try frequently have different strategies, growth opportunities, and pro¬tability, creating
comparability problems.
One way of dealing with these issues is to average across all ¬rms in the industry. The
analyst implicitly hopes that the various sources of noncomparability “cancel out,” so
that the ¬rm being valued is comparable to a “typical” industry member. Another ap
proach is to focus on only those ¬rms within the industry that are most similar.
For example, consider using multiples to value Nordstrom. Dow Jones Interactive
classi¬es the company in the Retail: Apparel industry. On July 16, 1999, Dow Jones re
ported that the industry priceearnings ratio was 24.0 and the average pricetobook ratio
412 Prospective Analysis: Valuation Theory and Concepts
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Prospective Analysis: Valuation Theory and Concepts
was 6.36 percent. In contrast, Nordstrom had a priceearnings ratio of 27.3 and a price
tobook ratio of 4.49 percent.
However, Dow Jones reported that Nordstrom™s competitors could be narrowed to the
following ¬rms: Ann Taylor, Brown Shoe, Dayton Hudson, Donna Karan, Dillards, Fed
erated Department Stores, The Gap, Lands™ End, The Limited, Mens Wearhouse, Ne
iman Marcus, May Department Stores, JC Penney, Saks, Spiegel, and Talbots. These
include other ¬rms that Dow Jones classi¬ed in the Retail: Apparel industry and several
¬rms in the Retail: Broadline segment. The average priceearnings ratio for these direct
competitors was 55.9 and the average pricetobook ratio was 3.81. Clearly, the market
expects that Nordstrom™s future performance will differ somewhat from that of the Re
tail: Apparel industry as a whole, and from that of its direct competitors.
Multiples for Firms with Poor Performance
Price multiples can be affected when the denominator variable is performing poorly.
This is especially common when the denominator is a ¬‚ow measure, such as earnings or
cash ¬‚ows. For example, Donna Karan, one of Nordstrom™s competitors, had earnings
per share of only 0.01 in 1998 and a priceearnings ratio of 434.4.
What are analysts™ options for handling the problems for multiples created by transi
tory shocks to the denominator? One option is to simply exclude ¬rms with large tran
sitory effects from the set of comparable ¬rms. If Donna Karan is excluded from
Nordstrom™s peer set, the average benchmark priceearnings ratio declines from 55.9 to
30.7. Alternatively, if the poor performance is due to a transitory shock, such as a write
off or special item, the transitory effect can be excluded from computation of the multi
ple. For Donna Karan this is not possible, since the temporary poor performance is not
attributable to any single event. Finally, the analyst can use a denominator that is a fore
cast of future performance rather than a past measure. Multiples based on forecasts are
termed leading multiples, whereas those based on historical data are called trailing mul
tiples. Leading multiples are less likely to include onetime gains and losses in the de
nominator, simply because such items are dif¬cult to anticipate. For Donna Karan, First
Call reported that analysts expected 1999 earnings to be $0.27, implying a leading price
earnings multiple of only 16.1.
Adjusting Multiples for Leverage
Price multiples should be calculated in a way that preserves consistency between the nu
merator and denominator. Consistency is an issue for those ratios where the denominator
re¬‚ects performance before servicing debt. Examples include the pricetosales multiple
and any multiple of operating earnings or operating cash ¬‚ows. When calculating these
multiples, the numerator should include not just the market value of equity, but the value
of debt as well.
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Prospective Analysis: Valuation Theory and Concepts
119 Part 2 Business Analysis and Valuation Tools
DETERMINANTS OF VALUETOBOOK
AND VALUEEARNINGS MULTIPLES
Even across relatively closely related ¬rms, price multiples can vary considerably. Care
ful analysis of this variation requires consideration of factors that might explain why one
¬rm™s multiples should be higher than those of benchmark ¬rms. We therefore return to
the abnormal earnings valuation method and show how it provides insights into differ
ences in valuetobook and valuetoearnings multiples across ¬rms
If the abnormal earnings formula is scaled by book value, the lefthand side becomes
the equity valuetobook ratio, as opposed to the equity value itself. The righthand side
variables are now earnings de¬‚ated by book value, or our old friend return on equity
(ROE), discussed in Chapter 9.5 The valuation formula becomes:
( ROE 2 “ re ) ( 1 + gbve 1 )
ROE 1 “ re
1 +  + 

Equity valuetobook ratio = 
( 1 + re ) 2
(1 + r ) e
( ROE 3 “ re ) ( 1 + gbve 1 ) ( 1 + gbve 2 )
+  + . . .

