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CHAPTER 8
EQUITY MULTIPLES
When investing in a stock, our interests primarily lie in whether the equity in a
company is fairly priced. It follows logically that we look at equity multiples, where we
relate the market value of equity to the earnings or book value of equity in that company.
In this chapter, we begin by looking at the variants on equity multiples ranging from the
widely used PE ratios to less common multiples such as price to free cash flow to equity.
We then examine the distributional characteristics of the most widely used equity
multiples and the determinants of these multiples. We close the chapter with a series of
applications where we use the analytical tools developed to make judgments on
valuation.
Definitions of Equity Multiples
An equity multiple requires two inputs, one for the market value of the equity and
one for the variable to which equity value is scaled – earnings, book value of equity or
revenues, for instance. In this section, we will first consider how best to estimate the
market value of equity and then move on to look at the choices when it comes to scaling
variables.
Measuring the Market Value of Equity
All equity multiples are scaled to the market value of equity. With publicly traded
firms, measuring the market value of equity may seem like a trivial exercise since there is
after all only one stock price at any point in time. There are, however, three decisions that
we have to make that can have consequences for how we measure equity value:
1. Per Share or Aggregate Equity Value: The market value of equity can be computed on
a per share basis or as an aggregate value (the market capitalization or market cap). Since
the latter is computed by multiplying the number of shares outstanding by the share price,
the effects of using one over the other on equity multiples may seem inconsequential but
there are conditions under which the two will diverge. One is when there are multiple
classes of shares in the same company, trading at different stock prices. The market
capitalization will include the market values of all outstanding shares, whereas the market
1
price will reflect only the class of shares considered. The other is when there is a
divergence between the number of shares outstanding today (primary shares) and the
potential number that can be outstanding if management options, convertibles and
warrants are exercised (diluted shares). The market capitalization is usually computed
using the former but the earnings per share and book value per share are often computed
using the latter.
2. Cum-Cash or Ex-Cash: The market value of equity for a publicly traded firm will
incorporate the company’s holdings of cash and marketable securities. Thus, the market
capitalization of $ 300 billion for Microsoft in November 2005 includes the $ 40 billion
in cash held by the company. The interest income earned by the company on its cash
holdings is reported as part of the overall net income of that company. In conventional
practice, analysts use the total market value of equity and the total net income or book
value of equity to compute equity multiples. While this is internally consistent, the risk
and return characteristics of cash holdings are so different from the risk and return
characteristics of operating assets, it may make sense (especially when cash balances
comprise a large proportion of the firm) to compute the market value of equity net of cash
holdings. This net market value of equity can be considered to be the market value of
equity in non-cash or operating assets.
3. Equity Options: One reason for the disconnect between per share and aggregate values
of equity is the existence of management options. Management options, in particular, and
company-issued equity options (including warrants and convertible bonds), in general,
create a second claim on the equity in a company (in addition to the primary claim from
common stockholders). The total market value of equity in a company with substantial
management and other equity options outstanding is therefore the market capitalization
plus the estimated or observed market value of equity options. In other words,
Microsoft’s market capitalization of $ 300 billion reflects the value of just the common
stock in the company; the estimated value of management options outstanding at the
company should be added to the market capitalization to get to total market value of
equity. Needless to say, most analysts do not make this adjustment and we will consider
the implications in the next section.
2
Scaling Variable
As we noted in chapter 7, consistency requires us to scale equity values to equity
variables. Equity multiples can be stated in terms of earnings, book value and revenues
and we will examine the choices in this section:
a. Equity Earnings Variables: In a conventional accounting statement, we begin with
revenues, net out operating expenses to arrive at operating income and subtract out
financial expenses and taxes to estimate net income. When computing equity multiples, it
is clearly inappropriate to use operating income as our measure of earnings because it
accrues to all claim holders in the firm. With net income, though, the measure that we
choose to use has to match up to how we compute market value of equity. Table 8.1
summarizes the consistent choices, given different measures of equity value:
Table 8.1: Equity Earnings Measures and Equity Market Value
Measure of Equity Value
Measure of Equity Earnings
Price per share
Earnings per share
Aggregate Market value of Equity
Net Income
Net Market Equity = Market Value of
Net Income minus After-tax interest
Equity minus Cash
income from cash
Option augmented Equity = Market Value
Net Income1
of Equity + Value of Management Options
With each of these measures, there are other judgments that will have to be made. For
instance, all of these measures of equity earnings can be computed before and after
extraordinary items. The key is to come up with a measure of earnings that is comparable
across different firms. With that objective in mind, it is quite clear that we should exclude
extraordinary items. However, there is one more measurement question that we will have
to confront when measuring earnings per share. Should we use primary, partially diluted
or fully diluted earnings per share? We believe that all of these measures create potential
comparison problems. If we use primary earnings per share, we are ignoring management
1
While it may seem logical to add back the expenses associated with new option grants back to net income
(especially in the aftermath of the new FASB 123R), we do not think it makes sense to do so. These
expenses are for the current period, whereas the options being added back to the value of equity reflect all
options granted historically which are still outstanding.
3
and other options outstanding and will bias our analyses towards finding companies that
have disproportionately large numbers of these options outstanding to be under valued. If
we use diluted earnings per share, we are assuming that the number of options
outstanding is a sufficient measure of the option overhang over equity and thus we meet
out equal penalties to firms with equivalent numbers of options outstanding. This can be
a problem when some companies have long-term, deep in-the-money options outstanding
and other companies have short term, at-the-money or out-of-the-money options
outstanding. Clearly, the options will affect equity value more at the former and less in
the latter, but using fully diluted earnings per share will bias us towards finding the
former to be under valued.2 The advantage of using the option augmented equity
approach is that it considers the values of options outstanding rather than just the number
of options.
b. Equity Cash flow Measures: There are many analysts and investors who are wary of
accounting measures of earnings and with good reason. They prefer cash flow measures
and they have two choices with equity multiples. One is an approximate measure of cash
earnings, obtained by adding depreciation and other non-cash charges back to net income.
The other is the measure of free cash flow to equity introduced in chapter 3, where we
netted out reinvestment needs and debt cashflows to get to a final measure of cash flow.
As with earnings numbers, the definitions of cash flow should be consistent with the
measure of equity value used. If the equity value is the aggregate market value of equity,
we should use total net income to estimate free cash flows to equity. If the equity value is
net of cash, the free cash flow to equity should also net out interest income from cash.
c. Equity Book Value Measures: The other logical measure to scale the market value of
equity to is to the book value of equity. Here again, the measure of book equity that we
use should be consistent with the measure of market equity. Table 8.2 summarizes the
choices:
Table 8.2: Book Equity Measures and Equity Market Value
Measure of Equity Value
2
Measure of Book Equity
To see why, note that the stock price will be depressed more when there are millions of deep in-themoney options outstanding than when these options are out-of-the-money. Dividing the price by the diluted
earnings per share will therefore yield a lower PE ratio and a stock that looks cheaper.
4
Price per share
Book Value of Equity per share
Aggregate Market value of Equity
Book Value of Equity (Shareholder’s
Equity on balance sheet)
Net Market Equity = Market Value of
Book Value of Equity minus Cash
Equity minus Cash
Option augmented Equity = Market Value
Book Value of Equity plus Book Value of
of Equity + Value of Management Options
Management Options granted (if any)
Note that shareholder’s equity (book value of equity) includes retained earnings and any
other accounting adjustments made to book equity. One big issue that faces analysts with
book equity is what to do with goodwill arising from acquisitions. The reason is that the
accounting for goodwill can make comparisons between acquisitive and non-acquisitive
firms difficult. To see why, note that companies that grow through internal investments
are not required to record the value of growth potential as part of their assets or in
shareholder’s equity. A company that grows through acquisitions has to record the
market value paid for the acquisition and the difference between the market value and
book value of the acquired company as goodwill; the goodwill can be considered to be a
premium paid for the growth assets of the acquired company.3 In practical terms, this will
mean that the price to book ratios of acquisitive companies will generally look lower (and
more attractive from an investment standpoint) than non-acquisitive companies.
d. Revenue Measures: There are many analysts who divide the market value of equity by
the revenues of the firm to estimate a price to sales ratio. This measure is inconsistent,
since revenues belong to the entire firm and not just to its equity investors.
Notwithstanding this, analysts often prefer to use price to sales ratios to enterprise value
to sales ratios (which would be more consistent). The reason they may be able to get
away with this practice, without major errors creeping into their analysis, may lie in the
sectors where the usage of this multiple is most common. One is technology, where firms
tend to have little or no debt, thus making firm value and equity value almost equivalent.
The other is retailing, where firms historically have maintained homogeneous debt ratios
3
Goodwill can also be a repository for synergy, control and over payment, thus making it an imperfect
measure of acquired company growth assets.
5
(usually in the form of operating leases). In both sectors, though, changes are underway
that put this long-standing practice at risk. In the technology sector, companies now often
hold large and divergent cash balances. Using price to sales ratios for these firms will
bias analysts towards finding companies with relatively small cash balances to be under
valued; one easy fix for this problem is to use equity values netted for cash. In retailing,
different companies have adopted different practices when it comes to opening new
stores. Some continue to use operating leases, but others have increasingly chosen to
invest in real estate directly by buying their store sites either with equity or debt. Using
price to sales ratios will bias analysts towards finding companies with more financial
leverage (either through operating leases or real estate debt) to be cheap relative to
companies without this leverage.
