Journal of Applied Corporate Finance S P R I N G 1.docx

Journal of Applied Corporate Finance
S P R I N G 1 9 9 7 V O L U M E 1 0 . 1
Two DCF Approaches for Valuing Companies Under Alternative
Financing
Strategies (And How to Choose Between Them)
by Isik Inselbag and Howard Kaufold,
University of Pennsylvania
114
JOURNAL OF APPLIED CORPORATE FINANCE
TWO DCF APPROACHES
FOR VALUING COMPANIES
UNDER ALTERNATIVE
FINANCING STRATEGIES
(AND HOW TO CHOOSE
BETWEEN THEM)
by Isik Inselbag and
Howard Kaufold,
University of Pennsylvania*

114
BANK OF AMERICA JOURNAL OF APPLIED
CORPORATE FINANCE
or decades now, finance theorists and
practitioners have been debating the
validity of various approaches to valuing
a levered corporation. The weighted
shown that, if the firm maintains a constant ratio of debt
to equity in market value terms, the weighted average
cost of capital method is an appropriate valuation
technique regardless of the pattern or duration of the
firm’s cash flows. In this paper, we take this finding a
step further to show that the two valuation methods
give the same answer—again, regardless of the pattern
and duration of the cash flows—for a much more
general set of financing strategies in which the debt/
equity ratio is changing over time. As one example, we
show the equivalence of the techniques for the case in
which a company commits to a schedule in which the
absolute dollar value of debt principal outstanding is
paid down over time.
We argue further that past confusion can prob-
ably be traced to assumptions the separate camps
have implicitly made about the corporation’s finan-
cial policy. While we will show the methods are
equivalent under different financing strategies, our
analysis suggests that it is more practical to apply the
APV technique when the firm targets the dollar level
of debt outstanding in the future, and the WACC
approach when the firm instead intends to hold the
debt/value ratio fixed in the future.

average cost of capital (WACC) method, in which a
firm’s value is determined by its unlevered cash flows
discounted by WACC, appears to be the reigning
favorite among practitioners. The main challenger is
the Adjusted Present Value (APV) technique, which
values the firm as an all-equity entity plus any
incremental worth created by leverage.1
Authors of corporate finance papers and text-
books seem to feel obligated to choose sides in this
debate. Proponents of WACC argue that, although
there are problems with this approach when the
firm’s capital structure is changing over time, it is
easier to use because the expected equity returns in
this approach can be directly observed. Those who
favor APV counter that the WACC method is correct
only under restrictive assumptions about the firm’s
cash flows and financing mix.
To our knowledge, there are only two studies—
one by one of the present writers—that have attempted
to reconcile the two views.2 Both of these studies have
*We wish to thank Jeffrey Jaffe and Saman Majd.
1. The Adjusted Present Value method was originally presented
by Stewart
Myers in “Interactions of Corporate Financing and Investment
Decisions—
Implications for Capital Budgeting,” Journal of Finance, March
1974, pp. 1-25.
While we cast our argument in terms of valuing an entire firm,
our findings are
equally relevant in a capital budgeting context. The reader need
only substitute the
marginal required return on assets and debt capacity appropriate

to the project in
question.
2. See I. Inselbag, “Project Evaluation and Weighted Average
Cost of Capital,”
in Cees van Dam, editor, Trends in Financial Decision-Making,
Martinus Nijhoff,
Boston, 1978, pp. 153-160; and J. Miles and R. Ezzell, “The
Weighted Average Cost
of Capital, Perfect Capital Markets and Project Life: A
Clarification,” Journal of
Financial and Quantitative Analysis, September 1980, pp. 719-
730. For a compari-
son of alternative approaches to valuing levered cash flows, see
D. Chambers, R.
Harris, and J. Pringle, “Treatment of Financing Mix in
Analyzing Investment
Opportunities,” Financial Management, Summer 1982, pp. 24-
41. In contrast to the
findings presented below, they conclude that the various
methods yield different
values. See footnote 7 for our explanation of their findings.
F
115
VOLUME 10 NUMBER 1 SPRING 1997
We illustrate these points by using the separate
valuation methods to appraise a hypothetical corpo-
ration under each of these financial policies. This
process shows how the required return on equity
and the weighted average cost of capital evolve

