FINDING VALUE WHERE by Laurence Booth,

University of Toronto
NONE EXISTS: PITFALLS
IN USING ADJUSTED
PRESENT VALUE

T
here are many different conceptually model could be used to examine interactions be-
“correct” methods for valuing firms and tween the investment decision and the financing
1
projects. Perhaps the best known is the decision. This use of the M&M valuation framework
weighted average cost of capital (WACC) has come to be called Adjusted Present Value (APV)
approach, which involves discounting unlevered or the valuation-by-components method. The cen-
(ie., pre-interest, but after-tax) cash flows at a rate tral idea is simply that the overall value of the firm
that reflects a blend of the costs of the different can be “unbundled” into two separate components:its
sources of finance. For example, the overall enter- debt-free or unlevered value and the value of its debt
prise value can be calculated by discounting the tax shield.
operating or unlevered cash flows to the firm as a Under normal simplifying assumptions, the
whole at the firm’s weighted average cost of capital. WACC, FTE, and APV frameworks should all yield
2
If desired, the firm’s equity value can then be the same answers if correctly implemented. But
calculated by subtracting the value of the debt to the problem has always been interpreting what
“back out” the equity value. Alternatively, the value “correctly implemented” means. The key issue is
of the equity can be calculated directly by discount- in the assumption about the firm’s debt policy—
ing the cash flows to the equity holders at the equity that is, whether that policy is framed in terms of
holders’ required rate of return. This latter approach maintaining a fixed debt ratio or a fixed dollar
3
is commonly referred to as the flows to equity (FTE) amount of debt. This distinction has been picked
method. Both the WACC and FTE frameworks have up by a number of researchers, who have demon-
been in use for many years. strated the advantages of APV by focusing on
In 1963, Franco Modigliani and Merton Miller highly-leveraged transactions (HLTs) like LBOs
4
(M&M) first analyzed how corporate income taxes and leveraged recapitalizations. Some have even
interact with a firm’s financing choices to create gone so far as to assert that “using the weighted
value. They showed that, under certain assumptions, average cost of capital (WACC) is obsolete...One
the value of a firm with debt was equal to the value alternative, called adjusted present value, is espe-
of the firm without debt plus the value of the tax cially versatile and reliable, and will replace
shields from using tax-deductible debt financing. WACC as the DCF [discounted cash flow] method-
5
Stewart Myers subsequently showed how the M&M ology of choice among generalists.”

1. S. Myers, “Interactions of Corporate Financing and Investment Decisions - 4. I. Inselbag and H. Kaufold, “How to Value Recapitalizations and Leveraged
Implications for Capital Budgeting,” Journal of Finance (March 1974), pp. 1-25. Buyouts,” Journal of Applied Corporate Finance, Vol. 2 (Summer 1989), pp. 87-93;
2. R. Taggart, “Capital Budgeting and the Financing Decision: An Exposition,” idem, “Two DCF Approaches for Valuing Companies under Alternative Financing
Financial Management (Summer 1977), pp. 59-64. Strategies (and How to Choose Between Them),” Journal of Applied Corporate
3. J. Miles and J. Ezzell, “The Weighted Average Cost of Capital, Perfect Capital Finance, Vol. 10 (Spring 1997), pp. 114-122; E. Arzac, “Valuation of Highly

Markets and Project Life: A Clarification,” Journal of Financial and Quantitative Leveraged Firms,” Financial Analysts Journal (July/August 1996); and T. Luehrman,
Analysis, Vol. 15 (September 1980), pp. 719-730; L. Booth, “Capital Budgeting “Using APV: A Better Tool for Valuing Operations,” Harvard Business Review (May-
Frameworks for the Multinational Corporation,” Journal of International Business June 1997), pp. 2-10,
(Fall 1982), pp. 113-123. 5. Luehrman (1997), cited above.

8
JOURNAL OF APPLIED CORPORATE FINANCE
 The goal of this paper is to examine the relative project or acquisition is similar to the firm’s existing
advantages of these frameworks and offer guidance projects, so that the firm can use its current cost of
as to when each is likely to be most useful. In this capital. In other words, business risk is held constant.
respect this paper is similar to the recent paper by Isik In the WACC framework, the cost of capital captures
Inselbag and Howard Kaufold that appeared in this the financing of the firm in the discount rate:
6
journal. Unlike previous work, however, my focus
is on how to implement the three valuation frame- E D
Ka = Ke + K d (1 − T )
works and on theproblems that are likely to arise in V V
actual applications.
The key recommendation of this paper is to where K is the weighted average of the equity cost
a

caution against the use of APV: it is frequently K and the after-tax debt cost K (1 – T), with the
e d

unreliable and should only be used in conjunction weights determined by the debt (D/V) and equity (E/
with more conventional valuation frameworks. In V) ratios based on market values. The critical as-
particular, it only has general applicability in trans- sumption is that the firm estimates the debt and
actions that involve a structured financing, like equity costs from current capital market data and
leveraged buyouts (LBOs), project financing, and uses its optimal or target capital structure to deter-
real estate financing. Even in these cases, however, mine the financing mix.
its use depends on theoretical concepts that in Using the perpetuity formula, the overall enter-
practical applications have a wide margin of error. prise (or project) value is simply

