Brealey, Myers. Principles of Corporate Finance. 7th edition
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Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
tion that the only financing side effects are the interest tax shields on debt supported
by the perpetual crusher project, and we consider corporate taxes only. (In other
words, .) As in Section 19.1, we assume that the perpetual crusher is an exact
match, in business risk and financing, to its parent, the Sangria Corporation.
Base-case NPV is found by discounting after-tax project cash flows of $1.355 mil-
lion at the opportunity cost of capital r of 12 percent and then subtracting the $12.5
million outlay. The cash flows are perpetual, so
Thus the project would not be worthwhile with all-equity financing. But it actually
supports debt of $5 million. At an 8 percent borrowing rate ( ) and a 35 percent
tax rate ( ), annual interest tax shields are , or $140,000.
What are those tax shields worth? It depends on the financing rule the company
follows. There are two common rules:
• Financing Rule 1: Debt fixed. Borrow a fraction of initial project value and make
any debt repayments on a predetermined schedule. We followed this rule in
Table 19.1.
• Financing Rule 2: Debt rebalanced. Adjust the debt in each future period to keep
it at a constant fraction of future project value.
What do these rules mean for the perpetual crusher project? Under Financing
Rule 1, debt stays at $5 million come hell or high water, and interest tax shields stay
at $140,000 per year. The tax shields are tied to fixed interest payments, so the 8 per-
cent cost of debt is a reasonable discount rate:
If the perpetual crusher were financed solely by equity, project value would be
$11.29 million. With fixed debt of $5 million, value increases by PV(tax shield) to
.
Under Financing Rule 2, debt is rebalanced to 40 percent of actual project value.
That means future debt levels are not known at the start of the project. They shift
up or down depending on the success or failure of the project. Interest tax shields
therefore pick up the project’s business risk.
If interest tax shields are just as risky as the project, they should be discounted
at the project’s opportunity cost of capital, in this case 12 percent.
We have now valued the perpetual crusher project three different ways:
1. APV (debt fixed) $.54 million.
2. APV (debt rebalanced) $.04 million.
3. NPV (discounting at WACC) $0 million.
The first APV is the highest, because it assumes that debt is fixed, not rebalanced,
and that interest tax shields are as safe as the interest payments generating them.
APV 1debt rebalanced21.21 1.17 $.04 million
PV1tax shields,
debt rebalanced2
140,000
.12
1, 170,000, or $1.17 million
11.29 1.75 $13.04 million
1.21 1.75 $.54
million
APV base-case NPV PV1tax shield2
PV1tax shields, debt fixed2
140,000
.08
$1,750,000, or $1.75 million
.35 .08 5 .14T
c
.35
r
D
.08
Base-case NPV 12.5
1.355
.12
$1.21 million
T* T
c
CHAPTER 19 Financing and Valuation 541
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
A Technical Point on Financing Rule 2
But why don’t APV calculations 2 and 3, which both follow Financing Rule 2, gen-
erate the same number? The answer is that our calculation of APV (debt rebal-
anced) gets the implications of Financing Rule 2 only approximately right.
Even when debt is rebalanced, next year’s interest tax shields are fixed. Year 1’s in-
terest tax shield is fixed by the amount of debt at date 0, the start of the project. There-
fore, year 1’s interest tax shield should have been discounted at 8, not 12 percent.
Year 2’s interest tax shield is not known at the start of the project, since debt is
rebalanced at date 1, depending on the first year’s performance. But once date 1’s
debt level is set, the interest tax shield is known. Therefore the forecasted interest
tax shield at date 2 ($140,000) should be discounted for one year at 12 percent and
one year at 8 percent.
The reasoning repeats. Every year, once debt is rebalanced, next year’s interest tax
shield is fixed. For example, year 15’s interest tax shield is fixed once debt is rebal-
anced in year 14. Thus the present value of the year 15 tax shield is the date 0 fore-
cast (again $140,000) discounted one year at 8 percent and 14 years at 12 percent.
So the procedure for calculating the exact value of tax shields under Financing
Rule 2 is as follows:
1. Discount at the opportunity cost of capital, because future tax shields are
tied to actual cash flows.
2. Multiply the resulting PV by , because the tax shields are
fixed one period before receipt.
For the perpetual crusher project, the forecasted interest tax shields are $140,000
or $.14 million. Their exact value is
The APV of the project, given these assumptions about future debt capacity, is
This calculation exactly matches our first valuation of the perpetual crusher proj-
ect based on WACC. Discounting at WACC implicitly recognizes that next year’s
interest tax shield is fixed by this year’s debt level.
21
1.21 1.21 $0 million
