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 2
Approaches to Valuation
Valuation Models
Asset Based Discounted Cashf low Relative Valuation Contingent Claim
Valuation Models Models
Liquidation Equity Sec tor Option to Option to Option to
Value delay expand liquidate
Stable Current Firm
Market
Young Equity in
Replac ement Tw o-s tage firms troubled
Cost Normalized firm
Three-stage
or n-stage Earnings Book Revenues Sec tor Undeveloped
Value specific land
Equity Valuation Firm Valuation
Models Models
Patent Undeveloped
Res erves
Dividends
Cost of capital APV Excess Return
Free Cashflow approach approach Models
to Firm
Aswath Damodaran 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 4
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.
Aswath Damodaran 5
Discounted Cashflow Valuation: Basis for
Approach
t = n CF
Value = t
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.
Aswath Damodaran 6
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
Aswath Damodaran 7
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.
t=n
CF to Equity t
Value of Equity = (1+ k )t
t=1 e
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.
Aswath Damodaran 8
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
CF to Firmt
Value of Firm = (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
Aswath Damodaran 9
Generic DCF Valuation Model
DISCOUNTED CASHFLOW VALUATION
Expe cte d Growth
Cash flows Firm: Growth in
Firm: Pre-debt cash Operating Earnings
flow Equity: Growth in
Equity: After debt Net Income/EPS Firm is in stable growth:
cash flows Grows at con stant rate
forever
Terminal Value
CF1 CF2 CF3 CF4 CF5 CFn
Value .........
Firm: Value of Firm Fore ver
Equity: Value of Equity
Le ngth of Pe riod of High Growth
Disc ount Rate
Firm:Cost of Capital
Equity: Cost of Equity
Aswath Damodaran 10
VALUING ABN AMRO
ROE = 16%
Retention
Ratio =
Dividends 41.56% Expe cte d Growth
EPS = 1.54 Eur 41.56% * g =4%: ROE = 8.95%(=Cost of equity)
* Payout Ratio 58.44% 16% = 6.65% Beta = 1.00
DPS = 0.90 Eur Payout = (1- 4/8.95) = .553
Terminal Value= EPS 6*Payout/(r-g)
= (2.21*.553)/(.0895-.04) = 24.69
EPS 1.64 Eur 1.75 Eur 1.87 Eur 1.99 Eur 2.12 Eur
Value of Equity per
share = 20.48 Eur DPS 0.96 Eur 1.02 Eur 1.09 Eur 1.16 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 Risk Premium
Beta 4%
4.95% + 0.95 X
Average beta for European banks =
0.95 Mature Market Country Risk
4% 0%
Aswath Damodaran 11
Aswath Damodaran 12
Avg Rein vestment Embraer: Status Quo ($)
ra te = 25 .08% Retu rn on Capital
21.85%
Reinvestme nt Rate
25.08% Stable Growth
Curre nt Cashf low to Firm Expe ct e d Growth g = 4.17%; Beta = 1.00;
EBIT(1- t) : $ 4 04 in EBIT ( 1-t) Country Premium= 5%
- Nt CpX 23 .2185*.2508=.0548 Cost of c apital = 8.76%
- Chg WC 9 5.48% ROC= 8.76%; Tax rate=34%
= FCFF $ 372 Reinvestme nt Rate=g /ROC
Reinvestme nt Rate = 32/404= 7.9% =4.17/8 .76= 47.62%
5=
Terminal Value 288/( .0 876-.0417) = 6272
$ Ca shflows
Op. Assets $ 5,2 72 Term Yr
+ Ca sh: 795 Year 1 2 3 4 5 549
- Debt 717 EBIT(1- t) 426 449 474 500 527 - 261