THE CLASSIC VALUATION FRAMEWORK: EBIT (1 − T )

V =
WACC Ka

There are several layers of difficulty in using We will illustrate how the methods differ in applica-
valuation techniques, and sometimes hidden as- tions, so let’s start with a firm (or project) with
sumptions creep in. For this reason, we will start with expected EBIT of $20 million. If the firm’s tax rate is
the simplest possible case, which is the standard 50%, the perpetuity free cash flows are $10 million.
M&M perpetuity framework. The main assumptions With a target capital structure of 50% debt, and debt
of this model will then be relaxed. But, as will and equity costs of 10% and 15%, respectively, then
become clear, most of the insights of the M&M model K = 10%. In this case, the total enterprise value is
a

continue to hold in the more complicated frame- $100 million ($20mm × 50%/10%).
works. At this point it is important to note the implicit
To start out, the firm has a series of expected free assumption of the WACC approach. The perpetuity
cash flows. These are estimated in the normal way formula uses the sum of an infinite series, with both
as after-tax operating earnings, calculated as earn- the expected free cash flows and the discount rate
ings before interest and taxes multiplied by one assumed to be constant (in addition to the normal
minus the tax rate [EBIT × (1 – T)], plus non-cash assumptions of constant tax rates, interest rates, and
charges, minus changes in net working capital and business risk premiums). For the WACC to be
capital expenditures. Since we are dealing with a constant, one of two assumptions must be made:
perpetuity, the depreciation cash flows fund capital either debt financing has no impact on the WACC,
7
expenditures and there are no net changes in which is the original M&M irrelevance argument; or
working capital. As a result, the free cash flows are the debt ratio, and thus the financial risk, is constant
simply the expected after-tax operating cash flows. through time. If debt financing affects the WACC and
The next step is to determine a discount rate and the future debt ratio is expected to change, then the
a valuation framework, which is where differences WACC will no longer be constant and thus techni-
8
in extant approaches arise. Let’s assume that the cally we cannot use the perpetuity formula. Of

6. Inselbag and Kaufold (1997), cited earlier. 8. There will still be a number that discounts the expected free cash flows and
7. See F. Modigliani and M. Miller, “The Cost of Capital, Corporate Finance and gives the correct market value, but it will not be the current WACC.
the Investment Decision,” American Economic Review (June 1958), pp. 261-297;
M. Miller, “Debt and Taxes,” Journal of Finance (May 1977), pp. 261-275.