Distributional Characteristics of Equity Multiples
In chapter 7, we noted that most multiples have distributions that are skewed
towards positive values and that the distributions themselves are volatile and change over
time. Equity multiples are no exception to this general rule. In this section, we will
examine the distributions of some widely used equity multiples.
a. Price Earnings Ratio
The price earnings ratio is the ratio of the market value of equity to the earnings
generated for equity investors:
PE =
Market Value of Equity
Equity Earnings
While it is conventionally computed using the current price price per share and diluted
earnings per share, the alternative measures of market equity – aggregate value of equity,
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equity net of cash and option-augmented equity – can be used with the consistent
measure of earnings (see table 8.1). Figure 8.1 presents the distribution of PE ratios for
U.S. stocks in January 2006. The current PE, trailing PE and forward PE ratios are all
presented in this figure.
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Table 8.3 presents summary statistics on all three measures of the price earnings ratio
starting with the mean and the standard deviation, and including the median, 10th and 90th
percentile values.4
Table 8.3: Summary Statistics – PE Ratios for U.S. Stocks
Mean
Standard Error
Median
Standard Deviation
Kurtosis
Skewness
Minimum
Maximum
Count
90th percentile
10th percentile
4
Current PE
43.58
3.74
20.67
241.96
1871.78
38.68
0.75
12712.82
4179
54.21
11.22
Trailing PE
40.52
7.38
19.04
463.62
3611.60
58.97
3.12
28518.28
3947
44.31
10.17
Forward PE
29.93
1.81
18.18
88.57
474.76
19.35
4.38
2710.00
2397
28.14
13.75
The mean and the standard deviation are the summary statistics that are most likely to be affected by these
outliers.
7
Looking at all three measures of the PE ratio, the average is consistently higher than the
median, reflecting the fact that PE ratios can be very high numbers but cannot be less
than zero. This asymmetry in the distributions is captured in the skewness values. The
current PE ratios are also higher than the trailing PE ratios, which, in turn, are higher than
the forward PE ratios.
There were 7123 firms in the overall sample, but only 4179 survived the positive
earnings cut and had PE ratios. With forward PE ratios, we lose more firms since we need
analyst estimates of earnings per share for the next year; any firm that is not followed by
analysts is eliminated from the sample. The bias that we averred to in chapter 7, resulting
from not being able to compute multiples for some firms, is clearly a significant problem
with PE ratios.
b. PEG Ratio
Portfolio managers and analysts sometimes compare PE ratios to the expected
growth rate to identify undervalued and overvalued stocks. As a natural outgrowth, the
PEG ratio is defined to be the price earnings ratio divided by the expected growth rate in
earnings per share:
PEG ratio =
PE ratio
Expected Growth Rate
For instance, a firm with a PE ratio of 20 and a growth rate of 10% is estimated to have a
PEG ratio of 2. Consistency requires the growth rate used in this estimate be the expected
growth rate in earnings per share or net income, rather than operating income, because
this is an equity multiple. Given the many definitions of the PE ratio, which version
should we use to estimate the PEG ratio? The answer depends upon the base on which the
expected growth rate is computed. If the expected growth rate in earnings per share is
based upon earnings in the most recent year (current earnings), the PE ratio that should be
used is the current PE ratio. If it based upon trailing earnings, the PE ratio used should be
the trailing PE ratio. The forward PE ratio should never be used in this computation,
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since it may result in a double counting of growth.5 The cross sectional distribution of
PEG ratios across all U.S. firms in January 2006 is examined in Figure 8.2.
In estimating these PEG ratios, the analyst estimates of growth in earnings per share over
the next 5 years is used in conjunction with the current PE. Any firm, therefore, that has
negative earnings per share or lacks an analyst estimate of expected growth is dropped
from the sample. This may be a source of bias, since larger and more liquid firms are
more likely to be followed by analysts.
PEG ratios are most widely used in analyzing technology firms. Figure 8.3
contains the distribution of PEG ratios for technology stocks in January 2006, using
analyst estimates of growth again to arrive at the PEG ratios.
5
Too see why, assume that the earnings per share is currently $1.00, is expected to double to $ 2.00 next
year and grow 4% a year for the following four years. The expected growth rate over the next 5 years will
be 18.53%, largely because of the expected growth next year. If we use the forward earnings per share of $
2.00 to compute the PE ratio and proceed to divide by the expected growth rate of 18.53% (to arrive at a
low PEG ratio), we have double counted next year’s growth.
9
Note that of the 516 technology firms for which PE ratios were estimated, only 279 have
PEG ratios available; the 237 firms for which analyst estimates of growth were not
available have been dropped from the sample.
Table 8.4 includes the summary statistics for PEG ratios for technology stocks
and non-technology stocks.
Table 8.4: PEG Ratios: Technology versus Non-technology Stocks
All firms
Technology firms
Mean
2.64
2.54
Standard Error
0.17
0.25
Median
1.70
1.66
Skewness
20.11
9.92
Range
234.24
60.43
Minimum
0.00
0.34
Maximum
234.24
60.78
Count
2178
279
Largest(100)
6.15
2.03
Smallest(100)
0.57
1.33
The mean PEG ratio for technology stocks is slightly lower than the mean PEG ratio for
all stocks. In addition, the mean is higher than the median for both groups. In both
groups, there are a significant number of firms with outlandishly high PEG ratios.
10
c. Price to Book Ratio
The market value of the equity in a firm reflects the market’s expectations of the
firm’s earning power and cashflows. The book value of equity is the difference between
the book value of assets and the book value of liabilities, a number that is largely
determined by accounting conventions. The price to book ratio is computed by dividing
the market value of equity by the current book value of equity.
Price to Book Ratio = PBV =
Market Value of Equity
Book value of Equity
To get a sense of what comprises a high, low or average price to book value ratio, we
computed the ratio for every !
firm listed in the United States and Figure 8.4 summarizes
the distribution of price to book ratios in January 2006.
Note that this distribution is heavily skewed, as is evidenced by the fact that the average
price to book value ratio of firms is 5.33 while the median price to book ratio is much
lower at 2.32. As with the earnings multiples, there is a large number of firms with very
high price to book ratios (exceeding 10).
Another point worth making about price to book ratios is that there are firms with
negative book values of equity – the result of continuously losing money – where price to
book ratios cannot be computed. In this sample of 7123 firms, there were 1467 firms
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where this occurred. In contrast, though, almost 3000 firms had negative earnings and PE
ratios could not be computed for them.
d. Price to Sales Ratio
A revenue multiple measures the value of the equity or a business relative to the
revenues that it generates. As with other multiples, other things remaining equal, firms
that trade at low multiples of revenues are viewed as cheap relative to firms that trade at
high multiples of revenues.
Price to Sales Ratio =
Market Value of Equity
Revenues
While this ratio is inconsistently defined, it is still widely used and figure 8.5 summarizes
!
the distribution of price to sales ratios for U.S. companies in January 2006.
One advantage that revenue multiples have over earnings and book value multiples is that
there are far fewer firms where the multiple cannot be computed and thus less bias in the
12
comparison process.6 The only firms that we lose in this computation are those where
there is no clearly specified revenue, as is the case with banks and other financial service
firms.
Another difference between the price to sales ratio and the other equity multiples
is in the nature of the distributions. Unlike the PE and PBV ratio distributions that have
sharply pronounced peaks, the price to sales ratio distribution is more uniformly
distributed. In other words, there are wide variations across sectors and there is no typical
price to sales ratio that applies across firms or sectors.
Analysis of Equity Multiples
There are two key questions that we need to address with every multiple. The first
relates to the variables that determine that multiple and the second to the relationship
between each of the variables and the multiple. In this section, we will consider both
issues.
Determinants of Equity Multiples
In chapter 7, we laid the groundwork for analyzing equity multiples by starting
with a stable growth dividend discount model and then stating multiples in terms of
fundamentals. Table 8.5 reviews our findings:
Table 8.5: Determinants of Equity Multiples: Stable Growth Model
Multiple Analyzed
Stable Growth DDM Model
Value of equity
P0 =
P0
Payout Ratio * (1 + g n )
= PE =
EPS 0
k e - gn
PE Ratio (using current earnings)
PE Ratio (using forward earnings)
DPS1
FCFE1
or P0 =
k e " gn
k e " gn
!
!
!
PEG Ratio
P0
Payout Ratio
= PE =
EPS1
k e - gn
PEG =
!
Payout Ratio
g( k - g )
e
n
!
6
While revenues can never be negative, they can be zero and there are about 100 firms in the sample with
no revenues but with some market value for equity. In addition, the definition of revenues is hazy for
financial service firms.
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P/FCFE
P0
1
=
FCFE1
k e - gn
Market to Book Equity
P0
ROE * Payout Ratio * (1 + g n )
= PBV =
BV0
k -g
!
Price to Sales Ratio
!
e
n
P0
Profit Margin * Payout Ratio * (1+ g n )
= PS =
Sales 0
k -g
e
n
The models can either be stated in terms of actual dividends (payout ratio) or potential
!
dividends (FCFE/ Earnings). All of the equity multiples, other than the PEG ratio,
increase as the payout ratio and the growth rate increase and decrease with the riskiness
of the firm. While these are the only variables that matter for the earnings multiples, the
return on equity and the net profit margin are the additional variables that determine price
to book and price to sales ratios respectively.