- Mino r. Int. 12 - Reinve stment 107 113 119 126 132 = 288
=Equity 5,34 9 = FCFF 319 336 355 374 395
-Optio ns 28
Value/Sh are $7.47
R$ 2 1.75 $
Discount at Cost o f Ca pital ( WACC) = 10 .52% ( .8 4) + 6.05% ( 0.16) = 9.81%
On October 6, 200 3
Embraer Pr ic e = R$15.5
Cost of Equit y Cost of De bt
10.52% (4 .17%+1%+4%) (1- .3 4) Weights
= 6.05% E = 84% D = 16%
Risk fre e Rate:
$ Risk fr ee Rate= 4 .17% Be ta M ature ma rke t Country Equity Ris k
+ 1.07 X pre mium + Lambda X Premium
4 % 0.27 7.67%
Unlever ed Beta for Firm’s D/E Rel Equity
Sectors : 0.95 Ratio: 19 % Country Defau lt Mkt Vol
Spre ad X
1.28
6.01%
Aswath Damodaran 13
Curr ent Curr ent
Revenue Margin: Stable Growth
$ 3,804 -4 9.82% Cap ex growth s lows Stable
and net cap ex Stable Stable ROC= 7.36%
decr eases Revenue EBITDA/ Reinvest
EBIT Growth: 5% Sales 67.93%
-1 895m Revenue EBITDA/Sales 30%
Growth: -> 30%
NOL: 13.33%
2,076m Terminal Value= 677( .0736- .0 5)
=$ 28,6 83
T erm. Year
Reven ues $3 ,8 04 $5 ,3 26 $6 ,9 23 $8 ,3 08 $9 ,1 39 $1 0,053 $ 11,058 $ 11,94 2 $12 ,6 59 $1 3,292 $1 3,902
EBIT DA ($95) $ 0 $3 46 $8 31 $1 ,3 71 $1 ,8 09 $2 ,3 22 $2 ,5 08 $3 ,0 38 $3 ,5 89 $ 4,18 7
EBIT ( ( ( $
($1,675 ) $1,738 ) $1,565 ) $1,272 ) 3 20 $1 ,0 74 $1 ,5 50 $1 ,6 97 $2 ,1 86 $2 ,6 94 $ 3,24 8
EBIT (1 -t ) ( ( ( $
($1,675 ) $1,738 ) $1,565 ) $1,272 ) 3 20 $1 ,0 74 $1 ,5 50 $1 ,6 97 $2 ,1 86 $2 ,2 76 $ 2,11 1
+ Depreciat ion $1 ,5 80 $1 ,7 38 $1 ,9 11 $2 ,1 02 $1 ,0 51 $7 36 $7 73 $8 11 $8 52 $8 94 $ 9 39
- Cap E x $3 ,4 31 $1 ,7 16 $1 ,2 01 $1 ,2 61 $1 ,3 24 $1 ,3 90 $1 ,4 60 $1 ,5 33 $1 ,6 09 $1 ,6 90 $ 2,35 3
- Chg WC $0 $4 6 $4 8 $4 2 $2 5 $2 7 $3 0 $2 7 $2 1 $1 9 $ 20
Value o f Op Assets $ 5,530FCFF ( (
($3,526 ) $1,761 ) $903 ) ($472 ) $2 2 $3 92 $8 32 $9 49 $1 ,4 07 $1 ,4 61 $ 6 77
+ Ca sh & Non- op $ 2,260 1 2 3 4 5 6 7 8 9 10
= Value of Firm $ 7,790 Fore ver
- Value o f De bt $ 4,923 Beta 3.00 3.00 3.00 3.00 3.00 2.60 2.20 1.80 1.40 1.00
= Value of Equity $ 2867 Co st o f Equity 16 .8 0% 16 .8 0% 16 .8 0% 16 .8 0% 16 .8 0% 15 .2 0% 13 .6 0% 12 .0 0% 10 .4 0% 8.80 %
- Equity Options $ 1 4 Co st o f Debt 12 .8 0% 12 .8 0% 12 .8 0% 12 .8 0% 12 .8 0% 11 .8 4% 10 .8 8% 9.92 % 8.96 % 6.76 %
Value p er share $ 3.22 Debt Ratio 74 .9 1% 74 .9 1% 74 .9 1% 74 .9 1% 74 .9 1% 67 .9 3% 60 .9 5% 53 .9 6% 46 .9 8% 40 .0 0%
Co st o f Cap it al 13 .8 0% 13 .8 0% 13 .8 0% 13 .8 0% 13 .8 0% 12 .9 2% 11 .9 4% 10 .8 8% 9.72 % 7.98 %
Cost of Equit y Cost of De bt Weights
16.80% 4.8%+8 .0%=12.8% Debt= 74.91% - > 40 %
Tax rate = 0% -> 35%
:
Risk fre e Rate
T. Bond rate = 4.8% Global Crossing
Risk Pre mium
Be ta 4% November 2001
+ 3.00> 1.10 X Stock price = $1.86
Inter net/ Operating Curr ent Base Equity Country Ris k
Reta il Lever age D/E: 4 41% Premium Premium
Aswath Damodaran 14
Valuing Global Crossing with Distress
Probability of distress
• Price of 8 year, 12% bond issued by Global Crossing = $ 653
t 8
120(1 Distress ) t 1000(1 Distress ) 8
653
t1
(1.05) t (1.05) 8
• 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
Aswath Damodaran 15
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.
