Valuation Models Aswath Damodaran 1

Valuation Models
Aswath Damodaran
Aswath Damodaran
1
Misconceptions about Valuation

Myth 1: A valuation is an objective search for “true” value
• Truth 1.1: All valuations are biased. The only questions are how much and
in which direction.
• Truth 1.2: The direction and magnitude of the bias in your valuation is
directly proportional to who pays you and how much you are paid.

Myth 2.: A good valuation provides a precise estimate of value
• Truth 2.1: There are no precise valuations
• Truth 2.2: The payoff to valuation is greatest when valuation is least
precise.

Myth 3: . The more quantitative a model, the better the valuation
• Truth 3.1: One’s understanding of a valuation model is inversely
proportional to the number of inputs required for the model.
• Truth 3.2: Simpler valuation models do much better than complex ones.
Aswath Damodaran
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Approaches to Valuation
Valuation Models
Asset Based
Valuation
Discounted Cashflow
Models
Relative Valuation
Liquidation
Value
Equity
Stable
Current
Contingent Claim
Models
Sector
Two-stage
Three-stage
or n-stage
Equity Valuation
Models
Normalized
Earnings
Book Revenues
Value
Sector
specific
Patent
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Option to
liquidate
Young
firms
Equity in
troubled
firm
Undeveloped
land
Firm Valuation
Models
Dividends
Free Cashflow
to Firm
Option to
expand
Firm
Market
Replacement
Cost
Option to
delay
Cost of capital
approach
APV
approach
Undeveloped
Reserves
Excess Return
Models
3
Basis for all valuation approaches

The use of valuation models in investment decisions (i.e., in decisions
on which assets are under valued and which are over valued) are based
upon
•
a perception that markets are inefficient and make mistakes in assessing
value
• an assumption about how and when these inefficiencies will get corrected

In an efficient market, the market price is the best estimate of value.
The purpose of any valuation model is then the justification of this
value.
Aswath Damodaran
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Discounted Cash Flow Valuation



What is it: In discounted cash flow valuation, the value of an asset is
the present value of the expected cash flows on the asset.
Philosophical Basis: Every asset has an intrinsic value that can be
estimated, based upon its characteristics in terms of cash flows, growth
and risk.
Information Needed: To use discounted cash flow valuation, you
need
• to estimate the life of the asset
• to estimate the cash flows during the life of the asset
• to estimate the discount rate to apply to these cash flows to get present
value

Market Inefficiency: Markets are assumed to make mistakes in
pricing assets across time, and are assumed to correct themselves over
time, as new information comes out about assets.
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Discounted Cashflow Valuation: Basis for
Approach
t = n CF
t
Value = 
t
t =1 (1+ r)
where CFt is the cash flow in period t, r is the discount rate appropriate
given the riskiness of the cash flow and t is the life of the asset.
Proposition 1: For an asset to have value, the expected cash flows
have to be positive some time over the life of the asset.
Proposition 2: Assets that generate cash flows early in their life will be
worth more than assets that generate cash flows later; the latter
may however have greater growth and higher cash flows to
compensate.
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Equity Valuation versus Firm Valuation


Value just the equity stake in the business
Value the entire business, which includes, besides equity, the other
claimholders in the firm
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I.Equity Valuation

The value of equity is obtained by discounting expected cashflows to equity, i.e., the
residual cashflows after meeting all expenses, tax obligations and interest and principal
payments, at the cost of equity, i.e., the rate of return required by equity investors in the
firm.
Value of Equity =
t=n CF

t=1
to Equity t
(1+ k e )t
where,
CF to Equityt = Expected Cashflow to Equity in period t
ke = Cost of Equity

Forms: The dividend discount model is a specialized case of equity valuation, and the
value of a stock is the present value of expected future dividends. In the more general
version, you can consider the cashflows left over after debt payments and reinvestment
needs as the free cashflow to equity.
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II. Firm Valuation

