Aswath Damodaran

VALUATION: LECTURE NOTE PACKET 1

INTRINSIC VALUATION
Aswath Damodaran
Updated: January 2015

The essence of intrinsic value

2

In intrinsic valuaJon, you value an asset based upon its

intrinsic characterisJcs.
For cash ow generaJng assets, the intrinsic value will
be a funcJon of the magnitude of the expected cash
ows on the asset over its lifeJme and the uncertainty
about receiving those cash ows.
Discounted cash ow valuaJon is a tool for esJmaJng
intrinsic value, where the expected value of an asset is
wriRen as the present value of the expected cash ows
on the asset, with either the cash ows or the discount
rate adjusted to reect the risk.

Aswath Damodaran

The two faces of discounted cash ow valuaJon

3

The value of a risky asset can be esJmated by discounJng the

expected cash ows on the asset over its life at a risk-adjusted
discount rate:

where the asset has a n-year life, E(CFt) is the expected cash ow in period t
and r is a discount rate that reects the risk of the cash ows.

AlternaJvely, we can replace the expected cash ows with the

guaranteed cash ows we would have accepted as an alternaJve
(certainty equivalents) and discount these at the riskfree rate:

where CE(CFt) is the certainty equivalent of E(CFt) and rf is the riskfree rate.

Aswath Damodaran

Risk Adjusted Value: Two Basic ProposiJons

4

If the value of an asset is the risk-adjusted present value of the cash ows:

1.

2.

3.

The IT proposiJon: If IT does not aect the expected cash ows or the
riskiness of the cash ows, IT cannot aect value.
The DUH proposiJon: For an asset to have value, the expected cash ows
have to be posiJve some Jme over the life of the asset.
The DONT FREAK OUT proposiJon: Assets that generate cash ows early in
their life will be worth more than assets that generate cash ows later; the
laRer may however have greater growth and higher cash ows to compensate.

Aswath Damodaran

DCF Choices: Equity ValuaJon versus Firm

ValuaJon
5

Firm Valuation: Value the entire business

Assets
Existing Investments
Generate cashflows today
Includes long lived (fixed) and
short-lived(working
capital) assets
Expected Value that will be
created by future investments

Liabilities

Assets in Place

Debt

Growth Assets

Equity

Fixed Claim on cash flows

Little or No role in management
Fixed Maturity
Tax Deductible

Residual Claim on cash flows

Significant Role in management
Perpetual Lives

Equity valuation: Value just the

equity claim in the business

Aswath Damodaran

Equity ValuaJon
6

Figure 5.5: Equity Valuation

Assets
Cash flows considered are
cashflows from assets,
after debt payments and
after making reinvestments
needed for future growth

Assets in Place

Growth Assets

Liabilities
Debt

Equity

Discount rate reflects only the

cost of raising equity financing

Present value is value of just the equity claims on the firm

Aswath Damodaran

Firm ValuaJon
7

Figure 5.6: Firm Valuation

Assets
Cash flows considered are
cashflows from assets,
prior to any debt payments
but after firm has
reinvested to create growth
assets

Assets in Place

Growth Assets

Liabilities
Debt

Equity

Discount rate reflects the cost

of raising both debt and equity
financing, in proportion to their
use

Present value is value of the entire firm, and reflects the value of
all claims on the firm.

Aswath Damodaran

Firm Value and Equity Value

8

a.
b.
c.
d.

a.
b.
c.

To get from rm value to equity value, which of the following

would you need to do?
Subtract out the value of long term debt
Subtract out the value of all debt
Subtract the value of any debt that was included in the cost of
capital calculaJon
Subtract out the value of all liabiliJes in the rm
Doing so, will give you a value for the equity which is
greater than the value you would have got in an equity valuaJon
lesser than the value you would have got in an equity valuaJon
equal to the value you would have got in an equity valuaJon

Aswath Damodaran

Cash Flows and Discount Rates

9

Assume that you are analyzing a company with the following

cashows for the next ve years.
Year CF to Equity
Interest Exp (1-tax rate)
1

$ 50

$ 40

2

$ 60

$ 40

3

$ 68

$ 40

4

$ 76.2
$ 40

5

$ 83.49
$ 40

Terminal Value $ 1603.0

CF to Firm
$ 90
$ 100
$ 108
$ 116.2
$ 123.49
$ 2363.008

Assume also that the cost of equity is 13.625% and the rm can
borrow long term at 10%. (The tax rate for the rm is 50%.)
The current market value of equity is $1,073 and the value of debt
outstanding is $800.

Aswath Damodaran

Equity versus Firm ValuaJon

10

Method 1: Discount CF to Equity at Cost of Equity to get value

of equity

Cost of Equity = 13.625%

Value of Equity = 50/1.13625 + 60/1.136252 + 68/1.136253 +
76.2/1.136254 + (83.49+1603)/1.136255 = $1073

Method 2: Discount CF to Firm at Cost of Capital to get value

of rm
Cost of Debt = Pre-tax rate (1- tax rate) = 10% (1-.5) = 5%
Cost of Capital = 13.625% (1073/1873) + 5% (800/1873) = 9.94%
PV of Firm = 90/1.0994 + 100/1.09942 + 108/1.09943 + 116.2/1.09944 +
(123.49+2363)/1.09945 = $1873

Value of Equity = Value of Firm - Market Value of Debt


= $ 1873 - $ 800 = $1073

Aswath Damodaran

10

First Principle of ValuaJon

11

DiscounJng Consistency Principle: Never mix and

match cash ows and discount rates.
Mismatching cash ows to discount rates is deadly.

DiscounJng cashows aper debt cash ows (equity cash

ows) at the weighted average cost of capital will lead to

an upwardly biased esJmate of the value of equity
DiscounJng pre-debt cashows (cash ows to the rm) at
the cost of equity will yield a downward biased esJmate of
the value of the rm.

Aswath Damodaran

11

The Eects of Mismatching Cash Flows and

Discount Rates
12

Error 1: Discount CF to Equity at Cost of Capital to get equity

value

Error 2: Discount CF to Firm at Cost of Equity to get rm value

PV of Equity = 50/1.0994 + 60/1.09942 + 68/1.09943 + 76.2/1.09944 +

(83.49+1603)/1.09945 = $1248
Value of equity is overstated by $175.
PV of Firm = 90/1.13625 + 100/1.136252 + 108/1.136253 +
116.2/1.136254 + (123.49+2363)/1.136255 = $1613

PV of Equity = $1612.86 - $800 = $813
Value of Equity is understated by $ 260.

Error 3: Discount CF to Firm at Cost of Equity, forget to

subtract out debt, and get too high a value for equity

Value of Equity = $ 1613

Value of Equity is overstated by $ 540

Aswath Damodaran

12

Discounted Cash Flow ValuaJon: The Steps

13

EsJmate the discount rate or rates to use in the valuaJon

1.
1.
2.
3.

2.

3.

4.

5.

Discount rate can be either a cost of equity (if doing equity valuaJon) or a cost of
capital (if valuing the rm)
Discount rate can be in nominal terms or real terms, depending upon whether
the cash ows are nominal or real
Discount rate can vary across Jme.

EsJmate the current earnings and cash ows on the asset, to either
equity investors (CF to Equity) or to all claimholders (CF to Firm)
EsJmate the future earnings and cash ows on the rm being valued,
generally by esJmaJng an expected growth rate in earnings.
EsJmate when the rm will reach stable growth and what
characterisJcs (risk & cash ow) it will have when it does.
Choose the right DCF model for this asset and value it.

Aswath Damodaran

13

Generic DCF ValuaJon Model

14

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

Aswath Damodaran

14

Same ingredients, dierent approaches

15

Input

Dividend Discount
Model

FCFE (Poten;al
FCFF (rm)
dividend) discount valua;on model
model

Cash ow

Dividend

PotenJal dividends
= FCFE = Cash ows
aper taxes,
reinvestment needs
and debt cash ows

FCFF = Cash ows

before debt
payments but aper
reinvestment needs
and taxes.

Expected growth

In equity income
and dividends

In equity income
and FCFE

In operaJng
income and FCFF

Discount rate

Cost of equity

Cost of equity

Cost of capital

Steady state

When dividends
grow at constant
rate forever

When FCFE grow at When FCFF grow at

constant rate
constant rate
forever
forever

Aswath Damodaran

15

Start easy: The Dividend Discount Model

16

Expected
growth in net
income

Net Income
* Payout ratio
= Dividends

Expected dividends = Expected net

income * (1- Retention ratio)

Length of high growth period: PV of dividends during

high growth
Value of equity
Cost of Equity
Rate of return
demanded by equity
investors

Aswath Damodaran

Retention ratio
needed to
sustain growth

Stable Growth
When net income and
dividends grow at constant
rate forever.

16

Moving on up: The potenJal dividends or

FCFE model
17

Expected growth in
net income
Free Cashflow to Equity
Non-cash Net Income
- (Cap Ex - Depreciation)
- Change in non-cash WC
- (Debt repaid - Debt issued)
= Free Cashflow to equity

Value of Equity in non-cash Assets

+ Cash
= Value of equity

Equity reinvestment
needed to sustain
growth

Expected FCFE = Expected net income *

(1- Equity Reinvestment rate)

Length of high growth period: PV of FCFE during high

growth

Stable Growth
When net income and FCFE
grow at constant rate forever.

Cost of equity
Rate of return
demanded by equity
investors

Aswath Damodaran

17

To valuing the enJre business: The FCFF model

18

Expected growth in
operating ncome
Free Cashflow to Firm
After-tax Operating Income
- (Cap Ex - Depreciation)
- Change in non-cash WC
= Free Cashflow to firm

Value of Operatng Assets

+ Cash & non-operating assets
- Debt
= Value of equity

Reinvestment
needed to sustain
growth

Expected FCFF= Expected operating

income * (1- Reinvestment rate)

Length of high growth period: PV of FCFF during high

growth

Stable Growth
When operating income and
FCFF grow at constant rate
forever.

Cost of capital
Weighted average of
costs of equity and
debt

Aswath Damodaran

18

Aswath Damodaran

DISCOUNTED CASH FLOW

VALUATION: THE INPUTS
Aswath Damodaran

19

Aswath Damodaran

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I. ESTIMATING DISCOUNT RATES

Discount rates maRer, but not as much as you think
they do!

EsJmaJng Inputs: Discount Rates

21

While discount rates obviously maRer in DCF valuaJon, they

dont maRer as much as most analysts think they do.
At an intuiJve level, the discount rate used should be
consistent with both the riskiness and the type of cashow
being discounted.

Equity versus Firm: If the cash ows being discounted are cash ows to
equity, the appropriate discount rate is a cost of equity. If the cash
ows are cash ows to the rm, the appropriate discount rate is the
cost of capital.
Currency: The currency in which the cash ows are esJmated should
also be the currency in which the discount rate is esJmated.
Nominal versus Real: If the cash ows being discounted are nominal
cash ows (i.e., reect expected inaJon), the discount rate should be
nominal

Aswath Damodaran

21

Risk in the DCF Model

22

Risk Adjusted
Cost of equity

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Risk free rate in the

currency of analysis

Relative risk of
company/equity in
questiion

Equity Risk Premium

required for average risk
equity

22

Not all risk is created equal

23

EsJmaJon versus Economic uncertainty

Micro uncertainty versus Macro uncertainty

EsJmaJon uncertainty reects the possibility that you could have the wrong
model or esJmated inputs incorrectly within this model.
Economic uncertainty comes the fact that markets and economies can change over
Jme and that even the best models will fail to capture these unexpected changes.
Micro uncertainty refers to uncertainty about the potenJal market for a rms
products, the compeJJon it will face and the quality of its management team.
Macro uncertainty reects the reality that your rms fortunes can be aected by
changes in the macro economic environment.

Discrete versus conJnuous uncertainty

Discrete risk: Risks that lie dormant for periods but show up at points in Jme.
(Examples: A drug working its way through the FDA pipeline may fail at some stage
of the approval process or a company in Venezuela may be naJonalized)
ConJnuous risk: Risks changes in interest rates or economic growth occur
conJnuously and aect value as they happen.

Aswath Damodaran

23

Risk and Cost of Equity: The role of the marginal

investor
24

Not all risk counts: While the noJon that the cost of equity should
be higher for riskier investments and lower for safer investments is
intuiJve, what risk should be built into the cost of equity is the
quesJon.
Risk through whose eyes? While risk is usually dened in terms of
the variance of actual returns around an expected return, risk and
return models in nance assume that the risk that should be
rewarded (and thus built into the discount rate) in valuaJon should
be the risk perceived by the marginal investor in the investment
The diversicaJon eect: Most risk and return models in nance
also assume that the marginal investor is well diversied, and that
the only risk that he or she perceives in an investment is risk that
cannot be diversied away (i.e, market or non-diversiable risk). In
eect, it is primarily economic, macro, conJnuous risk that should
be incorporated into the cost of equity.

Aswath Damodaran

24

The Cost of Equity: CompeJng Market Risk

Models
25

Model Expected Return

CAPM E(R) = Rf + (Rm- Rf)






APM E(R) = Rf + j (Rj- Rf)






MulJ E(R) = Rf + j (Rj- Rf)
factor





Proxy E(R) = a + bj Yj



Aswath Damodaran

Inputs Needed
Riskfree Rate
Beta relaJve to market porvolio
Market Risk Premium
Riskfree Rate; # of Factors;
Betas relaJve to each factor
Factor risk premiums
Riskfree Rate; Macro factors
Betas relaJve to macro factors
Macro economic risk premiums
Proxies
Regression coecients
25

The CAPM: Cost of Equity

26

Consider the standard approach to esJmaJng cost

of equity:
Cost of Equity = Riskfree Rate + Equity Beta * (Equity Risk
Premium)

In pracJce,
Government security rates are used as risk free rates
Historical risk premiums are used for the risk premium
Betas are esJmated by regressing stock returns against

market returns

Aswath Damodaran

26

I. A Riskfree Rate
27

On a riskfree asset, the actual return is equal to the

expected return. Therefore, there is no variance around
the expected return.
For an investment to be riskfree, then, it has to have
No default risk
No reinvestment risk

1.

2.

Time horizon maRers: Thus, the riskfree rates in

valuaJon will depend upon when the cash ow is
expected to occur and will vary across Jme.
Not all government securiJes are riskfree: Some
governments face default risk and the rates on bonds
issued by them will not be riskfree.

Aswath Damodaran

27

Test 1: A riskfree rate in US dollars!

28

In valuaJon, we esJmate cash ows forever (or at

least for very long Jme periods). The right risk free
rate to use in valuing a company in US dollars would
be
a.
b.
c.
d.
e.

A three-month Treasury bill rate (0.2%)

A ten-year Treasury bond rate (2%)
A thirty-year Treasury bond rate (3%)
A TIPs (inaJon-indexed treasury) rate (1%)
None of the above

Aswath Damodaran

28

Test 2: A Riskfree Rate in Euros

29

Euro Government Bond Rates - January 1, 2015

10.00%
9.00%
8.00%
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
0.00%

Aswath Damodaran

29

Test 3: A Riskfree Rate in Indian Rupees

30

The Indian government had 10-year Rupee bonds

outstanding, with a yield to maturity of about 7.87% on
January 1, 2015.
In January 2015, the Indian government had a local currency
sovereign raJng of Baa3. The typical default spread (over a
default free rate) for Baa3 rated country bonds in early 2014
was 2.2%. The riskfree rate in Indian Rupees is
a.
b.
c.
d.

The yield to maturity on the 10-year bond (5.67%)

The yield to maturity on the 10-year bond + Default spread (10.07%)
The yield to maturity on the 10-year bond Default spread (7.87%)
None of the above

Aswath Damodaran

30

Sovereign Default Spread: Three paths to the

same desJnaJon
31

Sovereign dollar or euro denominated bonds: Find

sovereign bonds denominated in US dollars, issued
by emerging markets. The dierence between the
interest rate on the bond and the US treasury bond
rate should be the default spread.
CDS spreads: Obtain the default spreads for
sovereigns in the CDS market.
Average spread: For countries which dont issue
dollar denominated bonds or have a CDS spread,
you have to use the average spread for other
countries in the same raJng class.