APV base-case NPV PV1tax shield2
PV1exact2 1.17 a
1.12
1.08
b $1.21 million
PV1approximate2
.14
.12
$1.17 million
11 r2/11 r
D
2
542 PART V Dividend Policy and Capital Structure
21
Miles and Ezzell (see footnote 5) have come up with a useful formula for modifying WACC:
where L is the debt-to-value ratio and is the net tax saving per dollar of interest paid. In practice
is hard to pin down, so the marginal tax rate is used instead.
The Miles–Ezzell formula assumes Financing Rule 2, that is, that debt is rebalanced at the end of
every period (although next year’s interest tax shield is fixed). You can check that it values the Sangria
project exactly .
In Section 19.3, we used a three-step procedure to calculate WACC at different debt ratios. It turns
out that this procedure is not exactly the same as the changes in WACC calculated by the Miles–Ezzell
formula. However, the numerical differences are in practice very small. In the Sangria example they are
lost in rounding.
1NPV $0 million2
T
c
T*T*
WACC r Lr
D
T* a
1 r
1 r
D
b
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
Which Financing Rule?
In practice it rarely pays to worry whether interest tax shields are valued approxi-
mately or exactly ($0 million). Your worrying time
will be much better spent in refining forecasts of operating cash flows and think-
ing through what-if scenarios.
But which financing rule is better—debt fixed or debt rebalanced?
Sometimes debt has to be paid down on a fixed schedule, as for the solar heater
project in Table 19.1. This is the case for most LBOs. But as a general rule we vote
for the assumption of rebalancing, that is, for Financing Rule 2. Any capital bud-
geting procedure that assumes debt levels are always fixed after a project is under-
taken is grossly oversimplified. Should we assume that the perpetual crusher proj-
ect contributes $5 million to the firm’s debt capacity not just when the project is
undertaken but from here to eternity? That amounts to saying that the future value
of the project will not change—a strong assumption indeed.
Financing Rule 2 is better: not “Always borrow $5 million,” but “Always bor-
row 40 percent of the perpetual crusher project value.” Then if project value in-
creases, the firm borrows more. If it decreases, the firm borrows less. Under this
policy you can no longer discount future interest tax shields at the borrowing rate
because the shields are no longer certain. Their size depends on the amount actu-
ally borrowed and, therefore, on the actual future value of the project.
APV and Hurdle Rates
APV tells you whether a project makes a net contribution to the value of the firm.
It can also tell you a project’s break-even cash flow or internal rate of return. Let’s
check this for the perpetual crusher project. We first calculate the income at which
. We will then determine the project’s minimum acceptable internal rate
of return (IRR).
or 10.84 percent of the $12.5 million outlay. In other words, the minimum accept-
able IRR for the project is 10.84 percent. At this IRR project APV is zero.
Suppose that we encounter another project with perpetual cash flows. Its op-
portunity cost of capital is also , and it also expands the firm’s borrowing
power by 40 percent of project value. We know that if such a project offers an IRR
greater than 10.84 percent, it will have a positive APV. Therefore, we could shorten
the analysis by just discounting the project’s cash inflows at 10.84 percent.
22
This
discount rate is the adjusted cost of capital. It reflects both the project’s business risk
and its contribution to the firm’s debt capacity.
We will call the adjusted cost of capital . To calculate we find the minimum
acceptable internal rate of return—the IRR at which . The rule is this: Ac-
cept projects which have a positive NPV at the adjusted cost of capital .r*
APV 0
r*r*
r .12
Annual income $1.355 million
annual income
.12
12.5 1.21 0
APV
annual income
r
investment PV1tax shield2
APV 0
1giving APV $.04 million2
CHAPTER 19 Financing and Valuation 543
22
Remember that forecasted project cash flows do not reflect the tax shields generated by any debt the
project may support. Project taxes are calculated assuming all-equity financing.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
The 10.84 percent adjusted cost of capital for the perpetual crusher project is (no
surprise) identical to Sangria Corporation’s WACC, calculated in Section 19.1.
A General Definition of the Adjusted Cost of Capital
We recapitulate the two concepts of cost of capital:
• Concept 1: The opportunity cost of capital (r). This is the expected rate of return
offered in capital markets by equivalent-risk assets. This depends on the risk
of the project’s cash flows. The opportunity cost of capital is the correct
discount rate for the project if it is all-equity-financed.
• Concept 2: The adjusted cost of capital (r*). This is an adjusted opportunity cost
or hurdle rate that reflects the financing side effects of an investment project.
Some people just say “cost of capital.” Sometimes their meaning is clear in con-
