### Price Multiples - American University

```FIN 468: Intermediate
Corporate Finance
Topic 7–Price Multiples
Larry Schrenk, Instructor
1 (of 22)
Topics

Relative Valuation

Price Multiples

P/E Ratio

Other Ratios
Relative Valuation
3 (of 36)
Relative Valuation

Value of an asset is compared to the values assessed by
the market for similar or comparable assets.

To do relative valuation


Identify comparable assets and obtain market values
Convert these market values into standardized values



Absolute prices cannot be compared
Standardizing creates price multiples.
Compare the standardized values/multiples


Controlling for any differences that might affect the multiple
Judge whether the asset is under or over valued
Relative Valuation

Most valuations on Wall Street are relative valuations.




Almost 85% of equity research reports are based upon a multiple and
comparables.
More than 50% of all acquisition valuations are based upon multiples
Rules of thumb based on multiples are not only common but are often
the basis for final valuation judgments.
While there are more discounted cashflow valuations in consulting
and corporate finance, they are often relative valuations
masquerading as discounted cash flow valuations.


The objective in many discounted cashflow valuations is to back into a
number that has been obtained by using a multiple.
The terminal value in a significant number of discounted cashflow
valuations is estimated using a multiple.
Four Steps
1.
Define the multiple

2.
Describe the multiple

3.
Know what the cross sectional distribution
Analyze the multiple

4.
Same multiple can be defined in different ways
Understand the fundamentals that drive each multiple
Apply the multiple


Define the comparable universe
Controlling for differences
Definitional Tests

Is the Multiple Consistently Defined?



Value (numerator) and the standardizing variable (denominator)
should apply to the same claimholders in the firm.
E.g., the value of equity should be divided by equity earnings or
equity book value, and firm value should be divided by firm
earnings or firm book value.
Is the Multiple Uniformly Estimated?


variables must be estimated uniformly across assets in the
“comparable firm” list.
For earnings- or book-based multiples, the accounting rules must
be applied consistently across assets.
Analytical Tests

What are the Fundamentals that Determine and Drive
these Multiples?



Constitutive of every multiple are variables that drive cash flow valuation,
e.g., growth, risk and cash flow patterns.
In theory, a simple discounted cash flow model should yield the
fundamentals that drive a multiple
How Do Changes in these Fundamentals Change the
Multiple?

Relationship between a fundamental (like growth) and a multiple (such
as PE) typically non-linear.


Twice the growth rate doe not imply twice the PE ratio
Cannot use multiple, if we do not know relationship between
fundamentals and multiple
Relative Value and
Fundamentals: Equity Multiples
DPS1
r - gn

Gordon Growth Model:
P0 =

Dividing both sides by the earnings,
P0
Payout Ratio *(1+ gn )
= PE =
EPS0
r-g
n

Dividing both sides by the book
value of equity,
P0
ROE * Payout Ratio *(1+ gn )
= PBV =
BV0
r-g
n


If the return on equity is written in
terms of the retention ratio and the
expected growth rate
Dividing by the Sales per share,
P0
ROE - gn
= PBV =
BV0
r-g
n
P0
Profit Margin * Payout Ratio *(1+ gn )
= PS =
Sales0
r-g
n
Determinants of Multiples
Value of Stock = DPS 1/(ke - g)
PE=Payout Ratio
(1+g)/(r-g)
PE=f (g, payout, risk)
PEG=Payout ratio
(1+g)/g(r-g)
PBV=ROE (Payout ratio)
(1+g)/(r-g)
PEG=f (g, payout, risk)
PBV=f(ROE,payout, g, risk)
PS= Net Margin (Payout ratio)
(1+g)/(r-g)
PS=f(Net Mgn, payout, g, risk)
Equity Multiple s
Fir m Multiple s
V/FCFF=f(g, WACC)
Value/FCFF=(1+g)/
(WACC-g)
V/EBIT(1-t)=f(g, RIR, WACC)
Value/EBIT(1-t) = (1+g)
(1- RIR)/(WACC-g)
V/EBIT=f (g, RIR, WACC, t)
Value/EBIT=(1+g)(1RiR)/(1-t)(WACC-g)
Value of Firm = FCFF1/(WACC -g)
VS=f(Oper Mgn, RIR, g, WACC)
VS= Oper Margin (1RIR) (1+g)/(WACC-g)
PE For a High Growth Firm


The price-earnings ratio for a high growth firm can be related to
fundamentals.
two-stage dividend discount model::
 (1+ g)n 
EPS0 *Payout Ratio *(1+ g)* 1
(1+ r)n  EPS0 *Payout Ration *(1+ g)n *(1+ gn )

P0 =
+
r -g
(r - gn )(1+ r)n


For a firm that does not pay what it can afford to in dividends, substitute
FCFE/Earnings for the payout ratio.