9
VOLUME 15 NUMBER 1 SPRING 2002
course, temporary deviations from the optimal capi- of the acquisition itself, which belongs to the equity
tal structure will occur over time. These deviations holders who own the project. In a fundamental
do not invalidate the WACC approach, as long as sense, the financing follows from the valuation of the
they are not expected at the time of the analysis. project or acquisition—after it is accepted—and not
10
Now let’s consider how we implement the from its direct cost. In this way the frameworks for
WACC approach. Suppose, for example, the free valuing a standard project or an acquisition are both
cash flows in the example are from a project conceptually identical.
requiring an initial investment of $60 million. In this Understanding how the debt decision is treated
case, the project’s net present value is $40 million in the WACC approach is critical for understanding
($100mm – $60mm). For a standard project, this is all the differences between standard project valuation
the operating manager needs to know: that the NPV and the valuation of stand-alone investments. For
is $40 million and the project should therefore be standard project valuation, the financing is ignored
undertaken. In most capital budgeting decisions, since it is “in” the WACC. What this means is that the
there is a separation of responsibility between the operating manager is concerned only about the
operating and financing functions. The cost of project’s NPV—a value that implicitly “spills over” to
capital of 10% is centrally determined by the the firm as a whole. The actual financing costs of
Treasurer’s office, and the operating manager is then even large projects are thus not allocated to a
simply told to discount the operating cash flows of particular project, since every project’s value spills
potential investment projects at a 10% rate and over to the overall enterprise value. In this sense, the
recommend acceptance of all positive-NPV projects. $100 million project value will increase the enter-
This separation of financing from investment deci- prise value by the same amount. Consequently, the
sions is typical for most corporations since the firm’s use of debt is not the actual project debt, but
operating manager is usually unaware of the firm’s the firm’s optimal debt ratio times its market value.
financing policies or, for that matter, its tax status. In This spillover assumption in WACC is critical.
other words, most operating decisions are decentral- Consider, for example, a multinational’s foreign
ized and most financing decisions are centralized. investment decision, where the local government
The WACC approach is quite consistent with this limits the amount of debt financing to, say, 50% of
functional separation. This is probably why surveys the project cost. Such restrictions are common in
have found the WACC approach to be so popular, both developed and emerging markets, and are
even in the valuation of acquisitions, where there is often referred to as “thin capitalization” rules. They
generally some interaction between the financing are designed to limit the allowable interest tax
9
and investment decisions. deductions and prevent tax arbitrage across coun-
It is clear in the case of a project that the tries. If our project has this restriction, then the local
functional separation embodied in the WACC frame- debt financing is limited to $30 million, or half the
work normally makes sense. However, much the project cost. However, the spillover assumption in
same analysis follows for an acquisition. In this case, the WACC approach assumes that a further $20
the value of the target would be $100 million and the million in debt will be raised at the parent level. As
cost $60 million, again leaving a $40 million NPV. the profits from the subsidiary are consolidated and
However, the firm in all probability would now show up in the parent’s income stream, the parent’s
directly consider the acquisition financing. The market value will increase, allowing it to raise
assumed debt ratio is 50%. But the critical question additional debt to maintain its optimal debt ratio. If,
is 50% of what? The right answer, at least in theory, on the other hand, local debt is subsidized, so that
is that it is 50% of the target’s total market value. In the firm is able to raise $70 million in local debt, the
this case the firm would raise $50 million in debt and firm will reduce its borrowing elsewhere to maintain
$10 million in equity. The extra $40 million in equity its 50% debt ratio. In both cases, the spillover
necessary to maintain the 50% equity ratio is the NPV assumption in WACC assumes that the debt financ-

9. See the survey by John Graham and Campbell Harvey in this issue. Another M. Fall, D. Kaufman, and B. Winger, “Acquisition/Divestiture Valuation Practices
survey found that on a 1-7 scale, DCF was rated the highest at 6.1 for large firms, in Major U.S Firms,” Financial Practice and Education (Spring 1981), pp. 73-81.
whereas various valuation multiples such as earnings were generally rated at the 10. Note that if the firm borrowed 50% of the acquisition cost, it would end
4.0 level, and firms generally used the acquiring firm’s cost of capital; see N. Mohan, up with a 30% debt ratio: $30 million in debt and a $70 million equity market value.
In this case there are internal inconsistencies in the debt ratio.

10
JOURNAL OF APPLIED CORPORATE FINANCE
ing is 50% of the market value of the project, even With the cash flows extended into infinity by rolling
if the firm actually raises a different amount specifi- over any term debt (at comparable interest rates), the
cally for the project! expected cash flows to the equity holders are $7.5
The same logic for valuing a project also applies million per year discounted at 15%, or $50 million.
to an acquisition. Suppose that the financing for the Since $50 million of the $60 million acquisition cost is
acquisition is actually 50% of the $60 million cost, or financed by debt, the NPV from the equity holders’
$30 million. Once the acquisition is accepted, the perspective is $40 million ($50mm – $10mm).
value of the firm will still increase by $100 million and This example shows the consistency of the
the firm will still increase its debt financing by a total WACC and FTE models: they both give an NPV of $40
of $50 million. Otherwise, its debt ratio will gradually million. However, a closer reading will indicate
trend down with every profitable acquisition that it problems with the logic of the FTE method. To get
makes, contradicting the assumption embedded in the $5 million interest expense requires knowing
the WACC. As long as the firm maintains an optimal that the debt financing is $50 million at a 10% interest
debt ratio, the WACC assumption is that any unused cost. Yet how do we know that $50 million in debt
debt capacity will spill over to the firm as a whole and will be raised? All we know at the outset is that debt
the firm will raise debt according to the WACC is to be 50% of the market value of the project; but
weights applied to the project’s or acquisition’s that value is unknown until it is calculated.
market value. Suppose instead that the FTE value is estimated
by using the optimal debt ratio times the $60 million
THE CONTENDER: THE FLOWS TO EQUITY acquisition cost. In this case, interest costs would be
METHOD $3 million rather than $5 million and the equity value
would be after-tax net income of $8.5 million
Now consider the traditional challenger to the [($20mm – $3mm)(1 – 0.5)] discounted at 15%, or
WACC, which is the flows to equity or FTE method. $56.6 million. Although the equity value is $56.6
The cash flows to the equity holder are discounted million rather than our previous $50 million, there
at the cost of equity capital to determine equity value are two problems. First, the estimated NPV to the
directly, rather than backing it out by subtracting the equity holder is smaller, at $26.6 million, since the
debt value from the overall enterprise value: equity holder is now assumed to put up 50% of the
cost of the project or $30 million. Second, the 15%
( EBIT − K d D )(1 − T ) equity discount rate may be an overestimate since
E= (1)
Ke there is now less financial risk to the equity holder
if debt is only $30 million rather than the $50 million
The FTE framework is not normally used for indi- as assumed in the WACC.
vidual projects, since the analyst needs to know the One possibility is that we could “iterate” to-
11
debt costs, and most decentralized operating man- wards the optimal debt level. For example, starting
agers do not have the necessary financing expertise at $30 million in debt, the NPV is $26.6 million, so the
to estimate this. More to the point, it is difficult to debt ratio is 35% ($30mm/$86.6mm); therefore man-
imagine setting up an efficient capital budgeting agement should increase the debt level to say $35
framework, in which on top of all the operating cash million and keep increasing it until the target debt
flow data, the operating manager also has to deter- ratio is the optimal 50%. But rather than clumsily
mine the financing and tax status for each individual moving to the optimal debt ratio, we can substitute
project! it directly into the FTE equation, that is, q = D/V,
The FTE method is most relevant for acquisitions where q is the optimal debt ratio. However, as soon
and very large projects. Consider our acquisition target. as we do this, and solve for the unknown enterprise
With expected EBIT of $20 million, the manager could value, the FTE method collapses to the standard
project interest costs of $5 million, so that earnings WACC equation—in which case, we may as well use
12
before tax are $15 million and $7.5 million after tax. the WACC approach from the start.