text. At other times, they don’t know which concept they are referring to, and that
can sow widespread confusion.
When financing side effects are important, you should accept projects with pos-
itive APVs. But if you know the adjusted discount rate, you don’t have to calculate
APV: You just calculate NPV at the adjusted rate. The weighted-average cost of
capital formula is the most common way to calculate the adjusted cost of capital.
544 PART V
Dividend Policy and Capital Structure
19.5 DISCOUNTING SAFE, NOMINAL CASH FLOWS
Suppose you’re considering purchase of a $100,000 machine. The manufacturer
sweetens the deal by offering to finance the purchase by lending you $100,000 for
five years, with annual interest payments of 5 percent. You would have to pay 13
percent to borrow from a bank. Your marginal tax rate is 35 percent ( ).
How much is this loan worth? If you take it, the cash flows, in thousands of dol-
lars, are
T
c
.35
Period
01 2 3 4 5
Cash flow 100
Tax shield
After-tax cash flow 100 103.253.253.253.253.25
1.751.751.751.751.75
1055555
What is the right discount rate?
Here you are discounting safe, nominal cash flows—safe because your company
must commit to pay if it takes the loan,
23
and nominal because the payments would
be fixed regardless of future inflation. Now, the correct discount rate for safe, nom-
inal cash flows is your company’s after-tax, unsubsidized borrowing rate.
24
In this
case r* r
D
11 T
c
2 .1311 .352 .0845. Therefore
23
In theory, safe means literally “risk-free,” like the cash returns on a Treasury bond. In practice, it means
that the risk of not paying or receiving a cash flow is small.
24
In Section 13.1 we calculated the NPV of subsidized financing using the pretax borrowing rate. Now you
can see that was a mistake. Using the pretax rate implicitly defines the loan in terms of its pretax cash flows,
violating a rule promulgated way back in Section 6.1: Always estimate cash flows on an after-tax basis.
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
The manufacturer has effectively cut the machine’s purchase price from $100,000
to . You can now go back and recalculate the ma-
chine’s NPV using this fire-sale price, or you can use the NPV of the subsidized
loan as one element of the machine’s adjusted present value.
A General Rule
Clearly, we owe an explanation of why is the right discount rate for safe,
nominal cash flows. It’s no surprise that the rate depends on , the unsubsidized
borrowing rate, for that is investors’ opportunity cost of capital, the rate they
would demand from your company’s debt. But why should be converted to an
after-tax figure?
Let’s simplify by taking a one-year subsidized loan of $100,000 at 5 percent. The
cash flows, in thousands of dollars, are
r
D
r
D
r
D
11 T
c
2
$100,000 $20,520 $79,480
20.52, or $20,520
NPV 100
3.25
1.0845
3.25
11.08452
2
3.25
11.08452
3
3.25
11.08452
4
103.25
11.08452
5
CHAPTER 19 Financing and Valuation 545
Period 0 Period 1
Cash flow 100
Tax shield
After-tax cash flow 100 103.25
1.75
105
Now ask, What is the maximum amount X that could be borrowed for one year
through regular channels if $103,250 is set aside to service the loan?
“Regular channels” means borrowing at 13 percent pretax and 8.45 percent af-
ter tax. Therefore you will need 108.45 percent of the amount borrowed to pay back
principal plus after-tax interest charges. If , then .
Now if you can borrow $100,000 by a subsidized loan, but only $95,205 through
normal channels, the difference ($4,795) is money in the bank. Therefore, it must
also be the NPV of this one-period subsidized loan.
When you discount a safe, nominal cash flow at an after-tax borrowing rate, you
are implicitly calculating the equivalent loan, the amount you could borrow through
normal channels, using the cash flow as debt service. Note that
In some cases, it may be easier to think of taking the lender’s side of the equiva-
lent loan rather than the borrower’s. For example, you could ask, How much would
my company have to invest today in order to cover next year’s debt service on the
subsidized loan? The answer is $95,205: If you lend that amount at 13 percent, you
will earn 8.45 percent after tax, and therefore have . By
this transaction, you can in effect cancel, or “zero out,” the future obligation. If you
can borrow $100,000 and then set aside only $95,205 to cover all the required debt
service, you clearly have $4,795 to spend as you please. That amount is the NPV of
the subsidized loan.
95,20511.08452 $103,250
Equivalent loan PV a
cash flow available
for debt service
b
103,250
1.0845
95,205
X 95,2051.0845X 103,250
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
Therefore, regardless of whether it’s easier to think of borrowing or lending, the
correct discount rate for safe, nominal cash flows is an after-tax interest rate.
25
In some ways, this is an obvious result once you think about it. Companies are
free to borrow or lend money. If they lend, they receive the after-tax interest rate on