Aswath Damodaran

31

Local Currency Government Bond Rates

January 2015
32
Currency
Australian $
BriJsh Pound
Bulgarian Lev
Canadian $
Chilean Peso
Chinese Yuan
Colombian Peso
Czech Koruna
Danish Krone
Euro
HK $
Hungarian Forint
Iceland Krona
Indian Rupee
Indonesian Rupiah
Israeli Shekel
Japanese Yen
Kenyan Shilling
Korean Won
Kuna
Malyasian Ringgit

Aswath Damodaran

Govt Bond Rate (1/1/15 Currency

2.81%
Mexican Peso
1.73%
Naira
3.15%
Norwegian Krone
1.79%
NZ $
4.30%
Pakistani Rupee
3.65%
Peruvian Sol
7.17%
Phillipine Peso
0.47%
Polish Zloty
0.79%
Reai (Brazil)
0.54%
Romanian Leu
1.97%
Russian Ruble
3.69%
Singapore $
6.15%
South African Rand
7.87%
Swedish Krona
7.81%
Swiss Franc
2.30%
Taiwanese $
0.33%
Thai Baht
12.35%
Turkish Lira
2.60%
US $
3.78%
Venezuelan Bolivar
4.13%
Vietnamese Dong

Govt Bond Rate (1/1/15)

5.83%
15.13%
1.51%
3.67%
10.00%
5.43%
4.37%
2.53%
12.42%
3.68%
14.09%
2.33%
7.80%
0.90%
0.31%
1.61%
2.91%
8.09%
2.12%
10.05%
7.15%

32

Approach 1: Default spread from Government

Bonds

The Brazil Default Spread

Brazil 2020 Bond: 3.20%
US 2020 T.Bond: 1.65%
Spread:
1.55%

33

Approach 2: CDS Spreads January 2015

34
Country
Abu Dhabi
ArgenJna
Australia
Austria
Bahrain
Belgium
Brazil
Bulgaria
Chile
China
Colombia
Costa Rica
CroaJa
Cyprus
Czech Republic
Egypt
Estonia
Finland
France
Germany
Greece
Hong Kong

Moody's
CDS Spread
CDS Spread
Country
ra;ng
adj for US
Aa2
Caa1
Aaa
Aaa
Baa2
Aa3
Baa2
Baa2
Aa3
Aa3
Baa2
Ba1
Ba1
B3
A1
Caa1
A1
Aaa
Aa1
Aaa
Caa1
Aa1

1.43%
83.48%
0.97%
0.81%
3.18%
1.20%
3.17%
2.99%
1.77%
1.78%
2.57%
3.58%
3.65%
6.35%
1.25%
3.56%
1.20%
0.81%
1.22%
0.74%
10.76%
1.12%

Aswath Damodaran

1.12%
83.17%
0.66%
0.50%
2.87%
0.89%
2.86%
2.68%
1.46%
1.47%
2.26%
3.27%
3.34%
6.04%
0.94%
3.25%
0.89%
0.50%
0.91%
0.43%
10.45%
0.81%

Hungary
Iceland
India
Indonesia
Ireland
Israel
Italy
Japan
Kazakhstan
Korea
Latvia
Lebanon
Lithuania
Malaysia
Mexico
Netherlands
New Zealand
Norway
Pakistan
Panama
Peru
Philippines

Moody's
CDS Spread
CDS Spread
Country
ra;ng
adj for US
Ba1
Baa3
Baa3
Baa3
Baa1
A1
Baa2
A1
Baa2
Aa3
Baa1
B2
Baa1
A3
A3
Aaa
Aaa
Aaa
Caa1
Baa2
A3
Baa2

2.64%
2.27%
2.64%
2.82%
1.26%
0.42%
2.34%
1.55%
4.16%
1.17%
1.92%
4.69%
1.88%
2.15%
2.05%
0.78%
1.01%
0.61%
10.41%
2.09%
2.23%
1.98%

2.33%
1.96%
2.33%
2.51%
0.95%
0.11%
2.03%
1.24%
3.85%
0.86%
1.61%
4.38%
1.57%
1.84%
1.74%
0.47%
0.70%
0.30%
10.10%
1.78%
1.92%
1.67%

Poland
Portugal
Qatar
Romania
Russia
Saudi Arabia
Slovakia
Slovenia
South Africa
Spain
Sweden
Switzerland
Thailand
Tunisia
Turkey
Ukraine
United Arab Emirates
United Kingdom
United States of America
Venezuela
Vietnam

Moody's
CDS Spread
CDS Spread
ra;ng
adj for US
A2
Ba1
Aa2
Baa3
Baa2
Aa3
A2
Ba1
Baa2
Baa2
Aaa
Aaa
Baa1
Ba3
Baa3
Caa3
Aa2
Aa1
Aaa
Caa1
B1

1.46%
3.09%
1.57%
2.23%
5.63%
1.39%
1.32%
2.14%
2.96%
1.79%
0.65%
0.72%
1.91%
3.38%
2.77%
15.74%
1.54%
0.77%
0.31%
18.06%
3.15%

1.15%
2.78%
1.26%
1.92%
5.32%
1.08%
1.01%
1.83%
2.65%
1.48%
0.34%
0.41%
1.60%
3.07%
2.46%
15.43%
1.23%
0.46%
0.00%
17.75%
2.84%

34

Approach 3: Typical Default Spreads: January

2014
35

Aswath Damodaran

Sovereign
Rating
Aaa
Aa1
Aa2
Aa3
A1
A2
A3
Baa1
Baa2
Baa3
Ba1
Ba2
Ba3
B1
B2
B3
Caa1
Caa2
Caa3

Default Spread
over riskfree
0.00%
0.40%
0.50%
0.60%
0.70%
0.85%
1.20%
1.60%
1.90%
2.20%
2.50%
3.00%
3.60%
4.50%
5.50%
6.50%
7.50%
9.00%
10.00%

35

Ge}ng to a risk free rate in a currency: Example

36

The Brazilian government bond rate in nominal reais in

January 2015 was 12.42%. To get to a riskfree rate in nominal
reais, we can use one of three approaches.

Approach 1: Government Bond spread

The 2020 Brazil bond, denominated in US dollars, has a spread of
1.55% over the US treasury bond rate.
Riskfree rate in $R = 12.42% - 1.55%% = 10.87%
Approach 2: The CDS Spread
The CDS spread for Brazil, adjusted for the US CDS spread, on
January 1, 2015 was 2.86%.
Riskfree rate in $R = 12.42% - 2.86% = 9.56%
Approach 3: The RaJng based spread
Brazil has a Baa2 local currency raJng from Moodys. The default
spread for that raJng is 1.90%
Riskfree rate in $R = 12.42% - 1.90% = 10.52%

Aswath Damodaran

36

Test 4: A Real Riskfree Rate

37

In some cases, you may want a riskfree rate in real terms

(in real terms) rather than nominal terms.
To get a real riskfree rate, you would like a security with
no default risk and a guaranteed real return. Treasury
indexed securiJes oer this combinaJon.
In January 2015, the yield on a 10-year indexed treasury
bond was 1.00%. Which of the following statements
would you subscribe to?
This (1.00%) is the real riskfree rate to use, if you are valuing
US companies in real terms.
b. This (1.00%) is the real riskfree rate to use, anywhere in the
world
Explain.
a.

Aswath Damodaran

37

No default free enJty: Choices with riskfree

rates.
38

EsJmate a range for the riskfree rate in local terms:

Do the analysis in real terms (rather than nominal terms) using a

real riskfree rate, which can be obtained in one of two ways

Approach 1: Subtract default spread from local government bond rate:

Government bond rate in local currency terms - Default spread for
Government in local currency
Approach 2: Use forward rates and the riskless rate in an index currency
(say Euros or dollars) to esJmate the riskless rate in the local currency.

from an inaJon-indexed government bond, if one exists

set equal, approximately, to the long term real growth rate of the
economy in which the valuaJon is being done.

Do the analysis in a currency where you can get a riskfree rate, say
US dollars or Euros.

Aswath Damodaran

38

Risk free Rate: Dont have or trust the

government bond rate?
1.

Build up approach: The risk free rate in any currency can be

wriRen as the sum of two variables:
Risk free rate = Expected InaJon in currency + Expected real interest rate
The expected real interest rate can be computed in one of two ways: from
the US TIPs rate or set equal to real growth in the economy. Thus, if the
expected inaJon rate in a country is expected to be 15% and the TIPs rate
is 1%, the risk free rate is 16%.

2.

US $ rate & DierenJal InaJon: AlternaJvely, you can scale up

the US $ risk free rate by the dierenJal inaJon between the US
$ and the currency in quesJon:
Risk free rateCurrency=

Thus, if the US $ risk free rate is 3.04%, the inaJon rate in the foreign
currency is 15% and the inaJon rate in US $ is 2%, the foreign currency risk
free rate is as follows:
1!=!16.17%!
Risk free rate = 1.0304 !.!"
!.!"
39

0.00%

-2.00%
Japanese Yen
Czech Koruna
Swiss Franc
Euro
Danish Krone
Swedish Krona
Taiwanese $
Hungarian Forint
Bulgarian Lev
Kuna
Thai Baht
BriJsh Pound
Romanian Leu
Norwegian Krone
HK $
Israeli Shekel
Polish Zloty
Canadian $
Korean Won
US $
Singapore $
Phillipine Peso
Pakistani Rupee
Venezuelan Bolivar
Vietnamese Dong
Australian $
Malyasian Ringgit
Chinese Yuan
NZ $
Chilean Peso
Iceland Krona
Peruvian Sol
Mexican Peso
Colombian Peso
Indonesian Rupiah
Indian Rupee
Turkish Lira
South African Rand
Kenyan Shilling
Reai
Naira
Russian Ruble

Why do risk free rates vary across currencies?

January 2015 Risk free rates

40

Riskfree Rates: January 2015

14.00%

12.00%

10.00%

8.00%

6.00%

4.00%

2.00%

Risk free Rate

Aswath Damodaran

40

One more test on riskfree rates

41

In January 2015, the 10-year treasury bond rate in the

United States was 2.17%, a historic low. Assume that you
were valuing a company in US dollars then, but were
wary about the risk free rate being too low. Which of the
following should you do?
a.

b.

c.

Replace the current 10-year bond rate with a more reasonable

normalized riskfree rate (the average 10-year bond rate over
the last 30 years has been about 5-6%)
Use the current 10-year bond rate as your riskfree rate but
make sure that your other assumpJons (about growth and
inaJon) are consistent with the riskfree rate
Something else

Aswath Damodaran

41

Some perspecJve on risk free rates

42

Interest rate fundamentals: T. Bond rates, Real growth and inaDon

20.00%

15.00%

10.00%

Real GDP growth

InaJon rate
Ten-year T.Bond rate

2012

2010

2008

2006

2004

2002

2000

1998

1996

1994

1992

1990

1988

1986

1984

1982

1980

1978

1976

1974

1972

1970

1968

1966

1964

1962

1960

1958

1956

0.00%

1954

5.00%

-5.00%

Aswath Damodaran

42

II. Equity Risk Premiums

The ubiquitous historical risk premium
43

The historical premium is the premium that stocks have historically

earned over riskless securiJes.
While the users of historical risk premiums act as if it is a fact (rather than
an esJmate), it is sensiJve to
How far back you go in history
Whether you use T.bill rates or T.Bond rates
Whether you use geometric or arithmeJc averages.
For instance, looking at the US:

Arithmetic Average
Geometric Average

Stocks - T. Bills Stocks - T. Bonds Stocks - T. Bills Stocks - T. Bonds

1928-2014
8.00%
6.25%
6.11%
4.60%

2.17%
2.32%

1965-2014
6.19%
4.12%
4.84%
3.14%

2.42%
2.74%

2005-2014
7.94%
4.06%
6.18%
2.73%

6.05%
8.65%

Aswath Damodaran

43

The perils of trusJng the past.

44

Noisy esJmates: Even with long Jme periods of history,

the risk premium that you derive will have substanJal
standard error. For instance, if you go back to 1928
(about 80 years of history) and you assume a standard
deviaJon of 20% in annual stock returns, you arrive at a
standard error of greater than 2%:
Standard Error in Premium = 20%/80 = 2.26%
Survivorship Bias: Using historical data from the U.S.
equity markets over the twenJeth century does create a
sampling bias. Aper all, the US economy and equity
markets were among the most successful of the global
economies that you could have invested in early in the
century.

Aswath Damodaran

44

Risk Premium for a Mature Market? Broadening

the sample to 1900-2013
45

Historical Equity Risk Premiums - Global: 1900-2013

7.00%
6.00%

5.70%
5.30%

5.30%

5.40%

5.10%

5.00%

4.50%
3.90%

4.00%
3.00%

3.50%
2.90%
2.40%

3.20%

3.40%
2.60%

2.10%

3.40%

3.90%
3.10%

2.40%

2.20%

2.10%

3.30% 3.30%
2.90%

Stocks - ST Government
Stocks - LT Government

2.00%
1.00%
0.00%

Aswath Damodaran

45

The simplest way of esJmaJng an addiJonal

country risk premium: The country default spread
46

Default spread for country: In this approach, the country equity

risk premium is set equal to the default spread for the country,
esJmated in one of three ways:

The default spread on a dollar denominated bond issued by the country.

(In January 2015, that spread was 1.55% for the Brazilian $ bond)
The sovereign CDS spread for the country. In January 2015, the ten year
CDS spread for Brazil was 2.86%.
The default spread based on the local currency raJng for the country.
Brazils sovereign local currency raJng is Baa2 and the default spread for a
Baa2 rated sovereign was about 1.90% in January 2015.

Add the default spread to a mature market premium: This

default spread is added on to the mature market premium to
arrive at the total equity risk premium for Brazil, assuming a
mature market premium of 5.75%.

Country Risk Premium for Brazil = 1.90%

Total ERP for Brazil = 5.75% + 1.90% = 7.65%

Aswath Damodaran

46

An equity volaJlity based approach to

esJmaJng the country total ERP
47

This approach draws on the standard deviaJon of two equity

markets, the emerging market in quesJon and a base market
(usually the US). The total equity risk premium for the
emerging market is then wriRen as:

Total equity risk premium = Risk PremiumUS* Country Equity / US Equity

The country equity risk premium is based upon the volaJlity

of the market in quesJon relaJve to U.S market.

Assume that the equity risk premium for the US is 5.75%.

Assume that the standard deviaJon in the Bovespa (Brazilian equity) is
21% and that the standard deviaJon for the S&P 500 (US equity) is
18%.
Total Equity Risk Premium for Brazil = 5.75% (21%/18%) = 6.71%
Country equity risk premium for Brazil = 6.71% - 5.75% = 0.96%

Aswath Damodaran

47

A melded approach to esJmaJng the addiJonal

country risk premium
48

Country raJngs measure default risk. While default risk premiums

and equity risk premiums are highly correlated, one would expect
equity spreads to be higher than debt spreads.
Another is to mulJply the bond default spread by the relaJve
volaJlity of stock and bond prices in that market. Using this
approach for Brazil in January 2014, you would get:

Country Equity risk premium = Default spread on country bond* Country

Equity / Country Bond
n Standard DeviaJon in Bovespa (Equity) = 21%
n Standard DeviaJon in Brazil government bond = 14%
n Default spread on C-Bond = 1.90%
Brazil Country Risk Premium = 1.90% (21%/14%) = 2.85%
Brazil Total ERP = Mature Market Premium + CRP = 5.75% + 2.85% = 8.60%

Aswath Damodaran

48

ERP : Jan 2015

Andorra
8.15% 2.40% Italy
Austria
5.75% 0.00% Jersey
Belgium
6.65% 0.90% Liechtenstein
Cyprus
15.50% 9.75% Luxembourg
Denmark
5.75% 0.00% Malta
Finland
5.75% 0.00% Netherlands
France
6.35% 0.60% Norway
Germany
5.75% 0.00% Portugal
Greece
17.00% 11.25% Spain
Guernsey
6.35% 0.60% Sweden
Iceland
9.05% 3.30% Switzerland
Ireland
8.15% 2.40% Turkey
Isle of Man 6.35% 0.60% UK
W. Europe

Canada
5.75%
US
5.75%
North America 5.75%
ArgenJna
Belize
Bolivia
Brazil
Chile
Colombia
Costa Rica
Ecuador
El Salvador
Guatemala
Honduras
Mexico
Nicaragua
Panama
Paraguay
Peru
Suriname
Uruguay
Venezuela
La;n America

0.00%
0.00%
0.00%

17.00%
19.25%
11.15%
8.60%
6.65%
8.60%
9.50%
15.50%
11.15%
9.50%
15.50%
7.55%
15.50%
8.60%
10.25%
7.55%
11.15%
8.60%
17.00%
9.95%

11.25%
13.50%
5.40%
2.85%
0.90%
2.85%
3.75%
9.75%
5.40%
3.75%
9.75%
1.80%
9.75%
2.85%
4.50%
1.80%
5.40%
2.85%
11.25%
4.20%

Angola
Botswana
Burkina Faso
Cameroon
Cape Verde
Congo (DR)
Congo (Republic)
Cte d'Ivoire
Egypt
Ethiopia
Gabon
Ghana
Kenya
Morocco
Mozambique
Namibia
Nigeria
Rwanda
Senegal
South Africa
Tunisia
Uganda
Zambia
Africa

8.60%
6.35%
5.75%
5.75%
7.55%
5.75%
5.75%
9.50%
8.60%
5.75%
5.75%
9.05%
6.35%
6.88%

2.85%
0.60%
0.00%
0.00%
1.80%
0.00%
0.00%
3.75%
2.85%
0.00%
0.00%
3.30%
0.60%
1.13%

10.25% 4.50%
7.03% 1.28%
15.50% 9.75%
14.00% 8.25%
14.00% 8.25%
15.50% 9.75%
11.15% 5.40%
12.50% 6.75%
17.00% 11.25%
12.50% 6.75%
11.15% 5.40%
14.00% 8.25%
12.50% 6.75%
9.50% 3.75%
12.50% 6.75%
9.05% 3.30%
11.15% 5.40%
14.00% 8.25%
12.50% 6.75%
8.60% 2.85%
11.15% 5.40%
12.50% 6.75%
12.50% 6.75%
11.73% 5.98%

Albania
Armenia
Azerbaijan
Belarus
Bosnia

12.50%
10.25%
9.05%
15.50%
15.50%

6.75%
4.50%
3.30%
9.75%
.75%

Montenegro
Poland
Romania
Russia
Serbia

11.15%
7.03%
9.05%
8.60%
12.50%

5.40%
1.28%
3.30%
2.85%
6.75%

Bulgaria
CroaJa

8.60%
9.50%

2.85% Slovakia
3.75% Slovenia

7.03%
9.50%

1.28%
3.75%

Czech Repub
Estonia
Georgia
Hungary
Kazakhstan
Latvia
Lithuania
Macedonia
Moldova

6.80%
6.80%
11.15%
9.50%
8.60%
8.15%
8.15%
11.15%
15.50%

1.05% Ukraine
20.75%
1.05% E. Europe
9.08%
5.40%
Bangladesh
3.75%
Cambodia
2.85%
China
2.40%
Fiji
2.40%
Hong Kong
5.40%
India
9.75%
Indonesia
Japan
Korea
Macao
Abu Dhabi
6.50% 0.75%
Malaysia
Bahrain
8.60% 2.85%
MauriJus
Israel
6.80% 1.05%
Mongolia
Jordan
12.50% 6.75%
Pakistan
Kuwait
6.50% 0.75%
Papua New Guinea
Lebanon
14.00% 8.25%
Philippines
Oman
6.80% 1.05%
Singapore
Qatar
6.50% 0.75%
Sri Lanka
Ras Al Khaimah 7.03% 1.28%
Taiwan
Saudi Arabia
6.65% 0.90%
Thailand
Sharjah
7.55% 1.80%
Vietnam
UAE
6.50% 0.75%
Asia
Middle East
6.85% 1.10%

15.00%
3.33%

Black #: Total ERP

Red #: Country risk premium
AVG: GDP weighted average

11.15%
14.00%
6.65%
12.50%
6.35%
9.05%
9.05%
6.80%
6.65%
6.50%
7.55%
8.15%
14.00%
17.00%
12.50%
8.60%
5.75%
12.50%
6.65%
8.15%
12.50%
7.26%

5.40%
8.25%
0.90%
6.75%
0.60%
3.30%
3.30%
1.05%
0.90%
0.75%
1.80%
2.40%
8.25%
11.25%
6.75%
2.85%
0.00%
6.75%
0.90%
2.40%
6.75%
1.51%

Australia

5.75%

0.00%

Cook Islands
New Zealand

12.50%
5.75%

6.75%
0.00%

Australia & NZ

5.75%

0.00%

From Country Equity Risk Premiums to

Corporate Equity Risk premiums
50

Approach 1: Assume that every company in the country is equally

exposed to country risk. In this case,

Approach 2: Assume that a companys exposure to country risk is similar

to its exposure to other market risk.