Cost of capital approach: The value of the firm is obtained by
discounting expected cashflows to the firm, i.e., the residual cashflows
after meeting all operating expenses and taxes, but prior to debt
payments, at the weighted average cost of capital, which is the cost of
the different components of financing used by the firm, weighted by
their market value proportions.
t= n
Value of Firm =
CF to Firm t
 (1+ WACC)
t
t =1

APV approach: The value of the firm can also be written as the sum
of the value of the unlevered firm and the effects (good and bad) of
debt.
Firm Value = Unlevered Firm Value + PV of tax benefits of debt - Expected
Bankruptcy Cost
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Generic DCF Valuation Model
DISCOUNTED CASHFLOW VALUATION
Expected Growth
Firm: Growth in
Operating Earnings
Equity: Growth in
Net Income/EPS
Cash flows
Firm: Pre-debt cash
flow
Equity: After debt
cash flows
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value
Value
Firm: Value of Firm
CF1
CF2
CF3
CF4
CF5
CFn
.........
Forever
Equity: Value of Equity
Length of Period of High Growth
Discount Rate
Firm:Cost of Capital
Equity: Cost of Equity
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VALUING ABN AMRO
Retention
Ratio =
41.56%
Dividends
EPS =
1.54 Eur
* Payout Ratio 58.44%
DPS = 0.90 Eur
ROE = 16%
Expected Growth
41.56% *
16% = 6.65%
g =4%: ROE = 8.95%(=Cost of equity)
Beta = 1.00
Payout = (1- 4/8.95) = .553
Terminal Value= EPS 6*Payout/(r-g)
= (2.21*.553)/(.0895-.04) = 24.69
Value of Equity per
share = 20.48 Eur
EPS 1.64 Eur
DPS 0.96 Eur
1.75 Eur
1.02 Eur
1.87 Eur
1.09 Eur
1.99 Eur
1.16 Eur
2.12 Eur
1.24 Eur
.........
Forever
Discount at Cost of Equity
Cost of Equity
4.95% + 0.95 (4%) = 8.75%
Riskfree Rate:
Long term bond rate in
Euros
4.95%
+
Beta
0.95
X
Average beta for European banks =
0.95
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Risk Premium
4%
Mature Market
4%
Country Risk
0%
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Avg Reinvestment
rate = 25.08%
Embraer: Status Quo ($)
Reinvestment Rate
25.08%
Current Cashflow to Firm
EBIT(1-t) :
$ 404
- Nt CpX
23
- Chg WC
9
= FCFF
$ 372
Reinvestment Rate = 32/404= 7.9%
Return on Capital
21.85%
Stable Growth
g = 4.17%; Beta = 1.00;
Country Premium= 5%
Cost of capital = 8.76%
ROC= 8.76%; Tax rate=34%
Reinvestment Rate=g/ROC
=4.17/8.76= 47.62%
Expected Growth
in EBIT (1-t)
.2185*.2508=.0548
5.48 %
Terminal Value5= 288/(.0876-.0417) = 6272
$ Cashflows
Op. Assets $ 5,272
+ Cash:
795
- Debt
717
- Minor. Int.
12
=Equity
5,349
-Options
28
Value/Share $7.47
R$ 21.75
Year
EBIT(1-t)
- Reinvestment
= FCFF
1
426