Aswath Damodaran 16
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.
Aswath Damodaran 17
EQUITY VALUATION WITH EQUITY EVA
Firm is in stable gr owth:
Curre nt EVA Expe ct ed Growth Growth r ate = 5%
Net Income = $ 3104 .60 * 20% =12% Retu rn on Equ ity = 15%
- Eq uity cost = $ 1645 Cost of eq uity =9.40 %
Equity EVA = $ 1459
Terminal Value= $2220/(.094-.05) =50,45
Net Income $3,599 $4,031 $4,515 $5,057 $5,664
$1,908
- Eq uity Co st (se e below) $2,137 $2,393 $2,680 $3,002
Exce ss Eq uity Re tur n $1,692 $1,895 $2,122 $2,377 $2,662
Book Equity= 17997
+ PV of EVA= 38334
= Equity EVA=56331 Fore ver
Value/s h = $50.26 Cos
Discount at t of Equity
Cost of Equit y
10.60%
Risk Pre mium
Be ta 4.00%
:
Risk fre e Rate + 1.40 X
5.00%
Base Equity Country Ris k
Premium = 4% Premium=0%
Aswath Damodaran 18
Choosing the rightDiscounted Cashflow Model
Can you estimate cas h flows ? Are the c urre nt earnings What rate is th e fir m gr owing
positive & normal? at cur ren tly?
Yes No Yes No Gr owth ra te of
of eco nomy econo my
Use cur rent Is the cause
Is lever age sta ble or Use divid end ear ning s as tempo rar y? Stable gr owth Are the firm’s
lik ely to cha nge ov er discount mode l base model competitive
time? advan tges time
limited?
Yes No
Stable Unstable
levera ge levera ge Replace curr ent Is the firm Yes No
ear ning s with lik ely to
nor malized sur vive?
ear ning s 3- stage or
FCFE FCFF 2- stage n- stage
model model
Yes No
Adjust Does the fir m
margins over have a lot o f
time to nurs e debt?
fir m to finan cia l
health
No
Yes
Value Eq uity Estimate
as an option liquidation
to liq uida te value
Aswath Damodaran 19
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.
Aswath Damodaran 20
Variations on Multiples
Equity versus Firm Value
• Equity multiples (Price per share or Market value of equity)
• Firm value multiplies (Firm value or Enterprise 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
• Most recent financial year (Current)
• Last four quarters (Trailing)
• Average over last few years (Normalized)
• Expected future year (Forward)
Comparables
• Sector
• Market
Aswath Damodaran 21
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.
Aswath Damodaran 22
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
Aswath Damodaran 23
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?