( 1 + re ) 3
where gbvet = growth in book value (BVE) from year t1 to year t or
BVE t “ BVE t “1


BVE t “1
The formulation implies that a ¬rm™s equity valuetobook ratio is a function of three
factors: its future abnormal ROEs, its growth in book equity, and its cost of equity capital.
Abnormal ROE is de¬ned as ROE less the cost of equity capital (ROE “ re ). Firms with
positive abnormal ROE are able to invest their net assets to create value for shareholders,
and have pricetobook ratios greater than one. Firms that are unable to generate returns
greater than the cost of capital have ratios below one.
The magnitude of a ¬rm™s valuetobook multiple also depends on the amount of
growth in book value. Firms can grow their equity base by issuing new equity or by re
investing pro¬ts. If this new equity is invested in positive valued projects for sharehold
ers, that is projects with ROEs that exceed the cost of capital, the ¬rm will boost its equity
valuetobook multiple. Of course, for ¬rms with ROEs that are less than the cost of cap
ital, equity growth further lowers the multiple.
The valuation task can now be framed in terms of two key questions about the ¬rm™s
“value drivers”:
• How much greater (or smaller) than normal will the firm ™s ROE be?
• How quickly will the firm™s investment base (book value) grow?
If desired, the equation can be rewritten so that future ROEs are expressed as the prod
uct of their components: pro¬t margins, sales turnover, and leverage. Thus, the approach
permits us to build directly on projections of the same accounting numbers utilized in
414 Prospective Analysis: Valuation Theory and Concepts
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Prospective Analysis: Valuation Theory and Concepts
¬nancial analysis (see Chapter 9) without the need to convert projections of those num
bers into cash ¬‚ows. Yet in the end, the estimate of value should be the same as that from
the dividend discount model.6
It is also possible to structure the multiple valuation as the debt plus equity valueto
book assets ratio by scaling the abnormal NOPAT formula by book value of net operating
assets. The valuation formula then becomes:
( ROA 2 “ WACC ) ( 1 + gbva )
ROA 1 “ WACC
1 +  + 

Debt plus equity valuetobook ratio =
( 1 + WACC ) ( 1 + WACC ) 2
( ROA 3 “ WACC ) ( 1 + gbva 1 ) ( 1 + gbva 2 )
+  + . . .

( 1 + WACC ) 3
where ROA = operating return on assets = NOPAT/(Operating working capital + Net longterm assets)
WACC = weighted average cost of debt and equity
gbvan = growth in book value of assets (BVA) from year t1 to year t or
BVA t “ BVA t 1


BVA t 1
The value of a ¬rm™s debt and equity to net operating assets multiple therefore depends
on its ability to generate asset returns that exceed its WACC, and its ability to grow its
asset base. The value of equity under this approach is then the estimated multiple times
the current book value of assets less the market value of debt.
Returning to the Down Under Company example, the implied equity valuetobook
multiple can be estimated as follows:
Year 1 Year 2 Year 3
Beginning book value $60m $40m $20m
Earnings $20m $30m $40m
33% 75% 200%
ROE
’ Cost of capital 10% 10% 10%
= Abnormal ROE 23% 65% 190%
— (1+ cumulative book value growth) 1.00 0.67 0.33
= Abnormal ROE scaled by book value growth 23% 43% 63%
— PV factor 0.9091 0.8264 0.7513
= PV of abnormal ROE scaled by book value
growth 21.2% 35.8% 47.6%
Cumulative PV of abnormal ROE scaled by
book value growth 104.6%
+ 1.00 100.0
= Equity valuetobook multiple 204.6%
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Prospective Analysis: Valuation Theory and Concepts
1111 Part 2 Business Analysis and Valuation Tools
The equity valuetobook multiple for Down Under is therefore 204.6 percent, and the
implied stock value is $122.8 ($60 . 2.046), once again identical to the dividend dis
count model value. Recall that Down Under is an allequity ¬rm, so that the abnormal
ROE and abnormal ROA structures for valuing the ¬rm are the same.
The equity valuetobook formulation can also be used to construct the equity value
earnings multiple as follows:
Book value of equity
Equity value tobook multiple — 