under the separate policies. The result is a clearer
understanding of the appropriate application of each
of the valuation techniques.
To make these points, we invoke three as-
sumptions that are standard in the related literature.
The required return on the firm’s assets is taken as
given and fixed over time. We also ignore costs of
financial distress, since our objective is to clarify
the effect of the corporate tax subsidy of debt
financing per se in several popular valuation ap-
proaches. Finally, we finesse issues arising from the
differential personal taxation of debt and equity
returns to investors.
In the next section, we present the unlevered
free cash flows for a hypothetical company used
throughout the paper to illustrate the financing
strategies and resulting valuations. Then we com-
pare the APV and WACC methods under the assump-
tion that the firm targets the absolute dollar value of
debt outstanding. Next we present the same com-
parison for the case in which the firm maintains a
constant debt/value blend. Finally, we discuss the
implications of our analysis for a third popular
valuation approach that involves capitalizing the
firm’s flows to equity.
AN EXAMPLE
A newspaper chain is planning to set up a new
division, Media, Inc., with projected cash flows as
presented in Table 1. The new operation would
require an initial investment in plant and equip-
ment of $100 million, plus an infusion of $7.5
million of working capital (equal to 10% of ex-

pected first-year sales). Media’s sales are projected
to be $75 million during the first year of operation.
Sales are expected to rise 12% per year over the
next two years, with growth stabilizing at a 4% rate
indefinitely thereafter. Management estimates that
cash costs (cost of goods sold, general and admin-
istrative expenses, etc.) will constitute 60% of rev-
enue. New investments in plant and equipment
will match depreciation each year, starting at 10%
of the initial $100 million asset cost and growing in
tandem with sales thereafter. The firm plans to
maintain working capital levels at 10% of the fol-
lowing year’s projected sales. With Media in the
35% tax bracket, unlevered free cash flow (asset
cash flow) would approach $16 million in three
years, and grow 4% per year thereafter.
The all-equity value of a firm at any point in time
should equal the discounted value of future unlevered
free cash flows, which we will denote as Ci:
(1)
TABLE 1
PROJECTED CASH FLOW
STATEMENT OF MEDIA,
INC. ($000’s)
Year 0 Year 1 Year 2 Year 3 Year 4
Sales 75,000 84,000 94,080 97,843
Cash Costs 45,000 50,400 56,448 58,706
Depreciation 10,000 11,200 12,544 13,046
Earnings before interest and taxes 20,000 22,400 25,088 26,092
Corporate tax 7,000 7,840 8,781 9,132

Earnings before interest after taxes 13,000 14,560 16,307
16,959
+Depreciation 10,000 11,200 12,544 13,046
Gross cash flow 23,000 25,760 28,851 30,005
Investments into:
Fixed Assets 100,000 10,000 11,200 12,544 13,046
Net Working Capital 7,500 900 1,008 376 391
Unlevered free cash flow (107,500) 12,100 13,552 15,931
16,568
V
C
(1 r )
U,t
i
A
i t
i t 1
=
+ −= +
∞
∑
116

where rA is the required return on the firm’s assets.
In the example, with growth constant after year 3, the
current all-equity value of Media takes the form:
VU,0 = C1/(1 + rA) + C2/(1 + rA)
2 + C3/(1 + rA)
2(rA – g).
We will take the asset return as given in our
analysis, and assume it is fixed at 18%. Applying this
discount rate to the free cash flows given in Table 1
implies that Media is worth approximately $102
million in unlevered form:
VU,0 = 12.1/(1.18) + 13.6/(1.18)
2 + 15.9/(1.18)2(.18 – .04).
≅ $101.7 million.
One can use equation (1) to trace the evolution
of Media’s all-equity value through time. The result-
ing estimates are shown in Table 2.
Media’s value as a levered company depends on
the financing policy the firm pursues. We now
outline two plausible financing strategies, indicating
how the APV and WACC methods can be applied in
either context. In the first case, Media chooses a
target for the absolute dollar value of its outstanding
debt. In the second, the company instead chooses to
fix its market debt/value ratio over time.
TARGETING THE DOLLAR VALUES OF

DEBT OUTSTANDING
Many firms agree to financing contracts that
specify debt service payments and outstanding fu-
ture debt levels over the life of the contract, as
opposed to adhering to a target capital structure by
fixing the firm’s debt as a constant proportion of firm
value. In leveraged buyouts, for example, owners
typically finance the newly acquired company with
unusually high debt amounts, and then gradually
pay down debt principal over the life of the transac-
tion.3 At some point, the firm again achieves its
desired long-run debt/value ratio.
Suppose, for example, that Media, Inc. arranges
to borrow $77.5 million initially. The firm agrees to
repay $8.5 million of principal at the end of each of
the first three years of the contract, bringing debt
outstanding at the end of the third year to $52 million
(see Table 3). From that point on, Media will increase
debt outstanding by 4% per year, in line with the
expected growth of operating cash flows. Because of
the firm’s highly levered position in the early years,
we assume the borrowing rate is 11% initially, falling
to 9% once it re-achieves a stable capital structure
(after year 3).
One can use either the APV or WACC method
to value a company choosing this type of financial
policy. But, under these circumstances, we will show
that the APV method is more direct.
The APV Method
The APV method treats the value of a levered

