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ples, value-to-book and value-earnings ratios. Value-to book multiples are shown to be
a function of future abnormal ROEs, book value growth, and the ¬rm™s cost of equity.
Value-earnings multiples are driven by the same factors and also the current ROE.


DEFINING VALUE FOR SHAREHOLDERS
How should shareholders think about the value of their equity claims on a ¬rm? Finance
theory holds that the value of any ¬nancial claim is simply the present value of the cash
payoffs that its claim holders receive. Since shareholders receive cash payoffs from a
company in the form of dividends, the value of their equity is the present value of future
dividends (including any liquidating dividend).
Equity value = PV of expected future dividends
If we denote the expected future dividend for a given year as DIV and re as the cost of
equity capital (the relevant discount rate), the stock value is as follows:
DIV 1 DIV 2 DIV 3
Equity value = ----------------------- + -------------------------- + -------------------------- + . . .
( 1 + re ) ( 1 + re ) 2 ( 1 + re ) 3
Notice that the valuation formula views a ¬rm as having an inde¬nite life. Of course, in
reality ¬rms go bankrupt and get taken over. In these situations, shareholders effectively
receive a terminating dividend on their stock.
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If a ¬rm had a constant dividend growth rate (gd) inde¬nitely, its value would simplify
to the following formula:
DIV1
Equity value = -------------------
-
d
re “ g
To better understand how the discounted dividend approach works, consider the fol-
lowing example. At the beginning of year 0 Down Under Company raises $60 million
of equity and uses the proceeds to buy a ¬xed asset. Operating pro¬ts before deprecia-
tion (all received in cash) and dividends for the company are expected to be $40 million
in year 1, $50 million in year 2, and $60 million in year 3, at which point the company
terminates. The ¬rm pays no taxes. If the cost of equity capital for this ¬rm is 10%, the
value of the ¬rm™s equity is computed as follows:
Year Dividend PV Factor PV of Dividend
1 $40m 0.9091 $36.4m
2 50 0.8264 41.3
3 60 0.7513 45.1
Equity value $122.8m

The above valuation formula is called the dividend discount model. It forms the basis
for most of the popular theoretical approaches for stock valuation. The remainder of the
chapter discusses how this model can be recast to generate the discounted abnormal
earnings and discounted cash ¬‚ow models of value.


THE DISCOUNTED ABNORMAL EARNINGS
VALUATION METHOD
As discussed in Chapter 3, there is a link between dividends and earnings. If all equity
effects (other than capital transactions) ¬‚ow through the income statement,1 the expected
book value of equity for existing shareholders at the end of year one (BVE1) is simply
the book value at the beginning of the year (BVE0) plus expected net income (NI1) less
expected dividends (DIV1).2 This relation can be rewritten as follows:
DIV 1 = NI 1 + BVE 0 “ BVE 1

By substituting this identity for dividends into the dividend discount formula and
rearranging the terms, stock value can be rewritten as follows 3 :
Equity value = Book value of equity + PV of expected future abnormal earnings

Abnormal earnings are net income adjusted for a capital charge computed as the dis-
count rate multiplied by the beginning book value of equity. Abnormal earnings there-
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fore make an adjustment to re¬‚ect the fact that accountants do not recognize any
opportunity cost for equity funds used. Thus, the discounted abnormal earnings valua-
tion formula is:
NI 1 “ re … BVE 0 NI 2 “ re … BVE 1 NI 3 “ re … BVE 2
Equity value = BVE 0 + ------------------------------------------ + ----------------------------------------- + ----------------------------------------- + . . .
- - -
( 1 + re ) ( 1 + re ) ( 1 + re )
2 3