107
319
3
474
119
355
4
500
126
374
Term Yr
549
- 261
= 288
5
527
132
395
Discount at$ Cost of Capital (WACC) = 10.52% (.84) + 6.05% (0.16) = 9.81%
Cost of Equity
10.52 %
Riskfree Rate :
$ Riskfree Rate= 4.17%
On October 6, 2003
Embraer Price = R$15.51
Cost of Debt
(4.17%+1%+4%)(1-.34)
= 6.05%
+
Beta
1.07
Unlevered Beta for
Sectors: 0.95
Aswath Damodaran
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449
113
336
X
Weights
E = 84% D = 16%
Mature market
premium
4%
Firm’s D/E
Ratio: 19%
+
Lambda
0.27
X
Country Equity Risk
Premium
7.67%
Country Default
Spread
6.01%
X
Rel Equity
Mkt Vol
1.28
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Current
Revenue
$ 3,804
Current
Margin:
-49.82%
Stable Growth
Cap ex growth slows
and net cap ex
decreases
EBIT
-1895m
Revenue
Growth:
13.33%
NOL:
2,076m
Stable
Revenue
Growth: 5%
EBITDA/Sales
-> 30%
Stable
EBITDA/
Sales
30%
Stable
ROC=7.36%
Reinvest
67.93%
Terminal Value= 677(.0736-.05)
=$ 28,683
Value of Op Assets $ 5,530
+ Cash & Non-op
$ 2,260
= Value of Firm
$ 7,790
- Value of Debt
$ 4,923
= Value of Equity
$ 2867
- Equity Options
$
14
Value per share
$ 3.22
Revenues
EBITDA
EBIT
EBIT (1-t)
+ Depreciation
- Cap Ex
- Chg WC
FCFF
$3,804
($95)
($1,675)
($1,675)
$1,580
$3,431
$0
($3,526)
1
$5,326
$0
($1,738)
($1,738)
$1,738
$1,716
$46
($1,761)
2
$6,923
$346
($1,565)
($1,565)
$1,911
$1,201
$48
($903)
3
$8,308
$831
($1,272)
($1,272)
$2,102
$1,261
$42
($472)
4
$9,139
$1,371
$320
$320
$1,051
$1,324
$25
$22
5
$10,053 $11,058 $11,942 $12,659 $13,292
$1,809 $2,322 $2,508 $3,038 $3,589
$1,074 $1,550 $1,697 $2,186 $2,694
$1,074 $1,550 $1,697 $2,186 $2,276
$736
$773
$811
$852
$894
$1,390 $1,460 $1,533 $1,609 $1,690
$27
$30
$27
$21
$19
$392
$832
$949
$1,407 $1,461
6
7
8
9
10
Beta
Cos t of Equity
Cos t of Debt
Debt Ratio
Cos t of Capital
3.00
16.80%
12.80%
74.91%
13.80%
3.00
16.80%
12.80%
74.91%
13.80%
3.00
16.80%
12.80%
74.91%
13.80%
3.00
16.80%
12.80%
74.91%
13.80%
3.00
16.80%
12.80%
74.91%
13.80%
2.60
15.20%
11.84%
67.93%
12.92%
Cost of Equity
16.80%
Cost of Debt
4.8%+8.0%=12.8%
Tax rate = 0% -> 35%
Riskfree Rate :
T. Bond rate = 4.8%
+
Beta
3.00> 1.10
Internet/
Retail
Aswath Damodaran
2.20
13.60%
10.88%
60.95%
11.94%
Operating
Leverage
X
1.80
12.00%
9.92%
53.96%
10.88%
1.40
10.40%
8.96%
46.98%
9.72%
Forever
1.00
8.80%
6.76%
40.00%
7.98%
Weights
Debt= 74.91% -> 40%
Global Crossing
November 2001
Stock price = $1.86
Risk Premium
4%
Current
D/E: 441%
Term. Year
$13,902
$ 4,187
$ 3,248
$ 2,111
$ 939
$ 2,353
$ 20
$ 677
Base Equity
Premium
Country Risk
Premium
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Valuing Global Crossing with Distress

