On the Applicability of WACC for Investment Decisions

On the Applicability of WACC for Investment Decisions

Prof. Dr. Jaime Sabal
Department of Financial Management and Control
ESADE. Ramon Llull University

December 2004



Abstract

Although WACC is appropriate for project and firm valuation, it is not a good
rule for investment decision making. The reason is that by mixing up the value
of the project itself with the tax shield, WACC can often turn unattractive
projects into apparently acceptable ones. Real investments must be accepted
only if they yield positive NPVs when discounted at the unleveraged discount
rate, that is, without accounting for the tax shield. WACC enters the picture
only to assess the impact of a new project on firm value, once it has been
accepted, and when a fixed debt ratio policy is in place.







1

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Introduction

According to Miller & Modigliani (1958, 1963), hereinafter MM, the
cost of capital WACC of a firm after corporate taxes (but before personal
taxes) is given by the formula:1

D
=
⋅(
E
WACC
1−T ⋅ r +
⋅ r (1)
C )
D
E
V
V
The following relationship also holds:

DT 
WACC = 1
C
−
⋅ r


(2)
0

V 
Where,
ro is the asset discount rate after taxes
D is the market value of debt
TC is the corporate tax rate
V is the market value of the firm
rD is the cost of debt
E is the market value of equity
rE is the cost of equity
If the terms are reordered, the following expression is found for the
return on equity with taxes:

1 I would like to thank Randolph Westerfield,Carlos Jaramillo, Carlos Molina, and Maximiliano González
for helpful comments.
2

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D
r = r +
⋅  r − r ⋅ 1−T 
E
0
( 0
D ) (
C )
E
 (3)
There is also the following equivalent formula:
V = V + DT (4)
u
C
Where Vu is the value of the unleveraged firm after taxes.
This last formula shows that the value of the firm rises with debt by an
amount equal to DTC. This amount is known as the tax shield.
The above results are based on the following assumptions:


No transaction costs

This assumption ensures that everyone has the same access to financial
markets. For example, with transaction costs the possibility of adjusting
personal portfolios to compensate for the firms’ financing decisions
would be costly, and might not be valid. Therefore, leverage would not
be irrelevant when computing firm value.


Perfectly competitive financial markets

With this condition nobody has advantages in the financial markets. If
this were not the case, leverage preferences could differ among market
participants and debt levels would not be irrelevant.





3

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No agency costs

This implies that the manager’s sole objective is to maximize
shareholders’ wealth. Therefore, the financial mix does not have any
relation with the particular interests of administrators nor any impact on
firm value.


No personal taxes

Individuals do not pay taxes.2


All cash flows are no-growth perpetuities

This assumption merely helps to simplify the formulas for the cost of
capital and the value of the firm.

MM’s work gave rise to two equivalent approaches for firm and project
valuation.3 The value of a firm or a project can be computed either by
discounting asset cash flows after taxes at WACC, or by discounting
asset cash flows after taxes at the unleveraged discount rate r0 and adding
the PV of the tax shield. The latter approach is known as Adjusted
Present Value (APV).4
In the following, it will be shown that although discounting at WACC is
appropriate for project and firm valuation, it is not a good rule for
investment decision making. For the sake of simplicity the argument will
be illustrated with a practical example.

2 Miller (1977) shows how MM’s results are modified in the presence of personal taxes.
3 Ruback (2002) proposes a third equivalent method: Capital Cash Flows.
4 APV has been generalized to include other effects on value besides the tax shield. For further
information refer to Ross, Westerfield & Jaffe (1999).
4

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WACC and Project Valuation

Assume that a firm is started with a project yielding a $1 million yearly
perpetual cash flow after taxes.5 The project requires an initial
investment of $100 million and will be fully financed with equity. The
project demands 12% annual return after taxes.6
The project’s present value PV is:
10MM
PV =
= $83.34
+
MM (5)
0.12
The NPV will be:
NPV = 83.34
+
MM −100MM = −$16.67MM (6)
Thus, the project must be rejected.7
In the event of the project being undertaken the financial balance sheet8
of the firm would look like this:

Assets Liabilities
Project: +$83.34MM
Equity: +$83.34MM

Investors would have put up $100 million in exchange for equity worth
just $83.34 million. A bad decision, clearly. The present value rule has
guided us wisely.
But, what is behind the present value rule?

5 In reality cash flows are not certain but expected.
6 The discount rate can be determined by the CAPM or any other asset pricing model such as the
APT.
7 Throughout the paper it is assumed that management maximizes firm value (i.e. there are no
agency problems) and that there are no costs of financial distress.
8 Meaning a balance sheet in market value terms.
5

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Its key assumption is that all investors have equal access to financial
markets and that these markets are complete and efficient. In our
example, this implies that the investor always has the choice of placing
the $100 million in a comparable portfolio of financial assets.
In an efficient financial market the return on this portfolio must be
equivalent to a $12 million annual perpetuity and the NPV of the
financial investment would be zero. Hence, the investor will never
undertake a negative NPV project if he has the choice of investing in a
zero NPV portfolio. This is why the present value rule dictates that only
positive NPV projects must be accepted.
Let us now see what happens when the same firm decides to take
leverage to finance the project.