their investment; if they borrow in the capital market, they pay the after-tax inter-
est rate. Thus, the opportunity cost to companies of investing in debt-equivalent
cash flows is the after-tax interest rate. This is the adjusted cost of capital for debt-
equivalent cash flows.
26
Some Further Examples
Here are some further examples of debt-equivalent cash flows.
Payout Fixed by Contract Suppose you sign a maintenance contract with a truck
leasing firm, which agrees to keep your leased trucks in good working order for
the next two years in exchange for 24 fixed monthly payments. These payments are
debt-equivalent flows.
27
Depreciation Tax Shields Capital projects are normally valued by discounting
the total after-tax cash flows they are expected to generate. Depreciation tax shields
contribute to project cash flow, but they are not valued separately; they are just
folded into project cash flows along with dozens, or hundreds, of other specific in-
flows and outflows. The project’s opportunity cost of capital reflects the average
risk of the resulting aggregate.
However, suppose we ask what depreciation tax shields are worth by them-
selves. For a firm that’s sure to pay taxes, depreciation tax shields are a safe,
nominal flow. Therefore, they should be discounted at the firm’s after-tax bor-
rowing rate.
28
Suppose we buy an asset with a depreciable basis of $200,000, which can be de-
preciated by the five-year tax depreciation schedule (see Table 6.4). The resulting
tax shields are
546 PART V
Dividend Policy and Capital Structure
25
Borrowing and lending rates should not differ by much if the cash flows are truly safe, that is, if the
chance of default is small. Usually your decision will not hinge on the rate used. If it does, ask which
offsetting transaction—borrowing or lending—seems most natural and reasonable for the problem at
hand. Then use the corresponding interest rate.
26
All the examples in this section are forward-looking; they call for the value today of a stream of future
debt-equivalent cash flows. But similar issues arise in legal and contractual disputes when a past cash
flow has to be brought forward in time to a present value today. Suppose it’s determined that company
A should have paid B $1 million ten years ago. B clearly deserves more than $1 million today, because
it has lost the time value of money. The time value of money should be expressed as an after-tax bor-
rowing or lending rate, or if no risk enters, as the after-tax risk-free rate. The time value of money is not
equal to B’s overall cost of capital. Allowing B to “earn” its overall cost of capital on the payment allows
it to earn a risk premium without bearing risk. For a broader discussion of these issues, see F. Fisher and
C. Romaine, “Janis Joplin’s Yearbook and Theory of Damages,” Journal of Accounting, Auditing & Finance
5 (Winter/Spring 1990), pp. 145–157.
27
We assume you are locked into the contract. If it can be canceled without penalty, you may have a
valuable option.
28
The depreciation tax shields are cash inflows, not outflows as for the contractual payout or the subsi-
dized loan. For safe, nominal inflows, the relevant question is, How much could the firm borrow today
if it uses the inflow for debt service? You could also ask, How much would the firm have to lend today
to generate the same future inflow?
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
The after-tax discount rate is . (We continue to
assume a 13 percent pretax borrowing rate and a 35 percent marginal tax rate.) The
present value of these shields is
A Consistency Check
You may have wondered whether our procedure for valuing debt-equivalent cash
flows is consistent with the WACC and APV approaches presented earlier in this
chapter. Yes, it is consistent, as we will now illustrate.
Let’s look at another very simple numerical example. You are asked to value
a $1 million payment to be received from a blue-chip company one year hence.
After taxes at 35 percent, the cash inflow is $650,000. The payment is fixed by
contract.
Since the contract generates a debt-equivalent flow, the opportunity cost of cap-
ital is the rate investors would demand on a one-year note issued by the blue-chip
company, which happens to be 8 percent. For simplicity, we’ll assume this is your
company’s borrowing rate too. Our valuation rule for debt-equivalent flows is
therefore to discount at :
What is the debt capacity of this $650,000 payment? Exactly $617,900. Your com-
pany could borrow that amount and pay off the loan completely—principal and
after-tax interest—with the $650,000 cash inflow. The debt capacity is 100 percent
of the PV of the debt-equivalent cash flow.
If you think of it that way, our discount rate is just a special case of
WACC with a 100 percent debt ratio ( ).
Now let’s try an APV calculation. This is a two-part valuation. First, the $650,000
inflow is discounted at the opportunity cost of capital, 8 percent. Second, we add
the present value of interest tax shields on debt supported by the project. Since the