11. Arzac (1996, cited earlier) tries this in a slightly different context. 12. Let E = (EBIT – Kd qV)(1 – T))/Ke where E and V are unknown. Multiplying
by Ke, rearranging, factoring for V, and dividing while noting that E/V is just (1–
q) allows us to solve for V as EBIT(1 – T)/Ka, which is just the WACC value.

11
VOLUME 15 NUMBER 1 SPRING 2002
 The conflict over financing assumptions is the change over time. Again let’s consider the simplest
central difference between the two valuation meth- perpetuity case, in which the tax advantage to debt
ods. The use of WACC assumes that the optimal or is the corporate tax rate multiplied by each period’s
target debt ratio is given, so that value and the interest payment. This assumption is the one made
amount of debt financing spills over to the firm as by M&M and used in most APV examples. The M&M
whole. A project is thus implicitly credited with the model is
target debt capacity, even if it is not immediately
used. In contrast, the FTE framework requires the EBIT (1 − T )
V = + DT (2)
optimal amount of debt both for the projected K0
interest cost as well as the net equity investment. The
FTE approach can thus be useful when dealing with In the first term, the after-tax EBIT is discounted at
absolute amounts of debt, although once a target the equity cost for an all-equity firm, K . This term is
0

debt ratio is substituted into the FTE it becomes then simply the value of an unlevered firm. The
indistinguishable from the WACC method. This in second term is the value of the tax shield from debt
turn means that either there is a complete absence financing, with the debt, like EBIT, assumed to be a
of any spillover from the project to the firm as a perpetuity (or, equivalently, term debt that will be
whole, or that prior to using FTE we already know rolled over at the same interest rate).
the project value—that is, we already know the value In our example, the firm has $50 million in debt.
before we calculate it! So with a 50% corporate tax rate the value of the tax
To be sure, FTE will consistently give the same shield is $25 million. If the unlevered equity cost is
13
answer as WACC when the NPV is zero. In this case, 13.33%, then the unlevered equity value is $10
the optimal amount of financing is the same whether million discounted in perpetuity at 13.33%, or $75
we multiply by the cost or the value of the project, million. The total APV of $100 million is then
and by definition there can be no spillover of the consistent with both the WACC and FTE estimates.
NPV to the firm as a whole. Otherwise, as the NPV However, APV has a further advantage in that this
changes so will the optimal amount of debt. Another $100 million is allocated into its separate compo-
way of stating this is to recognize that FTE gives the nents—the $75 million value of the operating cash
correct NPV only if the NPV has no impact on the flows and the $25 million debt tax shield value. This
subsequent financing decision. In this case, the in turn allows a sensitivity analysis with respect to the
financing isfixed regardless of whether the project’s different components of value, namely the firm’s
14
NPV is $5 million, $50 million, or $500 million. For operating cash flows and its capital structure.
most valuations, however, this assumption is not The APV framework is clearly attractive in that
likely to be appropriate in either the short or long it allows a deeper understanding of what creates
run. value. However, a closer reading of the above
example again reveals logical problems (in this case
THE GREAT HOPE: ADJUSTED PRESENT not one as with FTE, but two!) First, similar to FTE,
VALUE? we need to know the optimal amount of debt to
determine the value of the debt tax shield. However,
Once the constant debt ratio assumption is before knowing the NPV (APV), how can we know
violated, the cost of equity has to be changed to how much debt is optimal? If there is any spillover
reflect changing financial risk. This requires adjust- from the NPV, APV will give an incorrect answer.
ments in both the WACC and FTE methods, making Second, and even more problematic, where did the
them both more difficult to implement. It is the great unlevered equity cost of 13.33% come from? In fact,
hope of proponents of Adjusted Present Value that it has to be 13.33% to give the right answer. But
APV solves this problem, which is why most ex- without knowing that, how do we calculate it?
amples advocating APV involve valuing highly le- In the APV framework, the absolute amount of
vered transactionsin which the debt ratio tends to debt must be known before we can calculate the tax

