Updated: August 2009

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

1

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 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.

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

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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 Confectionary

Total assets $300 million

Book value of equity $200 million Revenues $600 million

Earnings $90 million Cash flow from operations $110 million

Growth in revenues 7% per year

Growth in earnings 9% per year

Number of employees 2,500

Now consider publicly-traded companies in the confectionary industry, using fiscal year 2005 values:

Hershey Tootsie Roll Wm. Wrigley

Total assets $4,295.2 million $813.7 million $4,460.2 million Book value of shareholders’ equity $1,021.1 million $617.4 million $2,214.4 million

Revenues $4,836.0 million $487.7 million $4,159.3 million Earnings $493.2 million $77.2 million $517.3 million

Cash flow from operations $461.8 million $82.5 million $757.6 million

Growth in revenues 5.5% 5.5% 9% Growth in earnings 10% 6.50% 10%

Number of employees 40,523 1,950 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

3

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 of equityMarket value-earnings ratio =

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:

Market price per sharePrice-earnings ratio =

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 price-

earnings 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:

4

0

t

Let

P = Price per share at time 0,

D = 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 m

010

00

0

00 0

0

00

00

odel,

D (1+g)DP = =

r-g r-g

DRecognizing that the dividend payout ratio is , where E is earnings per share, and

ED

substituting E for D ,E

DE (1+g)

EP = .

r-g

Dividing by earnings per share, 0

0

00

0

E ,

D(1+g)

E Dividend payout ratio (1+g)P= = .

E r-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 equityMarket 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:

Market price per sharePrice-to-book ratio =

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.

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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 price-

to-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:

010

00

0

00 0

0

00

00

Starting with the dividend valuation model,

D (1+g)DP = =

r-g r-g

DRecognizing that the dividend payout ratio is , where E is earnings per share, and

ED

substituting E for D ,E

DE (1+

EP =

0

0 0 0

0 0 00

0

g)

.r-g

Dividing by the book value of equity per share, B ,

E D D(1+g) Return on equity (1+g)

B E EP= = .

B r-g r-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 of equityMarket value-sales ratio =

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:

Market price per sharePrice-sales ratio =

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.

6

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:

010

00

0

00 0

0

00

00

Starting with the dividend valuation model,

D (1+g)DP = =

r-g r-g

DRecognizing that the dividend payout ratio is , where E is earnings per share, and

ED

substituting E for D ,E

DE (1+

EP =

0

0 0 0

0 0 00

0

g)

.r-g

Dividing by sales per share, S ,

E D D(1+g) Net profit margin (1+g)

S E EP= = .

S r-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:

share perflow Cash

share per Price

flows Cash

equity of value Market ratioflow cash-Price

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:

(expressed as a whole number)

PE ratioPEG ratio =

Growth rate of earnings

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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:

Hershey Tootsie Roll Wm. Wrigley Average Market price per share 3/31/2006* $52.23 $29.27 $64.00 Market price per share 12/31/2005* $55.25 $28.93 $66.49 Number of shares outstanding 238,949,667 53,069,531 277,278,198 Earnings $567.3 million $65.6 million $544.3 million Book value of equity $1,021.1 million $617.4 million $2,214.4 million Sales $4,836.0 million $487.7 million $4,159.3 million Earnings growth rate 10% 6.5% 10% Price-earnings ratio 21.9995 23.6790 32.6030 26.0939 Price-book ratio 12.2224 2.5159 8.0138 7.5841 Price-sales ratio 2.5807 3.1850 4.2665 3.3441 PEG ratio 2.1995 3.6429 3.2603 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 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.

The classification of leases, e.g., capital v. operating. If the subject company uses capital

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.

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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 Tootsie Roll Wm. Wrigley Average

Market value-earnings ratio $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 1,911.03 2,559.92 2,006.46

PEG ratio 1,781.96 2,950.77 2,640.84 2,457.86

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 3.958

Value weighted arithmetic mean 2.618 Median 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

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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 non-representative, 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 Cannot be used when … Price-earnings Earnings are zero or negative

Price-book Equity is zero or negative Price-cash flow Cash flow is zero or negative

PEG 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

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. 4 If the denominator is zero, the ratio cannot be calculated. If the denominator is negative, this will result in a meaningless ratio.

0%

10%

20%

30%

40%

50%

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

Percentage of companies with

zero or negative amounts

Earnings available for common shareholders before extraordinary items

Cash flow from operations

Book value of equity

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So, what is an analyst to do? One approach that analysts use is to invert a multiple. Consider the price-

earnings 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:

Price-earnings Earnings yield

Number of observations 3,991 5,534

Median 18.98 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 long-term.

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Exhibit 3 The Price-Earnings Ratio for the S&P 500 First Quarter 1988 through First Quarter 2009

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, 1997-2006

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.

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P/E of the S&P 500

Quarter end

0

5

10

15

20

$0.00

$0.20

$0.40

$0.60

$0.80

$1.00

$1.20

$1.40

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006

P/EEPS

EPS PE

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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