Enter leverage

In general, the financial balance sheet of a leveraged firm9 is given by:

Assets Liabilities
Investments Debt
Tax shield (DTC) Equity
Total value
Total value

Now imagine that our firm has a 50% corporate tax rate and decides to
partially finance the project with $50 million of debt at a 4% annual
interest. Notice that it is understood that the borrowing and investment
decisions are independent.

9 Assuming all cash flows are no-growth perpetuities.
6

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If the project is accepted the financial balance sheet of the firm will be:

Assets Liabilities
Project: +$83.34MM
Debt: $50MM
Tax shield: +$50MMx0.5 = $25MM
Equity: $58.34MM
Total value: $108.34MM
Total value: $108.34MM

Using MM’s formulas:

The value of WACC is:

DT 

$50MM ⋅0.5 
WACC = r ⋅ 1
C
−
= 0.12⋅ 1−
= 9.23% (7)
0 




V 

$108.34MM 
And the value of rE is:
D
$50MM
r = r +
⋅  r − r ⋅ 1−T  = 0.12 +
⋅  0.12 − 0.04 ⋅ 1− 0.5  = 15.43%
E
0
( 0
D ) (
C )
(
) (
)
E
$58.34MM

(8)
Discounting at WACC, the PV of the project will now be:

$10MM
PV =
= $108.34MM (9)
0.0923
And its NPV:
NPV = $108.34MM − $100MM = +$8.34MM (10)
So, it seems that the use of leverage has turned an unattractive project
into an acceptable one.

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Why WACC is not Appropriate for Investment Decision Making

The difference in PVs between the unleveraged and the leveraged project
is:
108.34 − 83.34 = $25MM (11)
This amounts exactly to the tax shield. The result can be more clearly
appreciated if APV is used instead. The APV of the leveraged project
equals the PV of the unleveraged project plus the PV of the tax shield:
APV = E (PV
+ DT (12)
unleveraged )
C
In our example:
APV = 83.34 + 50⋅ 0.5 = $108.34MM (13)
But, is it correct to accept a negative (unleveraged) NPV project just
because of the tax shield it generates?
I think the answer is no, in general. If all investors have equal access to
complete and efficient financial markets it will still be possible to invest
$100 million in an equivalent portfolio of financial assets. This portfolio
will be equivalent to a $12 million annual perpetuity after taxes. And
since, like the real project, it will be partially financed by $50 million of
debt, the investor will conserve the benefit of the tax shield.
Let us recalculate the financial balance sheet in the event of the project
being rejected and the $100 million being invested instead in the
equivalent financial portfolio:








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Assets Liabilities
Financial portfolio: +$100MM Debt:
$50MM
Tax shield: +$50MMx0.5 = $25MM
Equity: $75MM
Total value: $125MM
Total value: $125MM

The new WACC will be:

$25MM 
WACC = 0.12⋅ 1−
= 9.6%


(14)

$125MM 
The new PV will be:
12
PV =
= $125MM (15)
0.096
Or, using APV:
APV = 100 + 25 = $125MM (16)
A result that is clearly superior to the $108.34 million obtained by
investing in the project.
Therefore, the rule must be that whenever,
a) All investors have equal access to complete and efficient financial
markets and,
b) Investment and borrowing decisions are independent of each other,
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Then, a real investment must be accepted only if it yields a positive NPV
when discounted at the unleveraged discount rate. Discounting at WACC
might lead to unfavorable decisions.10


What Happens When the Assumptions do not Hold

Unleveraged negative NPV projects might be acceptable only when these
assumptions do not hold. First, if an investor faces restrictions to access
financial markets and/or financial markets are not complete or efficient, a
financial portfolio equivalent to the project might not be attainable. In
this instance, investing in an unleveraged negative NPV project might be
justified as long as the benefit stemming from the expanded investment
opportunity set is large enough.

Second, if the investment and borrowing decisions are closely tied, then
the tax shield might not be possible without the project. Here again an
unleveraged negative NPV project might be acceptable.
Nonetheless, we should be aware that the lack of validity of the
assumptions does not justify the use of WACC for investment decision
making. WACC remains an unsafe rule for the simple reason that it
mixes up the value of the project itself with the tax shield, not allowing
the valuation of projects on their own merits. In no case must an
unleveraged negative NPV project be accepted.
As long as the investment and borrowing decisions are independent, it is
always preferable to evaluate each investment opportunity on its own
merits, meaning that the project’s cash flows must be discounted at the
unleveraged discount rate. Only then, its PV must be adjusted for the

10 The conclusion is not altered when personal taxes are considered. The only difference is that the
WACC tax rate and the tax shield are combined expressions including both the corporate and the
personal tax rates.
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