13. Booth (1982), cited earlier. difficult to believe that there is a complete disconnect between the actual NPV and
14. This explains why most applications of FTE, like APV, involve high-debt future financing.
transactions like leveraged buyouts or project financing. However, even here it is

12
JOURNAL OF APPLIED CORPORATE FINANCE
shield value, in the same way that we needed the of debt. The WACC NPV estimate of $40 million
absolute amount of debt to calculate the interest implicitly assumes that another $20 million in debt is
payments and equity investment with FTE. We might raised based on the estimated NPV: the calculation
then ask what happens when we incorporate an is automatic. As with FTE, for APV to give the same
optimal debt ratio assumption, that is, q = D/V, into value as WACC requires that an additional tax shield
the APV equation? We start with value of $10 million be included. Only if there is no
debt spillover or, equivalently, no impact of the NPV
EBIT (1 − T ) on the debt financing will APV give the right answer.
V = + TθV
K0 Yet it is difficult to conceive of a situation where
knowing the NPV does not affect the financing
16,17
However, solving for V gives: decision.

V = EBIT (1 – T)/ K0(1 – Tq) (3) GROWTH OPPORTUNITIES

This may look different from the standard WACC The previous results are based on a perpetuity
equation, but the denominator is just the M&M framework, but very few investments are perpetu-
expression for the WACC (as I will show formally ities. What happens, for example, if there is growth
later). With our numbers, K is 13.33%, T = 50%, and in the expected EBIT? For WACC, if EBIT is expected
0

q = 50%. And so K 0
q
(1 – T ) is 13.33% × 0.75, or 10%. to grow at an average long-run growth rate g, we get
18
This 10% is just the WACC we calculated initially. the standard constant growth formula:
Consequently, iterating the amount of debt or incor-
porating the optimal debt ratio into the APV equation EBIT (1 − T )
V =
causes it to collapse to the standard WACC. Ka − g
As with FTE, the APV framework will give the
same answer as WACC as long as the optimal amount If the firm starts at its optimal debt ratio, the
of debt is used. Again, however, it is a question of equivalent APV formula is
how APV is used in practice. Suppose APV is
implemented by estimating the amount of debt EBIT (1 − T ) K 0 TD
V = + (4)
based on the debt ratio multiplied by the project’s K0 − g K0 − g
15
cost. If the unlevered equity cost is correctly
estimated at 13.33%, the unlevered project value is This is the same as the perpetuity model. APV gives
$75 million. The value of the tax shield then depends the value of the operating cash flows and the value
on whether the firm is using the optimal amount of of the tax shield. In both cases they are expected to
debt. With the project cost of $60 million and debt grow at the long-run growth rate. However, the tax
of $30 million, the tax shield value will be $15 million advantage to debt needs some explanation. The
for a total project value of $90 million. This under- perpetuity tax shield from existing debt, TD, has
estimates the WACC value by $10 million, or the been converted to a flow by multiplying by the
value of the tax shield from the additional $20 million unlevered equity cost, K . Since the firm is expected
0

in debt that results from knowing that the total to grow at the long-run average growth rate, we can
project value is $100 million and the NPV is $40 find the current value of this growing flow of tax
million. This is the spillover of the NPV to the firm’s benefits by discounting at K . We use the unlevered
0

financing decisions. equity cost (K ) to discount the future flow of debt

0

As in the case of FTE, The critical question with tax shields because they stem from the expected
APV is whether knowing the NPV affects the amount growth in EBIT. Consequently, and unlike the exist-

15. I have yet to come across an analysis that has based the debt financing on will differ across all three methods since the discount rate is either the WACC, the
the ultimate project value. In almost all cases the estimated financing comes from unlevered equity cost (APV), or the levered equity cost (FTE). What is then critical
the target debt ratio times the project cost. is the objecive of the sensitivity analysis: Is it to consider the effect of an EBIT change
16. Of course the optimal amount of debt may not be $20 million, but say $10 in isolation (APV), or the cumulative effect of the EBIT change with the associated
million. As a result, the WACC estimate is incorrect, but this just means that the optimal financing change, or neither (FTE)?
optimal debt ratio has not been used in the WACC estimate. 18. This is from the Gordon constant growth model; see M. Gordon, The
17. The same valuation problems exist if the analyst performs a sensitivity Investment, Financing and Valuation of the Corporation (Homewood, Illinois:

analysis, for example with respect to forecase EBIT. In this case the change in NPV Richard D. Irwin, 1961).

