Valuation multiples
A reading prepared by Pamela Peterson Drake
James Madison University
Table of Contents
Introduction........................................................................................................................................1
Understanding the use of multiples ......................................................................................................1
Identifying the comparables ................................................................................................................1
Choosing a multiple .............................................................................................................................2
Price-earnings ratio ..........................................................................................................................3
Price-book ratio ...............................................................................................................................4
Price-sales ratio ...............................................................................................................................5
Price-cash flow ratio ........................................................................................................................6
PEG ratio.........................................................................................................................................6
Calculating the multiples ..................................................................................................................7
Adjusting for differences in accounting .................................................................................................7
Applying the multiples .........................................................................................................................8
Issues multiples ..................................................................................................................................8
To average or not to average?..........................................................................................................8
Problems with the denominator ........................................................................................................9
The Moldovsky effect ..................................................................................................................... 10
Summary .......................................................................................................................................... 12
For further information ...................................................................................................................... 12
Index ............................................................................................................................................... 12
Updated: August 2009
Introduction
There are many approaches to valuing a company, a division, or any other business unit, including
discounted cash flows methods and valuation multiples. The discounted cash flow methods require
estimates of cash flows for a number of periods into the future, a discount rate that reflects the riskiness
of these cash flows, and either an assumption regarding the growth rate of cash flows into the future or
a terminal or horizon value of the business unit at some point in the future. The valuation multiples
require selection of a comparable or comparable businesses units and a multiple or set of multiples for
valuation, such as a price-earnings ratio. The focus of this reading is on the valuation multiples
approach.
Understanding the use of multiples
The process of valuation using multiples requires
the use of information on comparable firms, some
adjustments to improve comparability, and then the
application of the multiple derived from the
comparable firms to the subject firm, as shown in
Exhibit 1.
This process will lead to an estimate of value for a
company which is just that: an estimate. As you
can see in Exhibit 1, this process involves a great
deal of guess-work along the way, such that errors
in estimates are compounded. A prudent approach
is to use more than one multiple, evaluate the
sensitivity of the estimates to the choice of
comparables, and consider the amount of error that
is present in the estimates.
Identifying the comparables
Exhibit 1
Valuation using multiples
Identify comparable firms and determine
values from market data
Adjust values for different accounting
methods
Calculate the multiple based on the
comparable firms’ base and values
Estimate the base of the multiple for the
subject business unit or company
Apply the multiple from the comparables
to the subject business unit or company
To make comparisons, the analyst most likely will want to compare the firm with other firms. But
identifying the other firms in the same or similar lines of business presents a challenge. A system that has
been used for many years for classifying firms by lines of business is the Standard Industrial Classification
(SIC) system, which was developed by the Office of Management and Budget. However, starting in 1997,
another classification system, North American Industry Classification System (NAICS) replaces SIC codes
with a system that better represents the current lines of business. Using the NAICS, we can classify a
firm and then compare this firm with other of that class.
Classifying firms into industry groups is difficult because most firms have more than one line of business.
Most large corporations operate in several lines of business. Do we classify a firm into an industry by the
line of business that represents:
The most sales revenue generated?
The greatest investment in assets?
The greatest share of the firm's profits?
It is not clear which is the most appropriate method and a firm may be classified into different industries
by different financial services and analysts.
1
When identifying comparables, it is important to identify, if possible, companies that are most similar
according to a number of dimensions:





Line of business and, specifically, products
Asset size
Number of employees
Growth in revenues and earnings
Cash flow
Often, when we evaluate a company that is not publicly-traded, we are comparing a smaller company
with larger, publicly-traded companies. Therefore, it is often difficult to match up the subject company
with a similar-size company in terms of assets and number of employees. However, matching up on as
many factors as possible is useful, especially with respect to the line of business.