firm at any point in time (VL,t) as its value as an all-
equity entity (VU,t), plus the discounted value of the
interest tax shields from the debt its assets will
support (DVTSt):
4
VL,t = VU,t + DVTSt. (2)
The principle is straightforward. The firm’s
unlevered value is determined by the operating
TABLE 2
ALL-EQUITY VALUE OF
MEDIA, INC. ($000’s)
Value as of time: Year 0 Year 1 Year 2 Year 3
Unlevered Value 101,711 107,919 113,792 118,344
TABLE 3
DEBT REPAYMENT
SCHEDULE OF TARGETED
DEBT POLICY OF MEDIA,
INC. ($000’s)
As of time: Year 0 Year 1 Year 2 Year 3 Year 4
Debt Level 77,500 69,000 60,500 52,000 54,080
3. For a discussion of such an example, see I. Inselbag and H.
Kaufold, “How
to Value Recapitalizations and Leveraged Buyouts,” Journal of
Applied Corporate
Finance, Volume 2, Number 2, Summer 1989, pp. 87-96.

4. To be entirely true to Myers’ concept, we should also deduct
from this value
any costs of having the debt outstanding, such as the costs of
liquidating the firm’s
assets if it is unable to service the debt (costs of financial
distress). We ignore these
costs to focus on the tax effects of leverage.
117
income generated by its assets (as illustrated in the
projections presented above). The debt supported
by these operating cash flows increases levered
value because interest (unlike dividends) is deduct-
ible from the firm’s income for corporate tax pur-
poses. As a result, for given operating income, the
after-tax amount available for payment to both
bondholders and stockholders taken together in-
creases as more of the payout is in the form of interest
rather than dividends.
Under this financial policy, projected debt lev-
els are “exogenous”—that is to say, they do not
depend on future firm performance, but are pre-
determined by the schedule of debt service. As a
result, the borrowing rate, rD, is the appropriate
discount rate for current and future interest tax shields:
= T[ + + + ...] (3)
where T is the corporate tax rate, and Di is the
outstanding debt balance at the end of year i.

In the Media example, the value of interest tax
shields as of the beginning of the first year is:
DVTS0 = T[ + + +
≅ $30.5 million.
The value of the company is easily calculated as
$132.2 million, the sum of these tax shields and the
value of the all-equity company (see Table 2). Using
the fact that the levered value of the company is
equal to the sum of its debt and equity, VL,t = Dt + Et,
the evolution of corporate value, debt and equity is
given in Table 4.
The Weighted Average Cost of Capital (WACC)
Method
Under the WACC method, a widely used ap-
proach to corporate valuation, the firm’s value in a
given period is calculated as the discounted value of
its projected unlevered free cash flows, discounted
by the weighted average cost of capital:
(4)
The weighted average cost of capital for each
period is the weighted average of the after-tax debt
and equity required returns, weighted by the relative
size of each source of financing in the market value
capital structure of the firm:
(5)

If the firm targets dollar future debt levels in
absolute terms, the debt/value ratio changes over
time, thus causing changes in both the required
equity return and the weighted average cost of
capital. To see how a company’s required equity
return is affected by changes in its debt/value ratio,
consider equation (6a), which shows how the firm’s
after-tax income stream (represented by its asset
returns plus its annual tax savings) is divided among
the bondholders and stockholders:
(6a)
On the left-hand side of the equation, the
unlevered value of the asset cash flows is VU, the all-
equity value of the company. These assets generate
an annual expected return of rA, which is determined
by the riskiness of the operating cash flows. As we
have seen, this all-equity value is supplemented by
the value of interest tax shields, DVTS. Given the
“exogenous,” or pre-determined, character of future
debt levels and interest tax shields, this asset gener-
ates the return of rD, which is compatible with the
lower risk of these cash flows.
As shown on the right-hand side of the equa-
tion, these two sources of after-tax income are shared
TABLE 4
DEBT, EQUITY AND TOTAL
VALUE OF MEDIA, INC.:
DOLLAR VALUE OF DEBT
TARGETED ($000’s)
DVTSt
r D

(1 + r )
D t
D
r D
(1+ r )
D t+1
D
2
r D
(1+ r )
D t+2
D
3
.11(77,500)
(1.11)
.11(69,000)
(1.11)
2

.11(60,500)
(1.11)3
.09(52,000)
(1.11) (.09-.04)3
V
C
r
C
r r
L,t
t
WACC t
t
WACC t WACC t
=
+
+
+ +
+ +
+