13
VOLUME 15 NUMBER 1 SPRING 2002
ing tax benefits, they are as risky as the future ( EBIT − K d D )(1 − T )
unlevered cash flows and should be discounted at
Ke =
E
19
the same rate.
Similar to the perpetuity case, with an optimal This is just M&M’s equity cost equation rearranged.
debt ratio we can set q = D/V to find the conditions However, we can solve for EBIT(1 – T) from the
for consistent valuation between APV and WACC. M&M valuation equation and substitute to get
Subtracting the tax shield advantages from the
project value in equation (4), multiplying by the K 0 ( V − DT ) − K d D(1 − T )
Ke =
adjusted discount rate (K – g), and setting EBIT(1 – E
0

T) equal in both equations, we can solve for the

WACC as Since the enterprise value is the market value of the
debt and equity (V = D + E) we can rearrange to get
K a = K 0 (1 − Tθ )
M&M’s equity cost equation:

which is the same as previously: the traditional cost D

K e = K 0 + [ K 0 − K d (1 − T )] (5)
of capital (WACC) is equal to the M&M expression E
for WACC. Adding future growth in EBIT does not
affect the prior results, as long as the tax shields from This simply states that the equity cost is equal to K ,
0

the growth in EBIT are recognized to be as risky as the cost for an all-equity firm, plus a financial
EBIT itself. leverage risk premium. As the use of debt financing
By assuming an optimal or target capital struc- increases, common equity becomes riskier and
ture, WACC automatically adjusts financing for fu- attracts a financial leverage risk premium in addition
ture growth opportunities. To be consistent with this to the business risk premium. The “pure” financial
approach, the future tax shields in the growth- leverage effect is the unlevered equity cost multi-
extended APV equation need to be discounted at the plied by (1 + D/E). However, with the M&M assump-
unlevered equity cost. If the future tax shield ben- tion of a tax shield value of TD, the negative effect
efits, as well as the current tax benefits, are dis- of increased financial risk on firm value is partially
counted at the cost of debt, or a rate close to it, the offset by the positive effect of the tax shield. Conse-
tax shield value is vastly overstated and the results quently, the increase in the equity cost is moderated
20 21
are inconsistent with the WACC estimates. The by (1 – T). With a constant debt cost, the equity cost
critical assumption in comparing APV, WACC, and increases by [1 + (1 – T)D/E]. Many readers will notice
FTE is not the time pattern of the expected cash a similarity to the familiar beta adjustment formula
22
flows, but the financing assumption. developed by Robert Hamada. In that formula, the
beta of an unlevered firm (derived from the Capital
CHANGING DEBT RATIOS Asset Pricing Model) also increases by (1 + (1 – T)D/
E) with the addition of debt to the capital structure,
As long as there is a constant optimal debt ratio, so that b L
= b 0
(1 + (1 – T)D/E).
APV and FTE valuations turn into WACC valuations. The M&M equity cost equation indicates how
But what happens when the debt ratio is changed? the equity risk premium changes with the firm’s use
Since the existence of growth does not change the of debt. As a result, we can reverse the process and
results in a material way, we can revert to the standard calculate the unlevered equity cost from either
M&M perpetuity model. In this case, the levered equity equation. In our example, the levered equity cost at
cost is the earnings yield, or simplythe expected net a 50% debt ratio and a 50% tax rate was 15%. Inserting
income divided by the market value of equity: these values into equation (5), we estimate the

19. The financing of existing assets generates an interest tax shield whose value unlevered equity value is $157 million and the value of the interest tax shields $102
is derived by discounting at the cost of debt. It is the tax shields from the growth million—we could all wish that the government were this generous!
in EBIT that are as risky as the EBIT growth. If the growth rate is zero, the tax shield 21. M&M assumed zero bankruptcy costs, so the debt is risk-free debt; see F.
is the standard perpetuity formula for the tax shields from existing debt. Modigliani and M. Miller, “Corporate Income Taxes and the Cost of Capital,”
20. See Luehrman (1997, cited earlier) for an inappropriate application of APV, American Economic Review (June 1963), pp. 433-443.

where future tax shields are valued at a rate “a bit higher than the average cost of 22. R. Hamada, “The Effect of the Firm’s Capital Structure on the Systematic
debt” to vastly overstate the value of interest tax shields. In his example, the Risk of Common Stocks,” Journal of Finance (May 1972), pp. 435-452.