Aswath Damodaran 24
PE Ratio: Descriptive Statistics
Aswath Damodaran 25
PE: Deciphering the Distribution
Current PE Trailing PE Forward PE
Mean 36.04 34.14 30.79
Standard Error 1.94 2.93 1.15
Median 18.25 17.25 18.52
Standard Deviation 123.36 176.34 57.56
Skewness 23.13 28.40 13.66
Minimum 0.65 1.35 3.30
Maximum 5103.50 6914.50 1414.00
Count 4024 3627 2491
Largest(500) 48.00 39.60 34.49
Smallest(500) 9.38 9.62 12.94
Aswath Damodaran 26
8 Times EBITDA is not cheap…
Aswath Damodaran 27
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.
Aswath Damodaran 28
Relative Value and Fundamentals
Value o f Stock = DPS1/(ke - g)
PE=Payout Ra tio PEG=Payout ratio PBV=ROE (Payout ratio) PS= Net Ma rgin (Payout ratio)
(1 +g)/(r-g) (1 +g)/g(r-g) (1+g)/(r-g) (1 +g)/(r-g)
PE=f(g, payout, risk) PEG=f(g, payou t, risk) PBV=f(ROE,payout, g, risk) PS=f(Net Mgn, payout, g, risk)
Equity Multiple s
Firm M ultiple s
V/FCFF=f(g, WACC) V/EBIT(1-t)=f(g, RIR, WACC) V/EBIT=f(g, RIR, WACC, t) VS=f(Oper Mgn, RIR, g , WACC)
Value/FCFF=(1+g)/ Value/EBIT(1 -t) = (1+g) Value/EBIT=(1+g)(1- VS= Ope r Margin (1-
(WACC-g) (1 - RIR)/(WACC-g) RiR)/(1-t)(WACC-g) RIR) (1+g)/(WACC-g)
Value o f Firm = FCFF /(WACC -g)
1
Aswath Damodaran 29
What to control for...
Multiple Variables that determine it…
PE Ratio Expected Growth, Risk, Payout Ratio
PBV Ratio Return on Equity, Expected Growth, Risk, Payout
PS Ratio Net Margin, Expected Growth, Risk, Payout Ratio
EVV/EBITDA Expected Growth, Reinvestment rate, Cost of capital
EV/ Sales Operating Margin, Expected Growth, Risk, Reinvestment
Aswath Damodaran 30
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.
Aswath Damodaran 31
Comparing PE Ratios across a Sector
Co mpan y Name PE Growth
PT Ind osa t ADR 7.8 0.06
Te le bras ADR 8.9 0.07 5
Te le com Co rp oratio n of Ne w Zeal an d ADR 11 .2 0.11
Te le com Arge ntin a Ste t - Fra nce Tel eco m SA ADR B 12 .5 0.08
He ll eni c Tele co mmun icatio n Org ani za ti on SA A DR 12 .8 0.12
Te le comuni ca ci one s de Chi l e ADR 16 .6 0.08
Swi ssco m A G A DR 18 .3 0.11
Asia Sa te ll i te Tel eco m Hol di ngs A DR 19 .6 0.16
Po rtuga l Te le com SA A DR 20 .8 0.13
Te le fo nos d e Mexi co A DR L 21 .1 0.14
Matav RT ADR 21 .5 0.22
Te lstra ADR 21 .7 0.12
Gi la t Co mmun icatio ns 22 .7 0.31
De utsch e Tel ekom AG ADR 24 .6 0.11
Bri ti sh Tel eco mmun icatio ns PL C A DR 25 .7 0.07
Te le Da nma rk A S A DR 27 0.09
Te le komuni ka si Ind one si a ADR 28 .4 0.32
Ca ble & Wi rel ess P LC ADR 29 .8 0.14
APT S atel li te Hol di ngs A DR 31 0.33
Te le fo ni ca SA ADR 32 .5 0.18
Ro yal KPN NV ADR 35 .7 0.13
Te le com Ital ia SP A A DR 42 .2 0.14
Ni ppo n Tel eg ra ph & Tel ep hon e ADR 44 .3 0.2
Fran ce Te le com SA ADR 45 .2 0.19
Ko rea Tel eco m ADR 71 .3 0.44
Aswath Damodaran 32
PE, Growth and Risk
Dependent variable is: PE
R squared = 66.2% R squared (adjusted) = 63.1%
Variable Coefficient SE t-ratio prob
Constant 13.1151 3.471 3.78 0.0010
Growth rate 121.223 19.27 6.29 ≤ 0.0001
Emerging Market -13.8531 3.606 -3.84 0.0009
Emerging Market is a dummy: 1 if emerging market
0 if not
Aswath Damodaran 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
Adjus t e d R St d. Er ro r o f th e
a
Mo de l R R Sq ua r e Sq ua r e Es tim a te