The equity multiple for a high growth firm can also be related to fundamentals. In
the special case of the two-stage dividend discount model, this relationship can be made
explicit fairly simply. When a firm is expected to be in high growth for the next n years
and stable growth thereafter, the dividend discount model can be written as follows:
#
(EPS0 )(Payout Ratio )(1 +g)%%1"
$
P0 =
(1+g) n &(
(1+ k e,hg) n ('
k e,hg - g
+
(EPS0 )(Payout Ratio n )(1 +g)n (1 + gn )
(k e,st - gn )(1 + k e,hg)n
where,
EPS0 = Earnings per share in year 0 (Current year)
g = Growth rate in the first n years
ke,hg = Cost of equity in high growth period
ke,st = Cost of equity in stable growth period
Payout = Payout ratio in the first n years
gn = Growth rate after n years forever (Stable growth rate)
Payout Ration = Payout ratio after n years for the stable firm
Divide both sides of the equation by EPS0, we can estimate the PE ratio for a high
growth firm:
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P0
=
EPS0
"
(1+ g)n %
'
Payout Ratio * (1+ g)* $ 1!
n
# (1 + k e,hg ) &
ke, h g - g
Payout Ratio n * (1+ g)n *(1 + gn )
+
n
(ke, st - gn )(1 + k e,hg )
Thus the PE ratio for a high growth firm is determined by the same three variables that
determined PE ratios for a stable growth firm – the payout ratio, the riskiness of the firm
and the expected growth rate in earnings. The only practical difference is that we have to
estimate these inputs twice a high growth firm, once for the high growth period and once
for stable growth. This formula is general enough to be applied to any firm, even one
that is not paying dividends right now. In fact, the ratio of FCFE to earnings can be
substituted for the payout ratio for firms that pay significantly less in dividends than they
can afford to.
Extending the same approach, we can derive the fundamental equations for PEG,
price to book and price to sales ratios:
#
n &
1 + g) (
(
%
(Payout Ratio )(1+ g)%%1"
n(
(
n
$ (1 + k e,hg) ' (Payout Ratio n )(1+ g) (1 + gn )
PEG =
+
n
g(k e,hg - g)
g(k e,st - g n )(1+ k e,hg)
)
,
# (1 + g)n &
+
.
%1"
(
Payout
Ratio
1+
g
(
)
(
)
%
(
n
+
P0
$
'
(Payout Ratio n )(1+ g) (1+ g n )..
= ++(ROE h g)
+ (ROE st )
n
.
BV0
k e,hg - g
(k e,st - g n )(1+ k e,hg)
+
.
+*
.#
&
#
n &
1+ g) (
(
%
(
%
% (Payout Ratio )(1+ g)%%1"
(
n(
(
n
%
Price
$ (1+ k e,hg) ' (Payout Ratio n )(1+ g) (1+ g n ) (
= (Net Margin)%
+
(
n
Sales
k e,hg - g
%
(
(k e,st - g n )(1+ k e,hg)
%
(
%
(
$
'
While the equations look daunting, the conclusions are comforting. The determinants for
all three of these multiples, like the PE ratio, are unchanged from the stable growth
setting.
While all of the equations above are based upon a two-stage dividend discount
model, they can be generalized to the FCFE model by replacing the payout ratio with the
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ratio of FCFE to net income. There are two advantages to this substitution. The first is
that we get more realistic estimates of the multiples for companies that are not paying out
their FCFE as dividends. The second is that that the FCFE/Net income or potential
payout ratio is not constrained to be greater than zero. In other words, if the FCFE is
negative because the firm reinvests more than its net income, the potential payout ratio
can be negative at least for the high growth phase. A negative potential payout ratio
indicates that the firm will have to raise new equity during its high growth phase to fund
its reinvestment, and this expected dilution will push the PE ratio down today.
Illustration 8.1: Estimating equity multiples for a high growth firm in the two-stage
model
Assume that we are estimating equity multiples for a firm that had the following
characteristics:
• The firm reported net income of $15 million on revenues of $150 million last year and
equity invested of $75 million. The resulting net margin and return on equity are
shown below.
Net Margin = 15/150 = 10%
Sales/ Book Value of Equity = 150/75 = 2.00
Return on Equity = Net Margin * Sales/ BV of Equity = 10% *2 = 20%
The firm is expected to maintain these values in perpetuity.
• The firm paid out 10% of its earnings as dividends, resulting in a retention ratio of
90%. Assume also that the firm pays out its FCFE as dividends and that it is expected
to maintain this payout ratio for the next 5 years.
• The expected growth rate in net income over the next five years can be computed from
the retention ratio and the return on equity:
Expected growth rate = Return on equity * Retention ratio = 20%*.90 = 18%
• After the fifth year, we will assume that the expected growth rate in net income will
drop to 4%. Since the return on equity continues to be 20%, the stable period payout
ratio is 80%:
Stable period payout ratio = 1 – g/ ROE = 1- .04/.20 = .80 or 80%
• We will assume that the beta for equity is 1.00 in perpetuity. With a riskfree rate of 5%
and a market risk premium of 4%, the cost of equity is 9%.
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Cost of equity = Riskfree Rate + Beta * Risk Premium =5% + 1*4% = 9%
We can now estimate the price earnings ratio for this firm:
# 1.18 5 &
(
(0.1)(1.18)%%1"
5
5(
1.09
$
' (0.8)(1.18) (1.04)
PE =
+
= 25.38
0.09 " 0.18
(0.09 " 0.04)(1.09) 5
The estimated PE ratio for this firm is 25.38 and the PEG ratio for the firm is 1.41:
!
#
(1.18) 5 &(
%
0.1
1.18
1"
( )( )%
5(
(0.8)(1.18) 5 (1.04)
$ (1.09) '
PEG =
+
= 141 or 1.41
5
0.18(0.09 - 0 .18)
0.18(0.09 - 0.04)(1.09)
The price to book ratio for this firm can be estimated using the return on equity of 20% as
!
an input:
#
1.18 5 &
(
5(
(0.8) 1.18 5 (1.04)
$ 1.09 '
+ 0.20
= 5.08
0.09 " 0.18
(0.09 " 0.04) 1.09 5
(0.1)(1.18)%%1"
PBV = 0.20
(
)
(
)
This stock trades at well above book value, which should come as no surprise since its
!
return on equity is much higher than its cost of equity. The price to sales ratio can be
computed with the net profit margin (of 10%):
#
&
5 &
#
% (0.1)(1.25)%1" (1.25) (
(
5
%
% (1.115) 5 (
(0.50)(1.25) (1.08) ((
$
'
PS = 0.10%
+
= 2.54
5
%
0.115 - 0.25
0.115 - 0.08)(1.115) (
(
%
(
%
(
$
'
Based upon this firm’s fundamentals, you would expect its equity to trade at 2.54 times
!
revenues.
Relationship between Multiples and Fundamentals
In the last section, we laid out equations that make explicit the relationship
between the fundamental variables that drive value – cash flows, growth and risk – and
equity multiples. When analyzing companies, though, we are called upon to make
judgments on how differences on a variable translate into difference in a multiple. For
instance, while we can show fairly easily that, other things remaining equal, companies
with higher growth should trade at higher equity multiples, we need to be explicit about
17
how these multiples will change as growth changes. In this section, we will use the
fundamental equations from the last section to try to address this question.
The Growth Effect
Equity values are sensitive to expectations about the growth rate during the high
growth period. Thus, in the illustration above, the expected growth rate of 18% during the
high growth period of five years played a significant role in determining all of the equity
multiples. But what if the expected growth rate is different from our expectations?
Clearly, equity values will increase if the expected growth rate turns out to be higher than
18% and decrease if it turns out to be lower. In table 8.6, we summarize the effects of
changing the expected growth rate during the high growth period on equity multiples,
while holding all other inputs (payout ratio, return on equity, cost of equity, length of the
high growth period and stable growth inputs) fixed.
Table 8.6: Equity Multiples and Expected Growth Rate
Growth Rate during high growth period
0%
PE
11.20
PEG
∞
PBV
2.24
PS
1.12
2%
12.35
6.18
2.47
1.24
4%
13.59
3.40
2.72
1.36
6%
14.93
2.49
2.99
1.49
8%
16.38
2.05
3.28
1.64
10%
12%
14%
16%
18%
20%
22%
24%
26%
28%
30%
32%
34%
36%
38%
40%
17.93
19.60
21.40
23.32
25.38
27.58
29.94
32.45
35.13
37.99
41.03
44.26
47.69
51.34
55.20
59.29
1.79
1.63
1.53
1.46
1.41
1.38
1.36
1.35
1.35
1.36
1.37
1.38
1.40
1.43
1.45
1.48
3.59
3.92
4.28
4.66
5.08
5.52
5.99
6.49
7.03
7.60
8.21
8.85
9.54
10.27
11.04
11.86
1.79
1.96
2.14
2.33
2.54
2.76
2.99
3.25
3.51
3.80
4.10
4.43
4.77
5.13
5.52
5.93
18
All of the equity multiples, other than the PEG ratio, of a high growth firm increase with
the expected extraordinary growth rate - the higher the expected growth, the higher the
values for the multiples. In Illustration 8.1, for instance, the PE ratio that was estimated to
be 25.38, with a growth rate of 18%, drops to 16.38, if the expected growth rate during
the high growth period is only 8%. Similar trends are visible with price to book and price
to sales ratios.
With PEG ratios, however, the ratio initially decreases as the expected growth
increases but after bottoming out at about 1.35 when the expected growth rate is 24-26%,
it begins rising again. There are two immediate and important implications. The first is
that, contrary to the claims of its adherents, the PEG ratio does not fully control for
differences in growth across companies. As a general rule, lower growth companies will
look over valued on a PEG ratio basis and this is a direct result of the assumption of
linearity made in the PEG ratio; after all, if linearity held, the PEG ratio for a firm with an
expected growth rate of 0 should also be zero. The second is that, unlike other multiples
where the direction of the relationship between growth and the value of the multiple is
predictable, the effect of growth on PEG ratios can vary depending upon the expected
growth rates being compared. Put another way, when comparing two companies, one
with an expected growth rate of 4% and the other with an expected growth rate of 15%,
we know that the PEG ratio will bias us against the lower growth firm and towards the
higher growth firm. However, when comparing two companies with expected growth
rates of 30% and 40%, the PEG ratio may bias us against the higher growth firm and
towards the lower growth firm.