Probability of distress
• Price of 8 year, 12% bond issued by Global Crossing = $ 653
120(1  Distress) t 1000(1   Distress) 8

(1.05) t
(1.05) 8
t1
t 8
653  
• Probability of distress = 13.53% a year

• Cumulative
probability of survival over 10 years = (1- .1353)10 = 23.37%

Distress sale value of equity
•
•
•
•

Book value of capital = $14,531 million
Distress sale value = 15% of book value = .15*14531 = $2,180 million
Book value of debt = $7,647 million
Distress sale value of equity = $ 0
Distress adjusted value of equity
• Value of Global Crossing = $3.22 (.2337) + $0.00 (.7663) = $0.75
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Adjusted Present Value Model


In the adjusted present value approach, the value of the firm is written
as the sum of the value of the firm without debt (the unlevered firm)
and the effect of debt on firm value
Firm Value = Unlevered Firm Value + (Tax Benefits of Debt Expected Bankruptcy Cost from the Debt)
• The unlevered firm value can be estimated by discounting the free
cashflows to the firm at the unlevered cost of equity
• The tax benefit of debt reflects the present value of the expected tax
benefits. In its simplest form,
Tax Benefit = Tax rate * Debt
• The expected bankruptcy cost is a function of the probability of
bankruptcy and the cost of bankruptcy (direct as well as indirect) as a
percent of firm value.
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Excess Return Models

You can present any discounted cashflow model in terms of excess
returns, with the value being written as:
• Value = Capital Invested + Present value of excess returns on current
investments + Present value of excess returns on future investments

This model can be stated in terms of firm value (EVA) or equity value.
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EQUITY VALUATION WITH EQUITY EVA
Current EVA
Net Income =
- Equity cost =
Equity EVA =
Expected Growth
.60 * 20% =12%
$ 3104
$ 1645
$ 1459
Net Income
$3,599
- Equity Cost (see below) $1,908
Excess Equity Return
$1,692
Book Equity= 17997
+ PV of EVA= 38334
= Equity EVA=56331
Value/sh = $50.26
$4,031
$2,137
$1,895
Firm is in stable growth:
Growth rate = 5%
Return on Equity = 15%
Cost of equity =9.40%
Terminal Value= $2220/(.094-.05)=50,459
$4,515
$5,057
$5,664
$2,393
$2,680
$3,002
$2,122
$2,377
$2,662
Forever
Discount atCost of Equity
Cost of Equity
10.60%
Riskfree Rate :
5.00%
+
Beta
1.40
X
Risk Premium
4.00%
Base Equity
Premium = 4%
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Country Risk
Premium=0%
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Choosing the right Discounted Cashflow Model
Can you estimate cash flows?
Yes
No
Is leverage stable or
likely to change over
time?
Use dividend
discount model
Are the current earnings
positive & normal?
Yes
No
Use current
earnings as
base
< Growth rate
of economy
Is the cause
temporary?
Yes
Stable
leverage
Unstable
leverage
FCFE
FCFF
What rate is the firm growing
at currently?
Are the firm’s
competitive
advantges time
limited?
Stable growth
model
No
Replace current
earnings with
normalized
earnings
Is the firm
likely to
survive?
Yes
2-stage
model
Yes
No
3-stage or
n-stage
model
No
Adjust
margins over
time to nurse
firm to financial
health
Does the firm
have a lot of
debt?
Yes
Value Equity
as an option
to liquidate
Aswath Damodaran
> Growth rate of
economy
No
Estimate
liquidation
value
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Relative Valuation



What is it?: The value of any asset can be estimated by looking at
how the market prices “similar” or ‘comparable” assets.
Philosophical Basis: The intrinsic value of an asset is impossible (or
close to impossible) to estimate. The value of an asset is whatever the
market is willing to pay for it (based upon its characteristics)
Information Needed: To do a relative valuation, you need
• an identical asset, or a group of comparable or similar assets
• a standardized measure of value (in equity, this is obtained by dividing the
price by a common variable, such as earnings or book value)
• and if the assets are not perfectly comparable, variables to control for the
differences

Market Inefficiency: Pricing errors made across similar or
comparable assets are easier to spot, easier to exploit and are much
more quickly corrected.
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Variations on Multiples

Equity versus Firm Value
•
•

Scaling variable
•
•
•
•

Earnings (EPS, Net Income, EBIT, EBITDA)
Book value (Book value of equity, Book value of assets, Book value of capital)
Revenues
Sector specific variables
Base year
•
•
•
•

Equity multiples (Price per share or Market value of equity)
Firm value multiplies (Firm value or Enterprise value)
Most recent financial year (Current)
Last four quarters (Trailing)
Average over last few years (Normalized)
Expected future year (Forward)
Comparables
•
•
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Sector
Market
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Definitional Tests

Is the multiple consistently defined?
• Proposition 1: Both the value (the numerator) and the standardizing
variable ( the denominator) should be to the same claimholders in the
firm. In other words, the value of equity should be divided by equity
earnings or equity book value, and firm value should be divided by
firm earnings or book value.