Consider the 2005 fiscal year data of a company that is the subject of a valuation:
Line of business
Total assets
Book value of equity
Revenues
Earnings
Cash flow from operations
Confectionary
$300 million
$200 million
$600 million
$90 million
$110 million
Growth in revenues
Growth in earnings
Number of employees
7% per year
9% per year
2,500
Now consider publicly-traded companies in the confectionary industry, using fiscal year 2005 values:
Total assets
Book value of shareholders’ equity
Revenues
Earnings
Cash flow from operations
Growth in revenues
Growth in earnings
Number of employees
Hershey
$4,295.2 million
$1,021.1 million
$4,836.0 million
$493.2 million
$461.8 million
5.5%
10%
40,523
Tootsie Roll
$813.7 million
$617.4 million
$487.7 million
$77.2 million
$82.5 million
5.5%
6.50%
1,950
Wm. Wrigley
$4,460.2 million
$2,214.4 million
$4,159.3 million
$517.3 million
$757.6 million
9%
10%
43,555
Which firm is most comparable? Tootsie Roll is the smallest of the three possible comparables, but is it
the most comparable in other dimensions? Should we take an average of the three companies’ values in
some way? Should we restrict the comparables to U.S. companies, or should we expand the eligible
companies to include Lindt & Sprüngli or Nestlé?
While the choice of comparables is important, analysts will also examine the sensitivity of their valuation
to the choice of the comparable and develop a range of estimates based on alternative comparables.
Choosing a multiple
There are a large number of multiples that an analyst can apply in a valuation situation. These multiples
include the price-earnings ratio, the price-book ratio, and the price-sales ratio. In addition, we may want
to compare PEG ratios as well
2
Price-earnings ratio
The price-earnings ratio, also referred to as the PE or P/E ratio, is simply the ratio of the market
value of the stock to the earnings or net income:
Market value-earnings ratio =
Market value of equity
Net income
We can also restate the price-earnings ratio in the more familiar, but numerically equivalent, per-share
basis as the ratio of the price of a share of stock to the earnings per share:
Price-earnings ratio =
Market price per share
Earnings per share
But it really is not as simple as that:


Do we use earnings for the most recent four quarters of earnings? This is referred to as the
trailing PE.
Or do we use forecasted earnings? This is referred to as the leading PE.
The most important issue is that you are consistent. When you gather the information for the
comparables, you should make sure that the multiples are determined in the same manner and then
applied consistently to the subject company. For example, many analysts remove non-recurring items
from earnings before calculating this ratio so that we get a better picture of the underlying earnings of a
company. When using price-earnings ratios calculated from a third party, it is important to understand
how these ratios are calculated:
Before or after extraordinary earnings?
Leading or trailing earnings?
The price-earnings ratio is considered useful in valuation because earnings are a primary driver in a
company’s value. In cases in which a company does not have positive earnings, however, the priceearnings ratio cannot be used, and in cases in which a company has volatile earnings, the price-earnings
ratio as a multiple may not be very reliable.
We can relate the price-earnings ratio to fundamental factors using the familiar dividend valuation model:
3
Let
P0 = Price per share at time 0,
Dt = Dividend per share at the end of period t,
g = Expected growth rate of dividends, and
r = Required rate of return.
Starting with the dividend valuation model,
P0 =
D1 D0 (1+g)
=
r-g
r-g
Recognizing that the dividend payout ratio is
D0
substituting E0
P0 =
E0
D0
E0
E0
D0
E0
, where E0 is earnings per share, and
for D0 ,
(1+g)
.
r-g
Dividing by earnings per share, E0 ,
P0
D0
E0
=
E0
(1+g)
r-g
=
Dividend payout ratio (1+g)
.
r-g
We see from this that the price-earnings ratio is related to the dividend payout ratio and the
plowback ratio (which is the complement of the dividend payout ratio), expected growth, and the
required rate of return.1
Price-book ratio
The price-book ratio, or price-to-book ratio, is the ratio of the market value of the equity to the
book value of equity:2
Market value of equity
Market value-book ratio =
Book value of equity
We can also phrase this in terms on a per-share basis as the ratio of the market price per share of a
stock to the book value of equity per share:
Price-to-book ratio =
Market price per share
Book value of equity per share
This ratio is also known as the price-equity ratio.