The effect of changes in the expected growth rate on equity multiples can also
vary depending upon the level of interest rates. The intuition for this is straightforward.
The value of growth lies in the future and as interest rates rise, the value of expected
growth decreases. Consequently, surprises about expected growth have a bigger impact
when interest rates are low than when they are high. This is illustrated in figure 8.6,
where we look at the impact of changing the expected growth rate on the PE ratio under
four different riskless rates – 4%, 6%, 8% and 10%.
19
The PE ratio is much more sensitive to changes in expected growth rates when interest
rates are low than when they are high. There is a possible link between this finding and
how markets react when firms announce earnings. When a firm reports earnings that are
significantly higher than expected (a positive surprise) or lower than expected (a negative
surprise), investors’ perceptions of the expected growth rate for this firm can change
concurrently, leading to a price effect. We would expect to see much greater price
reactions for a given earnings surprise, positive or negative, in a low-interest rate
environment than you would in a high-interest rate environment.
There is one other dimension on which we can examine the effect of high growth
and that is through the length of the growth period (while holding the expected growth
rate fixed). In other words, what if the firm, instead of maintaining an 18% growth rate
for the next 5 years was able to do so for only 3 years? What if it could keep high growth
going for 8 years? Table 8.7 summarizes the impact of lengthening the growth period of
each of the equity multiples:
Table 8.7: Length of Growth Period and Equity Multiples
Growth Years
0
PE
16.64
PEG
0.92
PBV
3.33
PS
1.66
20
1
18.12 1.01 3.62 1.81
2
19.73 1.10 3.95 1.97
3
21.46 1.19 4.29 2.15
4
23.34 1.30 4.67 2.33
5
25.38 1.41 5.08 2.54
6
27.58 1.53 5.52 2.76
7
29.97 1.66 5.99 3.00
8
32.55 1.81 6.51 3.26
9
35.35 1.96 7.07 3.53
10
38.38 2.13 7.68 3.84
The effects are predictable. If the firm is able to sustain high growth for longer, all of the
equity multiples will register higher values. In chapter 4, we argued that the key
determinant of the length of the growth period was the competitive position of the firm;
the larger and more sustainable its competitive advantages, the longer the growth period,
we argued. This table suggests that, other things remaining equal, firms in stronger
competitive positions will trade at higher multiples, for any given expected growth rate,
than firms with weaker competitive positions.
The Risk Effect
Risk enters the equation through the cost of equity. While we use beta as our
measure of equity risk, the logic of higher risk increasing the cost of equity will apply no
matter what risk and return model we choose to use. Holding other variables constant,
increasing the risk of equity will decrease all equity multiples. In table 8.8, we examine
the effect of changing the beta (and through it the cost of equity) on all of the equity
multiples:
Table 8.8: Risk and Equity Multiples
Beta
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
Cost of
Equity
7.00%
8.00%
9.00%
10.00%
11.00%
12.00%
13.00%
14.00%
15.00%
PE
45.91
33.04
25.38
20.32
16.74
14.09
12.05
10.44
9.14
PEG
2.55
1.84
1.41
1.13
0.93
0.78
0.67
0.58
0.51
PBV
9.18
6.61
5.08
4.06
3.35
2.82
2.41
2.09
1.83
PS
4.59
3.30
2.54
2.03
1.67
1.41
1.20
1.04
0.91
21
As risk increases, equity multiples decrease across the board. A firm with a cost of equity
of 15% will trade at 9.14 times earnings, even though its expected earnings growth rate is
18%. The same can be said about PEG, price to book and price to sales ratios.
From a practical standpoint, this should add a note of caution to those analyses
where the PE ratios of PEG ratios of firms in a sector are compared to each other with the
intent of finding under and over valued stocks. Without controlling for differences in risk,
this type of analysis will be biased towards finding riskier companies to be cheap
(because they will trade at lower multiples) and safer companies to be expensive. From
the firm’s viewpoint, this relationship also suggests that at very high risk levels, a firm’s
equity multiples are likely to increase more as the risk decreases than as growth
increases. For many young firms that are viewed as both very risky and having good
growth potential, reducing risk may increase equity value much more than increasing
expected growth.
The Quality of Investments Effect
The focus on expected earnings growth among investors and analysts can
sometimes blind us to an obvious fact. Not all growth is created equal and companies that
generate growth more efficiently (with less investment) should trade at higher equity
values than firms that generate the same growth less efficiently. The simplest way to see
this is to go back to the fundamental determinants of expected earnings growth:
Earnings growth rate = Retention ratio * Return on equity
In our base case, we used a return on equity of 20% and a retention ratio of 90% to arrive
at an expected growth rate of 18%. But there are other combinations of return on equity
and retention ratios that would have generated the same growth rate. For instance, a firm
with a 30% return on equity would have been able to grow its earnings at 18% while
retaining only 60% of its earnings. Conversely, a firm with a return on equity of 15%
would have required a retention ratio of 120% to generate a growth rate of 18%; in effect,
the firm would have to issue new equity each year.7 In table 8.9, we summarize the
7
There is also a secondary effect. The retention ratio in stable growth also changes to allow the firm to
continue growing at 4% forever. As the return on equity drops, the terminal value of equity will also
decrease as a consequence.
22
impact of changing the return on equity, while keeping the expected growth rate at 18%,
on equity multiples:
Table 8.9: Return on Equity and Equity Multiples
Implied
Return on
Retention
Ratio
Equity
8%
225%
10%
180%
12%
150%
14%
129%
16%
113%
18%
100%
20%
90%
22%
82%
24%
75%
26%
69%
28%
64%
30%
60%
As the return on equity increases,
PE
PEG
7.48
0.42
13.45
0.75
17.43
0.97
20.27
1.13
22.40
1.24
24.05
1.34
25.38
1.41
26.46
1.47
27.37
1.52
28.13
1.56
28.79
1.60
29.36
1.63
the equity multiples all go up.
PBV
PS
0.60
0.75
1.34
1.34
2.09
1.74
2.84
2.03
3.58
2.24
4.33
2.41
5.08
2.54
5.82
2.65
6.57
2.74
7.31
2.81
8.06
2.88
8.81
2.94
At very low returns on
equity, the firm will have to issue substantial new equity to sustain its high earnings
growth, and the equity value per share decreases to reflect the potential dilution. If returns
on equity dip below the cost of equity, growth can start destroying equity value. In this
particular illustration, when the return on equity drops below the cost of equity of 10%,
increasing the growth rate will reduce equity values. In our discussion of companion
variables in chapter 7, we argued that the multiple that is most closely connected with
return on equity is the price to book equity ratio. If we define the difference between the
return on equity and the cost of equity as the measure of excess returns to equity
investors, there is clearly a link between the excess returns earned and whether a firm
trades at below or above book equity. In figure 8.7, we present the effects of changing
excess equity returns on the price to book equity ratio:
23
When the excess returns are negative, the stock trades at below book equity. In fact, when
the return on equity is expected to be equal to the cost of equity in perpetuity, the stock
trades at book value. Ignoring return on equity differences when comparing price to book
equity ratios across companies would be folly and lead us to conclude that low return on
equity stocks are cheap (since they trade at low multiples of book equity).
Another, albeit less direct, measure of earnings quality is the net profit margin
that a company generates. Again, using the linkage between net margins and returns on
equity stated in the earlier section, we can state the expected growth rate as a function of
the net margin:
Expected Growth rate = Net Margin * Sales/BV of Equity * Retention Ratio
In illustration 8.1, we assumed that the firm maintained a net margin of 10% and had a
sales to book equity ratio of 2.00, thus allowing us to have a return on equity of 20%. In
table 8.10, we examine the impact of changing the net margin, while keeping the
expected growth rate and sales to book equity ratio fixed. In other words, if the margin
drops to 5%, we will assume that the retention ratio will have to change to allow the firm
to grow at 18% for the high growth period:
24
Table 8.10: Net Margin and Equity Multiples
Net Margin
4%
6%
8%
10%
12%
14%
16%
18%
20%
PE
7.48
17.43
22.40
25.38
27.37
28.79
29.85
30.68
31.35
PEG
0.42
0.97
1.24
1.41
1.52
1.60
1.66
1.70
1.74
PBV
0.60
2.09
3.58
5.08
6.57
8.06
9.55
11.05
12.54
PS
0.30
1.05
1.79
2.54
3.28
4.03
4.78
5.52
6.27
As the net margin increases, all of the equity values increase. Since net margin is the
companion variable for price to sales ratios, we examine the impact of changing the
margin on price to sales ratios in figure 8.8:
When comparing companies on a price to sales ratio basis, we have to bring in the effect
of net margins. Companies that have low net margins, either because they have no pricing
power or because they adopt high volume/low price strategies (discount retailers, for
25
example) should trade at lower multiples of revenues than firms that maintain higher
margins.
A Bias Summary
With each of the variables we have discussed in this section, we have listed some
of the potential problems that can be created when they are ignored while doing analyses.
At the risk of repeating much of what we have said, we can summarize the biases that can
be created by ignoring any or all of the variables in table 8.11:
Table 8.11: Comparison Biases created by Omitting Variables
Variable ignored
Companies that will look
cheap
Expected
growth
rate Low growth companies
during high growth period
(with PE, PBV and PS)
High growth companies
(with PEG ratios)
Length of Growth Period
Companies with minimal or
short-lived
competitive
advantages
Risk of equity
Companies with high equity
risk, either because they are
in riskier businesses or
because they have high debt
ratios.