E(Return) = Riskfree Rate + CRP + Beta (Mature ERP)

Implicitly, this is what you are assuming when you use the local Governments
dollar borrowing rate as your riskfree rate.

E(Return) = Riskfree Rate + Beta (Mature ERP+ CRP)

Approach 3: Treat country risk as a separate risk factor and allow rms to
have dierent exposures to country risk (perhaps based upon the
proporJon of their revenues come from non-domesJc sales)

E(Return)=Riskfree Rate+ (Mature ERP) + (CRP)

Mature ERP = Mature market Equity Risk Premium

CRP = AddiJonal country risk premium

Aswath Damodaran

50

Approaches 1 & 2: EsJmaJng country risk

premium exposure
51

LocaJon based CRP: The standard approach in valuaJon is to

aRach a country risk premium to a company based upon its
country of incorporaJon. Thus, if you are an Indian company,
you are assumed to be exposed to the Indian country risk
premium. A developed market company is assumed to be
unexposed to emerging market risk.
OperaJon-based CRP: There is a more reasonable modied
version. The country risk premium for a company can be
computed as a weighted average of the country risk
premiums of the countries that it does business in, with the
weights based upon revenues or operaJng income. If a
company is exposed to risk in dozens of countries, you can
take a weighted average of the risk premiums by region.

Aswath Damodaran

51

OperaJon based CRP: Single versus MulJple

Emerging Markets
52

Single emerging market: Embraer, in 2004, reported that it derived 3% of

its revenues in Brazil and the balance from mature markets. The mature
market ERP in 2004 was 5% and Brazils CRP was 7.89%.

MulJple emerging markets: Ambev, the Brazilian-based beverage

company, reported revenues from the following countries during 2011.

Aswath Damodaran

52

Extending to a mulJnaJonal: Regional breakdown

Coca Colas revenue breakdown and ERP in 2012
53

Things to watch out for

1. Aggregation across regions. For instance, the Pacific region often includes Australia & NZ with Asia
2. Obscure aggregations including Eurasia and Oceania
53

Two problems with these approaches..

54

Focus just on revenues: To the extent that revenues are

the only variable that you consider, when weighJng risk
exposure across markets, you may be missing other
exposures to country risk. For instance, an emerging
market company that gets the bulk of its revenues
outside the country (in a developed market) may sJll
have all of its producJon faciliJes in the emerging
market.
Exposure not adjusted or based upon beta: To the extent
that the country risk premium is mulJplied by a beta, we
are assuming that beta in addiJon to measuring
exposure to all other macro economic risk also measures
exposure to country risk.

Aswath Damodaran

54

Approach 3: EsJmate a lambda for country risk

55

Source of revenues: Other things remaining equal, a company should be

more exposed to risk in a country if it generates more of its revenues
from that country.
Manufacturing faciliJes: Other things remaining equal, a rm that has all
of its producJon faciliJes in a risky country should be more exposed to
country risk than one which has producJon faciliJes spread over mulJple
countries. The problem will be accented for companies that cannot move
their producJon faciliJes (mining and petroleum companies, for
instance).
Use of risk management products: Companies can use both opJons/
futures markets and insurance to hedge some or a signicant porJon of
country risk.
Government naJonal interests: There are sectors that are viewed as
vital to the naJonal interests, and governments open play a key role in
these companies, either ocially or unocially. These sectors are more
exposed to country risk.

Aswath Damodaran

55

EsJmaJng Company Exposure to Country Risk

The factor l measures the relaJve exposure of a rm to country
risk. One simplisJc soluJon would be to do the following:
= % of revenues domesJcallyrm/ % of revenues domesJcallyaverage

rm

Consider two rms Tata Motors and Tata ConsulJng Services,

both Indian companies. In 2008-09, Tata Motors got about 91.37%
of its revenues in India and TCS got 7.62%. The average Indian rm
gets about 80% of its revenues in India:

Tata Motors= 91%/80% = 1.14

TCS= 7.62%/80% = 0.09

There are two implicaJons

A companys risk exposure is determined by where it does business and

not by where it is incorporated.
Firms might be able to acJvely manage their country risk exposures

56

A richer lambda esJmate: Use stock returns and country

bond returns: EsJmaJng a lambda for Embraer in 2004
57

ReturnEmbraer = 0.0195 + 0.2681 ReturnC Bond

ReturnEmbratel = -0.0308 + 2.0030 ReturnC Bond
Embraer versus C Bond: 2000-2003

Embratel versus C Bond: 2000-2003

40

100
80
60

Return on Embrat el

Return on Embraer

20

-20

40
20
0
-20
-40

-40

-60

-60
-30

-80

-20

-10

Return on C-Bond

Aswath Damodaran

10

20

-30

-20

-10

10

20

Return on C-Bond

57

EsJmaJng a US Dollar Cost of Equity for

Embraer - September 2004
58

Assume that the beta for Embraer is 1.07, and that the US $ riskfree rate
used is 4%. Also assume that the risk premium for the US is 5% and the
country risk premium for Brazil is 7.89%. Finally, assume that Embraer
gets 3% of its revenues in Brazil & the rest in the US.
There are ve esJmates of $ cost of equity for Embraer:

Approach 1: Constant exposure to CRP, LocaJon CRP

n E(Return) = 4% + 1.07 (5%) + 7.89% = 17.24%
Approach 2: Constant exposure to CRP, OperaJon CRP
n E(Return) = 4% + 1.07 (5%) + (0.03*7.89% +0.97*0%)= 9.59%
Approach 3: Beta exposure to CRP, LocaJon CRP
n E(Return) = 4% + 1.07 (5% + 7.89%)= 17.79%
Approach 4: Beta exposure to CRP, OperaJon CRP
n E(Return) = 4% + 1.07 (5% +( 0.03*7.89%+0.97*0%)) = 9.60%
Approach 5: Lambda exposure to CRP
n E(Return) = 4% + 1.07 (5%) + 0.27(7.89%) = 11.48%%

Aswath Damodaran

58

Valuing Emerging Market Companies with

signicant exposure in developed markets
59

The convenJonal pracJce in investment banking is to add the country

equity risk premium on to the cost of equity for every emerging market
company, notwithstanding its exposure to emerging market risk. Thus, in
2004, Embraer would have been valued with a cost of equity of 17-18%
even though it gets only 3% of its revenues in Brazil. As an investor, which
of the following consequences do you see from this approach?
a.
Emerging market companies with substanJal exposure in developed
markets will be signicantly over valued by equity research analysts.
b.
Emerging market companies with substanJal exposure in developed
markets will be signicantly under valued by equity research analysts.
Can you construct an investment strategy to take advantage of the
misvaluaJon? What would need to happen for you to make money of this
strategy?

Aswath Damodaran

59

Implied Equity Premiums

60

Lets start with a general proposiJon. If you know the price

paid for an asset and have esJmates of the expected cash
ows on the asset, you can esJmate the IRR of these cash
ows. If you paid the price, this is what you have priced the
asset to earn (as an expected return).
If you assume that stocks are correctly priced in the
aggregate and you can esJmate the expected cashows from
buying stocks, you can esJmate the expected rate of return
on stocks by nding that discount rate that makes the
present value equal to the price paid. SubtracJng out the
riskfree rate should yield an implied equity risk premium.
This implied equity premium is a forward looking number and
can be updated as open as you want (every minute of every
day, if you are so inclined).

Aswath Damodaran

60

Implied Equity Premiums: January 2008

61

We can use the informaJon in stock prices to back out how risk averse the market is and how much of a risk
premium it is demanding.
Between 2001 and 2007
dividends and stock
buybacks averaged 4.02%
of the index each year.

Analysts expect earnings to grow 5% a year for the next 5 years. We

will assume that dividends & buybacks will keep pace..
Last years cashflow (59.03) growing at 5% a year
61.98

65.08

68.33

71.75

After year 5, we will assume that

earnings on the index will grow at
4.02%, the same rate as the entire
economy (= riskfree rate).
75.34

January 1, 2008
S&P 500 is at 1468.36
4.02% of 1468.36 = 59.03

If you pay the current level of the index, you can expect to make a return of 8.39% on stocks (which is obtained by
solving for r in the following equaJon)

1468.36 =

61.98 65.08
68.33
71.75
75.34
75.35(1.0402)
+
+
+
+
+
(1+ r) (1+ r) 2 (1+ r) 3 (1+ r) 4 (1+ r) 5 (r .0402)(1+ r) 5

Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 8.39% - 4.02% = 4.37%

Aswath Damodaran

61

Implied Risk Premium Dynamics

62

a.
b.

a.
b.

a.
b.

Assume that the index jumps 10% on January 2 and that nothing else
changes. What will happen to the implied equity risk premium?
Implied equity risk premium will increase
Implied equity risk premium will decrease
Assume that the earnings jump 10% on January 2 and that nothing else
changes. What will happen to the implied equity risk premium?
Implied equity risk premium will increase
Implied equity risk premium will decrease
Assume that the riskfree rate increases to 5% on January 2 and that
nothing else changes. What will happen to the implied equity risk
premium?
Implied equity risk premium will increase
Implied equity risk premium will decrease

Aswath Damodaran

62

A year that made a dierence.. The implied

premium in January 2009
63
Year
2001
2002
2003
2004
2005
2006
2007
2008
Normalized

Market value of index

1148.09
879.82
1111.91
1211.92
1248.29
1418.30

1468.36

903.25

903.25

Dividends
15.74
15.96
17.88
19.01
22.34
25.04
28.14
28.47
28.47

Buybacks
14.34
13.87
13.70
21.59
38.82
48.12
67.22
40.25
24.11

Cash to equity Dividend yield Buyback yield

30.08
1.37%
1.25%
29.83
1.81%
1.58%
31.58
1.61%
1.23%
40.60
1.57%
1.78%
61.17
1.79%
3.11%
73.16
1.77%
3.39%
95.36
1.92%
4.58%
68.72
3.15%
4.61%
52.584
3.15%
2.67%

In 2008, the actual cash

returned to stockholders was
68.72. However, there was a
Analysts expect earnings to grow 4% a year for the next 5 years. We
41% dropoff in buybacks in
will assume that dividends & buybacks will keep pace..
Q4. We reduced the total
buybacks for the year by that Last years cashflow (52.58) growing at 4% a year
amount.
54.69
56.87
59.15
61.52

January 1, 2009
S&P 500 is at 903.25
Adjusted Dividends &
Buybacks for 2008 = 52.58

Aswath Damodaran

903.25 =

Total yield
2.62%
3.39%
2.84%
3.35%
4.90%
5.16%
6.49%
7.77%
5.82%

After year 5, we will assume that

earnings on the index will grow at
2.21%, the same rate as the entire
economy (= riskfree rate).
63.98

54.69 56.87 59.15 61.52 63.98

63.98(1.0221)
+
+
+
+
+
2
3
4
5
(1+ r) (1+ r) (1+ r) (1+ r) (1+ r) (r .0221)(1+ r)5
Expected Return on Stocks (1/1/09) = 8.64%
Riskfree rate
= 2.21%
Equity Risk Premium
= 6.43%

63

The Anatomy of a Crisis: Implied ERP from

September 12, 2008 to January 1, 2009
64

Aswath Damodaran

64

An Updated Equity Risk Premium: January

2015
65

Base year cash flow (last 12 mths)

Dividends (TTM):
38.57
+ Buybacks (TTM):
61.92
= Cash to investors (TTM): 100.50
Earnings in TTM:
114.74
E(Cash to investors)

100.5 growing @
5.58% a year

112.01

106.10

S&P 500 on 1/1/15=

2058.90
2058.90 =

Expected growth in next 5 years

Top down analyst estimate of earnings
growth for S&P 500 with stable
payout: 5.58%

118.26

124.85

131.81

106.10 112.91 118.26 124.85 131.81 131.81(1.0217)

+
+
+
+
+
(1+ r) (1+ r)2 (1+ r)3 (1+ r)4 (1+ r)5 (r .0217)(1+ r)5

Beyond year 5
Expected growth rate =
Riskfree rate = 2.17%
Expected CF in year 6 =
131.81(1.0217)

r = Implied Expected Return on Stocks = 7.95%

Minus
Risk free rate = T.Bond rate on 1/1/15= 2.17%
Equals
Implied Equity Risk Premium (1/1/15) = 7.95% - 2.17% = 5.78%

Aswath Damodaran

65

4.00%

3.00%
Implied Premium

Implied Premiums in the US: 1960-2014

66

Implied Premium for US Equity Market: 1960-2014

7.00%

6.00%

5.00%

2.00%

1.00%

2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
0.00%

Year

66
Aswath Damodaran

Implied Premium versus Risk Free Rate

67

Implied ERP and Risk free Rates

25.00%
Expected Return on Stocks = T.Bond Rate + Equity Risk
Premium

20.00%

15.00%

Implied Premium (FCFE)

Since 2008, the expected return

on stocks has stagnated at about
8%, but the risk free rate has
dropped dramatically.

10.00%

5.00%

1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014

0.00%

T. Bond Rate

Aswath Damodaran

67

Equity Risk Premiums and Bond Default Spreads

68

Figure 16: Equity Risk Premiums and Bond Default Spreads

7.00%

9.00
8.00

6.00%

7.00
6.00
4.00%

5.00

3.00%

4.00
3.00

ERP / Baa Spread

Premium (Spread)

5.00%

2.00%
2.00
1.00%

1.00

0.00%

0.00

ERP/Baa Spread

Aswath Damodaran

Baa - T.Bond Rate

ERP

68

Equity Risk Premiums and Cap Rates (Real

Estate)
69

Figure 17: Equity Risk Premiums, Cap Rates and Bond Spreads
8.00%

6.00%

4.00%

2.00%

0.00%

1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014

ERP
Baa Spread
Cap Rate premium

-2.00%

-4.00%

-6.00%

-8.00%

Aswath Damodaran

69

Why implied premiums maRer?

70

a.
b.
c.

In many investment banks, it is common pracJce (especially

in corporate nance departments) to use historical risk
premiums (and arithmeJc averages at that) as risk premiums
to compute cost of equity. If all analysts in the department
used the arithmeJc average premium (for stocks over T.Bills)
for 1928-2014 of 8% to value stocks in January 2014, given
the implied premium of 5.75%, what are they likely to nd?
The values they obtain will be too low (most stocks will look
overvalued)
The values they obtain will be too high (most stocks will
look under valued)
There should be no systemaJc bias as long as they use the
same premium to value all stocks.

Aswath Damodaran

70

Which equity risk premium should you use?

71

If you assume this

Premium to use

Premiums revert back to historical norms Historical risk premium

and your Jme period yields these norms
Market is correct in the aggregate or that Current implied equity risk premium
your valuaJon should be market neutral
Marker makes mistakes even in the
aggregate but is correct over Jme

Aswath Damodaran

Average implied equity risk premium

over Jme.

71

And the approach can be extended to emerging markets

Implied premium for the Sensex (September 2007)
72

Inputs for the computaJon

Sensex on 9/5/07 = 15446

Dividend yield on index = 3.05%
Expected growth rate - next 5 years = 14%
Growth rate beyond year 5 = 6.76% (set equal to riskfree rate)

Solving for the expected return:

15446 =

537.06 612.25 697.86 795.67 907.07

907.07(1.0676)
+
+
+
+
+
(1+ r) (1+ r) 2 (1+ r) 3 (1+ r) 4 (1+ r) 5 (r .0676)(1+ r) 5

Expected return on stocks = 11.18%

Implied equity risk premium for India = 11.18% - 6.76% =
4.42%

Aswath Damodaran

72

Can country risk premiums change? Brazil CRP

& Total ERP from 2000 to 2013
73

Figure 15: Implied Equity Risk Premium - Brazil

9.00%
0.69%

8.00%
7.00%

Risk Premium

6.00%

4.00%4.31%
3.70%
3.23%

3.15%
5.00%
4.06%
4.00%

0.65%
1.34%1.87%

2.28%

2.43%
0.86%0.70%

0.82%

Brazil Country Risk

7.64%

3.00%
5.10%
4.55%4.86%
4.05%4.12%3.95%3.88%3.95%4.04%
2.00%
3.51%
2.50%
1.00%

US premium

6.35%
5.59%5.28%

0.00%

Aswath Damodaran

73

The evoluJon of Emerging Market Risk

74

Aswath Damodaran

74

Measuring Relative Risk

MPT Quadrant

APM/ Multi-factor Models

Estimate 'betas' against
multiple macro risk factors,
using past price data

Sector-average Beta
Average regression beta
across all companies in the
business(es) that the firm
operates in.