1 2
11 1 1( ) ( )( ), , ,
+
+ + +
++
+ +
C
r r r
t
WACC t WACC t WACC t
3
1 21 1 1( )( )( )
....
, , ,
r r T
D
V
r
E
V
WACC t D t
t

L,t
E t
t
L,t
, , ,( )= − +1
V r DVTS r D r E rU t A t D t D t E t, ,( ) ( ) ( ) ( )+ = +
Unlevered value 101,711 107,919 113,792 118,344
Discounted value of tax shields 30,501 30,872 31,612 32,760
Levered value 132,212 138,791 145,404 151,104
Value of debt 77,500 69,000 60,500 52,000
Value of equity 54,712 69,791 84,904 99,104
Our analysis suggests that it is more practical to apply the APV
technique when the
firm targets the dollar level of debt outstanding in the future,
and the WACC
approach when the firm instead intends to hold the debt/value
ratio fixed in
the future.
118
between the bondholders and the equityholders
according to their proportional representation in the
capital structure and the returns required by these

two investor groups (rD and rE, respectively).
Then, by manipulating the basic balance sheet
identity, VL,t = VU,t + DVTSt = Et + Dt, we can solve for
(rE) as follows:
(7)
As Table 4 indicates, the debt/equity ratio, and
(Dt - DVTSt)/Et, change over the early years of the
transaction. The return the shareholders require
therefore fluctuates, and can be computed by direct
substitution from Table 4 into equation (7). These
returns are given in the first row of Table 5.
To calculate the weighted average cost of
capital, we substitute the required equity return
(equation (7)) into equation (5) to get:
(8)
In this targeted debt case, WACC also changes
if the debt/value ratio is not constant. Specifically, a
decline in the debt/value ratio implies an increase in
the cost of capital, since the reduction in leverage
means a loss of interest tax shields.5,6
The cost of capital for Media is given in the
second row of Table 5. After year 3, the value of the
firm (levered and unlevered), and the debt and
equity, grow at the steady-state rate of 4%. Therefore,
the required return on levered equity as well as the
weighted average cost of capital remain stable at the
level reached by the end of year 3.7

Using the WACC method to value Media, the
firm’s unlevered free cash flows are discounted by
the rates given in the second row of Table 5. The
value of the firm at time 0 is therefore:
VL,0 = + + +
= $132.2 million.
This solution is identical to that derived using
the APV method. Under this financial policy,
though, the APV approach is clearly preferred. In
fact, as equation (7) shows, one must know the
value of the firm’s tax shields to calculate the
correct equity return and weighted average cost of
capital. That is, one must already have calculated
the firm’s value (using APV or some other means)
to be able to derive the discount rates necessary to
value the firm using the WACC method.8 In addi-
tion, the variation in the WACC shown in Table 5
illustrates the well-known problem with using a
constant cost of capital, or “hurdle rate,” for
capital budgeting when capital structure is chang-
ing over time.
TABLE 5
REQUIRED RETURN TO
EQUITY AND WEIGHTED
AVERAGE COST OF
CAPITAL MEDIA, INC.:
TARGETED DEBT POLICY
For the Year: Year 0 Year 1 Year 2 Year 3 Year 4 ...
Required equity return 24.0% 21.8% 20.4% 19.7% 19.7%
Weighted average cost of capital 14.1% 14.5% 14.9% 15.0%

15.0%
5. This result may be altered in the presence of costs of
financial distress.
6. There is a related special case in which the equity return is
fixed, even
though the firm is targeting the dollar level of debt outstanding.
In the standard
textbook example, the firm’s expected unlevered cash flows are
assumed to be
constant and perpetual, and the firm sets borrowings at the same
dollar level, D,
in perpetuity. In this case, the present value of the tax shields is
simply TD, so that
the required equity return of equation (7) reduces to:
rE,t = rA + ((Dt – TDt)/Et)(rA – rD).
= rA + (Dt/Et)(1 – T)(rA – rD).
Since the expected future asset cash flows are constant, both the
debt and
equity values are stable as long as the firm makes a commitment
to maintaining
the same dollar debt level. The equity return is therefore
independent of time in
this case. Substituting the equity return into equation (5)
implies a weighted average
cost of capital of:
rWACC,t = rA(1 – T(D/VL)),
which, of course, is also constant over time. The reader will
recognize these
findings as the well-known Modigliani-Miller (1963) results.
(See F. Modigliani and