Is the multiple uniformally estimated?
• The variables used in defining the multiple should be estimated uniformly
across assets in the “comparable firm” list.
• If earnings-based multiples are used, the accounting rules to measure
earnings should be applied consistently across assets. The same rule
applies with book-value based multiples.
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An Example: Price Earnings Ratio: Definition
PE = Market Price per Share / Earnings per Share



There are a number of variants on the basic PE ratio in use. They are
based upon how the price and the earnings are defined.
Price:
is usually the current price
is sometimes the average price for the year
EPS:
earnings per share in most recent financial year
earnings per share in trailing 12 months (Trailing PE)
forecasted earnings per share next year (Forward PE)
forecasted earnings per share in future year
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Descriptive Tests


What is the average and standard deviation for this multiple, across the
universe (market)?
What is the median for this multiple?
• The median for this multiple is often a more reliable comparison point.

How large are the outliers to the distribution, and how do we deal with
the outliers?
• Throwing out the outliers may seem like an obvious solution, but if the
outliers all lie on one side of the distribution (they usually are large
positive numbers), this can lead to a biased estimate.


Are there cases where the multiple cannot be estimated? Will ignoring
these cases lead to a biased estimate of the multiple?
How has this multiple changed over time?
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PE Ratio: Descriptive Statistics
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PE: Deciphering the Distribution
Mean
Standard Error
Median
Standard Deviation
Skewness
Minimum
Maximum
Count
Largest(500)
Smallest(500)
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Current PE
36.04
1.94
18.25
123.36
23.13
0.65
5103.50
4024
48.00
9.38
Trailing PE
34.14
2.93
17.25
176.34
28.40
1.35
6914.50
3627
39.60
9.62
Forward PE
30.79
1.15
18.52
57.56
13.66
3.30
1414.00
2491
34.49
12.94
26
8 Times EBITDA is not cheap…
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Analytical Tests

What are the fundamentals that determine and drive these multiples?
• Proposition 2: Embedded in every multiple are all of the variables that
drive every discounted cash flow valuation - growth, risk and cash flow
patterns.
• In fact, using a simple discounted cash flow model and basic algebra
should yield the fundamentals that drive a multiple

How do changes in these fundamentals change the multiple?
• The relationship between a fundamental (like growth) and a multiple
(such as PE) is seldom linear. For example, if firm A has twice the growth
rate of firm B, it will generally not trade at twice its PE ratio
• Proposition 3: It is impossible to properly compare firms on a
multiple, if we do not know the nature of the relationship between
fundamentals and the multiple.
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Relative Value and Fundamentals
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 Multiples
Firm Multiples
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)
VS=f(Oper Mgn, RIR, g, WACC)
VS= Oper Margin (1RIR) (1+g)/(WACC-g)
Value of Firm = FCFF 1/(WACC -g)
Aswath Damodaran
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What to control for...
Multiple
Variables that determine it…
PE Ratio
PBV Ratio
PS Ratio
EVV/EBITDA
EV/ Sales
Expected Growth, Risk, Payout Ratio
Return on Equity, Expected Growth, Risk, Payout
Net Margin, Expected Growth, Risk, Payout Ratio
Expected Growth, Reinvestment rate, Cost of capital
Operating Margin, Expected Growth, Risk, Reinvestment
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Application Tests

Given the firm that we are valuing, what is a “comparable” firm?
• While traditional analysis is built on the premise that firms in the same
sector are comparable firms, valuation theory would suggest that a
comparable firm is one which is similar to the one being analyzed in terms
of fundamentals.
• Proposition 4: There is no reason why a firm cannot be compared
with another firm in a very different business, if the two firms have
the same risk, growth and cash flow characteristics.