The ratio captures the value that investors place on the company’s equity. In cases in which a company
has negative earnings, and hence the price-earnings ratio is meaningless, the price-book ratio may be
used as long as equity is positive. However, because the book value of a company’s assets will not often
1
The dividend payout ratio is the ratio of dividends to earnings. The plowback ratio, representing the proportion of
earnings reinvested into the firm, is one minus the dividend payout ratio.
2
The book value of equity in these ratios refers to common shareholders’ equity, which is total shareholders’
equity less any preferred stock equity. Some analysts use only tangible book equity, which is the book value of
common equity less the book value of intangibles assets.
4
be equivalent to the true value of its assets, this ratio may not be very meaningful for some companies.
For example, pharmaceutical companies have many patents on drugs, the value of which is not reflected
in the book value of assets and, hence, the book value of equity.
For investors who use a strategy of “value investing”, this ratio is often used to identify firms: low priceto-book stocks are typically viewed as under-priced value stocks. However, this may not be a correct
assessment because companies with financial problems often have low price-to-book ratios.
We can relate the price-book ratio to fundamental factors using the familiar dividend valuation model:
Starting with the dividend valuation model,
P0 =
D1 D0 (1+g)
=
r-g
r-g
Recognizing that the dividend payout ratio is
substituting E0
P0 =
E0
D0
D0
E0
D0
E0
, where E0 is earnings per share, and
for D0 ,
(1+g)
E0
.
r-g
Dividing by the book value of equity per share, B 0 ,
P0
E0
B0
=
B0
D0
E0
r-g
(1+g)
Return on equity
=
r-g
D0
E0
(1+g)
.
We see that the price-book ratio is related to the fundamentals of the return on equity (earnings
divided by the book value of equity), the plowback ratio, the expected growth rate, and the required rate
of return.
Price-sales ratio
The price-sales ratio, or price-to-sales ratio or PSR, is the ratio of the market value of the equity to
the company’s revenues for the period:
Market value-sales ratio =
Market value of equity
Revenues
We can also phrase this in terms on a per-share basis as the ratio of the market price per share of a
stock to the sales per share:
Price-sales ratio =
Market price per share
Revenues per share
The price-sales ratio permits comparisons among companies without the issue of dealing with different
accounting methods. This ratio also allows comparisons among companies that generate losses, in which
the price-earnings ratio is not applicable. For example, if there is year for, say, airlines in which most or
all airlines generate losses, the price-sales ratio gives us an idea of the valuation that investors apply to
revenue generation. The price-sales ratio may not reflect valuation comparatively if companies have
different cost structures, however.
5
A variation on this ratio is to include the market value of debt along with the market value of equity in
the numerator. This allows more comparability among companies that have different capital structures.
We can relate the price-sales ratio to fundamental factors using the familiar dividend valuation model:
Starting with the dividend valuation model,
P0 =
D1 D0 (1+g)
=
r-g
r-g
Recognizing that the dividend payout ratio is
D0
substituting E0
P0 =
E0
D0
E0
D0
E0
, where E0 is earnings per share, and
for D0 ,
(1+g)
E0
.
r-g
Dividing by sales per share, S 0 ,
P0
E0
S0
=
S0
D0
E0
r-g
(1+g)
Net profit margin
=
D0
E0
(1+g)
r-g
.
We see through this decomposition of the value of a share that the price-sales ratio is related to the
fundamentals of the net profit margin (through the inverse of earnings divided by sales), the plowback
ratio, expected growth, and the required rate of return.
Price-cash flow ratio
The price-cash flow ratio, or price-to-cash flow ratio, is the ratio of the market value of the equity
to the company’s cash flow for the period:
Price - cash flow ratio
Market value of equity
Cash flows
Price per share
Cash flow per share
There are several variants of the cash flow amount that is used. These variations include:
Simplified cash flow, which is earnings plus depreciation, amortization and depletion;
Cash flow from operations, from the statement of cash flows; and
Free cash flow, which is often calculated as cash flow from operations, less capital
expenditures, plus net borrowings.