14
JOURNAL OF APPLIED CORPORATE FINANCE
unlevered equity cost at 13.33%.
23
This is how we the general equation if we know l, but we can not
derived the baseline, unlevered equity cost and firm relever using l with different debt levels. This is
value of $75 million. With $50 million in debt there because l varies with the debt ratio depending on,
is an additional $25 million tax shield value to get the for example, the marginal agency or distress costs.
overall enterprise value of $100 million. To relever we need to know the functional form of
However, considering the effect of changes in both the advantages and disadvantages to debt.
leverage immediately brings out the fundamental Suffice it to say that generally we don’t know these.
weakness of M&M, which is that the value of the firm Further, these schedules differ from firm to firm, or
24
constantly increases with the use of debt. If that is at least industry to industry, which means that
true, why stop with $50 million in debt—why not $70 adjustments differ across firms, just as optimal capital
million or $80 million? After all, the M&M equation structures do. This destroys one of the key advan-
has no offset to the huge tax advantage to debt tages of using a constant adjustment formula across
financing. In practice, of course, firms cannot finance firms as well as across debt ratios.
with 100% debt, since in there are obvious problems This same reasoning applies to the Hamada beta
with a loss in financial flexibility and the increased adjustment. With an optimal capital structure, the
chance of financial distress. beta of a levered firm is b
L
= b (1 + (1 – l)D/E). But
0

Suppose we consider all of these factors in what the change in terms from T to l is not trivial. The tax
Stewart Myers has dubbed the static trade-off model, rate T can be looked up in the tax code, implying a
discussed throughout this journal issue (and in every standard beta adjustment formula that can be ap-
25
introductory finance textbook). In this case, the plied to any firm in a mechanical fashion. Yet
corporate tax and agency advantages to debt are financial distress and other agency cost advantages
offset by the personal tax, financial distress, and and disadvantages to debt depend on a variety of
agency cost disadvantages. At the firm’s optimal firm-specific factors, all of which interact to create
capital structure, the enterprise value can be ex- unique tax advantage and disadvantage schedules.
pressed as Consequently, levered betas cannot be mechanically
determined. Although the Hamada beta adjustment
EBIT (1 − T ) is commonly used, it is inconsistent with the exist-
V = + λD
K0 ence of an optimal capital structure and a gross
oversimplification of reality.
In this case, the net overall average advantage to The second implication is that the APV formula
using debt is l. Algebraically, this is identical with the allocates the overall enterprise value between the
M&M results, so that the equivalent equity cost is just debt-free value of the firm plus the value of other
effects, such as the net tax advantage and the agency/
D financial distress disadvantages of debt. Suppose, for
K e = K 0 + ( K 0 (1 − λ ) − K d (1 − T )) 28
E example, that there are no advantages to debt.
Then l = 0, the unlevered value of the firm is $100
However, although the equation looks similar to the million, and the unlevered equity cost is 10%. With
standard M&M equations, there are important differ- M&M, the unlevered cash flow/debt value split is $75
26
ences with profound implications. million/$25 million and the unlevered equity cost is
First, with M&M, the marginal and average 13.33%. With an optimal capital structure, the split in
advantages to using debt both equal the corporate value and unlevered equity cost would be some-
tax rate, T. Consequently, we can unlever and relever where in between. The state of financial knowledge
27
using the same corporate tax rate. However, with is such that we really don’t know exactly where,
29
an optimal capital structure, we can unlever using although APV assumes that we do!

23. Insert into the M&M equity cost equation or use K0 = WACC/(1 – TD/V). 26. For simplicity, a couple of issues are glossed over: whether the debt has
Since WACC is 10%, and T and D/V are both 50%, K0 is estimated as 13.33%. systematic risk and whether the promised yield or expected rate of return on debt
24. James Poterba points out that financial policy was much the same prior should be used in the WACC. These just compound the problems discussed below.
to the introduction of the corporate income tax as after it! See J. Poterba, “Tax Policy 27. Just use the M&M equation K0 = WACC/(1- lD/V). The only thing that is
and Corporate Savings,” Brookings Papers on Economic Activity, Vol. 18 (1987), pp. different is the average advantage to debt.
455-503. 28. Miller (1977), cited earlier.
25. Myers (1984), cited earlier. 29. We need a beta adjustment formula to unlever betas since most of the
observed betas are levered.