Return on equity
Companies that earn low
returns on equity, relative to
their costs of equity.
Net Profit Margin
Companies
that
adopt
volume leader strategies
(high volume, low price)
Companies that will look
expensive
High growth companies
(with PE, PBV and PS)
Low growth companies
(with PEG ratios)
Companies with strong and
sustainable
competitive
advantages
Companies with low equity
risk, either because they are
in more stable businesses or
because they are less
financially levered.
Companies that earn high
excess equity returns
Companies that adopt price
leader
strategies
(low
volume, high price)
The key question then becomes how best to control for differences in these variables
when doing relative valuation. That is the question we will examine in the next section.
Applications of Equity Multiples
Now that we have looked at the determinants of equity multiples and how the
multiples change as the fundamental variables change, we can turn our attention to the
proverbial bottom line. In this section, we will begin by looking at the conventional use
of multiples in sectors to make valuation judgments and then extend our discussion to
26
entire markets. We will also consider how to compare multiples across time and across
markets.
Comparing Equity Multiples across firms in a sector
The most common approach using equity multiples is to choose a group of firms
in the same sector as the firm that we are trying to value, to calculate the average value
for the multiple for this group and to subjectively adjust this average for differences
between the firm being valued and the comparable firms. While doing this, analysts
implicitly assume that firms in the same sector are equally risky and that controlling for
risk is therefore not necessary. Even if we accept this heroic assumption as reasonable,
relative valuations range the spectrum. Some relative valuations do not control for any of
the other variables that we argued affect the multiples that firms trade at while others do
control at least partially for some of the differences.
Reviewing the determinants of equity multiples from earlier in the chapter, we
outline all of the variables that affect each multiple in table 8.12:
Table 8.12: Equity Multiples and Fundamentals
Multiple Used
Fundamental Determinants
PE
Payout ratio, Expected Growth, Equity Risk
PEG
Payout ratio, Expected Growth, Equity Risk
P/FCFE
Risk, Expected Growth
P/BV of Equity
Payout ratio, Expected Growth, Equity Risk, Return on Equity
P/Sales
Payout ratio, Expected Growth, Equity Risk, Net Margin
Note that the companion variable for each multiple is italicized in the table. At the
minimum, we would expect analysts to control for at least this variable. However, the
other variables continue to affect multiples and assumptions, both explicit and implicit,
about these variables can determine what looks cheap or expensive.
The best way to see the biases created by not controlling for all of the variables
that affect multiples is by looking at relative valuations done across sectors. In the three
illustrations that follow, we will examine the use of equity multiples and different ways
of controlling for the fundamentals.
27
Illustration 8.2: Comparing PE across software companies
The following table summarizes the trailing PE ratios for software firms listed in
the United States in January 2006. The earnings per share used are estimated over the
most recent four quarters for each firm and the stock price is as of December 29, 2005.
Table 8.13: PE Ratios and Expected Growth Rates
Company Name
Accenture Ltd.
Adobe Systems
Affiliated Computer
ANSYS Inc.
Automatic Data Proc.
BearingPoint
BMC Software
Borland Software
CACI Int'l 'A'
Ceridian Corp.
Citrix Sys.
Cognizant Technology
Computer Sciences
Compuware Corp.
DST Systems
Electronic Data Sys.
Fair Isaac
First Data Corp.
Fiserv Inc.
Henry (Jack) & Assoc.
Infosys Techn. ADR
Intergraph Corp.
Intuit Inc.
Keane Inc.
Manhattan Assoc.
ManTech Int'l 'A'
McAfee Inc.
Mercury Interactive
Microsoft Corp.
Moldflow Corp.
Novell Inc.
Oracle Corp.
Paychex Inc.
Red Hat Inc.
PE
19.34
38.03
16.82
39.53
25.62
37.13
53.85
12.77
21.62
65.97
29.16
67.96
18.49
45.94
20.83
77.84
26.58
17.83
20.21
23.11
50.50
37.66
25.72
19.46
27.42
39.24
47.06
25.06
22.68
23.18
53.51
18.63
43.39
100.44
Expected Growth Rate
13.00%
19.50%
5.50%
16.00%
10.00%
21.50%
25.00%
8.00%
17.00%
17.00%
15.50%
29.00%
10.00%
21.50%
12.50%
26.50%
13.00%
7.00%
16.00%
16.50%
27.00%
29.00%
11.50%
19.00%
11.50%
17.50%
22.00%
18.50%
13.50%
27.00%
18.00%
19.50%
15.00%
34.50%
28
RSA Security
SEI Investments
Siebel Systems
Sybase Inc.
Symantec Corp.
Synopsys Inc.
Transaction Sys. 'A'
Verint Systems
23.74
22.61
47.64
30.27
33.57
18.44
30.50
61.51
31.00%
10.50%
14.00%
11.00%
15.00%
7.00%
17.50%
26.00%
Borland Software has the lowest PE ratio of 12.77 while Red Hat has the highest PE ratio
of 100.44. Even if we assume that these firms are of equivalent risk, the differences in PE
ratios can be explained by differences in growth potential. To capture this, the analyst
estimates of expected growth in earnings per share over the next 5 years for each
company are shown in the last column.
Regressing the PE ratio of each firm against the expected growth rate a yields the
following results (with t statistics in brackets below each coefficient).
PE Ratio = 4.24
R2 =42%
+ 177.12 Expected Growth
(0.71)
(5.59)
Firms with higher growth have significantly higher PE ratios than firms with lower
expected growth. In fact, every 1% difference in expected growth rates increases the PE
ratio by 1.77. Using this regression, we estimate the predicted PE ratio for Adobe
Systems, which has an expected growth rate of 19.50%:
Expected PE ratio for Adobe Systems = 4.24 + 177.12 (0.195) = 38.78
At its actual PE ratio of 38.03, Adobe is very slightly under valued (by approximately
1.93%):
Adobe under (over) valuation = (38.03/38.78) -1 = -1.93%
In table 8.14, we estimate the predicted PE ratios and the percent under or over valuation
for each of the companies in the sample.
Table 8.14: Predicted PE ratios for software companies
Company Name
Accenture Ltd.
Adobe Systems
Affiliated Computer
ANSYS Inc.
Automatic Data Proc.
BearingPoint
PE
19.34
38.03
16.82
39.53
25.62
37.13
Predicted PE
27.27
38.78
13.98
32.58
21.95
42.32
Under or Over Value
-29.07%
-1.93%
20.27%
21.32%
16.69%
-12.26%
29
BMC Software
Borland Software
CACI Int'l 'A'
Ceridian Corp.
Citrix Sys.
Cognizant Technology
Computer Sciences
Compuware Corp.
DST Systems
Electronic Data Sys.
Fair Isaac
First Data Corp.
Fiserv Inc.
Henry (Jack) & Assoc.
Infosys Techn. ADR
Intergraph Corp.
Intuit Inc.
Keane Inc.
Manhattan Assoc.
ManTech Int'l 'A'
McAfee Inc.
Mercury Interactive
Microsoft Corp.
Moldflow Corp.
Novell Inc.
Oracle Corp.
Paychex Inc.
Red Hat Inc.
RSA Security
SEI Investments
Siebel Systems
Sybase Inc.
Symantec Corp.
Synopsys Inc.
Transaction Sys. 'A'
Verint Systems
53.85
12.77
21.62
65.97
29.16
67.96
18.49
45.94
20.83
77.84
26.58
17.83
20.21
23.11
50.50
37.66
25.72
19.46
27.42
39.24
47.06
25.06
22.68
23.18
53.51
18.63
43.39
100.44
23.74
22.61
47.64
30.27
33.57
18.44
30.50
61.51
48.52
18.41
34.35
34.35
31.70
55.61
21.95
42.32
26.38
51.18
27.27
16.64
32.58
33.47
52.06
55.61
24.61
37.89
24.61
35.24
43.21
37.01
28.15
52.06
36.12
38.78
30.81
65.35
59.15
22.84
29.04
23.73
30.81
16.64
35.24
50.29
10.98%
-30.66%
-37.07%
92.05%
-7.99%
22.22%
-15.76%
8.54%
-21.03%
52.09%
-2.53%
7.16%
-37.97%
-30.94%
-3.00%
-32.27%
4.50%
-48.64%
11.42%
11.35%
8.92%
-32.29%
-19.44%
-55.48%
48.14%
-51.97%
40.82%
53.70%
-59.86%
-1.00%
64.07%
27.59%
8.94%
10.81%
-13.44%
22.30%
RSA Security is the most undervalued company in the sample (with a 59.86% under
valuation) and Ceridian is the most overvalued company in the group (with a 92.05%
over valuation).
30
Illustration 8.3: Comparing PEG ratios across semiconductor companies
Many analysts use the PEG ratio to compare the pricing of firms with different
expectations of growth. Table 8.15 summarizes the PE ratios, expected growth rates (as
predicted by analysts for the next 5 years) and the resulting PEG ratios of semiconductor
firms in January 2006.
Table 8.15: PEG Ratios for Semiconductor Firms
Company Name
Taiwan Semic. ADR
Mattson Technology Inc.
National Semic.
Int'l Rectifier
Bell Microproducts
MIPS Technologies Inc
Motorola Inc.
Altera Corp.
Maxim Integrated
Intel Corp.
Analog Devices
Cree Inc.
STMicroelectronics
Texas Instruments
Linear Technology
Semtech Corp.
QLogic Corp.
Microchip Technology
Fairchild Semic.
Xilinx Inc.