Given the comparable firms, how do we adjust for differences across
firms on the fundamentals?
• Proposition 5: It is impossible to find an exactly identical firm to the
one you are valuing.
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Comparing PE Ratios across a Sector
Comp any Name
PT Indosat ADR
Te leb ras ADR
Te lecom Corp orati on o f New Zeala nd ADR
Te lecom Arg enti na Stet - France Telecom SA ADR B
Hell enic Te lecommu nicatio n Organ ization SA ADR
Te lecomun ica cio nes de Ch ile ADR
Swisscom AG ADR
Asia Sa tell ite Tele com Holdi ngs ADR
Portugal Tel eco m SA ADR
Te lefo nos de Me xico ADR L
Mata v RT ADR
Te lstra ADR
Gila t Comm unicati ons
Deutsche Telek om AG ADR
British Tel eco mmun ica tion s PL C ADR
Te le Dan mark AS ADR
Te leko muni kasi Ind onesia ADR
Cab le & Wi reless PLC ADR
APT Satel lite Holdi ngs ADR
Te lefo nica SA ADR
Royal KPN NV ADR
Te lecom Italia SPA ADR
Nipp on Teleg raph & Tel epho ne ADR
Fra nce Tel eco m SA ADR
Kore a Te lecom ADR
Aswath Damodaran
PE
7.8
8.9
11 .2
12 .5
12 .8
16 .6
18 .3
19 .6
20 .8
21 .1
21 .5
21 .7
22 .7
24 .6
25 .7
27
28 .4
29 .8
31
32 .5
35 .7
42 .2
44 .3
45 .2
71 .3
Growth
0.06
0.075
0.11
0.08
0.12
0.08
0.11
0.16
0.13
0.14
0.22
0.12
0.31
0.11
0.07
0.09
0.32
0.14
0.33
0.18
0.13
0.14
0.2
0.19
0.44
32
PE, Growth and Risk
Dependent variable is:
R squared = 66.2%
PE
R squared (adjusted) = 63.1%
Variable
Coefficient SE
t-ratio
Constant
13.1151
3.471
3.78
Growth rate
121.223
19.27
6.29
Emerging Market
-13.8531
3.606
-3.84
Emerging Market is a dummy: 1 if emerging market
0 if not
Aswath Damodaran
prob
0.0010
≤ 0.0001
0.0009
33
Is Telebras under valued?


Predicted PE = 13.12 + 121.22 (.075) - 13.85 (1) = 8.35
At an actual price to earnings ratio of 8.9, Telebras is slightly
overvalued.
Aswath Damodaran
34
PE Ratio without a constant - US Stocks
Mo d e l Su mm a ry
Mo de l
1
a
R
R Sq ua r e
.8 5 6 b
.73 3
Adjus t e d R
Sq ua r e
.73 2
St d. Er ro r o f th e
Es tim a te
13 5 0.6 77 6 1 93 1 3
a . Fo r r e g re ss io n t hr ou gh th e or igin (th e n o - int e rc e pt
m od e l), R Squ a r e m e a su r e s t he pr o po rt ion of t he
va r ia b ility in th e de p e n de n t va ria ble a b ou t th e o rig in
ex pla ine d b y r e gr e s sion . T his CANNOT b e c o m p ar ed to R
Sq ua r e fo r m od e ls whic h inc lu d e a n int er c e p t.
b . Pr e d ic tor s: Valu e Line Bet a , P a you t Ra tio , Ex pe c te d
Gr owt h in EPS: ne x t 5 ye a rs
Co e f fici e n ts a,b ,c
Uns t an d ar d iz ed
Coe f fic ie nt s
Mo de l
1
B
Exp e ct e d Gro wth in
EPS: n e xt 5 ye ar s
Pa yo ut Ra tio
Va lu e Lin e Be ta
Std . Er r or
St a nd a r diz e d
C oe ffic ie n ts
Be t a
9 5% Co nf ide n ce Int e rva l f or
B
t
Sig .
Lo wer Bo un d
Up pe r Bo un d
1 .2 28
.05 5
.51 4
22 .1 87
.0 0 0
1 .1 19
1.3 3 6
- 1 .1 E- 0 2
.01 4
- .01 3
- .7 68
.4 4 3
- .03 9
.0 1 7
1 1. 70 5
.82 5
.38 4
14 .1 84
.0 0 0
1 0. 08 7
13 .3 24
a . De p e nd e n t Va r ia b le : Cu r re nt PE
b . Line a r Re g r e ss ion t hr ou gh th e Orig in
c . We igh te d Le a st Sq u ar e s Re g re ss ion - We ig h te d by Ma r ke t Ca p
Aswath Damodaran
35
Relative Valuation: Choosing the Right Model
Aswath Damodaran
36
Contingent Claim (Option) Valuation

