money in your pocket that you
have left over after Uncle Sam has had his dip from both. You want to reduce the tax obligation
both at the cash register and at your personal pocket. Corporate investors are no di¬erent from
your corner shop. They really care only about their after-tax personal income in the end, not
about whether the corporation pays taxes or they themselves pay taxes.


• Both corporate and personal taxes that can be avoided translates into cash
that the owners can keep.

• Reducing the total taxes ultimately collected by Uncle Sam (now and in the
future) increases the value of the ¬rm.

How Personal Taxes Enter The Firm™s Cost of Capital
How do corporate managers ¬nd the personal income tax rate applicable to their investors? Investors are the
corporate owners.
Importantly, they may not need to bother ¬nding it. This is because whatever the personal
Personal taxes matter to
income taxes may be, they manifest themselves in the cost of capital that investors demand the cost of capital
from the ¬rm. When a ¬rm o¬ers securities that cause a lot of personal tax liabilities, then demanded by investors.
investors will demand a higher expected rate of return. Securities that cause no personal tax
liabilities will be snapped up by our investors even at lower expected rates of return.
How do personal taxes enter the corporate cost of capital formula, i.e., the WACC formula Personal taxes do not
change the WACC or APV
in 22.18 and the APV formula in 22.6? The answer is that the formulas themselves do not
change. You can continue to use them. That is, as long as you use the two formulas on
the “after-corporate-income-tax cash ¬‚ows as if 100% equity ¬nanced” (and not on the “after-
corporate-income-tax and after-personal-income-tax cash ¬‚ows, as if 100% equity ¬nanced and
fully taxed at both corporate and personal level”), the formulas remain the right ones to use.
You can think of your investors™ personal income taxes only as in¬‚uencing the cost of capital
inputs into these two formulas”speci¬cally, the appropriate expected rates of return on debt
E(˜DT ) and equity E(˜EQ ) that investors demand. (These are the before-personal income tax
r r
rates of return, as you will see in the next paragraph.)
An example will make this clearer. Assume that the equilibrium is such that investors demand An example of how to
think about personal
an after-tax expected rate of return of 6% to hold risky equity capital. If the e¬ective personal
income taxes.
income tax rate on equity is 50%, then the market equilibrium would have shareholders demand
and receive an expected rate of return of E(rEQ ) = 12% from the corporation, because (1 ’
50%)·12% = 6%. The 12% is the input to the WACC and APV formulas”the rate of return that
investors demand before they have to pay their personal taxes. (The 6% rate of return after-
personal income tax is what matters to investors, but it does not show up numerically in either
¬le=caprest.tex: LP
584 Chapter 23. Other Capital Structure Considerations.

How should you as a CFO adjust for the e¬ects of changes in the personal taxation of investors
An example of how to
think about a cut in (e.g., the Bush dividend tax cuts of 2003)? For argument™s sake, presume that the e¬ective
personal income taxes.
personal income tax rate on equity drops from 50% to 25%. At what rate will the corporation
now be able to ¬nance projects? Our investors demand an expected after-tax rate of return
of 6%, so at an expected rate of return of E(rEQ ) = 8%, they will again come out with their
required (1 ’ 25%)·8% = 6% expected rate of return. From the perspective of the corporation,
the necessary and appropriate cost of capital E(rEQ ) in the formulas would have dropped from
12% to 8%. (Of course, this is a simpli¬cation. The tax cuts may also change other alternatives
available to investors. They could attract more ¬rms and investors into this market, too, which
could force the appropriate equilibrium after-tax expected rate of return on equity away from
6%, too.)


• The WACC or APV formulas from Chapter 22 remain applicable in the pres-
ence of personal income taxes.
• Personal income taxes are visible to corporate managers in the cost of capital
that they have to pay investors in order to obtain ¬nancing. Put di¬erently,
they manifest themselves in the expected-rates-of-return inputs to the WACC
and APV formulas.

In the real world, the ¬nancial markets provide managers with costs of capital that re¬‚ect not
only personal taxes, but also a host of other investor concerns that we will discuss next”but
the WACC and APV formulas always remain applicable.

23·1.C. Tax Clienteles

Your Problem ” How to Minimize Total IRS Receipts
Before we discuss how to minimize taxes, should we not weigh doing so (usually by ¬nanc-
Investors should care
only about value today! ing with more corporate debt) against such concerns as earnings dilution or the riskiness of
the equity? Worrying about these concerns too much is a mistake that the ¬nancially naïve
often make. The correct view is that reported earnings per s© are a less important concern.
Instead, what really matters is the after-tax money that investors get to keep in the end. To
the extent that Uncle Sam receives less money, owners ultimately get more money. It is money
that ultimately matter to them, not any ephemeral concerns about the debt-equity ratio or the
risk split-up or the earnings dilution, or any of a hundred other reasons sometimes given by
management. The capital markets are smart enough to know what really matters”money to
investors. (There is also good empirical evidence that capital markets indeed appreciate lower
income taxes, and reward their reduction with a higher market value.)
You now know the principle of joint tax avoidance, but you do not yet know how to implement
Companies can shift tax
burdens from it. You know that as manager acting on behalf of your corporate owners, you should try to
themselves to their
arrange the capital structure so as to minimize the sum of personal and corporate income


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