firm can borrow 100 percent of the cash flow’s value, the tax shield is APV, and
APV is
APV
650,000
1.08
.081.352APV
1.08
r
D
T
c
r
D
11 T
c
2 if D/V 1 and E/V 0
WACC r
D
11 T
c
2D/V r
E
E/V
D/V 1
r
D
11 T
c
2
PV
650,000
1.052
$617,900
r
*
r
D
11 T
c
2 .0811 .352 .052
56.2,
or $56,200
PV
14
1.0845
22.4
11.08452
2
13.4
11.08452
3
8.1
11.08452
4
8.1
11.08452
5
4.0
11.08452
6
r
D
11 T
c
2 .1311 .352 .0845
CHAPTER 19 Financing and Valuation 547
Period
12 3 4 5 6
Percentage deductions 20 32 19.2 11.5 11.5 5.8
Dollar deductions
(thousands) $40 $64 $38.4 $23 $23 $11.6
Tax shields at
(thousands) $14 $22.4 $13.4 $8.1 $8.1 $4.0T
c
.35
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
Solving for APV, we get $617,900, the same answer we obtained by discounting at
the after-tax borrowing rate. Thus our valuation rule for debt-equivalent flows is a
special case of APV.
548 PART V
Dividend Policy and Capital Structure
19.6 YOUR QUESTIONS ANSWERED
Question: All these cost of capital formulas—which ones do financial managers
actually use?
Answer: The after-tax weighted-average cost of capital, most of the time. WACC is
estimated for the company, or sometimes for an industry. We recommend industry
WACCs when data are available for several closely comparable firms. The firms
should have similar assets, operations, business risks, and growth opportunities.
Of course, conglomerate companies, with divisions operating in two or more un-
related industries, should not use a single company or industry WACC. Such firms
should try to estimate a different industry WACC for each operating division.
Question: But WACC is the correct discount rate only for “average” projects.
What if the project’s financing differs from the company’s or industry’s?
Answer: Remember, investment projects are usually not separately financed.
Even when they are, you should focus on the project’s contribution to the firm’s
overall debt capacity, not on its immediate financing. (Suppose it’s convenient to
raise all the money for a particular project with a bank loan. That doesn’t mean the
project itself supports 100 percent debt financing. The company is borrowing
against its existing assets as well as the project.)
But if the project’s debt capacity is materially different from the company’s ex-
isting assets, or if the company’s overall debt policy changes, WACC should be ad-
justed. The adjustment can be done by the three-step procedure explained in Sec-
tion 19.3.
Question: Could we do one more numerical example?
Answer: Sure. Suppose that WACC has been estimated as follows at a 30 percent
debt ratio:
What is the correct discount rate at a 50 percent debt ratio?
First, let’s repeat the three-step procedure.
Step 1. Calculate the opportunity cost of capital.
Step 2. Calculate the new costs of debt and equity. The cost of debt will be higher
at 50 percent debt than 30 percent. Say it is . The new cost of equity is
.169
or 16.9%
.132 1.132 .0952
50/50
r
E
r 1r r
D
2 D/E
r
D
.095
.091.32 .151.72 .132 or 13.2%
r r
D
D/V r
E
E/V
.0911 .352 1.32 .151.72 .1226, or 12.26%
WACC r
D
11 T
c
2
D
V
r
E
E
V
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
Step 3. Recalculate WACC.
Question: How do I use the capital asset pricing model to calculate the after-tax
weighted-average cost of capital?
Answer: First plug the equity beta into the capital asset pricing formula to cal-
culate , the expected return to equity. Then use this figure, along with the after-
tax cost of debt and the debt-to-value and equity-to-value ratios, in the WACC for-
mula. We covered this in Chapter 9. The only change here is use of the after-tax cost
of debt, .
Of course the CAPM is not the only way to estimate the cost of equity. For ex-
ample, you might be able to use arbitrage pricing theory (APT—see Section 8.4) or
the dividend-discount model (see Section 4.3).
Question: But suppose I do use the CAPM? What if I have to recalculate the eq-
uity beta for a different debt ratio?
Answer: The formula for the equity beta is
where is the equity beta, is the asset beta, and is the beta of the com-
pany’s debt.
Question: Can I use the capital asset pricing model to calculate the asset beta and
the opportunity cost of capital?
Answer: Sure. We covered this in Chapter 9. The asset beta is a weighted average
of the debt and equity betas:
29
Suppose you needed the opportunity cost of capital r. You could calculate and
then r from the capital asset pricing model.
Question: I think I understand how to adjust for differences in debt capacity or
debt policy. How about differences in business risk?
Answer: If business risk is different, then r, the opportunity cost of capital, is
different.
Figuring out the right r for an unusually safe or risky project is never easy.
Sometimes the financial manager can use estimates of risk and expected return
for companies similar to the project. Suppose, for example, that a traditional
pharmaceutical company is considering a major commitment to biotech research.
The financial manager could pick a sample of biotech companies, estimate their