PEG ratio
The PEG ratio is the ratio of the price-earnings ratio to the growth rate of earnings:
PEG ratio =
PE ratio
Growth rate of earnings
(expressed as a whole number)
6
The PEG ratio considers the company’s expected growth directly by comparing the market’s multiple
applied to earnings with the growth rate anticipated by the analyst. Effectively, this ratio is a comparison
of the market’s assessment of the company’s growth to that of the analyst. Though in most applications
the PEG ratio is calculated using anticipated growth, in valuation situations of a non-publicly-traded
company it may not be possible to estimate the future growth rate, but rather it may be possible to look
at the recent or historical growth rate of the companies.
The general belief is that if a company’s price-earnings ratio is approximately equal to the company’s
earnings growth rate – hence a PEG ratio of 1.0 -- the stock is appropriately priced; if the PEG ratio is
lower than one, this implies that the stock is under-priced, whereas if the PEG ratio is greater than one,
this implies that the stock is over-priced.
Calculating the multiples
For publicly-traded stocks the data used in the multiples is easy to obtain from the financial statements
and financial websites. For 2005, the comparable companies have the following data and multiples:
Market price per share 3/31/2006*
Market price per share 12/31/2005*
Number of shares outstanding
Earnings
Book value of equity
Sales
Earnings growth rate
Price-earnings ratio
Price-book ratio
Price-sales ratio
PEG ratio
Hershey
$52.23
$55.25
238,949,667
$567.3 million
$1,021.1 million
$4,836.0 million
10%
Tootsie Roll
$29.27
$28.93
53,069,531
$65.6 million
$617.4 million
$487.7 million
6.5%
Wm. Wrigley
$64.00
$66.49
277,278,198
$544.3 million
$2,214.4 million
$4,159.3 million
10%
21.9995
12.2224
2.5807
2.1995
23.6790
2.5159
3.1850
3.6429
32.6030
8.0138
4.2665
3.2603
Average
26.0939
7.5841
3.3441
1.2097
*
Source: Yahoo! Finance
Source: 10-K filings for fiscal year 2005, filed with the Securities and Exchange Commission
 Source: Value Line Investment Survey, various issues.


Based on the market value of stock on March 31, 2006.
Adjusting for differences in accounting
The adjustments for differences in accounting are necessary if the subject company and the comparable
companies use different methods of accounting such that these different methods may result in
distortions in comparability. The methods of accounting that may cause such an issue include:

The method of accounting for inventory, e.g., LIFO v. FIFO. If a company uses the LIFO
method and comparables use FIFO, or vice versa, there is sufficient information in the footnotes
to adjust the balance sheet and income statements to a FIFO basis.

The method of accounting for depreciation, e.g., accelerated v. straight-line. There is no

The classification of leases, e.g., capital v. operating. If the subject company uses capital
simple method of adjusting the two methods because the extent of the difference depends on
the age of the assets relative to their useful lives, information that is not readily available.
leases for all its leases and the comparables use operating leases, or vice versa, the simplest
method of achieving comparability is to capitalize the operating leases based on footnote
information and adjusting the balance sheet and the income statement appropriately.
7
Though there are some adjustments that are quite straight-forward, there are other adjustments that are
difficult to calculate and, effectively, must be guess-timated. The usefulness of any application of
multiples requires understanding the data limitations and the resulting sensitivity of the estimated value.
Applying the multiples
The analysis and calculation of multiples using comparables provides valuable information in the valuation
of the subject company.
Value based on multiple of …
Using …
Hershey
Market value-earnings ratio
Tootsie Roll
Wm. Wrigley
Average
$1,979.96
$2,131.11
$2,934.27
$2,348.45
Market value-book ratio
2,444.49
503.19
1,602.76
1,516.81
Market value-sales ratio
1,548.43
1,781.96
1,911.03
2,950.77
2,559.92
2,640.84
2,006.46
2,457.86
PEG ratio
As you can see, the valuation of the company of interest depends on the multiple that you apply, as well
as your definition of the comparable. The wide range, from $503 million to $2,951 million, may be too
wide to be practical. An analyst would delve deeper into the adjustments to the base (e.g., the
comparability of earnings and the book value or equity), the appropriateness of using one multiple versus
another in the particular case, and the most appropriate comparable.