M. Miller, “Corporate Income Taxes and the Cost of Capital: A
Correction,”
American Economic Review, June 1963, pp. 433-443.) While
the weighted average
cost of capital is independent of the absolute cost of borrowing
under these
conditions, this will not generally be true as shown by equation
(8).
7. In concluding that various methods imply different values for
the same cash
flows and financing policy, Chambers, Harris and Pringle
(1982) assume time-
independent discount rates for each of the valuation approaches.
As equations (7)
and (8) show, the costs of equity and the weighted average cost
of capital will
change over time as long as the capital structure is not constant
(as occurs in their
example). Applying equations (7) and (8) to their example
implies identical values
for their project, independent of the valuation method used.
8. We elaborate on this point in our discussion of the “flows to
equity”
approach later in the paper.
r r
D DVTS
E
r rE t A
t t
t

A D,
( )
( )= +
−
−
r r
DVTS
V
r
DVTS TD
V
WACC t A
t
L,t
D
t t
L,t
, ( )
( )
= − +
−
1

16.6
(1.141)(1.145)(1.149)(.15-.04)
12.1
(1.141)
13.6
(1.141)(1.145)
15.9
(1.141)(1.145)(1.149)
119
THE CONSTANT DEBT/VALUE RATIO CASE
In weighing the pros and cons of debt funding,
many firms conclude that it is optimal to set and
adhere to a targeted blend of debt and equity.9 In
these circumstances, unless the company’s cash
flows are constant over time, the firm will need to
undertake regular debt-equity swaps to maintain this
target capital structure. We now describe the proper
application of the APV and WACC methods under

this financing policy.
The APV Method
If the company maintains a fixed debt/value
capital structure in market value terms, the present
value of interest tax shields at time t will be:
(9)
Why this blending of rA and rD as discount rates
in this expression?10 Consider the calculation of DVTS
at time 0. At that time, the value of the levered firm,
and the dollar level of debt financing for that year
(equal to a fixed fraction of firm value), are known.
This debt level and borrowing rate fix the interest the
firm will pay at the end of the first year. The expected
tax savings resulting from this single year’s interest
tax shield is therefore pre-determined. As a result,
this cash flow is as risky as the interest payment itself,
so that rD is the appropriate discount rate.
But thereafter, because the firm expects to
maintain debt as a fixed fraction of total value, the
amount of debt and interest payments will vary with
the actual (rather than the expected) future asset
cash flow outcomes for the company. Since future
interest payments and tax shields will therefore be as
risky as the asset cash flows, one must use the higher
rate rA to discount tax shields after the first year.
Suppose, for example, that Media fixes its debt/
value ratio at 40% (debt/equity at 66.7%), and that the
firm can borrow at an interest rate of 9%. How much
would the resulting tax shields add to the all-equity
value? Since debt and levered firm value are simul-

taneously determined under this policy, we must
solve for the levered value of the firm using the
“iterative” process illustrated below.
Beginning at the end of year 3 (the point at
which growth stabilizes), we can use equations (2)
and (9) to determine the value of Media as:
Since the expected debt level grows at a constant rate
g after year 3, this relation can be simplified as:
Defining L to be the debt/value ratio, D/VL,
Media in period three will be worth:
From Table 2, the all-equity value of Media at the end
of year 3 is approximately $118 million. Substituting
this value and the other parameters into the expres-
sion for VL,3, the levered value of Media at the end
of year 3 is expected to be $131 million. The debt
level would be 40% of this amount, or $52 million.
The difference between the levered and unlevered
values of $13 ($131-$118) million is the value of all
interest tax shields expected from year 4 on.
Solving recursively, we can describe the ex-
pected evolution in the value, debt, and equity of
Media under the fixed debt/value policy. The value
of the firm at the end of year 2 is:
DVTS T
r D
r
r D

r r
r D
r r
t
D t
D
D t
D A
D t
D A
=
+
+
+ +
+
+ +
+

+
+
( ) ( )( )
( )( )
...
1 1 1
1 1
1
2
2
9. In this paper, we use a targeted blend of debt and equity
expressed in terms

of market values. Some companies, however, set capital
structure targets in terms
of book values. That characterization of debt capacity leads to a
somewhat different
financing strategy—one that requires a modification of the
analysis presented
below. Our focus on market values in this paper reflects the
well-known principle
that use of book values is likely to understate debt capacity
because the book values
of assets reflect “historical costs” rather than current values of
assets based on their
cash-flow-generating capacity. Nevertheless, for companies
whose current value
consists primarily of intangible future growth opportunities as
opposed to tangible
“assets in place,” targeting debt-equity ratios in terms of book
values may still make
sense. For an excellent discussion of these issues, see Michael
J. Barclay, Clifford
W. Smith, Jr. and Ross L. Watts,”The Determinants of
Corporate Leverage and
Dividend Policies,” Journal of Applied Corporate Finance, Vol.
7 No. 4 (Winter,
1996), 4-19.
10. The argument in the text is a heuristic version of ideas
presented in Miles
and Ezzell (1980). In that paper, the authors show the
equivalence of the APV and
WACC approaches in a finite-lived capital budgeting context
when the project is
financed with a constant blend of debt and equity. As we show,
their approach can
be extended to the case in which the firm’s unlevered cash

flows are expected to
continue indefinitely.
V V T
r D
r
r D
r r
r D
r r
L, U
D
D
D
D A
D
D A
3 3
3 4
5