Price Variance Model

Standard deviation, relative to the
average across all stocks

The CAPM Beta

Regression beta of
stock returns at
firm versus stock
returns on market
index

Accounting Risk
Quadrant
Accounting Earnings Volatility
How volatile is your company's
earnings, relative to the average
company's earnings?
Accounting Earnings Beta
Regression beta of changes
in earnings at firm versus
changes in earnings for
market index

Relative Risk Measure

How risky is this asset,
relative to the average
risk investment?

Balance Sheet Ratios

Risk based upon balance
sheet ratios (debt ratio,
working capital, cash, fixed
assets) that measure risk

Debt cost based

Estimate cost of equity based
upon cost of debt and relative
volatility

Price based, Model

Agnostic Quadrant

Implied Beta/ Cost of equity

Estimate a cost of equity for
firm or sector based upon
price today and expected
cash flows in future

Proxy measures
Use a proxy for risk
(market cap, sector).

Composite Risk Measures

Use a mix of quantitative (price,
ratios) & qualitative analysis
(management quality) to
estimate relative risk

Intrinsic Risk Quadrant

75

Aswath Damodaran

The CAPM Beta

76

The standard procedure for esJmaJng betas is to

regress stock returns (Rj) against market returns (Rm) -
Rj = a + b Rm
where a is the intercept and b is the slope of the regression.

The slope of the regression corresponds to the beta of

the stock, and measures the riskiness of the stock.
This beta has three problems:

It has high standard error

It reects the rms business mix over the period of the
regression, not the current mix
It reects the rms average nancial leverage over the period
rather than the current leverage.

Aswath Damodaran

76

Beta EsJmaJon: The Noise Problem

77

Aswath Damodaran

77

Beta EsJmaJon: The Index Eect

78

Aswath Damodaran

78

Stock-priced based soluJons to the Regression

Beta Problem
79

Modify the regression beta by

EsJmate the beta for the rm using

the standard deviaJon in stock prices instead of a regression against

an index
RelaJve risk = Standard deviaJon in stock prices for investment/
Average standard deviaJon across all stocks

EsJmate the beta for the rm from the boRom up without

employing the regression technique. This will require

changing the index used to esJmate the beta

adjusJng the regression beta esJmate, by bringing in informaJon
about the fundamentals of the company

understanding the business mix of the rm

esJmaJng the nancial leverage of the rm

Imputed or implied beta (cost of equity) for the sector.

Aswath Damodaran

79

AlternaJve measures of relaJve risk for equity

80

AccounJng risk measures: To the extent that you dont trust market-
priced based measures of risk, you could compute relaJve risk measures
based on

AccounJng earnings volaJlity: Compute an accounJng beta or relaJve volaJlity

Balance sheet raJos: You could compute a risk score based upon accounJng raJos
like debt raJos or cash holdings (akin to default risk scores like the Z score)

Proxies: In a simpler version of proxy models, you can categorize rms

into risk classes based upon size, sectors or other characterisJcs.
QualitaJve Risk Models: In these models, risk assessments are based at
least parJally on qualitaJve factors (quality of management).
Debt based measures: You can esJmate a cost of equity, based upon an
observable costs of debt for the company.

Cost of equity = Cost of debt * Scaling factor

Aswath Damodaran

80

Determinants of Betas & RelaJve Risk

81

Beta of Equity (Levered Beta)

Beta of Firm (Unlevered Beta)

Nature of product or
service offered by
company:
Other things remaining equal,
the more discretionary the
product or service, the higher
the beta.

Operating Leverage (Fixed

Costs as percent of total
costs):
Other things remaining equal
the greater the proportion of
the costs that are fixed, the
higher the beta of the
company.

Implications
1. Cyclical companies should
have higher betas than noncyclical companies.
2. Luxury goods firms should
have higher betas than basic
goods.
3. High priced goods/service
firms should have higher betas
than low prices goods/services
firms.
4. Growth firms should have
higher betas.

Implications
1. Firms with high infrastructure
needs and rigid cost structures
should have higher betas than
firms with flexible cost structures.
2. Smaller firms should have higher
betas than larger firms.
3. Young firms should have higher
betas than more mature firms.

Aswath Damodaran

Financial Leverage:
Other things remaining equal, the
greater the proportion of capital that
a firm raises from debt,the higher its
equity beta will be

Implciations
Highly levered firms should have highe betas
than firms with less debt.
Equity Beta (Levered beta) =
Unlev Beta (1 + (1- t) (Debt/Equity Ratio))

81

In a perfect world we would esJmate the beta

of a rm by doing the following
82

Start with the beta of the business that the firm is in

Adjust the business beta for the operating leverage of the firm to arrive at the
unlevered beta for the firm.

Use the financial leverage of the firm to estimate the equity beta for the firm
Levered Beta = Unlevered Beta ( 1 + (1- tax rate) (Debt/Equity))

Aswath Damodaran

82

AdjusJng for operaJng leverage

83

Within any business, rms with lower xed costs (as a

percentage of total costs) should have lower unlevered
betas. If you can compute xed and variable costs for
each rm in a sector, you can break down the unlevered
beta into business and operaJng leverage components.

Unlevered beta = Pure business beta * (1 + (Fixed costs/

Variable costs))

The biggest problem with doing this is informaJonal. It is

dicult to get informaJon on xed and variable costs for
individual rms.
In pracJce, we tend to assume that the operaJng
leverage of rms within a business are similar and use
the same unlevered beta for every rm.

Aswath Damodaran

83

AdjusJng for nancial leverage

84

ConvenJonal approach: If we assume that debt carries

no market risk (has a beta of zero), the beta of equity
alone can be wriRen as a funcJon of the unlevered beta
and the debt-equity raJo
L = u (1+ ((1-t)D/E))
In some versions, the tax eect is ignored and there is no (1-t) in
the equaJon.

Debt Adjusted Approach: If beta carries market risk and

you can esJmate the beta of debt, you can esJmate the
levered beta as follows:
L = u (1+ ((1-t)D/E)) - debt (1-t) (D/E)
While the laRer is more realisJc, esJmaJng betas for debt can be
dicult to do.

Aswath Damodaran

84

BoRom-up Betas
85
Step 1: Find the business or businesses that your firm operates in.
Possible Refinements
Step 2: Find publicly traded firms in each of these businesses and
obtain their regression betas. Compute the simple average across
these regression betas to arrive at an average beta for these publicly
traded firms. Unlever this average beta using the average debt to
equity ratio across the publicly traded firms in the sample.
Unlevered beta for business = Average beta across publicly traded
firms/ (1 + (1- t) (Average D/E ratio across firms))

Step 3: Estimate how much value your firm derives from each of
the different businesses it is in.

Step 4: Compute a weighted average of the unlevered betas of the

different businesses (from step 2) using the weights from step 3.
Bottom-up Unlevered beta for your firm = Weighted average of the
unlevered betas of the individual business

Step 5: Compute a levered beta (equity beta) for your firm, using
the market debt to equity ratio for your firm.
Levered bottom-up beta = Unlevered beta (1+ (1-t) (Debt/Equity))

Aswath Damodaran

If you can, adjust this beta for differences

between your firm and the comparable
firms on operating leverage and product
characteristics.

While revenues or operating income

are often used as weights, it is better
to try to estimate the value of each
business.

If you expect the business mix of your

firm to change over time, you can
change the weights on a year-to-year
basis.
If you expect your debt to equity ratio to
change over time, the levered beta will
change over time.

85

Why boRom-up betas?

86

The standard error in a boRom-up beta will be signicantly

lower than the standard error in a single regression beta.
Roughly speaking, the standard error of a boRom-up beta
esJmate can be wriRen as follows:
Average Std Error across Betas
Std error of boRom-up beta =

Number of firms in sample

The boRom-up beta can be adjusted to reect changes in the

rms business mix and nancial leverage. Regression betas

reect the past.

You can esJmate boRom-up betas even when you do not
have historical stock prices. This is the case with iniJal public
oerings, private businesses or divisions of companies.

Aswath Damodaran

86

EsJmaJng BoRom Up Betas & Costs of

Equity: Vale
Sample'

Sample'
size'

Metals'&'
Mining'

Global'firms'in'metals'&'
mining,'Market'cap>$1'
billion'

48'

0.86'

$9,013'

1.97'

$17,739'

16.65%'

Iron'Ore'

Global'firms'in'iron'ore'

78'

0.83'

$32,717'

2.48'

$81,188'

76.20%'

Fertilizers'

Global'specialty'
chemical'firms'

693'

0.99'

$3,777'

1.52'

$5,741'

5.39%'

Global'transportation'
firms'

223'

0.75'

$1,644'

1.14'

$1,874'

1.76%'

''

0.8440'

$47,151'

''

$106,543'

100.00%'

Business'

Logistics'
Vale'
Operations'

''

Aswath Damodaran

Unlevered'beta'
of'business'
Revenues'

Peer'Group'
EV/Sales'

Value'of'
Business'

Proportion'of'
Vale'

87

Embraers BoRom-up Beta

88

Business
Aerospace

a.
b.

Unlevered Beta D/E RaJo

0.95 18.95%

Levered beta
1.07

Levered Beta = Unlevered Beta ( 1 + (1- tax rate) (D/E RaJo)

= 0.95 ( 1 + (1-.34) (.1895)) = 1.07
Can an unlevered beta esJmated using U.S. and European
aerospace companies be used to esJmate the beta for a Brazilian
aerospace company?
Yes
No
What concerns would you have in making this assumpJon?

Aswath Damodaran

88

Gross Debt versus Net Debt Approaches

89

Analysts in Europe and LaJn America open take the dierence between
debt and cash (net debt) when compuJng debt raJos and arrive at very
dierent values.
For Embraer, using the gross debt raJo

Using the net debt raJo, we get

Gross D/E RaJo for Embraer = 1953/11,042 = 18.95%

Levered Beta using Gross Debt raJo = 1.07
Net Debt RaJo for Embraer = (Debt - Cash)/ Market value of Equity


= (1953-2320)/ 11,042 = -3.32%
Levered Beta using Net Debt RaJo = 0.95 (1 + (1-.34) (-.0332)) = 0.93

The cost of Equity using net debt levered beta for Embraer will be much
lower than with the gross debt approach. The cost of capital for Embraer
will even out since the debt raJo used in the cost of capital equaJon will
now be a net debt raJo rather than a gross debt raJo.

Aswath Damodaran

89

The Cost of Equity: A Recap

90

Preferably, a bottom-up beta,

based upon other firms in the
business, and firms own financial
leverage
Cost of Equity =

Riskfree Rate

Has to be in the same

currency as cash flows,
and defined in same terms
(real or nominal) as the
cash flows

Aswath Damodaran

Beta *

(Risk Premium)

Historical Premium
1. Mature Equity Market Premium:
Average premium earned by
stocks over T.Bonds in U.S.
2. Country risk premium =
Country Default Spread* ( Equity/Country bond)

or

Implied Premium
Based on how equity
market is priced today
and a simple valuation
model

90

EsJmaJng the Cost of Debt

91

The cost of debt is the rate at which you can borrow at

currently, It will reect not only your default risk but also the
level of interest rates in the market.
The two most widely used approaches to esJmaJng cost of
debt are:

Looking up the yield to maturity on a straight bond outstanding from

the rm. The limitaJon of this approach is that very few rms have
long term straight bonds that are liquid and widely traded
Looking up the raJng for the rm and esJmaJng a default spread
based upon the raJng. While this approach is more robust, dierent
bonds from the same rm can have dierent raJngs. You have to use a
median raJng for the rm

When in trouble (either because you have no raJngs or

mulJple raJngs for a rm), esJmate a syntheJc raJng for
your rm and the cost of debt based upon that raJng.

Aswath Damodaran

91

EsJmaJng SyntheJc RaJngs

92

The raJng for a rm can be esJmated using the nancial

characterisJcs of the rm. In its simplest form, the raJng
can be esJmated from the interest coverage raJo
Interest Coverage RaJo = EBIT / Interest Expenses

For Embraers interest coverage raJo, we used the

interest expenses from 2003 and the average EBIT from
2001 to 2003. (The aircrap business was badly aected
by 9/11 and its apermath. In 2002 and 2003, Embraer
reported signicant drops in operaJng income)
Interest Coverage RaJo = 462.1 /129.70 = 3.56

Aswath Damodaran

92

Interest Coverage RaJos, RaJngs and Default

Spreads: 2003 & 2004
93

If Interest Coverage RaJo is

EsJmated Bond RaJng Default Spread(2003)

Default Spread(2004)

> 8.50
6.50 - 8.50
5.50 - 6.50
4.25 - 5.50
3.00 - 4.25
2.50 - 3.00
2.25- 2.50
2.00 - 2.25
1.75 - 2.00
1.50 - 1.75
1.25 - 1.50
0.80 - 1.25
0.65 - 0.80
0.20 - 0.65
< 0.20 (<0.5)

AAA
AA
A+
A
A
BBB
BB+
BB
B+
B
B
CCC
CC
C

0.35%
0.50%
0.70%
0.85%
1.00%
1.50%
2.00%
2.50%
3.25%
4.00%
6.00%
8.00%
10.00%
12.00%
20.00%

(>12.50)
(9.5-12.5)
(7.5-9.5)
(6-7.5)
(4.5-6)
(4-4.5)
(3.5-4)
((3-3.5)
(2.5-3)
(2-2.5)
(1.5-2)
(1.25-1.5)
(0.8-1.25)
(0.5-0.8)
D

0.75%
1.00%
1.50%
1.80%
2.00%
2.25%
2.75%
3.50%
4.75%
6.50%
8.00%
10.00%
11.50%
12.70%
15.00%

The rst number under interest coverage raJos is for larger market cap companies and the second in
brackets is for smaller market cap companies. For Embraer , I used the interest coverage raJo table for
smaller/riskier rms (the numbers in brackets) which yields a lower raJng for the same interest coverage
raJo.

Aswath Damodaran

93

Cost of Debt computaJons

94

Companies in countries with low bond raJngs and high default risk
might bear the burden of country default risk, especially if they are
smaller or have all of their revenues within the country.
Larger companies that derive a signicant porJon of their revenues
in global markets may be less exposed to country default risk. In
other words, they may be able to borrow at a rate lower than the
government.
The syntheJc raJng for Embraer is A-. Using the 2004 default
spread of 1.00%, we esJmate a cost of debt of 9.29% (using a
riskfree rate of 4.29% and adding in two thirds of the country
default spread of 6.01%):
Cost of debt
= Riskfree rate + 2/3(Brazil country default spread) + Company default
spread =4.29% + 4.00%+ 1.00% = 9.29%

Aswath Damodaran

94

SyntheJc RaJngs: Some Caveats

95

The relaJonship between interest coverage raJos and

raJngs, developed using US companies, tends to travel
well, as long as we are analyzing large manufacturing
rms in markets with interest rates close to the US
interest rate
They are more problemaJc when looking at smaller
companies in markets with higher interest rates than the
US. One way to adjust for this dierence is modify the
interest coverage raJo table to reect interest rate
dierences (For instances, if interest rates in an
emerging market are twice as high as rates in the US,
halve the interest coverage raJo.

Aswath Damodaran

95

Default Spreads: The eect of the crisis of

2008.. And the apermath
96

Default spread over treasury

Rating
Aaa/AAA
Aa1/AA+
Aa2/AA
Aa3/AAA1/A+
A2/A
A3/A-

1-Jan-08
0.99%
1.15%
1.25%
1.30%
1.35%
1.42%
1.48%

12-Sep-08
1.40%
1.45%
1.50%
1.65%
1.85%
1.95%
2.15%

12-Nov-08
2.15%
2.30%
2.55%
2.80%
3.25%
3.50%
3.75%

1-Jan-09
2.00%
2.25%
2.50%
2.75%
3.25%
3.50%
3.75%

1-Jan-10
0.50%
0.55%
0.65%
0.70%
0.85%
0.90%
1.05%

1-Jan-11
0.55%
0.60%
0.65%
0.75%
0.85%
0.90%
1.00%

Baa1/BBB+
Baa2/BBB

1.73%
2.02%

2.65%
2.90%

4.50%
5.00%

5.25%
5.75%

1.65%
1.80%

1.40%
1.60%

Baa3/BBBBa1/BB+
Ba2/BB
Ba3/BBB1/B+
B2/B
B3/B-

2.60%
3.20%
3.65%
4.00%
4.55%
5.65%
6.45%

3.20%
4.45%
5.15%
5.30%
5.85%
6.10%
9.40%

5.75%
7.00%
8.00%
9.00%
9.50%
10.50%
13.50%

7.25%
9.50%
10.50%
11.00%
11.50%
12.50%
15.50%

2.25%
3.50%
3.85%
4.00%
4.25%
5.25%
5.50%

2.05%
2.90%
3.25%
3.50%
3.75%
5.00%
6.00%

Caa/CCC+
ERP

7.15%
4.37%

9.80%
4.52%

14.00%
6.30%

16.50%
6.43%

7.75%
4.36%

7.75%
5.20%96

Updated Default Spreads - January 2015

97

RaJng
Aaa/AAA
Aa1/AA+
Aa2/AA
Aa3/AA-
A1/A+
A2/A
A3/A-
Baa1/BBB+
Baa2/BBB
Baa3/BBB-
Ba1/BB+
Ba2/BB
Ba3/BB-
B1/B+
B2/B
B3/B-
Caa/CCC+

Aswath Damodaran

1 yr
0.05%
0.09%
0.13%
0.18%
0.23%
0.29%
0.40%
0.54%
0.65%
1.04%
1.93%
2.23%
2.52%
2.87%
3.17%
3.47%
3.81%

2 yr
0.08%
0.20%
0.32%
0.39%
0.45%
0.49%
0.61%
0.79%
0.96%
1.39%
2.06%
2.37%
2.68%
3.04%
3.35%
3.66%
4.02%

3 yr
0.12%
0.28%
0.44%
0.51%
0.58%
0.61%
0.74%
0.93%
1.14%
1.60%
2.21%
2.53%
2.85%
3.22%
3.54%
3.87%
4.23%

5 yr
0.18%
0.38%
0.58%
0.66%
0.74%
0.76%
0.89%
1.12%
1.36%
1.87%
2.36%
2.70%
3.03%
3.41%
3.75%
4.08%
4.46%

7 yr
0.28%
0.48%
0.68%
0.76%
0.85%
0.86%
0.99%
1.23%
1.51%
2.04%
2.48%
2.83%
3.17%
3.57%
3.92%
4.26%
4.65%

10 yr
0.42%
0.60%
0.78%
0.87%
0.96%
0.97%
1.10%
1.36%
1.67%
2.22%
2.61%
2.97%
3.33%
3.74%
4.10%
4.45%
4.86%

30 yr
0.65%
0.87%
1.09%
1.19%
1.28%
1.31%
1.44%
1.75%
2.15%
2.72%
2.83%
3.16%
3.50%
3.92%
4.29%
4.66%
5.08%

97

Subsidized Debt: What should we do?