As noted earlier, equity values can also be estimated by valuing the ¬rm™s assets and
then deducting its net debt. Under the earnings-based approach, this implies that the
value of the assets is:
NOPAT 1 “ WACC … BVA 0 NOPAT 2 “ WACC … BVA 1
Asset value = BVA 0 + ------------------------------------------------------------------- + --------------------------------------------------------------------- + . . .
- -
( 1 + WACC ) ( 1 + WACC ) 2
BVA is the book value of the ¬rm™s assets, NOPAT is net operating pro¬t (before interest)
after tax, and WACC is the ¬rm™s weighted-average cost of debt and equity. From this
asset value the analyst can deduct the market value of net debt to generate an estimate
of the value of equity.
The earnings-based formulation has intuitive appeal. It implies that if a ¬rm can earn
only a normal rate of return on its book value, then investors should be willing to pay no
more than book value for the stock. Investors should pay more or less than book value
if earnings are above or below this normal level. Thus, the deviation of a ¬rm™s market
value from book value depends on its ability to generate “abnormal earnings.” The for-
mulation also implies that a ¬rm™s stock value re¬‚ects the cost of its existing net assets
(that is, its book equity) plus the net present value of future growth options (represented
by cumulative abnormal earnings).


Key Analysis Questions
Valuation of equity (debt plus equity) under the discounted abnormal earnings
method requires the analyst to answer the following questions:
• What are expected future net income (NOPAT) and book values of equity
(assets) over a finite forecast horizon (usually 5 to 10 years)?
• What are expected future abnormal earnings (NOPAT), after deducting a cap-
ital charge from forecasts of net income (NOPAT)? The capital charge is the
firm™s cost of equity (WACC) multiplied by beginning book equity (assets).
• What is expected future abnormal net income (NOPAT) beyond the final year
of the forecast horizon (called the “terminal year”) based on some simplify-
ing assumption?
• What is the present value of abnormal earnings (NOPAT) discounted at the
cost of equity capital (WACC)?
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• What is the estimated value of equity, computed by adding the current book
value of equity (assets) to the cumulated present value of future abnormal
earnings (NOPAT)? Are there nonoperating assets held by the firm that have
been ignored in the previous abnormal earnings (NOPAT) forecasts (e.g., mar-
ketable securities or real estate held for sale)? If so, their values should be in-
cluded in the equity estimate.


To illustrate the earnings-based valuation approach, let™s return to the Down Under
Company example. Since the company is an all-equity ¬rm, the value of the ¬rm™s eq-
uity and its assets (debt plus equity) are the same. If the company depreciates its ¬xed
assets using the straight-line method, its beginning book equity, earnings, abnormal
earnings, and valuation will be as follows:
PV of
Beginning Abnormal Abnormal
Year Book Value Earnings Earnings PV Factor Earnings
1 $60m $20m $14m 0.9091 $12.7m
2 40 30 26 0.8264 21.5
3 20 40 38 0.7513 28.6
Cumulative PV of abnormal earnings 62.8
+ Beginning book value 60.0
= Equity value $122.8m

This stock valuation of $122.8 million is identical to the value estimated when the ex-
pected future dividends are discounted directly.
Recent research shows that abnormal earnings estimates of value outperform tradi-
tional multiples, such as price-earnings ratios, price-to-book ratios, and dividend yields,
for predicting future stock movements.4 Firms with high abnormal earnings model esti-
mates of value relative to current price show positive abnormal future stock returns,
whereas ¬rms with low estimated value-to-price ratios have negative abnormal stock
performance.