2
1 1 1
1 1
= +
+
+
+ +
+
+ +
+

,
( ) ( )( )
( )( )
.......
The APV method treats the value of a levered firm at any point
in time as its value as
an all-equity entity plus the discounted value of the interest tax
shields from the debt
its assets will support.
V V
Tr D r
r r g
L, U
D A
D A
3 3
3 1
1
= +
+
+ −,
( )

( )( )
V
V
Tr L r
r r g
L,
U
D A
D A
3
3
1
1
1
=
−
+
+ −

,
( )
( )( )
120
because of the dependence of the debt outstanding
on the realizations of future cash flows. It is not
surprising that the value of interest tax shields as of
the end of year 3 is much lower in this case than
under the targeted debt case ($12.8 million vs. $32.8
million; see Tables 6 and 4). Though the expected tax
savings are approximately the same from that point
on, the risk of these cash flows is significantly higher
in the constant debt/value case because future debt
levels depend on as yet unknown operating results
for the firm.11,12
The example reveals the complexity of us-
ing the APV technique to value a firm that fol-
lows the constant debt/value policy. Since the
amount of the firm’s outstanding debt depends
on realizations of future cash flows, dollar debt
levels are not pre-determined as in standard APV
calculations. The simultaneous determination of
debt and value requires an iterative solution.
While this method is perfectly legitimate, the

WACC method is simpler when the firm pursues
this financial strategy.
The Weighted Average Cost of Capital (WACC)
Method
Reconsider equation (5) describing the firm’s
weighted average cost of capital. If the company
follows a fixed debt/value policy, Dt/VLt and Et/VLt
will, by definition, be constant over time. If we
assume the borrowing rate is fixed, the weighted
average cost of capital will be independent of time
since the equity return will also be constant under
these conditions.
To show that the equity return will be constant
under this financial policy, let’s go back to the
analysis of the distribution of the firm’s income
V V T
r D
r
r D
r r
r D
r r
L, U
D

D
D
D A
D
D A
2 2
2 3
4
2
1 1 1
1 1
= +
+
+
+ +
+
+ +
+

,
( ) ( )( )
( )( )
.......
V V
Tr D
r
DVTS
r
L, U
D
D A

2 2
2 3
1 1
= +
+
+
+, ( ) ( )
V
V
DVTS
r
Tr L
r
L,
U
A
D
D
2
2
3

1
1
1
=
+
+
−
+
,
( )
( )
TABLE 6
DEBT, EQUITY AND TOTAL
VALUE OF MEDIA, INC.:
40% DEBT/VALUE MIX
($000’s))
Unlevered value 101,711 107,919 113,792 118,344
Levered value 113,012 119,712 126,076 131,110
Discounted value of tax shields 11,301 11,794 12,284 12,775
Value of Debt (40% of value) 45,205 47,885 50,430 52,447
Value of Equity (60% of value) 67,807 71,827 75,645 78,671
which can be rewritten as:
Since D2 = L VL,2, the value of the company at the
end of year 2 is:

Using the all-equity value as of the end of year
2 of $114 million, the end-of-year 3 tax shields of $13
million, and the other parameters of the example,
Media will be worth approximately $126 million at
the end of year 2. Debt and equity will again be 40%
and 60%, respectively, of the total value of the firm.
Continuing the solution process in this fashion,
one can calculate the present value of the company
and its debt and equity. Table 6 summarizes the
results of the recursive solution process. Media is
initially worth approximately $113 million: $45 mil-
lion (40%) is debt, $68 million (60%) is equity. The
present value of the interest tax shields on projected
borrowings is:
≅ $11 Million
To repeat, the return on assets plays a promi-
nent role in calculating the value of the tax shields
11. Even in the targeted debt example, one might argue that
after year 3 the
firm would vary its borrowings as future cash flow outcomes are
realized. One
would then value the tax shields from year 3 on using the
method described in
this section of the paper. We assume in the previous section that
the firm
commits to exogenous debt levels in order to show the two
financing policies in
their purest forms.
12. One should not conclude, however, that the targeted debt
policy is

superior to the constant debt/value strategy based on the levered
values as
calculated in the two examples. The former may involve higher
costs of financial
distress which are ignored in this analysis.
DVTS
Tr
r
D
D
r
D
D
r g
r
D
D A
A
A
0 0
1
2
3