Issues multiples
To average or not to average?
The choice of a comparable or set of comparable companies was discussed previously. However, there is
another issue that should be considered: How do you consider the multiples when you have more than
one comparable. The issues involve:
How do you treat companies that are different sizes?
How do you deal with outlier multiples in the set of comparable?
With regard to different size comparables, the issue is whether or not you use an equal weighted mean, a
value-weighted mean, or a median. Consider the tire and rubber industry. In 2006, the price-book ratio
calculated using these different metrics results in different values:
Equal weighted arithmetic mean
Value weighted arithmetic mean
Median
3.958
2.618
2.374
The equal weighted arithmetic mean is calculated by simply summing the values for the firms in the
industry and dividing this sum by the number of firms. The value weighted arithmetic mean is calculated
by summing the market values, summing the book values of equity, and then dividing the former sum by
the latter sum. In this manner, the larger firms receive a greater weight in the average. The median is
calculated as the center value of the ratio once the ratios are ranked in numerical order. The difference
in these metrics can make a significant difference in the estimated value of the subject company.
Which is best to use? It depends on the distribution of firms by size in the set of comparables, but also
on the size of the subject company. For example, if the subject company is similar in size to the larger
8
firms in the industry, the analyst would want to use the value-weighted mean, rather than the median or
the equal-weighted mean.
With regard to the outliers, the issue is whether or not you simply disregard the outliers as nonrepresentative, dropping them from consideration completely, or giving them less weight by using a
harmonic mean or a geometric mean of the comparables’ multiples.3 For example, using the same set of
price-book ratios, we observe two outliers – that is, values significantly different than the other values in
the sample. We could either calculate the harmonic mean, which results in a value of 2.309, or calculate
the arithmetic mean removing the two outliers, resulting in a mean of 3.079. The point of this is that the
there are remedies, but they may result in different multiples for the comparables.
Problems with the denominator
One of the issues that an analyst faces in using multiples is that the denominator may be negative,
resulting in a meaningless multiple. When looking at these multiples, we can see that there are cases in
which the multiple cannot be calculated or, if mechanically can be calculated, is meaningless:4
Multiple
Price-earnings
Price-book
Price-cash flow
PEG
Cannot be used when …
Earnings are zero or negative
Equity is zero or negative
Cash flow is zero or negative
Earnings are zero or negative
How often is the denominator in these common multiples negative? With sufficient frequency to cause
problems in applying multiples in some industries and in some economic environment, as shown in
Exhibit 2.
Exhibit 2
The proportion of NYSE, AMSE and Nasdaq traded companies that experience
negative earnings, cash flows, or book value of equity
Earnings available for common shareholders before extraordinary items
Cash flow from operations
Book value of equity
50%
40%
Percentage of
companies with 30%
zero or
20%
negative
amounts
10%
0%
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Source of data: Standard & Poor’s Compustat
3
The harmonic mean gives each value in the sample a weight that is inverse to its value.
If the denominator is zero, the ratio cannot be calculated. If the denominator is negative, this will result in a
meaningless ratio.
4
9
So, what is an analyst to do? One approach that analysts use is to invert a multiple. Consider the priceearnings ratio. The inverse of this ratio is the earnings yield. If a company’s earnings are negative, the
price-earnings ratio is meaningless, but the earnings yield is interpretable – it is the return (positive or
negative) per dollar of market value. Consider the price-earnings ratio (P/E) and earnings yield (E/P) for
the companies traded on the NYSE, AMSE and the Nasdaq at the end of 2006:
Number of observations
Median
Price-earnings
3,991
18.98
Earnings yield
5,534
4%
In other words, there were 1,543 of the 5,534 companies that had zero or negative earnings, and
therefore the price-earnings ratio was meaningless.
The Moldovsky effect
Nicholas Molodovsky observed that price-earnings ratios exhibit a countercyclical behavior: during poor
economic environment, price-earnings ratios tend to be inflated vis-a-vis those in good economic
environments, and that these multiples tend to be mean-reverting.56 This mean reverting behavior has
come to be referred to as the Moldovsky effect.