A

A

D
D
V

E
E
V

D

A

E

E

A
1
A

D
2
D
E
r
D
11 T
c
2
r
E
.09511 .3521.52 .1691.52 .1154, or about 11.5%
WACC r
D
11 T
c
2D/V r
E
E/V
CHAPTER 19 Financing and Valuation 549
29
This formula assumes Financing Rule 2. If debt is fixed, taxes complicate the formulas. For exam-
ple, if debt is fixed and permanent, and only corporate taxes are considered, the formula for
changes to

E

A
1
A

D
2 11 T
c
2D/E

E
Brealey−Meyers:
Principles of Corporate
Finance, Seventh Edition
V. Dividend Policy and
Capital Structure
19. Financing and
Valuation
© The McGraw−Hill
Companies, 2003
550 PART V Dividend Policy and Capital Structure
average beta and cost of capital, and use these estimates as benchmarks for the
biotech investment.
But in many cases it’s difficult to find a good sample of matching companies
for an unusually safe or risky project. Then the financial manager has to adjust
the opportunity cost of capital by judgment.
30
Section 9.5 may be helpful in
such cases.
Question: Let’s go back to the cost of capital formulas. The tax rates are confus-
ing. When should I use and when ?
Answer: Always use , the marginal corporate tax rate, (1) when calculating
WACC as a weighted average of the costs of debt and equity and (2) when dis-
counting safe, nominal cash flows. In each case the discount rate is adjusted only
for corporate taxes.
31
APV in principle calls for , the net tax saving per dollar of interest paid by
the firm. This depends on the effective personal tax rates on debt and equity
income. is almost surely less than , but it is very difficult to pin down
the numerical difference. Therefore in practice is almost always used as an
approximation.
Question: When do I need adjusted present value (APV)?
Answer: The WACC formula picks up only one financing side effect: the
value of interest tax shields on debt supported by a project. If there are other
side effects—subsidized financing tied to a project, for example—you should
use APV.
You can also use APV to show the value of interest tax shields:
where base-case NPV assumes all-equity financing. But it’s usually easier to do this
calculation in one step, by discounting project cash flows at an adjusted cost of cap-
ital (usually WACC). Remember, though, that discounting by WACC usually as-
sumes Financing Rule 2, that is, debt rebalanced to a constant fraction of future
project value. If this financing rule is not right, you may need APV to calculate
PV(tax shield), as we did for the solar heater project in Table 19.1.
32
Suppose, for example, that you are analyzing a company just after a leveraged
recapitalization. The company has a very high initial debt level but plans to pay
down the debt as rapidly as possible. APV could be used to obtain an accurate
valuation.
30
The judgment may be implicit. That is, the manager may not explicitly announce that the discount
rate for a high-risk project is, say, 2.5 percentage points above the standard rate. But the project will not
be approved unless it offers a higher-than-standard rate of return.
31
Any effects of personal income taxes are reflected in and , the rates of return demanded by debt
and equity investors.
32
Having read Section 19.5, you may be wondering why we did not discount at the after-tax borrowing
rate in Table 19.1. The answer is that we wanted to simplify and take one thing at a time. If debt is fixed
and the odds of financial distress are low, interest tax shields are safe, nominal flows, and there is a case
for using the after-tax rate. Doing so assumes that the firm will, or can, take out an additional loan with
debt service exactly covered by the interest tax shields.
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