21 1 1
=
+
+
+
+
+
−
+
( ) ( )
( )

( )
121
between bondholders and stockholders we pre-
sented earlier. Once again, the value of the company
is the sum of its all-equity value and the expected
present value of interest tax shields. As we argued
in the APV section above, the value of the interest
tax shield for the first year (TrDD/(1+rD)) is pre-
determined, and therefore earns a return of rD. But
since subsequent tax shields (DVTS-TrDD/(1+rD))
vary with future free cash flow outcomes for the firm,
the appropriate return for these tax shields is the
higher asset rate, rA.
Revising equation (6a) to take account of the
greater risk of future tax shields under this financial
policy,
(6b)
One can again use the balance-sheet equalities, VL,t
= VU,t + DVTSt = Et + Dt, to solve equation (6b) for
the equity return:13
(10)
It follows that the equity return is constant if the
firm fixes its debt/value (debt/equity) ratio. Using
the parameters of the example, the required equity
return is:

≅ $23.8%
Substituting this equity return (equation (10))
into the weighted average cost of capital (equa-
tion (5)), we obtain the following expression for
WACC:
(11)14
This constant weighted average cost of capital
properly accounts for the higher discount rate ap-
propriate given the greater riskiness of future interest
tax shields.
Using the parameters of our example in equa-
tion (11), the weighted average cost of capital for
Media, Inc. is found as:
rWACC,t = .18 - (.35)(.09)(.40)((1.18)/(1.09)) = 16.6%.
To value Media, we discount the unlevered cash
flows (given in Table 1) by this constant weighted
average cost of capital:
+ +
≅ $113.0 million.
This answer is identical to that derived using the
more complicated APV method (see Table 6). While
the APV and WACC methods yield the same results,
the simplicity of the WACC approach in this case
indicates that it is far more practical than APV if the
firm being valued follows a constant debt/value
policy.15,16

When a company’s debt ratio is changing over time, one must
already have
calculated the firm’s value (using APV or some other means) to
be able to derive the
discount rates necessary to value the firm using the WACC
method.
V r
Tr D
r
r
DVTS
Tr D
r
r D r E r
U t A
D t
D
D
t
D t
D
A t D t E t
,
,

( )
( )
( )
(
( )
)( ) ( ) ( )
+
+
+
−
+
= +
1
1
r r
D
E
Tr
r
r rE t A
t

t
D
D
A D, (
( )
)( )= + −
+
−1
1
rE = + − +
−. (
. (. )
.
)(. . )18
2
3
1
35 09
1 09
18 09
r r Tr L
r

r
WACC t A D
A
D
,
( )
( )
= −
+
+
1
1
13. For the reader who is uncomfortable with the informality of
this derivation,
one can calculate the return shareholders earn in the following
way. Note that the
cash flow to stockholders, CEt, is the unlevered free cash flow
net of debt service
and taxes:
CEt = Ct – rDDt–1(1 – T) + Dt – Dt–1 (F-1)
At any point in time, the required return on equity, rE,t, must
satisfy the
equality:
Et = (CEt+1 + Et+1)/(1 + rE,t) (F-2)

where Et and Et+1 are the values of equity at time t and t+1,
respectively.
Since VL,t+1 = Dt+1 + Et+1, equation (F-2) can be inverted and
rewritten using
equation (F-1) as:
(1 + rE,t) = (Ct+1 + VL,t+1 - Dt[1 + rD(1 – T)])/Et. (F-3)
From our prior observation that future interest tax shields are as
risky as
corresponding unlevered cash flows under this financial policy,
we know that the
firm’s value evolves intertemporally according to:
VL,t = (Ct+1)/(1 + rA) + (TrDDt)/(1 + rD) + (VL,t+1)/(1+rA).
Solving this relation for Ct+1 and substituting into equation (F-
3),
1 + rE,t = ((1 +rA)VL,t – Dt[1 + rD(1 – T) + TrD(1 + rA)/(1 +
rD)])/Et.
Finally, dividing the numerator and denominator of the right
hand side of this
expression by VLt, we can simplify to get:
rE,t = rA + (Dt/Et)(1 – [TrD/(1 + rD)])(rA – rD). (10)
14. This formula is derived in Miles and Ezzell (1980), equation
(20).
15. The relative simplicity of the WACC method for a firm
using a constant debt-
equity blend is recognized by R. Brealey and S. Myers,
Principles of Corporate