Catalyst Semiconductor Inc
Rudolph Technologies Inc
NVIDIA Corp.
Rambus Inc.
Supertex Inc.
Intersil Corp. 'A'
PE
16.12
13.68
25.11
27.34
21.13
17.44
29.35
27.99
23.29
21.36
24.97
34.63
27.55
29.31
26.86
23.90
16.86
30.76
36.79
30.05
21.68
33.72
63.08
49.73
87.71
41.98
Expected Growth Rate
50.00%
40.00%
65.00%
28.50%
20.00%
16.00%
26.50%
24.50%
19.50%
17.50%
19.00%
26.00%
20.00%
20.50%
18.00%
16.00%
9.50%
16.00%
19.00%
14.50%
10.00%
15.00%
26.00%
14.50%
25.00%
10.50%
PEG Ratio
0.32
0.34
0.39
0.96
1.06
1.09
1.11
1.14
1.19
1.22
1.31
1.33
1.38
1.43
1.49
1.49
1.77
1.92
1.94
2.07
2.17
2.25
2.43
3.43
3.51
4.00
Taiwan Semiconductor’s ADR, with a PEG ratio of 0.32, looks like the cheapest stock in
the group and Intersil with a PEG ratio of 4.00 comes out as the most over valued stock.
There does, however, seem to be a pattern with the higher growth companies bunched
together at the top of the table with low PEG ratios. The relationship between PEG ratios
31
and expected growth rates does not appear to be linear, as is clear when we look at the
scatter plot in figure 8.9:
Figure 8.9: PEG Ratios versus Expected Growth – Semiconductor Firms
5
PEG Ratio
4
3
2
1
0
0
10
20
30
40
50
60
70
Expected Growth Rate
To allow for the non-linear relationship, we regress the PEG ratio against the natural log
of the expected growth rate:8
PEG = -0.32 - 1.23 ln(Expected Growth Rate)
R2 = 33.52%
(0.58) (3.69)
Consider Intel. Intel with a PEG ratio of 1.22 is trading at a higher PEG ratio than the
average of 1.64 for the sector, suggesting, at least on a preliminary basis, an undervalued
stock. Plugging in the expected growth rate of 17.50%, the predicted PEG ratio based
upon this regression is:
Predicted PEG ratio = -0.32 - 1.23 ln(.175 ) = 1.82
Intel, given its expected growth rate, is undervalued by almost 33% on a PEG ratio basis,
at least based upon this regression.
8
Using the natural log of the expected growth rate narrows the differences across companies on the growth
dimension and makes the relationship between PEG and growth more linear.
32
As a final note, there is one other reason why Taiwan Semiconductor looks cheap
on a PEG ratio basis. It is one of the few emerging market companies in this sector and
the additional risk associated with its status may be depressing its PE ratio.
Illustration 8.4: Comparing PBV ratios across banks
If the essence of misvaluation is finding firms that have price to book ratios that
do not go with their equity return spreads, the mismatch can be brought home by plotting
the price to book value ratios of firms against their returns on equity. In figure 8.10, we
report on the price to book ratios for banks in the United States in January 2006 against
the returns on equity each reported over the most recent financial year.
Figure 8.10: Price to Book versus ROE: U.S. Banks in January 2006
4 .0
Cull en/F rost Banker s
Me llon Fina ncia l Cor
Synovus Fina ncial
Bank of Haw aii
State Stree t Corp.
Compa ss Bancshare s
3 .5
PBV
3 .0
We lls Fa rgo
Ba nk of New York
PNC Fina ncial Ser v.
2 .5
M&T Bank Corp .
2 .0
Ba nk of Ame rica
Wa chovia Corp.
SunTrust Banks
Nor th For k Bancorp
1 .5
JPMorga n Chase
1 .0
R sq = 0.6532
0
10
20
30
ROE
The firms that fall in the upper left hand quadrant (with high price to book ratios and low
returns on equity) are over valued, whereas those that fall in the lower right hand
quadrant (with low returns on equity and high price to book ratios) are under valued.
Note that 65.32% of the differences in price to book ratios across U.S. banks is explained
by differences in returns on equity. The regression line and the 95% confidence intervals
(represented by the outside lines) indicate that there are no banks that are under or over
valued enough to be outside this range. Put another way, once we adjust for differences
33
in returns on equity, all of the banks in this sample look fairly valued on a price to book
basis.
Regressing the price to book against return on equity for U.S. banks, we obtain
the following:
PBV = 0.434 +
14.12 ROE
(1.37)
R2 = 63.9%
(6.86)
This regression can be used to estimate predicted price to book ratios for the banks in the
sample in Table 8.17.
Table 8.17: Predicted Price to Book Ratios – U.S. Banks
Company Name
JPMorgan Chase
Regions Financial
North Fork Bancorp
SunTrust Banks
Wachovia Corp.
Popular Inc.
Bank of America
KeyCorp
TD Banknorth Inc.
BB&T Corp.
M&T Bank Corp.
Zions Bancorp.
PNC Financial Serv.
Mercantile Bankshares
AmSouth Bancorp.
Bank of New York
City National Corp.
Wells Fargo
Compass Bancshares
Wilmington Trust
State Street Corp.
Bank of Hawaii
Synovus Financial
Mellon Financial Corp.
Hudson United Bancorp
Cullen/Frost Bankers
Commerce Bancorp NJ
PBV
Predicted PBV
Under/Over value
1.31
1.53
-14.34%
1.46
1.58
-7.12%
1.51
1.31
14.69%
1.68
1.82
-7.61%
1.76
1.99
-11.42%
1.87
2.66
-29.88%
1.88
2.44
-22.72%
1.92
2.33
-17.61%
2.08
2.40
-13.33%
2.18
2.46
-11.46%
2.18
2.21
-1.65%
2.41
2.49
-3.24%
2.49
2.70
-7.51%
2.51
2.12
18.17%
2.65
3.11
-14.68%
2.69
2.62
2.59%
2.74
2.59
5.78%
2.84
3.05
-6.89%
3.02
2.99
1.01%
3.05
2.65
15.16%
3.14
2.36
33.41%
3.25
3.44
-5.36%
3.36
2.77
21.31%
3.49
3.19
9.59%
3.57
3.87
-7.85%
3.57
2.86
24.73%
3.66
2.75
33.18%
34
The most under valued firm in the group is Popular Inc., trading almost 30% below its
predicted value. State Street is the most over valued bank in the group, trading 33.41%
above its predicted value.
Illustration 8.5: Comparing price to sales ratios across specialty retailers
Price to sales ratios are used widely to analyze retail firms. In figure 8.11, the
price to sales ratios of specialty retail firms in the U.S. are plotted against the net profit
margins of these firms.
Figure 8.11: Price to Sales Ratios and Net Profit Margins
8
Coach Inc.
Chico's FAS
6
PS
We ight Watcher s
Urba n Outfi tters
NuCo2 Inc
4
Coldwa ter Cree k
b ebe store s inc
Cla ire 's Stores
2
Ame r. Eagle O utfi tte
Chil dren's Pl ace
RadioS hack Corp.
Cir cuit City Stor es
0
R sq = 0.6810
0
10
20
30
Net Margin
Firms with higher net margins tend to have higher price to sales ratios, while firms with
lower margins have lower price to sales ratios. As with PE, PEG and price to book ratios,
a regression of price to sales ratios against net profit margins for specialty retailers backs
up this conclusion.
Price to Sales Ratio = -0.107 + 25.45 Net Profit Margin
(0.67)
R2= 67.6%
(11.50)
This regression has 63 observations and the t-statistics are reported in brackets. The
predicted price to sales ratio for Coach, one of the specialty retailers in the group, which
has an net profit margin of 21.41%, can be estimated.
35
Predicted Value to Sales Ratio = -0.107
+ 25.452 (0.2141) = 5.34
With an actual value to sales ratio of 7.19, Talbot’s can be considered to be over valued,
relative to other firms in the specialty retail sector.
Comparing Equity Multiples across firms in the market
In the last section, comparable firms were narrowly defined to be other firms in
the same business. In this section, we consider ways in which we can expand the number
of comparable firms by looking at an entire sector or even the market. There are two
advantages to this more expansive analysis. The first is that the estimates may become
more precise as the number of comparable firms increase. The second is that it allows us
to pinpoint when firms in a small sub-group are being under or over valued relative to the
rest of the sector or the market. Since the differences across firms will increase when we
loosen the definition of comparable firms, we have to adjust for these differences. The
simplest way of doing this is with a multiple regression, with the equity multiples as the
dependent variable and proxies for risk, growth and payout forming the independent
variables. In this section, we present the results of market regressions for each of the
equity multiples.
a. PE Ratio
In the regression, run in January 2006, the PE ratios were regressed against
payout ratios (in most recent financial year), betas (from Value Line) and expected
growth (analyst consensus estimates for the next 5 years) for all firms in the market.
PE = 6.75
(4.83)
+ 113.10 (Expected Growth rate) -0.919 (Beta) + 7.33 (Payout ratio)
(29.66)
(0.76)
(5.64)
R squared = 30.6%
With the sample size expanding to 2163 firms, this regression represents a broader
measure of relative value. Other things remaining equal, this regression suggests that:
•
The PE ratio increases 1.131 for every 1% increase in the expected growth rate in
earnings per share over the next 5 years.