Options have several features
• They derive their value from an underlying asset, which has value
• The payoff on a call (put) option occurs only if the value of the underlying
asset is greater (lesser) than an exercise price that is specified at the time
the option is created. If this contingency does not occur, the option is
worthless.
• They have a fixed life

Any security that shares these features can be valued as an option.
Aswath Damodaran
37
Option Payoff Diagrams
Strike Price
Value of Asset
Put Option
Call Option
Aswath Damodaran
38
Underlying Theme: Searching for an Elusive
Premium

Traditional discounted cashflow models under estimate the value of
investments, where there are options embedded in the investments to
• Delay or defer making the investment (delay)
• Adjust or alter production schedules as price changes (flexibility)
• Expand into new markets or products at later stages in the process, based
upon observing favorable outcomes at the early stages (expansion)
• Stop production or abandon investments if the outcomes are unfavorable
at early stages (abandonment)

Put another way, real option advocates believe that you should be
paying a premium on discounted cashflow value estimates.
Aswath Damodaran
39
Three Basic Questions

When is there a real option embedded in a decision or an asset?
•
•

When does that real option have significant economic value?
•
•

There has to be a clearly defined underlying asset whose value changes over time
in unpredictable ways.
The payoffs on this asset (real option) have to be contingent on an specified event
occurring within a finite period.
For an option to have significant economic value, there has to be a restriction on
competition in the event of the contingency.
At the limit, real options are most valuable when you have exclusivity - you and
only you can take advantage of the contingency. They become less valuable as the
barriers to competition become less steep.
Can that value be estimated using an option pricing model?
•
•
•
Aswath Damodaran
The underlying asset is traded - this yield not only observable prices and volatility
as inputs to option pricing models but allows for the possibility of creating
replicating portfolios
An active marketplace exists for the option itself.
The cost of exercising the option is known with some degree of certaint
40
Putting Natural Resource Options to the Test

The Option Test:
•
•

The Exclusivity Test:
•
•

Natural resource reserves are limited (at least for the short term)
It takes time and resources to develop new reserves
The Option Pricing Test
•
•
•

Underlying Asset: Oil or gold in reserve
Contingency: If value > Cost of development: Value - Dev Cost
If value < Cost of development: 0
Underlying Asset: While the reserve or mine may not be traded, the commodity is. If we
assume that we know the quantity with a fair degree of certainty, you can trade the underlying
asset
Option: Oil companies buy and sell reserves from each other regularly.
Cost of Exercising the Option: This is the cost of developing a reserve. Given the experience
that commodity companies have with this, they can estimate this cost with a fair degree of
precision.
Bottom Line: Real option pricing models work well with natural resource options.
Aswath Damodaran
41
The Real Options Test: Patents and Technology

The Option Test:
•
•
Underlying Asset: Product that would be generated by the patent
Contingency:
If PV of CFs from development > Cost of development: PV - Cost
If PV of CFs from development < Cost of development: 0