Finance, 5th Edition, McGraw-Hill, New York, 1996. See
Chapter 19.
16. We have outlined two plausible financial policies. A third
case, observed
in many highly levered transactions, occurs when a firm is
required (by debt
covenants) to dedicate its entire free cash flow to interest and
principal payments.
Under these conditions, the amount of debt outstanding and,
therefore, the interest
tax shields at any point in time are a direct function of the
unlevered free cash flows
of the firm. Since the debt balance then becomes as risky as the
operating cash
flows, the required return on assets, rA, is the appropriate
discount rate to be used
in calculating the present value of interest tax shields. This is
yet another case in
which the APV and WACC methods yield identical values. One
can demonstrate
this equivalence using the procedures given in the previous
section with proper
adjustment of the discounting of the tax shields. This case
corresponds to the
“Compressed Adjusted Present Value” technique referred to in
S. Kaplan and R.
Ruback, “The Market Pricing of Cash Flow Forecasts:
Discounted Cash Flow vs. The
Method of ‘Comparables’,” Journal of Applied Corporate
Finance, Volume 8,
Number 4, Winter 1996, pp. 45-60.
VL,0 =
12.1

(1.166)
13.6
(1.166)
2
15.9
(1.166) (.166-.04)2
(11)14
122
SOME COMMENTS ON THE “FLOWS
TO EQUITY” APPROACH
A third approach to valuation, popular among
certain practitioners,17 is the “flows to equity” method.
To use this method to calculate the value of a
company, one first values the outstanding equity,
and then adds the market value of debt. To estimate
the value of the levered equity, one must first project
the cash flows the stockholders expect to receive net
of debt service (as described in equation (F-1) in
footnote 13). One must then discount these flows by
the required equity return as given by equation (7)
or (10), depending on the financial policy of the firm.

It is useful to recognize that, whether the firm
pursues the targeted debt strategy or the constant
debt/value policy, the flows to equity approach is
not an independent valuation technique. Suppose,
for example, that the firm targets an absolute dollar
debt level. Under these conditions, the cash flows to
the shareholders are exogenous, given the unlevered
cash flows and pre-determined debt repayment
schedule. However, as equation (7) shows, the
required return to equity (the discount rate to be
used in this approach) depends on the present value
of interest tax shields. If the value of these tax shields
is known, the value of the company can also be
calculated directly as the sum of the tax shields and
the firm’s unlevered value.
Suppose, instead, the firm pursues the constant
capital structure policy. It is then impossible to
estimate the equity cash flows without first having
used one of the two methods described above to
value the firm as a whole. While the projected
unlevered cash flow is assumed known, and the debt
level as of the beginning of the year is pre-deter-
mined, the debt outstanding at year end will depend
on the value of the company at that time. This value
fluctuates based on unlevered cash flows yet to be
realized. Thus, the change in outstanding debt
principal, and the equity cash flow, depend on the
value of the firm. It follows that, under the constant
capital structure financial policy, the estimation of
the flows to equity requires prior knowledge of total
firm value.
In sum, application of the “flows to equity”

approach to valuation in each financing case re-
quires prior knowledge of what the company is
worth. It still may be of interest, for purposes other
than valuation, to calculate the cash flow to share-
holders and the required equity return. But one will
already be in a position to use the APV or WACC
methods to value the company directly.
CONCLUSION
In this paper, we have compared two popular
approaches to valuing a company, the Adjusted
Present Value (APV) and the Weighted Average Cost
of Capital (WACC) methods. To illustrate the ap-
proaches, we have assumed that the company being
valued follows one of two plausible financing strat-
egies: In the first, the company commits to a pre-
determined schedule for the absolute amount of
debt to be used. Under a second scenario, the firm
is financed with a constant blend of debt and equity.
We have shown that both valuation methods,
when properly formulated to take into account the
evolution of the firm’s cash flows and capital struc-
ture, give identical results under each of these
financing alternatives. But, although the approaches
are equivalent, our analysis also reveals that it is more
practical to apply the APV technique when the firm
targets the dollar level of debt outstanding over time,
and the WACC approach when the firm instead
intends to maintain a fixed debt/value ratio.
17. Particularly those involved in real estate investments,
leveraged buyout,
leveraged leasing and project finance transactions.

ISIK INSELBAG
is Adjunct Professor of Finance, as well as the former Vice
Dean
and Director of the Graduate Division, at the University of
Pennsylvania’s Wharton School of Business.
HOWARD KAUFOLD
is Adjunct Professor of Finance and the Director of the
Executive
MBA Program at the Wharton School.
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