98

a.

b.

c.

Assume that the Brazilian government lends money to

Embraer at a subsidized interest rate (say 6% in dollar
terms). In compuJng the cost of capital to value
Embraer, should be we use the cost of debt based upon
default risk or the subisidized cost of debt?
The subsidized cost of debt (6%). That is what the
company is paying.
The fair cost of debt (9.25%). That is what the company
should require its projects to cover.
A number in the middle.

Aswath Damodaran

98

Weights for the Cost of Capital ComputaJon

99

In compuJng the cost of capital for a publicly traded

rm, the general rule for compuJng weights for debt
and equity is that you use market value weights (and
not book value weights). Why?
a.
b.
c.
d.

Because the market is usually right

Because market values are easy to obtain
Because book values of debt and equity are meaningless
None of the above

Aswath Damodaran

99

EsJmaJng Cost of Capital: Embraer in 2004

100

Equity

Cost of Equity = 4.29% + 1.07 (4%) + 0.27 (7.89%) = 10.70%

Market Value of Equity =11,042 million BR ($ 3,781 million)

Debt

Cost of debt = 4.29% + 4.00% +1.00%= 9.29%

Market Value of Debt = 2,083 million BR ($713 million)

Cost of Capital
Cost of Capital = 10.70 % (.84) + 9.29% (1- .34) (0.16)) = 9.97%

The book value of equity at Embraer is 3,350 million BR.

The book value of debt at Embraer is 1,953 million BR; Interest
expense is 222 mil BR; Average maturity of debt = 4 years
EsJmated market value of debt = 222 million (PV of annuity, 4 years,
9.29%) + $1,953 million/1.09294 = 2,083 million BR

Aswath Damodaran

100

If you had to do it.ConverJng a Dollar Cost of

Capital to a Nominal Real Cost of Capital
101

Approach 1: Use a BR riskfree rate in all of the calculaJons

above. For instance, if the BR riskfree rate was 12%, the cost
of capital would be computed as follows:

Cost of Equity = 12% + 1.07(4%) + 0.27 (7.89%) = 18.41%

Cost of Debt = 12% + 1% = 13%
(This assumes the riskfree rate has no country risk premium
embedded in it.)

Approach 2: Use the dierenJal inaJon rate to esJmate the

cost of capital. For instance, if the inaJon rate in BR is 8%
and the inaJon rate in the U.S. is 2%

" 1+ Inflation %
BR
'
Cost of capital= (1+ Cost of Capital$ )$
# 1+ Inflation$ &

= 1.0997 (1.08/1.02)-1 = 0.1644 or 16.44%

Aswath Damodaran

101

Dealing with Hybrids and Preferred Stock

102

When dealing with hybrids (converJble bonds, for

instance), break the security down into debt and equity
and allocate the amounts accordingly. Thus, if a rm has
$ 125 million in converJble debt outstanding, break the
$125 million into straight debt and conversion opJon
components. The conversion opJon is equity.
When dealing with preferred stock, it is beRer to keep it
as a separate component. The cost of preferred stock is
the preferred dividend yield. (As a rule of thumb, if the
preferred stock is less than 5% of the outstanding
market value of the rm, lumping it in with debt will
make no signicant impact on your valuaJon).

Aswath Damodaran

102

Decomposing a converJble bond

103

Assume that the rm that you are analyzing has $125

million in face value of converJble debt with a stated
interest rate of 4%, a 10 year maturity and a market
value of $140 million. If the rm has a bond raJng of A
and the interest rate on A-rated straight bond is 8%, you
can break down the value of the converJble bond into
straight debt and equity porJons.
Straight debt = (4% of $125 million) (PV of annuity, 10 years, 8%)
+ 125 million/1.0810 = $91.45 million
Equity porJon = $140 million - $91.45 million = $48.55 million

Aswath Damodaran

103

Recapping the Cost of Capital

104

Cost of borrowing should be based upon

(1) synthetic or actual bond rating
(2) default spread
Cost of Borrowing = Riskfree rate + Default spread
Cost of Capital =

Cost of Equity (Equity/(Debt + Equity))

Cost of equity
based upon bottom-up
beta

Aswath Damodaran

Cost of Borrowing

(1-t)

Marginal tax rate, reflecting

tax benefits of debt

(Debt/(Debt + Equity))

Weights should be market value weights

104

Aswath Damodaran

II. ESTIMATING CASH FLOWS

Cash is king

105

Steps in Cash Flow EsJmaJon

106

EsJmate the current earnings of the rm

Consider how much the rm invested to create future growth

If looking at cash ows to equity, look at earnings aper interest

expenses - i.e. net income
If looking at cash ows to the rm, look at operaJng earnings aper
taxes
If the investment is not expensed, it will be categorized as capital
expenditures. To the extent that depreciaJon provides a cash ow, it
will cover some of these expenditures.
Increasing working capital needs are also investments for future
growth

If looking at cash ows to equity, consider the cash ows

from net debt issues (debt issued - debt repaid)

Aswath Damodaran

106

Measuring Cash Flows

107

Cash flows can be measured to

All claimholders in the firm
EBIT (1- tax rate)
- ( Capital Expenditures - Depreciation)
- Change in non-cash working capital
= Free Cash Flow to Firm (FCFF)

Aswath Damodaran

Just Equity Investors

Net Income
- (Capital Expenditures - Depreciation)
- Change in non-cash Working Capital
- (Principal Repaid - New Debt Issues)
- Preferred Dividend

Dividends
+ Stock Buybacks

107

Measuring Cash Flow to the Firm

108

EBIT ( 1 - tax rate)

- (Capital Expenditures - DepreciaJon)
- Change in Working Capital
= Cash ow to the rm
Where are the tax savings from interest payments in
this cash ow?

Aswath Damodaran

108

From Reported to Actual Earnings

109

Firms
history

Comparable
Firms

Operating leases
- Convert into debt
- Adjust operating income

Normalize
Earnings

R&D Expenses
- Convert into asset
- Adjust operating income

Cleanse operating items of

- Financial Expenses
- Capital Expenses
- Non-recurring expenses

Measuring Earnings
Update
- Trailing Earnings
- Unofficial numbers

Aswath Damodaran

109

I. Update Earnings
110

When valuing companies, we open depend upon nancial

statements for inputs on earnings and assets. Annual reports are
open outdated and can be updated by using-

Trailing 12-month data, constructed from quarterly earnings reports.

Informal and unocial news reports, if quarterly reports are unavailable.

UpdaJng makes the most dierence for smaller and more volaJle
rms, as well as for rms that have undergone signicant
restructuring.
Time saver: To get a trailing 12-month number, all you need is one
10K and one 10Q (example third quarter). Use the Year to date
numbers from the 10Q:

Trailing 12-month Revenue = Revenues (in last 10K) - Revenues from rst 3
quarters of last year + Revenues from rst 3 quarters of this year.

Aswath Damodaran

110

II. CorrecJng AccounJng Earnings

111

Make sure that there are no nancial expenses mixed in with

operaJng expenses

Financial expense: Any commitment that is tax deducJble that you have to
meet no maRer what your operaJng results: Failure to meet it leads to
loss of control of the business.
Example: OperaJng Leases: While accounJng convenJon treats operaJng
leases as operaJng expenses, they are really nancial expenses and need
to be reclassied as such. This has no eect on equity earnings but does
change the operaJng earnings

Make sure that there are no capital expenses mixed in with the
operaJng expenses

Capital expense: Any expense that is expected to generate benets over

mulJple periods.
R & D Adjustment: Since R&D is a capital expenditure (rather than an
operaJng expense), the operaJng income has to be adjusted to reect its
treatment.

Aswath Damodaran

111

The Magnitude of OperaJng Leases

112
Operating Lease expenses as % of Operating Income
60.00%

50.00%

40.00%

30.00%

20.00%

10.00%

0.00%
Market

Aswath Damodaran

Apparel Stores

Furniture Stores

Restaurants

112

Dealing with OperaJng Lease Expenses

113

OperaJng Lease Expenses are treated as operaJng expenses

in compuJng operaJng income. In reality, operaJng lease
expenses should be treated as nancing expenses, with the
following adjustments to earnings and capital:
Debt Value of OperaJng Leases = Present value of OperaJng
Lease Commitments at the pre-tax cost of debt
When you convert operaJng leases into debt, you also create
an asset to counter it of exactly the same value.
Adjusted OperaJng Earnings
Adjusted OperaJng Earnings = OperaJng Earnings + OperaJng Lease
Expenses - DepreciaJon on Leased Asset
As an approximaJon, this works:
Adjusted OperaJng Earnings = OperaJng Earnings + Pre-tax cost of
Debt * PV of OperaJng Leases.

Aswath Damodaran

113

OperaJng Leases at The Gap in 2003

114

The Gap has convenJonal debt of about $ 1.97 billion on its balance sheet and its
pre-tax cost of debt is about 6%. Its operaJng lease payments in the 2003 were
$978 million and its commitments for the future are below:
Year
Commitment (millions)
Present Value (at 6%)
1

$899.00
$848.11
2

$846.00
$752.94
3

$738.00
$619.64
4

$598.00
$473.67
5

$477.00
$356.44
6&7
$982.50 each year
$1,346.04
Debt Value of leases =
$4,396.85 (Also value of leased asset)
Debt outstanding at The Gap = $1,970 m + $4,397 m = $6,367 m
Adjusted OperaJng Income = Stated OI + OL exp this year - Deprecn

= $1,012 m + 978 m - 4397 m /7 = $1,362 million (7 year life for assets)

Approximate OI = $1,012 m + $ 4397 m (.06) = $1,276 m

Aswath Damodaran

114

The Collateral Eects of TreaJng OperaJng

Leases as Debt
115

!
Conventional!Accounting!
Income!Statement!
EBIT&&Leases&=&1,990&
0&Op&Leases&&&&&&=&&&&978&
EBIT&&&&&&&&&&&&&&&&=&&1,012&

Balance!Sheet!
Off&balance&sheet&(Not&shown&as&debt&or&as&an&
asset).&Only&the&conventional&debt&of&$1,970&
million&shows&up&on&balance&sheet&
&
Cost&of&capital&=&8.20%(7350/9320)&+&4%&
(1970/9320)&=&7.31%&
Cost&of&equity&for&The&Gap&=&8.20%&
After0tax&cost&of&debt&=&4%&
Market&value&of&equity&=&7350&
Return&on&capital&=&1012&(10.35)/(3130+1970)&
&&&&&&&&&=&12.90%&

Operating!Leases!Treated!as!Debt!
!Income!Statement!
EBIT&&Leases&=&1,990&
0&Deprecn:&OL=&&&&&&628&
EBIT&&&&&&&&&&&&&&&&=&&1,362&
Interest&expense&will&rise&to&reflect&the&
conversion&of&operating&leases&as&debt.&Net&
income&should&not&change.&
Balance!Sheet!
Asset&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&Liability&
OL&Asset&&&&&&&4397&&&&&&&&&&&OL&Debt&&&&&4397&
Total&debt&=&4397&+&1970&=&$6,367&million&
Cost&of&capital&=&8.20%(7350/13717)&+&4%&
(6367/13717)&=&6.25%&
&
Return&on&capital&=&1362&(10.35)/(3130+6367)&
&&&&&&&&&=&9.30%&

&

Aswath Damodaran

115

The Magnitude of R&D Expenses

116
R&D as % of Operating Income
60.00%

50.00%

40.00%

30.00%

20.00%

10.00%

0.00%
Market

Aswath Damodaran

Petroleum

Computers

116

R&D Expenses: OperaJng or Capital Expenses

117

AccounJng standards require us to consider R&D as an

operaJng expense even though it is designed to
generate future growth. It is more logical to treat it as
capital expenditures.
To capitalize R&D,
Specify an amorJzable life for R&D (2 - 10 years)
Collect past R&D expenses for as long as the amorJzable life
Sum up the unamorJzed R&D over the period. (Thus, if the
amorJzable life is 5 years, the research asset can be obtained by
adding up 1/5th of the R&D expense from ve years ago, 2/5th
of the R&D expense from four years ago...:

Aswath Damodaran

117

Capitalizing R&D Expenses: SAP

118

R & D was assumed to have a 5-year life.

Year

Current
-1

-2

-3

-4

-5

R&D Expense
1020.02
993.99
909.39
898.25
969.38
744.67

UnamorJzed AmorJzaJon this year

1.00
1020.02
0.80
795.19 198.80
0.60
545.63 181.88
0.40
359.30 179.65
0.20
193.88 193.88
0.00
0.00
148.93

Value of research asset =

AmorJzaJon of research asset in 2004 =
Increase in OperaJng Income = 1020 - 903 =

Aswath Damodaran

2,914 million
903 million
117 million

118

The Eect of Capitalizing R&D at SAP

119

!
Conventional!Accounting!
Income!Statement!
EBIT&&R&D&&&=&&3045&
.&R&D&&&&&&&&&&&&&&=&&1020&
EBIT&&&&&&&&&&&&&&&&=&&2025&
EBIT&(1.t)&&&&&&&&=&&1285&m&

R&D!treated!as!capital!expenditure!
!Income!Statement!
EBIT&&R&D&=&&&3045&
.&Amort:&R&D&=&&&903&
EBIT&&&&&&&&&&&&&&&&=&2142&(Increase&of&117&m)&
EBIT&(1.t)&&&&&&&&=&1359&m&
Ignored&tax&benefit&=&(1020.903)(.3654)&=&43&
Adjusted&EBIT&(1.t)&=&1359+43&=&1402&m&
(Increase&of&117&million)&
Net&Income&will&also&increase&by&117&million&&
Balance!Sheet!
Balance!Sheet!
Off&balance&sheet&asset.&Book&value&of&equity&at&
Asset&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&Liability&
3,768&million&Euros&is&understated&because&
R&D&Asset&&&&2914&&&&&Book&Equity&&&+2914&
biggest&asset&is&off&the&books.&
Total&Book&Equity&=&3768+2914=&6782&mil&&
Capital!Expenditures!
Capital!Expenditures!
Conventional&net&cap&ex&of&2&million&
Net&Cap&ex&=&2+&1020&&903&=&119&mil&
Euros&
Cash!Flows!
Cash!Flows!
EBIT&(1.t)&&&&&&&&&&=&&1285&&
EBIT&(1.t)&&&&&&&&&&=&&&&&1402&&&
.&Net&Cap&Ex&&&&&&=&&&&&&&&2&
.&Net&Cap&Ex&&&&&&=&&&&&&&119&
FCFF&&&&&&&&&&&&&&&&&&=&&1283&&&&&&
FCFF&&&&&&&&&&&&&&&&&&=&&&&&1283&m&
Return&on&capital&=&1285/(3768+530)&
Return&on&capital&=&1402/(6782+530)&

Aswath Damodaran

119

III. One-Time and Non-recurring Charges

120

Assume that you are valuing a rm that is reporJng a

loss of $ 500 million, due to a one-Jme charge of $ 1
billion. What is the earnings you would use in your
valuaJon?
a.
b.

A loss of $ 500 million

A prot of $ 500 million

Would your answer be any dierent if the rm had

reported one-Jme losses like these once every ve
years?
a.
b.

Yes
No

Aswath Damodaran

120

IV. AccounJng Malfeasance.

121

Though all rms may be governed by the same accounJng

standards, the delity that they show to these standards can vary.
More aggressive rms will show higher earnings than more
conservaJve rms.
While you will not be able to catch outright fraud, you should look
for warning signals in nancial statements and correct for them:

Income from unspecied sources - holdings in other businesses that are

not revealed or from special purpose enJJes.
Income from asset sales or nancial transacJons (for a non-nancial rm)
Sudden changes in standard expense items - a big drop in S,G &A or R&D
expenses as a percent of revenues, for instance.
Frequent accounJng restatements
Accrual earnings that run ahead of cash earnings consistently
Big dierences between tax income and reported income

Aswath Damodaran

121

 V. Dealing with NegaJve or Abnormally Low

Earnings
122
A Framework for Analyzing Companies with Negative or Abnormally Low Earnings
Why are the earnings negative or abnormally low?