What is happening is that the denominator is depressed during poor economic periods, yet the value in
the numerator reflects investors’ expectations regarding future earnings. This is true even if a leading PE
is used because the expectations built in to the numerator go well beyond the next fiscal period. We can
see this in Exhibit 3, with the P/E ratio of the S&P 500 increasing substantially in the first quarter of 2009,
where earnings reflect the recessionary environment of 2008, but the prices are forward-looking to the
possible economic recovery in 2009.
5
Nicholas Molodovsky, “A Theory of Price-Earnings Ratios,” Financial Analysts Journal (January/February 1994) p.
31.
6
Mean reversion is the tendency of a value to remain near or converge upon the average value over the longterm.
10
Exhibit 3
The Price-Earnings Ratio for the S&P 500 First Quarter 1988 through First
Quarter 2009
140
120
100
80
60
P/E of the
S&P 500 40
20
12/31/2008
12/31/2007
12/31/2006
12/31/2005
12/31/2004
12/31/2003
12/31/2002
12/31/2001
12/31/2000
12/31/1999
12/31/1998
12/31/1997
12/31/1996
12/31/1995
12/31/1994
12/31/1993
12/31/1992
12/31/1991
12/31/1990
12/31/1989
12/31/1988
0
Quarter end
Source of data: Standard & Poor’s
Consider the furniture industry, which is a cyclical industry. I show the median earnings per share (EPS)
and price-earnings ratio for this industry over the ten years, 1997 through 2006, in Exhibit 4.
Exhibit 4
Earnings per share and price-earnings ratios for the furniture industry, 19972006
EPS
PE
$1.40
20
$1.20
15
$1.00
EPS
$0.80
10 P/E
$0.60
$0.40
5
$0.20
$0.00
0
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Source of data: Standard & Poor’s Compustat
First, you should notice that the two series tend to move in different directions. For example, the U.S.
economy was in a recession from March 2001 through November 2001, during which the price-earnings
ratios were higher than usual, and the EPS were lower than usual for this industry.
11
The Molodovsky effect is prevalent in any of the multiples that use earnings as a denominator, including
those that use cash flows that are calculated based on earnings. What is the importance of this effect?
Analysts using multiples to value a company should consider whether the multiple is affected by cycles in
the economy and, if so, how the valuation should be adjusted to consider that the multiples tend toward
a mean value over time, regardless of a particular economic cycle.
Summary
Analysts use multiples to value securities and there are many different multiples that can be used and
different methods of applying these multiples. The basic idea is that to value a particular company, the
analyst selects comparable companies, calculates the multiples that the market assigns to those
companies, and then applies these multiples to the subject company.
However, calculating and applying multiples is not straightforward, and the analyst must take care in the
selection of the comparables, the selection of the multiple, and adjustments for any accounting
differences.
For further information
1. Damodaran, Aswath, “PE Ratios,” http://pages.stern.nyu.edu/~adamodar/pdfiles/pe.pdf, a
lecture on the use of PE to value a company.
2. Motley Fool, “Earnings-Based Valuations,”
http://www.fool.com/School/EarningsBasedValuations.htm
3. Stowe, John D., Thomas R. Robinson, Jerald E. Pinto, and Dennis W. McLeavey, Analysis of
Equity Investments: Valuation, Association for Investment Management and Research, (United
Book Press, Inc., 2002), Chapter 4.
Index
Dividend payout ratio, 4
Free cash flow, 6
Leading PE, 3
Mean reversion, 10
Moldovsky effect, 10
Net profit margin, 6
P/E. See Price-earnings ratio
PE. See Price-earnings ratio
PEG ratio, 6
Plowback ratio, 4
Price-book ratio, 4
Price-cash flow ratio, 6
Price-earnings ratio, 3
Price-equity ratio, 4
Price-sales ratio, 5
Price-to-book ratio. See Price-book ratio
Price-to-cash flow ratio. See Price-cash flow ratio
Price-to-sales ratio. See Price-sales ratio
PSR. See Price-sales ratio
Return on equity, 5
Trailing PE, 3
12