•
An increase in the beta of 1 reduces the PE ratio by roughly 0.92
•
An increase in the payout ratio of 1% increases the PE ratio by 0.07
For instance, a firm with an expected growth rate of 12%, a beta of 1.2 and a payout ratio
of 20% will have a predicted PE ratio:
36
Predicted PE = 6.75 + 113.1 (0.12) – 0.919 (1.20) + 0.073 (0.20) = 20.68
This regression has a low R-squared, but it is more a reflection of the noise in PE
ratios than it is on the regression methodology. As we will see, the market regressions for
price to book value and price to sales ratios tend to be better behaved and have higher Rsquared than PE ratio regressions. While the coefficients in this regression all have the
predicted signs – PE ratios increase with growth and payout and decrease as risk
increases – this is not always the case. In fact, similar regressions run in 2003 and 2004
had the wrong sign for the beta coefficient, with higher beta companies have higher PE
ratios instead of lower ones. This occurs largely because the independent variables in this
regression are themselves correlated with each other, with high growth companies
tending to be risky with low payout ratios.9
b. PEG Ratio
When comparing PEG ratios across firms, then, it is important that we control for
differences in risk, growth and payout ratios when making the comparison. While we can
attempt to do this subjectively, the complicated relationship between PEG ratios and
these fundamentals can pose a challenge. A far more promising route is the regression
approach used for PE ratios and to relate the PEG ratios of the firms being compared to
measures of risk, growth potential and the payout ratio for these firms.
As with the PE ratio, the comparable firms in this analysis can be defined
narrowly (as other firms in the same business), more expansively as firms in the same
sector or as all firms in the market. In running these regressions, all the caveats that were
presented for the PE regression continue to apply. The independent variables continue to
be correlated with each other and the relationship is both unstable and likely to be nonlinear. In fact, Figure 8.12, which provides a scatter plot of PEG ratios against growth
rates, for all U.S. stocks in January 2006, indicates the degree of non-linearity.
9
This creates a phenomenon known as multicollinearity in the regression. To illustrate the problems this
will create, assume (as is reasonable) that high growth companies also have high betas and low payout
ratios. The beta then becomes a proxy not only for risk but also for growth, and the coefficient in the
regression will reflect the dominant factor. In 2003 and 2004, betas were better proxies for growth than
risk, which explains the positive coefficient on betas in the regressions from those years.
37
Figure 8.12: PEG Ratios versus Expected Growth Rates
20
10
PEG Ratio
0
-10
-20
0
20
40
60
80
1 00
Expected Growth in E PS: next 5 y ears
In running the regression, especially when the sample contains firms with very different
levels of growth, we should transform the growth rate to make the relationship more
linear. A scatter plot of PEG ratios against the natural log of the expected growth rate in
figure 8.13, for instance, yields a much more linear relationship.
38
Figure 8.13: PEG Ratios versus ln(Expected Growth Rate)
20
10
PEG Ratio
0
-10
-1
0
1
2
3
4
5
LNGR OWTH
The results of the regression of PEG ratios against ln(expected growth), beta and payout
ratio is reported below for the entire market.
PEG Ratio = 4.27
– 0.83 ln(Growth) -0.417 (Beta) + 0.769 (Payout)
(1.76)
R squared = 21.5%
(25.35)
(4.49)
(12.46)
Number of firms = 2159
(Growth is entered as an absolute value in this regression)
As with the PE ratio regression, this regression can be used to estimate predicted PEG
ratios for individual companies though the R-squared is even lower than it was for PE
ratios. Across the market, higher growth and higher risk companies tend to have lower
PEG ratios than the more stable, lower growth companies.
c. Price to Book Ratios
In the earlier section, we noted that price to book ratios are heavily influenced by
returns on equity. In January 2006, we regressed the price to book ratio against the
fundamentals identified in the last section – the return on equity (from the most recent
39
financial year), the payout ratio, the beta and the expected growth rate over the next 5
years (from analyst forecasts).
PBV = -0.49 + 17.60 ROE
(2.69) (47.51)
+0.16 Payout ratio
(3.06)
-0.534 Beta
(3.72)
+ 11.90 Growth rate
(26.91)
The regression has an R-squared of 55.6%, a significant improvement on the PE and PEG
ratio regressions. The return on equity is clearly the variable that has the strongest
relationship with the price to book ratio, as evidenced by the high t statistic on the
coefficient. Every 1% improvement in return increases the price to book ratio by 0.176.
The strong positive relationship between price to book ratios and returns on equity
is not unique to the United States. In fact, table 8.18 summarizes regression for other
countries of price to book against returns on equity run at different points in time:
Table 8.18: Price to Book and Returns on Equity: Market Regressions
Country
Regression Details
Regression Equation
Greece
May 2001
PBV = 2.11 + 11.63 ROE
Entire
(R2=17.5%)
market:
272firms
Brazil
October 2000
PBV = 0.77 + 3.78 (ROE)
(R2=17.3%)
(Entire market:
Portugal
June 1999
PBV = -1.94 + 16.34 ROE + 2.83 Beta
(R2=78%)
(Entire market – 74
firms)
India
November 1997
PBV = -1.68 + 24.03 ROE
(R2=51%)
(50 largest firms)
In each of the markets, firms with higher returns on equity have higher price to book
ratios, though the strength of the relationship is greater in Portugal and India and lesser in
Greece and Brazil.
d. Price to Sales Ratios
To examine differences in price to sales ratios across companies in the market, we
used the variables that we identified in the last section as its determinants – the expected
growth in earnings per share, the payout ratio, the beta and the net margin (again from the
most recent financial year):
40
PS = -1.648
+ 23.6 Net Margin +0.12 Payout ratio+0.361 Beta +8.80 Growth rate
(10.55) (46.89)
(3.49)
(3.72)
(19.63)
The R-squared on the regression is 58.4% and the sample size is 1877 firms with data
available on all of the independent variables. There are two troublesome components to
this regression. The first is that the coefficient on beta has the wrong sign – riskier firms
have higher price to sales ratios in this regression whereas our prediction would be that
they should have lower. We explained the reasons for this when we talked about price
earnings ratios. The second is that the intercept is a large negative number, which by
itself is not uncommon, but can result in negative predicted price to sales ratios at least
for some firms.
To alleviate the second problem, the regression was rerun without an intercept,
with the following results:
PS = 21.8 Net Margin
(44.76)
+0.06 Payout ratio
(3.49)
- 0.832 Beta +8.39 Growth rate
(8.78)
(18.26)
Not only is this regression less likely to yield negative predicted values, but the
coefficient on beta now has the right sign: higher beta companies have lower price to
sales ratios.
Comparing Equity Multiples across time
Analysts and market strategists often compare the PE ratio of a market to its
historical average to make judgments about whether the market is under or over valued.
Thus, a market which is trading at a PE ratio which is much higher than its historical
norm is often considered to be over valued, whereas one that is trading at a ratio lower is
considered under valued.
While reversion to historic norms remains a very strong force in financial
markets, we should be cautious about drawing too strong a conclusion from such
comparisons. As the fundamentals (interest rates, risk premiums, expected growth and
payout) change over time, the PE ratio will also change. Other things remaining equal,
for instance, we would expect the following.
•
An increase in interest rates should result in a higher cost of equity for the market and
a lower PE ratio.
41
•
A greater willingness to take risk on the part of investors will result in a lower risk
premium for equity and a higher PE ratio across all stocks.
•
An increase in expected growth in earnings across firms will result in a higher PE
ratio for the market.
•
An increase in the return on equity at firms will result in a higher payout ratio for any
given growth rate and a higher PE ratio for all firms.
In other words, it is difficult to draw conclusions about PE ratios without looking at these
fundamentals. A more appropriate comparison is therefore not between PE ratios across
time, but between the actual PE ratio and the predicted PE ratio based upon fundamentals
existing at that time.
Illustration 8.6: PE Ratios across time for the S&P 500
While PE ratios are more widely used in practice, market strategists often prefer
to focus on the inverse of the number, the earnings to price ratio (or the earnings yield).
To illustrate, a PE ratio of 20 translates into an earnings yield of 5%, which, in turn, can
be compared to the dividend yield or the treasury bond rate. Figure 8.14 summarizes the
Earnings/Price ratios for S&P 500 and treasury bond rates at the end of each year from
1960 to 2005.
There is a strong positive relationship between E/P ratios and T.Bond rates, as evidenced
42
by the correlation of 0.69 between the two variables. In addition, there is evidence that
the term structure also affects the E/P ratio. In the following regression, we regress E/P
ratios against the level of T.Bond rates and the yield spread (T.Bond - T.Bill rate), using
data from 1960 to 2005.
E/P = 0.0209 + 0.7437 T.Bond Rate – 0.3274 (T.Bond Rate-T.Bill Rate)
(2.44)
(6.64)
R2 = 49.09%
(1.33)
Other things remaining equal, this regression suggests that
•
Every 1% increase in the T.Bond rate increases the E/P ratio by 0.7437% (and thus
reduces the PE ratio). This is not surprising but it quantifies the impact that higher
interest rates have on the PE ratio.
•
Every 1% increase in the difference between T.Bond and T.Bill rates reduces the E/P
ratio by 0.3274%. Flatter or negative sloping term yield curves seem to correspond to
lower PE ratios and upwards sloping yield curves to higher PE ratios. While, at first
sight, this may seem surprising, the slope of the yield curve, at least in the United
States, has been a leading indicator of economic growth with more upward sloped
curves going with higher growth.
Based upon this regression, we predict E/P ratio at the beginning of 2006, with the T.Bill
rate at 4.31% and the T.Bond rate at 4.39%.
E/P2006 = 0.0209 + 0.7437 (0.0439)- 0.3274 (0.0439-0.0431)= 0.0533
PE2006
=
1
1
=
= 18.77
E/P2006
0.0533
Since the S&P 500 was trading at a multiple of 18.27 times earnings in early 2006, this
would !have indicated a market that is almost correctly priced. This regression can be
enriched by adding other variables, which should be correlated to the price-earnings ratio,
such as expected growth in GNP and payout ratios, as independent variables. In fact, a
fairly strong argument can be made that the influx of technology stocks into the S&P 500
over the last decade, the increase in return on equity at U.S. companies over the same
period and a decline in risk premiums could all explain the increase in PE ratios over the
period.