Dividing both sides by the earnings per share:
 (1+ g)n 
Payout Ratio *(1+ g)* 1
(1+ r)n  Payout Ration *(1+ g)n *(1+ gn )
P0

=
+
EPS0
r -g
(r - gn )(1+ r)n
Application Tests

What is a ‘Comparable’ Firm?


Traditional Analysis: Firms in the same sector are comparable firms
Valuation Theory: Comparable firm is determined by similar
fundamentals.


Firm can be compared with a firm in a very different business, if same risk,
growth and cash flow characteristics.
How Do We Adjust for Differences across Firms on the
Fundamentals?

Impossible to find two exactly identical firms
Price Multiples
Method of Comparables

Using a price multiple to evaluate whether an
asset is in relation to a benchmark multiple value:




relatively fairly valued,
relatively undervalued, or
relatively overvalued.
Benchmark value of a multiple could be…


A closely matched individual stock
Average or median value of the multiple for the stock’s
peer group of companies or industry.
Method of Comparables

Law of One Price

Two identical assets should sell at the same price.

Most widely used multiples approach for analysts

Assumption: Over/undervalued asset will under/outperform
the comparison asset(s) on a relative basis.

If the comparison asset or assets themselves are efficiently priced
Profitability Assumptions

Assumption 1: Markets are no perfectly
efficient.

Assumption 2: You have correctly identified a
mispricing.

Assumption 3: The market corrects this
mispricing–within a ‘reasonable’ time.
16 (of 70)
P/E Ratios
17 (of 36)
Rationales for Use of P/E Ratios

Earning power chief driver of value.

Earnings per share (EPS) perhaps the chief
focus of security analysts’ attention.

Differences in price/earnings ratios may be
related to differences in long-run average
returns, according to empirical research.
Drawbacks to P/E Ratios

EPS can be negative.


Two components of earnings



The P/E ratio does not make economic sense with a
negative denominator.
On-going or recurrent are most important in
Volatile, transient components
Management distortion of earnings
Accounting Issues with P/E Ratios

Price easily obtained and unambiguous.

Earnings not as straightforward.

Two issues are

Time horizon over which earnings are measured

Adjustments to accounting earnings to make P/Es comparable
across companies.

Trailing P/E (Current P/E):




Leading P/E (Forward P/E, Prospective P/E)


Current market price of the stock divided by the most recent four
quarters’ earnings per share.
EPS in such calculations are sometimes referred to as trailing
twelve months (TTM) EPS.
Trailing P/E is the price–earnings ratio published in stock listings
of financial newspapers.
Current market price of the stock divided by next year’s expected
earnings.
Other


First Call/Thomson Financial reports as the “current P/E” market
price divided by the last reported annual earnings per share.
Value Line reports as the “P/E” market price divided by the sum
of the preceding two quarters’ trailing earnings and the next two
quarters’ expected earnings.
Issues with Trailing P/E’s
EPS issues include
 Transitory, nonrecurring components of earnings
that are company-specific;
 Transitory components of earnings due to
 Differences in accounting methods; and
 Potential dilution of earnings per share.
Normalized P/E’s

Nomalized EPS can be used to create a normalized P/E.
Two methods for nomalizing EPS:



The Method of Historical Average EPS: Normal EPS is calculated
as average EPS over the most recent full cycle.
The Method of Average ROE: Normal EPS is calculated as the
average return on equity from the most recent full cycle,
multiplied by current book value per share.
Which method is preferred?


The first method is approach to cyclical earnings, but does not
account for changes in the business’s size.
The second method reflects more accurately the effect growth or
shrinkage in the company’s size.

The method of average ROE is sometimes preferred.
Justified P/E in a DCF Model

DCF valuation models can be used to develop an estimate of the justified P/E for a
stock.


In the Gordon growth form of the dividend discount model, the P/E is calculated using these
two expressions.
P0 D1 / E1 1  b


E1
rg
rg

The trailing P/E is:
P0 D0(1+g)/E0 (1-b)(1+g)
=
=
E0
r -g
r -g

Both expressions state P/E as a function of two fundamentals: the stock’s required
rate of return, r, reflecting its risk, and the expected (stable) dividend growth rate, g.