1 .8 5 6 b .73 3 .73 2 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 St a nd a r diz e d 9 5% Co nf ide n ce Int e rva l f or
Coe f fic ie nt s C oe ffic ie n ts B
Mo de l B Std . Er r or Be t a t Sig . Lo wer Bo un d Up pe r Bo un d
1 Exp e ct e d Gro wth in
1 .2 28 .05 5 .51 4 22 .1 87 .0 0 0 1 .1 19 1.3 3 6
EPS: n e xt 5 ye ar s
Pa yo ut Ra tio - 1 .1 E- 0 2 .01 4 - .01 3 - .7 68 .4 4 3 - .03 9 .0 1 7
e
Va lu e Lin e B ta 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 Ass et
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?
• 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.
When does that real option have significant economic value?
• 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?
• 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
Aswath Damodaran 40
Putting Natural Resource Options to the Test
The Option Test:
• Underlying Asset: Oil or gold in reserve
• Contingency: If value > Cost of development: Value - Dev Cost
If value Cost of development: PV - Cost
If PV of CFs from development Expansion Cost: PV - Expansion Cost
If PV of CF from expansion < Expansion Cost: 0
The Exclusivity Test
• Barriers may range from strong (exclusive licenses granted by the government) to weaker
(brand name, knowledge of the market) to weakest (first mover).
The Pricing Test
• 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 Discou nted Ca shf low Relative Valuatio n Contin gent Claim
Valuation M odels M odels
Liquidation Equity Sec tor Option to Option to Option to
Value delay ex pand liq uid ate
Stable Cur ren t Firm
Mark et
Youn g Equity in
Replac ement Tw o-s tage fir ms troub led
Cost Normalized fir m
Thr ee- stage
or n- stage Ear nings Book Revenues Sec tor Undeveloped
Value sp ecific land
Equity Valu ation Firm Valu ation
Models Models
Patent Undeveloped
Res erv es
Divid ends
Cost of capital APV Excess Return
Fr ee Cash flow ap proach ap proach Models
to Firm
Aswath Damodaran 45
Which approach should you use? Depends
upon the asset being valued..
Asset Marketab ility and Valua tion App roache s
Mature businesses Growth bu sin esses
Separable & marketable assets Linked and non-marketable assets
Liquidation & Other valua tion models
Replacement cost
valuation
Cash Flows and Valuation Approa ches
Cashflo ws cu rren tly o r Cashflo ws if a contingen cy Assets that will never
expe cted in nea r future occu rs generate cashflows
Discounted cashflow Option pricing models Relative valuation mo dels
or re lative valuation
models
Uniqueness of Asset and Va luation Approaches
Large number of simila r
Unique asset or business asse ts tha t are priced
Discounted cashflow Relative valuation mo dels
or optio n pricing
models
Aswath Damodaran 46
And the analyst doing the valuation….
Investor Time Horizo n and Valuation Approaches
Very sho rt time horizon
Long Time Horizon
Liquidation value Relative valuation Option pricing Discounted Cashflow value
models
Views on marke t and Valuatio n Approaches
Marke ts are correct o n Asset markets and finan cial Marke ts make mistakes but
average but make mistakes marke ts may diverge correct them o ver time
on ind ividual a ssets
Relative valuation Liquidation value Discounted Cashflow value
Option pricing models
Aswath Damodaran 47