Equity valuetoearnings multiple =
Earnings
Equity valuetobook multiple
Valuetoearnings multiple = 

ROE
In other words, the same factors that drive a ¬rm™s equity valuetobook multiple also
explain its equity valueearnings multiple. The key difference between the two multiples
is that the valueearnings multiple is affected by the ¬rm™s current level of ROE perfor
mance, whereas the valuetobook multiple is not. Firms with low current ROEs there
fore have very high valueearnings multiples and vice versa. If a ¬rm has a zero or
negative ROE, its PE multiple is not de¬ned. Valueearnings multiples are therefore more
volatile than valuetobook multiples.
The following data for a subset of ¬rms in the Retail: Apparel industry illustrate the
relation between ROE, equity growth, the pricetobook ratio, and the priceearnings
ratio:
Book Value Priceto PriceEarnings
Company ROE Growth Book Ratio Ratio
..........................................................................................................................
The Gap 48.5% “1% 2327% 50.1
The Limited 88.9% 9% 346% 5.5
Saks 2.1% 83% 262% 74.8
Donna Karan 0.2% 0% 135% 434.4
..........................................................................................................................
Both the pricetobook and priceearnings ratios are high for The Gap. Investors there
fore expect that in the future The Gap will generate even higher ROEs than its current
high level (48 percent). In contrast, the Limited has a high pricetobook ratio (346 per
cent) but a low priceearnings ratio. This indicates that investors expect that The Limited
will continue to generate positive abnormal ROEs, but that the current level of ROE
(89 percent) is not sustainable. Saks has a pricetobook ratio of 262 percent, indicating
that investors expect it to earn abnormal ROEs. However, it has a high priceearnings
multiple (75), suggesting that the current low ROE (2 percent) is considered temporary.
Finally, Donna Karan has a relatively low pricetobook ratio (135 percent) but a high
priceearnings multiple. Investors apparently do not expect Donna Karan™s poor perfor
mance to persist, but they also do not believe that the company will be able to sustain
high abnormal ROEs.
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Prospective Analysis: Valuation Theory and Concepts
Key Analysis Questions
To value a ¬rm using multiples, an analyst has to assess the quality of the variable
used as the multiple basis, and to determine the appropriate peer ¬rms to include
in the benchmark multiple. Analysts are therefore likely to be interested in answer
ing the following questions:
• What is the expected future growth in the variable to be used as the basis for
the multiple? For example, if the variable is earnings, has the firm made con
servative or aggressive accounting choices that are likely to unwind in the
coming years? If the multiple is book value, what is the sustainability of the
firm™s growth and ROE? What is the dynamics of the firm™s industry and
product market? Is it a market leader in a high growth industry, or is it in a
mature industry with fewer growth prospects? How is the firm™s future per
formance likely to be affected by competition or potential entry in the
industry?
• Who are the most suitable peer companies to include in the benchmark mul
tiple computation? Have these firms had comparable growth (earnings or
book values), profitability, and quality of earnings as the firm being ana
lyzed? Do they have the same risk characteristics?
SHORTCUT FORMS OF EARNINGSBASED VALUATION
The discounted abnormal earnings valuation formula can be simpli¬ed by making
assumptions about the relation between a ¬rm™s current and future abnormal earnings.