Temporary
Problems

Cyclicality:
Eg. Auto firm
in recession

Life Cycle related

reasons: Young
firms and firms with
infrastructure
problems

Leverage
Problems: Eg.
An otherwise
healthy firm with
too much debt.

Long-term
Operating
Problems: Eg. A firm
with significant
production or cost
problems.

Normalize Earnings

If firms size has not

changed significantly
over time

Average Dollar
Earnings (Net Income
if Equity and EBIT if
Firm made by
the firm over time

Aswath Damodaran

If firms size has changed

over time

Use firms average ROE (if

valuing equity) or average
ROC (if valuing firm) on current
BV of equity (if ROE) or current
BV of capital (if ROC)

Value the firm by doing detailed cash

flow forecasts starting with revenues and
reduce or eliminate the problem over
time.:
(a) If problem is structura
l: Target for
operating margins of stable firms in the
sector.
(b) If problem is leverage: Target for a
debt ratio that the firm will be comfortable
with by end of period, which could be its
own optimal or the industry average.
(c) If problem is operating: Target for an
industry-average operating margin.

122

What tax rate?

123

The tax rate that you should use in compuJng the aper-
tax operaJng income should be
a.
b.
c.
d.
e.
f.

The eecJve tax rate in the nancial statements (taxes paid/

Taxable income)
The tax rate based upon taxes paid and EBIT (taxes paid/EBIT)
The marginal tax rate for the country in which the company
operates
The weighted average marginal tax rate across the countries in
which the company operates
None of the above
Any of the above, as long as you compute your aper-tax cost
of debt using the same tax rate

Aswath Damodaran

123

The Right Tax Rate to Use

124

The choice really is between the eecJve and the marginal

tax rate. In doing projecJons, it is far safer to use the
marginal tax rate since the eecJve tax rate is really a
reecJon of the dierence between the accounJng and the
tax books.
By using the marginal tax rate, we tend to understate the
aper-tax operaJng income in the earlier years, but the aper-
tax tax operaJng income is more accurate in later years
If you choose to use the eecJve tax rate, adjust the tax rate
towards the marginal tax rate over Jme.

While an argument can be made for using a weighted average

marginal tax rate, it is safest to use the marginal tax rate of the
country

Aswath Damodaran

124

A Tax Rate for a Money Losing Firm

125

Assume that you are trying to esJmate the aper-tax

operaJng income for a rm with $ 1 billion in net
operaJng losses carried forward. This rm is expected to
have operaJng income of $ 500 million each year for the
next 3 years, and the marginal tax rate on income for all
rms that make money is 40%. EsJmate the aper-tax
operaJng income each year for the next 3 years.

Year 1
Year 2
Year 3
EBIT
500
500
500
Taxes
EBIT (1-t)
Tax rate

Aswath Damodaran

125

Net Capital Expenditures

126

Net capital expenditures represent the dierence

between capital expenditures and depreciaJon.
DepreciaJon is a cash inow that pays for some or a
lot (or someJmes all of) the capital expenditures.
In general, the net capital expenditures will be a
funcJon of how fast a rm is growing or expecJng to
grow. High growth rms will have much higher net
capital expenditures than low growth rms.
AssumpJons about net capital expenditures can
therefore never be made independently of
assumpJons about growth in the future.

Aswath Damodaran

126

Capital expenditures should include

127

Research and development expenses, once they have been

re-categorized as capital expenses. The adjusted net cap ex
will be

AcquisiJons of other rms, since these are like capital

expenditures. The adjusted net cap ex will be

Adjusted Net Capital Expenditures = Net Capital Expenditures +

Current years R&D expenses - AmorJzaJon of Research Asset

Adjusted Net Cap Ex = Net Capital Expenditures + AcquisiJons of other

rms - AmorJzaJon of such acquisiJons

Two caveats:
1. Most rms do not do acquisiJons every year. Hence, a normalized
measure of acquisiJons (looking at an average over Jme) should be used
2. The best place to nd acquisiJons is in the statement of cash ows,
usually categorized under other investment acJviJes

Aswath Damodaran

127

Ciscos AcquisiJons: 1999

128

Acquired
Method of AcquisiJon
GeoTel

Pooling

Fibex

Pooling

SenJent

Pooling

American Internet Purchase

Summa Four
Purchase

Clarity Wireless
Purchase

Selsius Systems
Purchase

PipeLinks

Purchase

Amteva Tech
Purchase






Aswath Damodaran

Price Paid
$1,344
$318
$103
$58
$129
$153
$134
$118
$159
$2,516

128

Ciscos Net Capital Expenditures in 1999

129

Cap Expenditures (from statement of CF) = $ 584 mil

- DepreciaJon (from statement of CF) = $ 486 mil
Net Cap Ex (from statement of CF)
= $ 98 mil
+ R & D expense


= $ 1,594 mil
- AmorJzaJon of R&D


= $ 485 mil
+ AcquisiJons



= $ 2,516 mil
Adjusted Net Capital Expenditures
= $3,723 mil

(AmorJzaJon was included in the depreciaJon number)

Aswath Damodaran

129

Working Capital Investments

130

In accounJng terms, the working capital is the dierence

between current assets (inventory, cash and accounts
receivable) and current liabiliJes (accounts payables, short
term debt and debt due within the next year)
A cleaner deniJon of working capital from a cash ow
perspecJve is the dierence between non-cash current
assets (inventory and accounts receivable) and non-debt
current liabiliJes (accounts payable)
Any investment in this measure of working capital Jes up
cash. Therefore, any increases (decreases) in working capital
will reduce (increase) cash ows in that period.
When forecasJng future growth, it is important to forecast
the eects of such growth on working capital needs, and
building these eects into the cash ows.

Aswath Damodaran

130

Working Capital: General ProposiJons

131

Changes in non-cash working capital from year to

year tend to be volaJle. A far beRer esJmate of non-
cash working capital needs, looking forward, can be
esJmated by looking at non-cash working capital as
a proporJon of revenues
Some rms have negaJve non-cash working capital.
Assuming that this will conJnue into the future will
generate posiJve cash ows for the rm. While this
is indeed feasible for a period of Jme, it is not
forever. Thus, it is beRer that non-cash working
capital needs be set to zero, when it is negaJve.

Aswath Damodaran

131

VolaJle Working Capital?

132

Revenues

Non-cash WC

% of Revenues
Change from last year
Average: last 3 years
Average: industry

Amazon
$ 1,640
-$419
-25.53%
$ (309)
-15.16%
8.71%

Cisco
$12,154
-$404
-3.32%
($700)
-3.16%
-2.71%

Motorola
$30,931
$2547
8.23%
($829)
8.91%
7.04%

WC as % of Revenue

3.00%

0.00%

8.23%

Aswath Damodaran

132

Dividends and Cash Flows to Equity

133

In the strictest sense, the only cash ow that an investor

will receive from an equity investment in a publicly
traded rm is the dividend that will be paid on the stock.
Actual dividends, however, are set by the managers of
the rm and may be much lower than the potenJal
dividends (that could have been paid out)
managers are conservaJve and try to smooth out dividends
managers like to hold on to cash to meet unforeseen future
conJngencies and investment opportuniJes

When actual dividends are less than potenJal dividends,

using a model that focuses only on dividends will under
state the true value of the equity in a rm.

Aswath Damodaran

133

Measuring PotenJal Dividends

134

Some analysts assume that the earnings of a rm represent its

potenJal dividends. This cannot be true for several reasons:

Earnings are not cash ows, since there are both non-cash revenues and
expenses in the earnings calculaJon
Even if earnings were cash ows, a rm that paid its earnings out as
dividends would not be invesJng in new assets and thus could not grow
ValuaJon models, where earnings are discounted back to the present, will
over esJmate the value of the equity in the rm

The potenJal dividends of a rm are the cash ows lep over aper
the rm has made any investments it needs to make to create
future growth and net debt repayments (debt repayments - new
debt issues)

The common categorizaJon of capital expenditures into discreJonary and

non-discreJonary loses its basis when there is future growth built into the
valuaJon.

Aswath Damodaran

134

EsJmaJng Cash Flows: FCFE

135

Cash ows to Equity for a Levered Firm

Net Income
- (Capital Expenditures - DepreciaJon)
- Changes in non-cash Working Capital
- (Principal Repayments - New Debt Issues)
= Free Cash ow to Equity

I have ignored preferred dividends. If preferred

stock exist, preferred dividends will also need to be
neRed out

Aswath Damodaran

135

EsJmaJng FCFE when Leverage is Stable

136

Net Income
- (1- ) (Capital Expenditures - DepreciaJon)
- (1- ) Working Capital Needs
= Free Cash ow to Equity
= Debt/Capital RaJo
For this rm,

Proceeds from new debt issues = Principal Repayments +

(Capital Expenditures - DepreciaJon + Working Capital Needs)

In compuJng FCFE, the book value debt to capital raJo

should be used when looking back in Jme but can be
replaced with the market value debt to capital raJo,
looking forward.

Aswath Damodaran

136

EsJmaJng FCFE: Disney

137

Net Income=$ 1533 Million

Capital spending = $ 1,746 Million
DepreciaJon per Share = $ 1,134 Million
Increase in non-cash working capital = $ 477 Million
Debt to Capital RaJo = 23.83%
EsJmaJng FCFE (1997):
Net Income

- (Cap. Exp - Depr)*(1-DR)
Chg. Working Capital*(1-DR)
= Free CF to Equity

$1,533 Mil
$465.90 [(1746-1134)(1-.2383)]
$363.33 [477(1-.2383)]
$ 704 Million

Dividends Paid

$ 345 Million

Aswath Damodaran

137

FCFE and Leverage: Is this a free lunch?

138
Debt Ratio and FCFE: Disney
1600

1400

1200

FCFE

1000

800

600

400

200

0
0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

Debt Ratio

Aswath Damodaran

138

FCFE and Leverage: The Other Shoe Drops

139
Debt Ratio and Beta
8.00

7.00

6.00

Beta

5.00

4.00

3.00

2.00

1.00

0.00
0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

Debt Ratio

Aswath Damodaran

139

Leverage, FCFE and Value

140

In a discounted cash ow model, increasing the debt/equity

raJo will generally increase the expected free cash ows to
equity investors over future Jme periods and also the cost of
equity applied in discounJng these cash ows. Which of the
following statements relaJng leverage to value would you
subscribe to?
a.
b.
c.
d.

Increasing leverage will increase value because the cash ow eects

will dominate the discount rate eects
Increasing leverage will decrease value because the risk eect will be
greater than the cash ow eects
Increasing leverage will not aect value because the risk eect will
exactly oset the cash ow eect
Any of the above, depending upon what company you are looking at
and where it is in terms of current leverage

Aswath Damodaran

140

Aswath Damodaran

III. ESTIMATING GROWTH

Growth can be good, bad or neutral

141

Ways of EsJmaJng Growth in Earnings

142

Look at the past

The historical growth in earnings per share is usually a

good starJng point for growth esJmaJon

Look at what others are esJmaJng

Analysts esJmate growth in earnings per share for many

rms. It is useful to know what their esJmates are.

Look at fundamentals
UlJmately, all growth in earnings can be traced to two

fundamentals - how much the rm is invesJng in new

projects, and what returns these projects are making for
the rm.

Aswath Damodaran

142

I. Historical Growth in EPS

143

Historical growth rates can be esJmated in a

number of dierent ways
ArithmeJc versus Geometric Averages
Simple versus Regression Models

Historical growth rates can be sensiJve to

the period used in the esJmaJon

In using historical growth rates, the following factors

have to be considered
how to deal with negaJve earnings
the eect of changing size

Aswath Damodaran

143

Motorola: ArithmeJc versus Geometric Growth

Rates
144

Aswath Damodaran

144

A Test
145

a.
b.
c.
d.

You are trying to esJmate the growth rate in

earnings per share at Time Warner from 1996 to
1997. In 1996, the earnings per share was a decit of
$0.05. In 1997, the expected earnings per share is $
0.25. What is the growth rate?
-600%
+600%
+120%
Cannot be esJmated

Aswath Damodaran

145

Dealing with NegaJve Earnings

146

When the earnings in the starJng period are negaJve,

the growth rate cannot be esJmated. (0.30/-0.05 =
-600%)

There are three soluJons:

Use the higher of the two numbers as the denominator

(0.30/0.25 = 120%)
Use the absolute value of earnings in the starJng period as the
denominator (0.30/0.05=600%)
Use a linear regression model and divide the coecient by the
average earnings.

When earnings are negaJve, the growth rate is

meaningless. Thus, while the growth rate can be
esJmated, it does not tell you much about the future.

Aswath Damodaran

146

The Eect of Size on Growth: Callaway Golf

147

Year Net Prot Growth Rate

1990 1.80
1991 6.40
255.56%
1992 19.30
201.56%
1993 41.20
113.47%
1994 78.00
89.32%
1995 97.70
25.26%
1996 122.30
25.18%
Geometric Average Growth Rate = 102%
Aswath Damodaran

147

ExtrapolaJon and its Dangers

148

Year Net Prot

1996 $ 122.30
1997 $ 247.05
1998 $ 499.03
1999 $ 1,008.05
2000 $ 2,036.25
2001 $ 4,113.23
If net prot conJnues to grow at the same rate as it has
in the past 6 years, the expected net income in 5 years
will be $ 4.113 billion.
Aswath Damodaran

148

II. Analyst Forecasts of Growth

149

While the job of an analyst is to nd under and over

valued stocks in the sectors that they follow, a signicant
proporJon of an analysts Jme (outside of selling) is
spent forecasJng earnings per share.
Most of this Jme, in turn, is spent forecasJng earnings per share
in the next earnings report
While many analysts forecast expected growth in earnings per
share over the next 5 years, the analysis and informaJon
(generally) that goes into this esJmate is far more limited.

Analyst forecasts of earnings per share and expected

growth are widely disseminated by services such as
Zacks and IBES, at least for U.S companies.

Aswath Damodaran

149

How good are analysts at forecasJng growth?

150

Analysts forecasts of EPS tend to be closer to the actual EPS than

simple Jme series models, but the dierences tend to be small

Study Group tested

Collins & Hopwood Value Line Forecasts
Brown & Roze Value Line Forecasts
Fried & Givoly Earnings Forecaster

The advantage that analysts have over Jme series models

Analyst Time Series

Error Model Error
31.7% 34.1%
28.4% 32.2%
16.4% 19.8%

tends to decrease with the forecast period (next quarter versus 5 years)
tends to be greater for larger rms than for smaller rms
tends to be greater at the industry level than at the company level

Forecasts of growth (and revisions thereof) tend to be highly

correlated across analysts.

Aswath Damodaran

150

Are some analysts more equal than others?

151

A study of All-America Analysts (chosen by InsJtuJonal

Investor) found that

There is no evidence that analysts who are chosen for the All-America
Analyst team were chosen because they were beRer forecasters of
earnings. (Their median forecast error in the quarter prior to being
chosen was 30%; the median forecast error of other analysts was 28%)
However, in the calendar year following being chosen as All-America
analysts, these analysts become slightly beRer forecasters than their
less fortunate brethren. (The median forecast error for All-America
analysts is 2% lower than the median forecast error for other analysts)
Earnings revisions made by All-America analysts tend to have a much
greater impact on the stock price than revisions from other analysts
The recommendaJons made by the All America analysts have a
greater impact on stock prices (3% on buys; 4.7% on sells). For these
recommendaJons the price changes are sustained, and they conJnue
to rise in the following period (2.4% for buys; 13.8% for the sells).

Aswath Damodaran

151

The Five Deadly Sins of an Analyst

152

Tunnel Vision: Becoming so focused on the sector and

valuaJons within the sector that you lose sight of the bigger
picture.
LemmingiJs: Strong urge felt to change recommendaJons &
revise earnings esJmates when other analysts do the same.
Stockholm Syndrome: Refers to analysts who start idenJfying
with the managers of the rms that they are supposed to
follow.
Factophobia (generally is coupled with delusions of being a
famous story teller): Tendency to base a recommendaJon on
a story coupled with a refusal to face the facts.
Dr. Jekyll/Mr.Hyde: Analyst who thinks his primary job is to
bring in investment banking business to the rm.

Aswath Damodaran

152

ProposiJons about Analyst Growth Rates

153

ProposiJon 1: There if far less private informaJon and far more

public informaJon in most analyst forecasts than is generally
claimed.
ProposiJon 2: The biggest source of private informaJon for
analysts remains the company itself which might explain

why there are more buy recommendaJons than sell recommendaJons

(informaJon bias and the need to preserve sources)
why there is such a high correlaJon across analysts forecasts and revisions
why All-America analysts become beRer forecasters than other analysts
aper they are chosen to be part of the team.

ProposiJon 3: There is value to knowing what analysts are

forecasJng as earnings growth for a rm. There is, however,
danger when they agree too much (lemmingiJs) and when they
agree to liRle (in which case the informaJon that they have is so
noisy as to be useless).