Accounting Methods and Discounted Abnormal Earnings
It may seem odd that ¬rm value can be expressed as a function of accounting numbers.
After all, accounting methods per se should have no in¬‚uence on ¬rm value (except as
those choices in¬‚uence the analyst™s view of future real performance). Yet the valuation
approach used here is based on numbers”earnings and book value”that vary with
accounting method choices. How, then, can the valuation approach deliver correct
estimates?
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It turns out that because accounting choices affect both earnings and book value, and
because of the self-correcting nature of double-entry bookkeeping (all “distortions” of
accounting must ultimately reverse), estimated values based on the discounted abnormal
earnings method will not be affected by accounting choices per se. For example, assume
that Down Under Company™s managers choose to be conservative and expense some un-
usual costs that could have been capitalized as inventory at year 1, causing earnings and
ending book value to be lower by $10 million. This inventory is then sold in year 2. For
the time being, let™s say the accounting choice has no in¬‚uence on the analyst™s view of
the ¬rm™s real performance.
Managers™ choice reduces abnormal earnings in year 1 and book value at the begin-
ning of year 2 by $10 million. However, future earnings will be higher, for two reasons.
First, future earnings will be higher (by $10 million) when the inventory is sold in year
2 at a lower cost of sales. Second, the benchmark for normal earnings (based on book
value of equity) will be lower by $10 million. The $10 million decline in abnormal earn-
ings in year 1 is perfectly offset (on a present value basis) by the $11 million higher ab-
normal earnings in year 2. As a result, the value of Down Under Company under
conservative reporting is identical to the value under the earlier accounting method
($122.8 million).
PV of
Beginning Abnormal Abnormal
Year Book Value Earnings Earnings PV Factor Earnings
1 $60m $10m $ 4m 0.9091 $ 3.6m
2 30 40 37 0.8264 30.6
3 20 40 38 0.7513 28.6
Cumulative PV of abnormal earnings 62.8
+ Beginning book value 60.0
= Equity value $122.8m


Consequently, provided the analyst is aware of biases in accounting data as a result
of the use of aggressive or conservative accounting choices by management, abnormal
earnings-based valuations are unaffected by the variation in accounting decisions. This
implies that strategic and accounting analyses are critical precursors to abnormal earn-
ings valuation. The strategic and accounting analysis tools help the analyst to identify
whether abnormal earnings arise from sustainable competitive advantage or from
unsustainable accounting manipulations. For example, consider the implications of fail-
ing to understand the reasons for a decline in earnings from a change in inventory policy
for Down Under Company. If the analyst mistakenly interpreted the decline as indicating
that the ¬rm was having dif¬culty moving its inventory, rather than that it had used con-
servative accounting, she might reduce expectations of future earnings. The estimated
value of the ¬rm would then be lower than that reported in our example.
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VALUATION USING PRICE MULTIPLES
Valuations based on price multiples are widely used by analysts. The primary reason for
their popularity is their simplicity. Unlike the discounted abnormal earnings, discounted
dividend, and discounted cash ¬‚ow methods, they do not require detailed multiple-year
forecasts about a variety of parameters, including growth, pro¬tability, and cost of
capital.
Valuation using multiples involves the following steps:
Step 1: Select a measure of performance or value (e.g., earnings, sales, cash ¬‚ows, book
equity, book assets) as the basis for multiple calculations.
Step 2: Estimate price multiples for comparable ¬rms using the measure of performance
or value.
Step 3: Apply the comparable ¬rm multiple to the performance or value measure of the
¬rm being analyzed.
Under this approach, the analyst relies on the market to undertake the dif¬cult task of
considering the short- and long-term prospects for growth and pro¬tability and their im-
plications for the values of the “comparable” ¬rms. Then the analyst assumes that the
pricing of those other ¬rms is applicable to the ¬rm at hand.
On the surface, using multiples seems straightforward. Unfortunately, in practice it is
not as simple as it would appear. Identi¬cation of “comparable” ¬rms is often quite dif-
¬cult. There are also some choices to be made concerning how multiples will be calcu-
lated. Finally, explaining why multiples vary across ¬rms, and how applicable another
¬rm™s multiple is to the one at hand, requires a sound understanding of the determinants
of each multiple.


Selecting Comparable Firms
Ideally, price multiples used in a comparable ¬rm analysis are those for ¬rms with sim-
ilar operating and ¬nancial characteristics. Firms within the same industry are the most
obvious candidates. However, even within narrowly de¬ned industries, it is often dif¬-
cult to ¬nd multiples for similar ¬rms. Many ¬rms are in multiple industries, making it

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