The dividend payout ratio, 1 – b, also enters into the expression. The stock’s justified
P/E based on forecasted fundamentals.
Justified P/E Example
For FPL Group, Inc. (FPL), a utility analyst, forecasts a
long-term payout rate of 50 percent, a long-term growth
rate of 5 percent, and a required rate of return of 9
percent. Based upon these forecasts of fundamentals,
what is FPL’s justified leading P/E and trailing P/E?
P0 1-b
1- 0.50
=
=
=12.5
E1 r - g 0.09- 0.05
Trailing Justified P/E:
P0 (1- b)(1+ g) (1- 0.5)(1+ 0.05)
=
=
=13.125
E0
r -g
0.09 - 0.05
Benchmark P/E’s

The choices for the benchmark value of the P/E:






The P/E of the most closely matched individual stock.
The average or median value of the P/E for the company’s peer
group of companies within an industry.
The average or median value of the P/E for the company’s
industry or sector.
The P/E for a representative equity index
An average past value of the P/E for the stock.
Valuation errors are probably less likely when we use an
equity index or a group of stocks than when we use a
single stock, because the former choices involve an
averaging.
Other Ratios
27 (of 36)
PEG Ratios

P/E to growth (PEG) ratio addresses the impact of
earnings growth on P/E ratios is P/E to growth (PEG)
ratio.




Stock’s P/E divided by the expected earnings growth rate.
Stock’s P/E per unit of expected growth.
Stocks with lower PEGs are more attractive
Cautions:

Assumes a linear relationship between P/E ratios and growth.



The model for P/E in terms of DDM shows that in theory the relationship is not
linear.
Does not factor in differences in risk
Does not account for differences in the duration of growth.

For example, dividing P/E ratios by short-term (5 year) growth forecasts may
not capture differences in growth in long-term growth prospects.
Price to Book (P/B) Ratio

Book value per share, the measure of value in the P/B
ratio, is a stock or level variable coming from the balance
sheet.


Contrast EPS, a flow variable from the income statement
Intuitively, book value per share represents the
investment that common shareholders have made in the
company, on a per-share basis.
Rationales for Use of P/B Ratio

Book value is generally positive even when EPS is negative.


Book value per share is more stable than EPS



P/B may be more meaningful than P/E when EPS are abnormally high or low, or
are highly variable.
Book value per share appropriate for valuing companies composed
chiefly of liquid assets, such as finance, investment, insurance, and
banking institutions.


We can generally use P/B when EPS is negative, whereas P/E based on a
negative EPS is not meaningful.
For such companies, book values of assets may approximate market values.
Book value used to valuation companies not expected to continue
as a going concern.
Differences in P/B ratios may be related to differences in long-run
average returns, according to empirical research.
Possible Drawbacks to P/B Ratios

Other assets besides those recognized in accounting may be critical
operating factors.



P/B can be misleading as a valuation indicator when there are
significant differences among the level of assets employed by
companies.
Accounting effects on book value may compromise book value as a
measure of shareholders’ investment in the company.


For example, in many service companies human is more important than physical
capital as an operating factor.
As one example, book value can understate shareholders’ investment as a result
of the expensing of investment in research and development (R&D). Such
expenditures often positively affect income over many periods and in principle
create assets.
Book value largely reflects the historical purchase costs of assets,
as well as accumulated accounting depreciation expenses.


Inflation as well as technological change eventually drive a wedge between the
book value and the market value of assets.
Book value per share often poorly reflects the value of shareholders’ investments.
Computation of Book Value

Calculation of Book Value:
Shareholders’ Equity – Senior Equity Claims
= Common Shareholders’ Equity
Common Shareholder Equity/Common Stock Shares Outstanding
= Book Value per Share

Possible Senior Claims


value of preferred stock
dividends in arrears on preferred stock

Tangible book value per share




Significant off-balance sheet assets and liabilities
Internationally, accounting methods currently report some
assets/liabilities at historical cost (with some adjustments) and
others at fair value.



Subtracting reported intangible assets from the balance sheet from common
shareholders’ equity
Following financial theory, the general exclusion of intangibles is not warranted
For example, assets such as land or equipment are reported at their historical
acquisitions cost, and in the case of equipment are being depreciated over their
useful lives.