Aswath Damodaran

153

III. Fundamental Growth Rates

154

Investment
in Existing
Projects
$ 1000

Investment
in Existing
Projects
$1000

Investment
in Existing
Projects
$1000

Current Return on
Investment on
Projects
12%

Next Periods
Return on
Investment
12%

Change in
ROI from
current to next
period: 0%

Aswath Damodaran

Current
Earnings
$120

Investment
in New
Projects
$100

Investment
in New
Projects
$100

Return on
Investment on
New Projects
12%

Return on
Investment on
New Projects
12%

Next
Periods
Earnings
132

Change in Earnings

= $ 12

154

Growth Rate DerivaJons

155

In the special case where ROI on existing projects remains unchanged and is equal to the ROI on new projects
Investment in New Projects
Current Earnings
100
120
Reinvestment Rate
83.33%

X
X
X
X

Return on Investment

Change in Earnings
Current Earnings

12%

$12
$120

Return on Investment
12%

=
=

Growth Rate in Earnings

10%

in the more general case where ROI can change from period to period, this can be expanded as follows:
Investment in Existing Projects*(Change in ROI) + New Projects (ROI)
Investment in Existing Projects* Current ROI

Change in Earnings
Current Earnings

For instance, if the ROI increases from 12% to 13%, the expected growth rate can be written as follows:
$1,000 * (.13 - .12) + 100 (13%)
$ 1000 * .12

Aswath Damodaran

$23
$120

19.17%

155

EsJmaJng Fundamental Growth from new

investments: Three variaJons
156

Earnings Measure

Reinvestment Measure

Return Measure

Earnings per share

RetenJon RaJo = % of net

income retained by the
company = 1 Payout
raJo

Return on Equity = Net

Income/ Book Value of
Equity

Net Income from non-cash Equity reinvestment Rate =

assets
(Net Cap Ex + Change in
non-cash WC Change in
Debt)/ (Net Income)

Non-cash ROE = Net

Income from non-cash
assets/ (Book value of
equity Cash)

OperaJng Income

Return on Capital or ROIC

= Aper-tax OperaJng
Income/ (Book value of
equity + Book value of
debt Cash)

Aswath Damodaran

Reinvestment Rate = (Net

Cap Ex + Change in non-
cash WC)/ Aper-tax
OperaJng Income

156

I. Expected Long Term Growth in EPS

157

When looking at growth in earnings per share, these inputs

can be cast as follows:

Reinvestment Rate = Retained Earnings/ Current Earnings = RetenJon

RaJo
Return on Investment = ROE = Net Income/Book Value of Equity

In the special case where the current ROE is expected to

remain unchanged
gEPS = Retained Earnings t-1/ NI t-1 * ROE

= RetenJon RaJo * ROE

= b * ROE
ProposiJon 1: The expected growth rate in earnings for a
company cannot exceed its return on equity in the long term.

Aswath Damodaran

157

EsJmaJng Expected Growth in EPS: Wells Fargo

in 2008
158

Return on equity (based on 2008 earnings)= 17.56%

RetenJon RaJo (based on 2008 earnings and
dividends) = 45.37%
Expected growth rate in earnings per share for Wells
Fargo, if it can maintain these numbers.
Expected Growth Rate = 0.4537 (17.56%) = 7.97%

Aswath Damodaran

158

Regulatory Eects on Expected EPS growth

159

Assume now that the banking crisis of 2008 will have

an impact on the capital raJos and protability of
banks. In parJcular, you can expect that the book
capital (equity) needed by banks to do business will
increase 30%, starJng now.
Assuming that Wells conJnues with its exisJng
businesses, esJmate the expected growth rate in
earnings per share for the future.
New Return on Equity =
Expected growth rate =

Aswath Damodaran

159

One way to pump up ROE: Use more debt

160

ROE = ROC + D/E (ROC - i (1-t))

where,
ROC = EBITt (1 - tax rate) / Book value of Capitalt-1
D/E = BV of Debt/ BV of Equity
i = Interest Expense on Debt / BV of Debt
t = Tax rate on ordinary income
Note that Book value of capital = Book Value of Debt
+ Book value of Equity- Cash.
Aswath Damodaran

160

Decomposing ROE: Brahma in 1998

161

Brahma (now Ambev) had an extremely high return

on equity, partly because it borrowed money at a
rate well below its return on capital
Return on Capital = 19.91%
Debt/Equity RaJo = 77%
Aper-tax Cost of Debt = 5.61%
Return on Equity = ROC + D/E (ROC - i(1-t))

= 19.91% + 0.77 (19.91% - 5.61%) = 30.92%

This seems like an easy way to deliver higher growth

in earnings per share. What (if any) is the downside?

Aswath Damodaran

161

Decomposing ROE: Titan Watches (India)

162

Return on Capital = 9.54%

Debt/Equity RaJo = 191% (book value terms)
Aper-tax Cost of Debt = 10.125%
Return on Equity = ROC + D/E (ROC - i(1-t))

= 9.54% + 1.91 (9.54% - 10.125%) = 8.42%

Aswath Damodaran

162

II. Expected Growth in Net Income from non-

cash assets
163

The limitaJon of the EPS fundamental growth equaJon is that it

focuses on per share earnings and assumes that reinvested
earnings are invested in projects earning the return on equity. To
the extent that companies retain money in cash balances, the
eect on net income can be muted.
A more general version of expected growth in earnings can be
obtained by subsJtuJng in the equity reinvestment into real
investments (net capital expenditures and working capital) and
modifying the return on equity deniJon to exclude cash:

Net Income from non-cash assets = Net income Interest income from
cash (1- t)
Equity Reinvestment Rate = (Net Capital Expenditures + Change in
Working Capital) (1 - Debt RaJo)/ Net Income from non-cash assets
Non-cash ROE = Net Income from non-cash assets/ (BV of Equity Cash)
Expected GrowthNet Income = Equity Reinvestment Rate * Non-cash ROE

Aswath Damodaran

163

EsJmaJng expected growth in net income from

non-cash assets: Coca Cola in 2010
164

In 2010, Coca Cola reported net income of $11,809 million. It had a

total book value of equity of $25,346 million at the end of 2009.
Coca Cola had a cash balance of $7,021 million at the end of 2009,
on which it earned income of $105 million in 2010.
Coca Cola had capital expenditures of $2,215 million, depreciaJon
of $1,443 million and reported an increase in working capital of
$335 million. Coca Colas total debt increased by $150 million
during 2010.

Equity Reinvestment = 2215- 1443 + 335-150 = $957 million

Non-cash Net Income = $11,809 - $105 = $ 11,704 million
Non-cash book equity = $25,346 - $7021 = $18,325 million
Reinvestment Rate = $957 million/ $11,704 million= 8.18%
Non-cash ROE = $11,704 million/ $18,325 million = 63.87%
Expected growth rate = 8.18% * 63.87% = 5.22%

Aswath Damodaran

164

III. Expected Growth in EBIT And Fundamentals:

Stable ROC and Reinvestment Rate
165

When looking at growth in operaJng income, the

deniJons are

Reinvestment Rate = (Net Capital Expenditures + Change in

WC)/EBIT(1-t)
Return on Investment = ROC = EBIT(1-t)/(BV of Debt + BV of
Equity-Cash)

Reinvestment Rate and Return on Capital

Expected Growth rate in OperaJng Income

= (Net Capital Expenditures + Change in WC)/EBIT(1-t) * ROC
= Reinvestment Rate * ROC

ProposiJon: The net capital expenditure needs of a rm,

for a given growth rate, should be inversely proporJonal
to the quality of its investments.

Aswath Damodaran

165

EsJmaJng Growth in OperaJng Income

166

Ciscos Fundamentals
Reinvestment Rate = 106.81%
Return on Capital =34.07%
Expected Growth in EBIT =(1.0681)(.3407) = 36.39%

Motorolas Fundamentals
Reinvestment Rate = 52.99%
Return on Capital = 12.18%
Expected Growth in EBIT = (.5299)(.1218) = 6.45%

Aswath Damodaran

166

IV. OperaJng Income Growth when Return on

Capital is Changing
167

When the return on capital is changing, there will be a

second component to growth, posiJve if the return on
capital is increasing and negaJve if the return on capital
is decreasing.
If ROCt is the return on capital in period t and ROC t+1 is
the return on capital in period t+1, the expected growth
rate in operaJng income will be:
Expected Growth Rate = ROC t+1 * Reinvestment rate



+(ROC t+1 ROCt) / ROCt
If the change is over mulJple periods, the second
component should be spread out over each period.

Aswath Damodaran

167

Motorolas Growth Rate

168

Motorolas current return on capital is 12.18% and its reinvestment rate

is 52.99%.
We expect Motorolas return on capital to rise to 17.22% over the next 5
years (which is half way towards the industry average)
Expected Growth Rate
= ROC New Investments*Reinvestment Rate Current+ {[1+(ROC In 5 years-ROC Current)/ROC
1/5
Current] -1}
= .1722*.5299 +{ [1+(.1722-.1218)/.1218]1/5-1}
= .1629 or 16.29%

One way to think about this is to decompose Motorolas expected

growth into

Growth from new investments: .1722*5299= 9.12%

Growth from more eciently using exisJng investments: 16.29%-9.12%= 7.17%

Note that I am assuming that the new investments start making 17.22%
immediately, while allowing for exisJng assets to improve returns gradually
Aswath Damodaran

168

The Value of Growth

169

Expected growth = Growth from new investments + Efficiency growth

= Reinv Rate * ROC
+ (ROCt-ROCt-1)/ROCt-1
Assume that your cost of capital is 10%. As an investor, rank these
firms in the order of most value growth to least value growth.

Aswath Damodaran

169

V. EsJmaJng Growth when OperaJng Income is

NegaJve or Margins are changing
170

All of the fundamental growth equaJons assume that the rm has a

return on equity or return on capital it can sustain in the long term.
When operaJng income is negaJve or margins are expected to change
over Jme, we use a three step process to esJmate growth:

EsJmate growth rates in revenues over Jme

n Use historical revenue growth to get esJmates of revenue growth in the near
future
n Decrease the growth rate as the rm becomes larger
n Keep track of absolute revenues to make sure that the growth is feasible
EsJmate expected operaJng margins each year
n Set a target margin that the rm will move towards
n Adjust the current margin towards the target margin
EsJmate the capital that needs to be invested to generate revenue growth and
expected margins
n EsJmate a sales to capital raJo that you will use to generate reinvestment
needs each year.

Aswath Damodaran

170

Sirius Radio: Revenues and Revenue Growth-

June 2006
171

Year

Revenue Revenue OperaJng

OperaJng

Growth $

Margin

Income

Current

$187

-419.92%

-$787

200.00% $562

-199.96%

-$1,125

100.00% $1,125

-89.98%

-$1,012

80.00%

$2,025

-34.99%

-$708

60.00%

$3,239

-7.50%

-$243

40.00%

$4,535

6.25%

$284

25.00%

$5,669

13.13%

$744

20.00%

$6,803

16.56%

$1,127

15.00%

$7,823

18.28%

$1,430

10.00%

$8,605

19.14%

$1,647

10

5.00%

$9,035

19.57%

$1,768

Aswath Damodaran

Target margin based upon

Clear Channel

171

Sirius: Reinvestment Needs

172
Year
Revenues Change in revenue
Sales/Capital Ratio
Reinvestment
Current
$187
1
$562
$375
1.50
$250
2
$1,125
$562
1.50
$375
3
$2,025
$900
1.50
$600
4
$3,239
$1,215
1.50
$810
5
$4,535
$1,296
1.50
$864
6
$5,669
$1,134
1.50
$756
7
$6,803
$1,134
1.50
$756
8
$7,823
$1,020
1.50
$680
9
$8,605
$782
1.50
$522
10
$9,035
$430
1.50
$287

Capital Invested
Operating Income (Loss)
Imputed ROC
$
1,657
-$787
$
1,907
-$1,125
-67.87%
$
2,282
-$1,012
-53.08%
$
2,882
-$708
-31.05%
$
3,691
-$243
-8.43%
$
4,555
$284
7.68%
$
5,311
$744
16.33%
$
6,067
$1,127
21.21%
$
6,747
$1,430
23.57%
$
7,269
$1,647
17.56%
$
7,556
$1,768
15.81%

Capital invested in year t+!=

Capital invested in year t +
Reinvestment in year t+1
Industry average Sales/Cap Ratio

Aswath Damodaran

172

Expected Growth Rate

Equity Earnings

Analysts

Fundamentals

Operating Income

Historical

Fundamentals

Stable ROC

Changing ROC

ROC *
Reinvestment Rate

ROCt+1*Reinvestment Rate
+ (ROCt+1-ROCt)/ROCt

Earnings per share

Stable ROE

ROE * Retention Ratio

173

Changing ROE

ROEt+1*Retention Ratio
+ (ROEt+1-ROEt)/ROEt

Aswath Damodaran

ROE * Equity
Reinvestment Ratio

Negative Earnings

1. Revenue Growth
2. Operating Margins
3. Reinvestment Needs

Net Income

Stable ROE

Historical

Changing ROE

ROEt+1*Eq. Reinv Ratio

+ (ROEt+1-ROEt)/ROEt

Aswath Damodaran

IV. CLOSURE IN VALUATION

The Big Enchilada

174

Ge}ng Closure in ValuaJon

175

A publicly traded rm potenJally has an innite life. The value is

therefore the present value of cash ows forever.
t= CF
t
Value =
t
t=1 (1+r)

Since we cannot esJmate cash ows forever, we esJmate cash ows for a
growth period and then esJmate a terminal value, to capture the value
at the end of the period:
t=N CF
t + Terminal Value
Value =
N
t
(1+r)
t=1 (1+r)

Aswath Damodaran

175

Ways of EsJmaJng Terminal Value

176

Terminal Value

Liquidation
Value

Most useful
when assets
are separable
and
marketable

Aswath Damodaran

Multiple Approach

Easiest approach but

makes the valuation
a relative valuation

Stable Growth
Model

Technically soundest,
but requires that you
make judgments about
when the firm will grow
at a stable rate which it
can sustain forever,
and the excess returns
(if any) that it will earn
during the period.
176

Ge}ng Terminal Value Right

1. Obey the growth cap
177

When a rms cash ows grow at a constant rate forever, the present value of
those cash ows can be wriRen as:
Value = Expected Cash Flow Next Period / (r - g)
where,
r = Discount rate (Cost of Equity or Cost of Capital)
g = Expected growth rate

The stable growth rate cannot exceed the growth rate of the economy but it can
be set lower.

If you assume that the economy is composed of high growth and stable growth rms, the
growth rate of the laRer will probably be lower than the growth rate of the economy.
The stable growth rate can be negaJve. The terminal value will be lower and you are assuming
that your rm will disappear over Jme.
If you use nominal cashows and discount rates, the growth rate should be nominal in the
currency in which the valuaJon is denominated.

One simple proxy for the nominal growth rate of the economy is the riskfree rate.

Aswath Damodaran

177

Ge}ng Terminal Value Right

2. Dont wait too long
178

Assume that you are valuing a young, high growth rm with

great potenJal, just aper its iniJal public oering. How long
would you set your high growth period?
a.
b.
c.
d.

< 5 years
5 years
10 years
>10 years

While analysts rouJnely assume very long high growth

periods (with substanJal excess returns during the periods),
the evidence suggests that they are much too opJmisJc.
Most growth rms have diculty sustaining their growth for
long periods, especially while earning excess returns.

Aswath Damodaran

178

And the key determinant of growth periods is

the companys compeJJve advantage
179

Recapping a key lesson about growth, it is not

growth per se that creates value but growth with
excess returns. For growth rms to conJnue to
generate value creaJng growth, they have to be able
to keep the compeJJon at bay.
ProposiJon 1: The stronger and more sustainable
the compeJJve advantages, the longer a growth
company can sustain value creaJng growth.
ProposiJon 2: Growth companies with strong and
sustainable compeJJve advantages are rare.

Aswath Damodaran

179

Dont forget that growth has to be earned..

3. Think about what your rm will earn as returns forever..
180

In the secJon on expected growth, we laid out the fundamental

equaJon for growth:
Growth rate = Reinvestment Rate * Return on invested capital

+ Growth rate from improved eciency
In stable growth, you cannot count on eciency delivering growth
(why?) and you have to reinvest to deliver the growth rate that you
have forecast. Consequently, your reinvestment rate in stable
growth will be a funcJon of your stable growth rate and what you
believe the rm will earn as a return on capital in perpetuity:

Reinvestment Rate = Stable growth rate/ Stable period Return on capital

A key issue in valuaJon is whether it okay to assume that rms can

earn more than their cost of capital in perpetuity. There are some
(McKinsey, for instance) who argue that the return on capital =
cost of capital in stable growth

Aswath Damodaran

180

There are some rms that earn excess returns

181

While growth rates seem to fade quickly as rms become larger, well
managed rms seem to do much beRer at sustaining excess returns for
longer periods.

Aswath Damodaran

181

And dont fall for sleight of hand

182

A typical assumpJon in many DCF valuaJons, when it

comes to stable growth, is that capital expenditures
oset depreciaJon and there are no working capital
needs. Stable growth rms, we are told, just have to
make maintenance cap ex (replacing exisJng assets ) to
deliver growth. If you make this assumpJon, what
expected growth rate can you use in your terminal value
computaJon?
What if the stable growth rate = inaJon rate? Is it okay
to make this assumpJon then?

Aswath Damodaran

182

Ge}ng Terminal Value Right

4. Be internally consistent..
183

Risk and costs of equity and capital: Stable growth rms tend
to

Have betas closer to one

Have debt raJos closer to industry averages (or mature company
averages)
Country risk premiums (especially in emerging markets should evolve
over Jme)

The excess returns at stable growth rms should approach

(or become) zero. ROC -> Cost of capital and ROE -> Cost of
equity
The reinvestment needs and dividend payout raJos should
reect the lower growth and excess returns:

Stable period payout raJo = 1 - g/ ROE

Stable period reinvestment rate = g/ ROC

Aswath Damodaran

183

Aswath Damodaran

184

V. BEYOND INPUTS: CHOOSING

AND USING THE RIGHT MODEL
Choosing the right model

Summarizing the Inputs

185

In summary, at this stage in the process, we should have

an esJmate of the
the current cash ows on the investment, either to equity
investors (dividends or free cash ows to equity) or to the rm
(cash ow to the rm)
the current cost of equity and/or capital on the investment
the expected growth rate in earnings, based upon historical
growth, analysts forecasts and/or fundamentals

The next step in the process is deciding

which cash ow to discount, which should indicate
which discount rate needs to be esJmated and
what paRern we will assume growth to follow

Aswath Damodaran

185

Which cash ow should I discount?