The Exclusivity Test:
•
•

The Pricing Test
•
•
•

Patents restrict competitors from developing similar products
Patents do not restrict competitors from developing other products to treat the same disease.
Underlying Asset: Patents are not traded. Not only do you therefore have to estimate the present
values and volatilities yourself, you cannot construct replicating positions or do arbitrage.
Option: Patents are bought and sold, though not as frequently as oil reserves or mines.
Cost of Exercising the Option: This is the cost of converting the patent for commercial
production. Here, experience does help and drug firms can make fairly precise estimates of the
cost.
Bottom Line: Use real option pricing arguments with caution.
Aswath Damodaran
42
The Real Options Test for Growth (Expansion)
Options

The Options Test
• Underlying Asset: Expansion Project
• Contingency
If PV of CF from expansion > Expansion Cost: PV - Expansion Cost
If PV of CF from expansion < Expansion Cost: 0

The Exclusivity Test
•

The Pricing Test
•
•
•

Barriers may range from strong (exclusive licenses granted by the government) to weaker
(brand name, knowledge of the market) to weakest (first mover).
Underlying Asset: As with patents, there is no trading in the underlying asset and you have to
estimate value and volatility.
Option: Licenses are sometimes bought and sold, but more diffuse expansion options are not.
Cost of Exercising the Option: Not known with any precision and may itself evolve over time
as the market evolves.
Bottom Line: Using option pricing models to value expansion options will not only
yield extremely noisy estimates, but may attach inappropriate premiums to discounted
cashflow estimates.
Aswath Damodaran
43
Summarizing the Real Options Argument




There are real options everywhere.
Most of them have no significant economic value because there is no
exclusivity associated with using them.
When options have significant economic value, the inputs needed to
value them in a binomial model can be used in more traditional
approaches (decision trees) to yield equivalent value.
The real value from real options lies in
• Recognizing that building in flexibility and escape hatches into large
decisions has value
• Insights we get on understanding how and why companies behave the way
they do in investment analysis and capital structure choices.
Aswath Damodaran
44
Valuation Models
Asset Based
Valuation
Discounted Cashflow
Models
Relative Valuation
Liquidation
Value
Equity
Stable
Current
Contingent Claim
Models
Sector
Two-stage
Three-stage
or n-stage
Equity Valuation
Models
Normalized
Earnings
Book Revenues
Value
Sector
specific
Dividends
Cost of capital
approach
Aswath Damodaran
Option to
liquidate
Young
firms
Equity in
troubled
firm
Undeveloped
land
Firm Valuation
Models
Patent
Free Cashflow
to Firm
Option to
expand
Firm
Market
Replacement
Cost
Option to
delay
APV
approach
Undeveloped
Reserves
Excess Return
Models
45
Which approach should you use? Depends
upon the asset being valued..
Asset Marketability and Valuation Approaches
Mature businesses
Separable & marketable assets
Growth businesses
Linked and non-marketable assets
Liquidation &
Replacement cost
valuation
Other valuation models
Cash Flows and Valuation Approaches
Cashflows currently or
expected in near future
Discounted cashflow
or relative valuation
models
Cashflows if a contingency
occurs
Option pricing models
Assets that will never
generate cashflows
Relative valuation models
Uniqueness of Asset and Valuation Approaches
Unique asset or business
Discounted cashflow
or option pricing
models
Aswath Damodaran
Large number of similar
assets that are priced
Relative valuation models
46
And the analyst doing the valuation….
Investor Time Horizon and Valuation Approaches
Very short time horizon
Liquidation value
Long Time Horizon
Relative valuation
Option pricing
models
Discounted Cashflow value
Views on market and Valuation Approaches
Markets are correct on
average but make mistakes
on individual assets
Relative valuation
Asset markets and financial
markets may diverge
Liquidation value
Markets make mistakes but
correct them over time
Discounted Cashflow value
Option pricing models
Aswath Damodaran
47
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