15
VOLUME 15 NUMBER 1 SPRING 2002
 Finally, it is important to recognize that APV Further, it is inconceivable that a valuation
simply allocates the enterprise value based on the be conducted without some form of sensitivity
estimate of the unlevered equity cost. As long as analysis. If the expected operating cash flows
we are consistent in using the same capital struc- are varied, the three valuation methods will
ture model to unlever betas as well as to add up give different results. The reason again is sim-
the components in APV, the only change is the ply the different financing assumptions. Both
allocation of value. If we estimate the WACC APV and FTE assume that the financing is
correctly at 10%, regardless of how we adjust for always constant, whereas WACC automatically
leverage/unlever the equity cost, we will always assumes a financing adjustment. FTE further
get back an APV value of $100 million. However, assumes that the cost of equity is independent
our components of value are radically different! of financial risk.
It is possible to fix the problems with APV and
CONCLUSIONS FTE by incorporating the interaction between
operating and financing decisions, but at a signifi-
This paper has a number of important conclu- cant cost to their simplicity. However, the most
sions, some of which have already appeared in the serious problem with APV is its misleading signals
literature but are worth revisiting. In general, the about the value of debt financing. Normal appli-
WACC is an appropriate valuation framework as cation of APV relies on the M&M tax model, which
long as the debt ratio is expected to be constant. implies that the firm should optimally use 100%
Further, APV and FTE can be formulated to be debt financing to take maximum advantage of the
consistent with the WACC valuation. The issue, debt tax shield. And yet such a model is inconsis-
however, is not whether the techniques can be tent with the reality of corporate practice or the
rendered consistent through relatively complex ad- intent of most tax authorities. Moreover, it is also
justments by sophisticated users, but rather what troubling that people can simultaneously recom-
happens when they are used in everyday practice by mend the use of APV, an equity cost (or beta)
practitioners unfamiliar with the somewhat arcane adjustment model, and the existence of an optimal
valuation issues involved. capital structure (implicitly acknowledging that
The critical question in choosing among the there are disadvantages to debt). It is important to
three frameworks was first raised in a paper I recognize that the latter two models are mutually
wrote 20 years ago, in which I said, “For APV and inconsistent.
FTE to provide consistent results the amount of If disadvantages to debt are acknowledged,
debt financing must equal the optimal debt ratio the APV equation needs significant modification
times the value of the project and not the cost of to lower the tax shield value. The reality, of
the project [emphasis added].” In other words, if course, is that the tax advantage to debt is not
the firm has an optimal debt ratio, FTE and APV simply the corporate tax rate, and that financial
require the project value as an input in order to distress and other agency cost factors all affect the
perform the valuation! In contrast, APV and FTE optimal capital structure and with it the cost of
are useful when knowing the NPV has no impact capital and the value of the firm.
on the financing of the project. If the project is to It is clear that traditional valuation methods
be financed with $10 million in debt, and its NPV based on WACC are more robust than either APV
is subsequently estimated at $100 million, then or FTE. If the firm or project has an optimal debt
this knowledge cannot feed back into the analysis ratio, use WACC. If the firm hasn’t got an optimal
and prompt the company to take on more debt. debt ratio, perhaps this means that the cost of
Obviously, complete independence between the capital is constant—in which case companies
valuation and the financing is a very restrictive should still use WACC! If a firm knows how its cost
assumption and some iteration is inevitable. How- of capital varies with its debt financing and can
ever, this paper shows that if the iteration is accurately estimate this, please let people know,
towards an optimal debt ratio, then both the APV since it is not obvious how to do it. Quite simply,
and FTE techniques end up turning into the capital structure problems are too complex to
standard WACC analysis, which renders the value allow us to use mechanical formulas to separate
of the exercise moot. firm value into its unlevered and debt value

16
JOURNAL OF APPLIED CORPORATE FINANCE
components (or to accurately unlever and relever as separate components of value. Similarly, if there
30
betas). is a low-interest loan, it is straightforward to include
Finally, APV is not necessarily the same as the true interest cost in the WACC and then add the
valuation by components. In a corporate valuation, value of the interest subsidy as a separate component
there are always extra pieces of value not captured of value. This use of valuation by components is
in the discounted cash flow itself and it is important appropriate. What this paper takes issue with is the
to remember that the DCF valuation only values the much more contentious APV approach of unbun-
assets needed to generate the expected stream of dling the core WACC valuation into that of the
cash flows. As a result, we always add in the value unlevered free cash flows and the tax and other
of redundant assets or subtract contingent liabilities advantages and disadvantages to using debt.

30. A final caution is that many “solutions” to minimize WACC and determine implied by bond ratings. However, the yield on corporate debt is a promised yield,
the optimal capital structure rely on an increasing yield to maturity schedule, as not an expected rate of return.

LAURENCE BOOTH

holds the CIT Chair in Structured Finance at the University of

Toronto’s Rotman School of Management.

17
VOLUME 15 NUMBER 1 SPRING 2002