Other assets such as investments in marketable securities are reported at fair
market value.

One company may be using FIFO and a peer company may be using LIFO
Justified P/B Ratio

Fundamental forecasts to estimate a stock’s justified P/B ratio. For example,
using Gordon growth model and sustainable growth rate (g = b  ROE), the
expression for the justified P/B ratio based on the most recent book value
(B0) is
P0 ROE - g
=
B0
r -g


For example, if a business’s ROE is 12 percent, its required rate of return is
10 percent, and its expected growth rate is 7 percent, then its justified P/B
based on fundamentals is (0.12  0.07)/(0.10  0.07) = 1.7.
Further insight into the P/B ratio comes from the residual income model.
The expression for the justified P/B ratio based on the residual income
valuation is
P0
Present value of expected future residual earnings
=1+
B0
B0
Rationales for Price/Sales Ratios

Sales less subject to distortion or manipulation than
other fundamentals such as EPS or book value.


Sales are positive even when EPS is negative.





Therefore, we can use P/S when EPS is negative, whereas P/E based
on a negative EPS is not meaningful.
Sales are generally more stable than EPS


Total sales, as the top line in the income statement, is prior to any
expenses.
EPS reflects operating and financial leverage
P/S is generally more stable than P/E
P/S may be more meaningful than P/E when EPS is abnormally high or
low.
P/S appropriate for valuing the stock of mature, cyclical,
and zero income companies.
Differences in P/S ratios may relate to differences in
long-run average returns
Drawbacks to P/S Ratios

High growth in sales not imply operating
profitably as judged by earnings and cash flow
from operations.



To have value as a going concern, a business must
ultimately generate earnings and cash.
P/S ratio does not reflect differences in cost
structures across companies.
Manipulation potential through revenue
recognition practices
Justified P/S Ratio


Like other multiples, the P/S multiple can be
In terms of the Gordon growth model, we can
state P/S as
P0 (E0 / S0 )(1-b)(1+g)
=
S0
r -g
Rationales for Price/Cash Flow
Ratios

Cash flow less manipulation by management than
earnings.


Cash flow is generally more stable than earnings



Cash flow manipulated only through ‘real’ activities, such as the
sale of receivables.
Price-to-cash flow is generally more stable than P/E.
Avoids issue of differences in accounting conservatism
between companies (differences in the quality of
earnings).
Differences in price to cash flow may be related to
differences in long-run average returns
Drawbacks to Price/Cash Flow
Ratios

Non-cash revenue and net changes in working
capital are ignored.

Free cash flow rather than cash flow as the
appropriate variable for valuation.

We can use P/FCFE ratios but FCFE


More volatile than CF for many businesses, and
More frequently negative than CF.
Common Cash Flow Measures

In practice, use simple approximations to cash flow from
operations:





Earnings-plus-Non-Cash Charges (CF): approximation specifies cash
flow per share as EPS plus per-share depreciation, amortization, and
depletion.
Cash Flow from Operations (CFO)
Free Cash Flow to Equity (FCFE), and
EBITDA, an Estimate of Pre-interest, Pre-tax Operating Cash Flow.
Most frequently, trailing price-to-cash flow ratios are
reported.

Current market price divided by the sum of the most recent four
quarters’ cash flow per share.
Enterprise Value/EBITDA

A P/EBITDA multiple is flawed

EBITDA is a flow to both debt and equity.

Enterprise value to EBITDA is better.

Enterprise value (EV)


Total company value (the market value of debt, common equity,
and preferred equity) minus the value of cash and investments.
EV/EBITDA is a valuation indicator for the overall
company rather than common stock.
Rationales for EV/EBITDA

Comparing companies with different financial leverage



EBITDA is a pre-interest earnings figure,
EPS, which is post-interest.
By adding back depreciation and amortization, EBITDA
controls for differences in depreciation and amortization

EV/EBITDA is frequently used in the valuation of capital-intensive
businesses (for example, cable companies and steel companies).


EBITDA is frequently positive when EPS is negative.
Possible Drawbacks to EV/EBITDA

EBITDA will overestimate cash flow from operations if
working capital is growing.

EBITDA also ignores the effects of differences in
revenue recognition policy on cash flow from operations.

Free cash flow to the firm, which directly reflects the
amount of required capital expenditures, has a stronger
link to valuation theory than EBITDA.

Only if depreciation expenses match capital expenditures do we
expect EBITDA to reflect differences in businesses’ capital
programs.
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