Illustration 8.7: Comparing Price to Book Value Ratios across time
In illustration 8.6, we looked at changes in the price to earnings ratios for the U.S,
market from 1960 to 2005. Over that period, the price to book value ratio for the market
43
has also increased. In Figure 8.15, we report on the price to book ratio for the S&P 500
on one axis and the return on equity for S&P 500 firms on the other.
The increase in the price to book ratio over the last two decades can be at least partially
explained by the increase in return on equity over the same period.
Comparing Equity Multiples across Countries
Comparisons are often made between price-earnings ratios in different countries
with the intention of finding undervalued and overvalued markets. Markets with lower
PE ratios are viewed as under valued and those with higher PE ratios are considered over
valued. Given the wide differences that exist between countries on fundamentals, it is
clearly misleading to draw these conclusions. For instance, you would expect to see the
following, other things remaining equal:
•
Countries with higher real interest rates should have lower PE ratios than countries
with lower real interest rates.
•
Countries with higher expected real growth should have higher PE ratios than
countries with lower real growth.
44
•
Countries that are viewed as riskier (and thus command higher risk premiums) should
have lower PE ratios than safer countries
•
Countries where companies are more efficient in their investments (and earn a higher
return on these investments) should trade at higher PE ratios.
Illustration 8.8: Comparing PE ratios across markets
This principle can be extended to broader comparisons of PE ratios across
countries. Table 8.19 summarizes PE ratios across different countries in January 2006,
together with interest rates (short term and long term) at the time.
Table 8.19: PE Ratios for Markets – January 2006
Country
Argentina
Australia
Austria
Belgium
Brazil
Canada
Chile
China
Colombia
Czech Republic
Denmark
Finland
France
Germany
Greece
Hong Kong
Hungary
India
Indonesia
Italy
Japan
Malaysia
Mexico
Netherlands
Norway
Peru
Philipines
Poland
PE
Dividend Yield
10 yr rate
14.65
2.03%
14.00%
16.98
3.86%
5.19%
16.93
1.29%
3.30%
12.74
3.21%
3.30%
14.59
5.70%
21.00%
20.88
1.97%
3.95%
16.45
3.15%
7%
18.36
3.30%
3.09%
12.84
1.54%
8.25%
29.06
1.58%
3.69%
13.98
1.62%
3.28%
16.90
2.64%
3.23%
15.00
2.42%
3.30%
15.02
2.14%
3.30%
20.83
2.49%
3.30%
14.45
3.50%
4.19%
13.52
2.37%
8.00%
20.33
1.28%
7.10%
11.06
2.89%
13.54%
14.70
3.84%
3.30%
45.01
0.95%
1.46%
14.19
4.67%
4.11%
11.30
1.80%
5.30%
17.69
3.46%
3.29%
14.43
3.20%
3.63%
13.14
3.30%
9%
11.15
2.63%
11.90%
11.76
2.20%
5.07%
Short term
rate
8.00%
5.64%
2.48%
2.48%
18.03%
3.35%
5.28%
2.90%
6.35%
2.16%
2.46%
2.41%
2.48%
2.48%
2.48%
4.18%
6.30%
5.64%
15.00%
2.48%
0.25%
3.20%
8.14%
1.70%
2.60%
3.44%
7.69%
4.62%
45
Portugal
Russia
Singapore
South Africa
South Korea
Spain
Sweden
Switzerland
Taiwan
Thailand
Turkey
UK
USA
Venezuela
16.59
8.89
13.03
11.09
11.67
16.38
16.02
18.29
13.81
10.33
11.44
18.60
18.27
5.17
3.19%
1.80%
4.29%
2.76%
0.56%
2.85%
2.39%
1.59%
3.83%
3.64%
1.94%
3.56%
1.80%
12.19%
3.30%
15.01%
3.18%
7.45%
5.59%
3.30%
3.28%
1.96%
3.77%
5.38%
15.50%
4.09%
4.37%
13.50%
2.48%
13.00%
3.22%
7.15%
4.07%
2.48%
1.68%
0.99%
1.35%
4.50%
14.77%
4.59%
4.23%
11.50%
A naive comparison of PE ratios suggests that Japanese stocks, with a PE ratio of 45.01,
are overvalued, while Russian and Venezuelan stocks are undervalued, with single digit
PE ratios. However, differences in PE ratios across countries reflect differences in
interest rates across countries, with lower (higher) PE ratios in countries with higher
(lower) interest rates. Table 8.20 summarizes the correlation between PE ratios, interest
rates and dividend yields:
Table 8.20: Correlation Matrix: PE Ratio and Interest Rates- January 2006
PE Ratio
LT Rate
ST Rate
LT minus ST
Rate
PE Ratio
LT Rate
1.00
-0.425
-0.448
-0.041
1.00
0.939
0.406
1.00
0.066
ST Rate
LT – ST Rate
1.00
Across the sample, PE ratios are higher in countries with lower interest rates – both short
and long term. In addition, PE ratios tend to be higher in countries with more upward
sloping yield curves (measured by the difference between short term and long term rates),
reflecting their role as proxies for future growth.
There is a mix of developed market and emerging market countries in our sample
and the PE ratios tend to be lower for the latter. To provide at least partial control for this
difference, we introduce a dummy variable, set to 1 for emerging markets and 0 for
46
developed markets. A cross-sectional regression of PE ratio on the long term interest rate,
the slope of the yield curve (the difference between the long term and short term rate) and
the emerging market dummy variable (EMDUM) yields the following:
PE Ratio = 22.51 – 67.78 (LT rate) + 96.85 (LT rate– ST rate) -4.83 EMDUM
(11.03)
(3.33)
(1.59)
(2.35)
The R-squared of the regression is 24.7% and the coefficients indicate statistical
significance. Other things remaining equal, this regression suggests that a 1% difference
in long-term rates translates into a difference of 0.68 in the PE ratio and that emerging
markets trade at lower PE ratios than developed markets. Based upon this regression, the
predicted PE ratios for the countries are shown in Table 8.21.
Table 8.21:Predicted PE Ratios for Markets – January 2006
Country
Australia
China
Hong Kong
India
Indonesia
Japan
Malaysia
Philipines
Singapore
South Korea
Taiwan
Thailand
UK
Germany
France
Spain
Switzerland
Belgium
Italy
Sweden
Netherlands
Greece
Norway
Finland
Portugal
South Africa
PE Predicted PE Under(Over) Value
16.98
18.55
-8.48%
18.36
15.77
16.45%
14.45
14.85
-2.67%
20.33
14.28
42.38%
11.06
7.09
56.09%
45.01
22.69
98.38%
14.19
15.77
-10.04%
11.15
13.69
-18.55%
13.03
15.48
-15.84%
11.67
15.36
-24.03%
13.81
17.47
-20.93%
10.33
14.88
-30.59%
18.60
19.25
-3.38%
15.02
16.23
-7.48%
15.00
16.23
-7.61%
16.38
16.23
0.89%
18.29
17.29
5.79%
12.74
16.23
-21.53%
14.7
16.23
-9.45%
16.02
17.00
-5.79%
17.69
16.99
4.14%
20.83
16.23
28.30%
14.43
16.21
-11.01%
16.9
16.28
3.79%
16.59
16.23
2.19%
11.09
17.75
-37.51%
47
Russia
Poland
Hungary
Czech Republic
Austria
Denmark
Turkey
USA
Canada
Mexico
Brazil
Argentina
Venezuela
Chile
Colombia
Peru
8.89
11.76
13.52
29.06
16.93
13.98
11.44
18.27
20.88
11.3
14.59
14.65
5.17
16.45
12.84
13.14
9.45
14.68
13.90
16.66
21.06
21.08
12.71
19.68
20.41
11.33
6.32
14.00
10.46
14.60
13.93
16.96
-5.91%
-19.87%
-2.74%
74.45%
-19.63%
-33.67%
-9.97%
-7.17%
2.30%
-0.31%
130.88%
4.65%
-50.59%
12.68%
-7.80%
-22.53%
Brazil emerges as the most over valued market in the group, whereas Venezuela is the
most under valued market.
Conclusion
With equity multiples, we scale the market value of equity to some measure of
equity earnings, book value or even revenues. The most commonly used equity multiple
is the price earnings ratio, where the market value of equity is scaled to net income. Even
that simple ratio is defined in different ways by different analysts, and we began this
chapter by looking at the variations. We then considered variations on the PE ratio as
well as price to book equity and price to sales ratios; the latter is not a consistently
defined multiple but still remains widely used.
Equity multiples are ultimately determined by the same fundamentals that
determine the value of equity in a discounted cash flow model - expected growth in
earnings, equity risk and cash flow potential. Firms with higher growth, lower risk and
higher payout ratios, other things remaining equal, should trade at much higher multiples
of earnings, book value of equity and revenues than other firms. To the extent that there
are differences in fundamentals across countries, across time and across companies, the
multiples will also vary. A failure to control for these differences in fundamentals can
lead to erroneous conclusions based purely upon a direct comparison of multiples.
48
There are several ways in which equity multiples can be used in valuation. One
way is to compare multiples across a narrowly defined group of comparable firms and to
control for differences in growth, risk and payout subjectively. Another is to expand the
definition of a comparable firm to the entire sector (such as technology) or the market
and to control for differences in fundamentals using statistical techniques, such as
regressions.