186

Use Equity ValuaJon

(a) for rms which have stable leverage, whether high or not, and
(b) if equity (stock) is being valued

Use Firm ValuaJon

(a) for rms which have leverage which is too high or too low, and
expect to change the leverage over Jme, because debt payments
and issues do not have to be factored in the cash ows and the
discount rate (cost of capital) does not change dramaJcally over
Jme.
(b) for rms for which you have parJal informaJon on leverage
(eg: interest expenses are missing..)
(c) in all other cases, where you are more interested in valuing the
rm than the equity. (Value ConsulJng?)

Aswath Damodaran

186

Given cash ows to equity, should I discount

dividends or FCFE?
187

Use the Dividend Discount Model

(a) For rms which pay dividends (and repurchase stock) which are
close to the Free Cash Flow to Equity (over a extended period)
(b)For rms where FCFE are dicult to esJmate (Example: Banks
and Financial Service companies)

Use the FCFE Model

(a) For rms which pay dividends which are signicantly higher or
lower than the Free Cash Flow to Equity. (What is signicant? ... As
a rule of thumb, if dividends are less than 80% of FCFE or dividends
are greater than 110% of FCFE over a 5-year period, use the FCFE
model)
(b) For rms where dividends are not available (Example: Private
Companies, IPOs)

Aswath Damodaran

187

What discount rate should I use?

188

Cost of Equity versus Cost of Capital

If discounJng cash ows to equity -> Cost of Equity

If discounJng cash ows to the rm
-> Cost of Capital

What currency should the discount rate (risk free rate)

be in?

Match the currency in which you esJmate the risk free rate to
the currency of your cash ows

Should I use real or nominal cash ows?

If discounJng real cash ows

-> real cost of capital
If nominal cash ows

-> nominal cost of capital
If inaJon is low (<10%), sJck with nominal cash ows since
taxes are based upon nominal income
If inaJon is high (>10%) switch to real cash ows

Aswath Damodaran

188

Which Growth PaRern Should I use?

189

If your rm is

large and growing at a rate close to or less than growth rate of the economy, or
constrained by regulaJon from growing at rate faster than the economy
has the characterisJcs of a stable rm (average risk & reinvestment rates)

Use a Stable Growth Model

If your rm

is large & growing at a moderate rate ( Overall growth rate + 10%) or

has a single product & barriers to entry with a nite life (e.g. patents)

Use a 2-Stage Growth Model

If your rm

is small and growing at a very high rate (> Overall growth rate + 10%) or
has signicant barriers to entry into the business
has rm characterisJcs that are very dierent from the norm

Use a 3-Stage or n-stage Model

Aswath Damodaran

189

The Building Blocks of ValuaJon

190

Choose a
Cash Flow

Dividends
Expected Dividends to
Stockholders

Cashflows to Equity

Cashflows to Firm

Net Income

EBIT (1- tax rate)

- (Capital Exp. - Deprecn)
- (1- ) (Capital Exp. - Deprecn)
- Change in Work. Capital
- (1- ) Change in Work. Capital
= Free Cash flow to Equity (FCFE) = Free Cash flow to Firm (FCFF)
[ = Debt Ratio]

& A Discount Rate

Cost of Equity

Basis: The riskier the investment, the greater is the cost of equity.

Models:

& a growth pattern

Cost of Capital
WACC = ke ( E/ (D+E))
+ kd ( D/(D+E))

CAPM: Riskfree Rate + Beta (Risk Premium)

kd = Current Borrowing Rate (1-t)

APM: Riskfree Rate + Betaj (Risk Premiumj): n factors

E,D: Mkt Val of Equity and Debt

Stable Growth

Two-Stage Growth
g

Three-Stage Growth
g

|
t

Aswath Damodaran

High Growth

|
Stable

High Growth

Transition

Stable

190

Aswath Damodaran

191

6. TYING UP LOOSE ENDS

The trouble starts aper you tell me you are done..

But what comes next?

192
Value of Operating Assets

Since this is a discounted cashflow valuation, should there be a real option

premium?

+ Cash and Marketable

Securities

Operating versus Non-opeating cash

Should cash be discounted for earning a low return?

+ Value of Cross Holdings

How do you value cross holdings in other companies?

What if the cross holdings are in private businesses?

+ Value of Other Assets

What about other valuable assets?

How do you consider under utlilized assets?
Should you discount this value for opacity or complexity?
How about a premium for synergy?
What about a premium for intangibles (brand name)?

Value of Firm

- Value of Debt

What should be counted in debt?

Should you subtract book or market value of debt?
What about other obligations (pension fund and health care?
What about contingent liabilities?
What about minority interests?

= Value of Equity

Should there be a premium/discount for control?

Should there be a discount for distress

- Value of Equity Options

What equity options should be valued here (vested versus non-vested)?

How do you value equity options?

= Value of Common Stock

Should you divide by primary or diluted shares?

/ Number of shares
= Value per share

Aswath Damodaran

Should there be a discount for illiquidity/ marketability?

Should there be a discount for minority interests?

192

1. The Value of Cash

193

The simplest and most direct way of dealing with cash and
marketable securiJes is to keep it out of the valuaJon - the
cash ows should be before interest income from cash and
securiJes, and the discount rate should not be contaminated
by the inclusion of cash. (Use betas of the operaJng assets
alone to esJmate the cost of equity).
Once the operaJng assets have been valued, you should add
back the value of cash and marketable securiJes.
In many equity valuaJons, the interest income from cash is
included in the cashows. The discount rate has to be
adjusted then for the presence of cash. (The beta used will be
weighted down by the cash holdings). Unless cash remains a
xed percentage of overall value over Jme, these valuaJons
will tend to break down.

Aswath Damodaran

193

An Exercise in Cash ValuaJon

194

Enterprise Value
Cash

Return on Capital
Cost of Capital
Trades in

Aswath Damodaran

Company A Company B Company C

$ 1 billion
$ 100 mil
10%
10%
US

$ 1 billion
$ 100 mil
5%

10%
US

$ 1 billion
$ 100 mil
22%
12%
ArgenJna

194

Should you ever discount cash for its low

returns?
195

There are some analysts who argue that companies with a lot of
cash on their balance sheets should be penalized by having the
excess cash discounted to reect the fact that it earns a low return.

Excess cash is usually dened as holding cash that is greater than what the
rm needs for operaJons.
A low return is dened as a return lower than what the rm earns on its
non-cash investments.

This is the wrong reason for discounJng cash. If the cash is

invested in riskless securiJes, it should earn a low rate of return. As
long as the return is high enough, given the riskless nature of the
investment, cash does not destroy value.
There is a right reason, though, that may apply to some
companies Managers can do stupid things with cash (overpriced
acquisiJons, pie-in-the-sky projects.) and you have to discount
for this possibility.

Aswath Damodaran

195

Cash: Discount or Premium?

196

Aswath Damodaran

196

The Case of Closed End Funds: Price and NAV

197

Aswath Damodaran

197

A Simple ExplanaJon for the Closed End

Discount
198

Assume that you have a closed-end fund that invests

in average risk stocks. Assume also that you
expect the market (average risk investments) to
make 11.5% annually over the long term. If the
closed end fund underperforms the market by
0.50%, esJmate the discount on the fund.

Aswath Damodaran

198

A Premium for Marketable SecuriJes: Berkshire

Hathaway
199

Aswath Damodaran

199

2. Dealing with Holdings in Other rms

200

Holdings in other rms can be categorized into

Minority passive holdings, in which case only the dividend

from the holdings is shown in the balance sheet

Minority acJve holdings, in which case the share of equity
income is shown in the income statements
Majority acJve holdings, in which case the nancial
statements are consolidated.

Aswath Damodaran

200

An Exercise in Valuing Cross Holdings

201

Assume that you have valued Company A using consolidated

nancials for $ 1 billion (using FCFF and cost of capital) and that
the rm has $ 200 million in debt. How much is the equity in
Company A worth?
Now assume that you are told that Company A owns 10% of
Company B and that the holdings are accounted for as passive
holdings. If the market cap of company B is $ 500 million, how
much is the equity in Company A worth?
Now add on the assumpJon that Company A owns 60% of
Company C and that the holdings are fully consolidated. The
minority interest in company C is recorded at $ 40 million in
Company As balance sheet. How much is the equity in Company A
worth?

Aswath Damodaran

201

More on Cross Holding ValuaJon

202

Building on the previous example, assume that

You have valued equity in company B at $ 250 million

(which is half the markets esJmate of value currently)

Company A is a steel company and that company C is a
chemical company. Furthermore, assume that you have
valued the equity in company C at $250 million.
EsJmate the value of equity in company A.

Aswath Damodaran

202

If you really want to value cross holdings right.

203

Step 1: Value the parent company without any cross

holdings. This will require using unconsolidated nancial
statements rather than consolidated ones.
Step 2: Value each of the cross holdings individually. (If
you use the market values of the cross holdings, you will
build in errors the market makes in valuing them into
your valuaJon.
Step 3: The nal value of the equity in the parent
company with N cross holdings will be:
Value of un-consolidated parent company
Debt of un-consolidated parent company
j= N
+

% owned of Company j * (Value of Company j -

Debt of Company j)

j=1

Aswath Damodaran

203

Valuing Yahoo as the sum of its intrinsic

pieces
204

Aswath Damodaran

204

If you have to seRle for an approximaJon, try

this
205

For majority holdings, with full consolidaJon, convert the

minority interest from book value to market value by
applying a price to book raJo (based upon the sector average
for the subsidiary) to the minority interest.

EsJmated market value of minority interest = Minority interest on

balance sheet * Price to Book raJo for sector (of subsidiary)
Subtract this from the esJmated value of the consolidated rm to get
to value of the equity in the parent company.

For minority holdings in other companies, convert the book

value of these holdings (which are reported on the balance
sheet) into market value by mulJplying by the price to book
raJo of the sector(s). Add this value on to the value of the
operaJng assets to arrive at total rm value.

Aswath Damodaran

205

Yahoo: A pricing game?

206

Aswath Damodaran

206

3. Other Assets that have not been counted

yet..
207

Assets that you should not be counJng (or adding on to DCF values)

If an asset is contribuJng to your cashows, you cannot count the market value of
the asset in your value. Thus, you should not be counJng the real estate on which
your oces stand, the PP&E represenJng your factories and other producJve
assets, any values aRached to brand names or customer lists and denitely no non-
assets (such as goodwill).

Assets that you can count (or add on to your DCF valuaJon)

Overfunded pension plans: If you have a dened benet plan and your assets
exceed your expected liabiliJes, you could consider the over funding with two
caveats:
n CollecJve bargaining agreements may prevent you from laying claim to these
excess assets.
n There are tax consequences. Open, withdrawals from pension plans get taxed at
much higher rates.
UnuJlized assets: If you have assets or property that are not being uJlized to
generate cash ows (vacant land, for example), you have not valued it yet. You can
assess a market value for these assets and add them on to the value of the rm.

Aswath Damodaran

207

4. A Discount for Complexity:

An Experiment
208

Company A Company B
OperaJng Income
$ 1 billion $ 1 billion
Tax rate


40%
40%
ROIC


10%
10%
Expected Growth
5%
5%
Cost of capital

8%
8%
Business Mix

Single
MulJple
Holdings


Simple
Complex
AccounJng

Transparent Opaque
Which rm would you value more highly?
Aswath Damodaran

208

Measuring Complexity: Volume of Data in

Financial Statements
209

Company
General Electric
Microsoft
Wal-mart
Exxon Mobil
Pfizer
Citigroup
Intel
AIG
Johnson & Johnson
IBM

Aswath Damodaran

Number of pages in last 10Q

65
63
38
86
171
252
69
164
63
85

Number of pages in last 10K

410
218
244
332
460
1026
215
720
218
353

209

Measuring Complexity: A Complexity Score

210

Aswath Damodaran

210

Dealing with Complexity

211

In Discounted Cashow ValuaJon

The Aggressive Analyst: Trust the rm to tell the truth and value the rm
based upon the rms statements about their value.
The ConservaJve Analyst: Dont value what you cannot see.
The Compromise: Adjust the value for complexity
n Adjust cash ows for complexity
n Adjust the discount rate for complexity
n Adjust the expected growth rate/ length of growth period
n Value the rm and then discount value for complexity

In relaJve valuaJon
In a relaJve valuaJon, you may be able to assess the price that the market
is charging for complexity:
With the hundred largest market cap rms, for instance:
PBV = 0.65 + 15.31 ROE 0.55 Beta + 3.04 Expected growth rate 0.003 #
Pages in 10K

Aswath Damodaran

211

5. Be circumspect about dening debt for cost

of capital purposes
212

General Rule: Debt generally has the following characterisJcs:

Dened as such, debt should include

All interest bearing liabiliJes, short term as well as long term

All leases, operaJng as well as capital

Debt should not include

Commitment to make xed payments in the future

The xed payments are tax deducJble
Failure to make the payments can lead to either default or loss of control
of the rm to the party to whom payments are due.

Accounts payable or supplier credit

Be wary of your conservaJve impulses which will tell you to count

everything as debt. That will push up the debt raJo and lead you to
understate your cost of capital.

Aswath Damodaran

212

Book Value or Market Value

213

You are valuing a distressed telecom company and have

arrived at an esJmate of $ 1 billion for the enterprise value
(using a discounted cash ow valuaJon). The company has $
1 billion in face value of debt outstanding but the debt is
trading at 50% of face value (because of the distress). What is
the value of the equity to you as an investor?
a.
b.

The equity is worth nothing (EV minus Face Value of Debt)

The equity is worth $ 500 million (EV minus Market Value of Debt)

Would your answer be dierent if you were told that the

liquidaJon value of the assets of the rm today is $1.2 billion
and that you were planning to liquidate the rm today?

Aswath Damodaran

213

But you should consider other potenJal

liabiliJes when ge}ng to equity value
214

If you have under funded pension fund or health care

plans, you should consider the under funding at this
stage in ge}ng to the value of equity.

If you do so, you should not double count by also including a

cash ow line item reecJng cash you would need to set aside
to meet the unfunded obligaJon.
You should not be counJng these items as debt in your cost of
capital calculaJons.

If you have conJngent liabiliJes - for example, a

potenJal liability from a lawsuit that has not been
decided - you should consider the expected value of
these conJngent liabiliJes

Value of conJngent liability = Probability that the liability will

occur * Expected value of liability

Aswath Damodaran

214

6. Equity OpJons issued by the rm..

215

Any opJons issued by a rm, whether to

management or employees or to investors
(converJbles and warrants) create claims on the
equity of the rm.
By creaJng claims on the equity, they can aect the
value of equity per share.
Failing to fully take into account this claim on the
equity in valuaJon will result in an overstatement of
the value of equity per share.

Aswath Damodaran

215

Why do opJons aect equity value per share?

216

It is true that opJons can increase the number of shares

outstanding but diluJon per se is not the problem.
OpJons aect equity value at exercise because
Shares are issued at below the prevailing market price. OpJons
get exercised only when they are in the money.
AlternaJvely, the company can use cashows that would have
been available to equity investors to buy back shares which are
then used to meet opJon exercise. The lower cashows reduce
equity value.

OpJons aect equity value before exercise because we

have to build in the expectaJon that there is a
probability and a cost to exercise.

Aswath Damodaran

216

A simple example
217

XYZ company has $ 100 million in free cashows to

the rm, growing 3% a year in perpetuity and a cost
of capital of 8%. It has 100 million shares
outstanding and $ 1 billion in debt. Its value can be
wriRen as follows:
Value of rm = 100 / (.08-.03)
Debt



= Equity


Value per share

Aswath Damodaran

= 2000
= 1000
= 1000
= 1000/100 = $10

217

Now come the opJons

218

XYZ decides to give 10 million opJons at the money

(with a strike price of $10) to its CEO. What eect
will this have on the value of equity per share?
a.
b.

c.

None. The opJons are not in-the-money.

Decrease by 10%, since the number of shares could
increase by 10 million
Decrease by less than 10%. The opJons will bring in cash
into the rm but they have Jme value.

Aswath Damodaran

218

Dealing with Employee OpJons: The Bludgeon

Approach
219

The simplest way of dealing with opJons is to try to

adjust the denominator for shares that will become
outstanding if the opJons get exercised.
In the example cited, this would imply the following:

Value of rm = 100 / (.08-.03)

Debt



= Equity


Number of diluted shares
Value per share

Aswath Damodaran

= 2000
= 1000
= 1000
= 110
= 1000/110 = $9.09

219

Problem with the diluted approach

220

The diluted approach fails to consider that exercising

opJons will bring in cash into the rm.
Consequently, they will overesJmate the impact of
opJons and understate the value of equity per
share.
The degree to which the approach will understate
value will depend upon how high the exercise price
is relaJve to the market price.
In cases where the exercise price is a fracJon of the
prevailing market price, the diluted approach will
give you a reasonable esJmate of value per share.

Aswath Damodaran

220

The Treasury Stock Approach

221

The treasury stock approach adds the proceeds from

the exercise of opJons to the value of the equity
before dividing by the diluted number of shares
outstanding.
In the example cited, this would imply the following:

Value of rm = 100 / (.08-.03)

Debt



= Equity


Number of diluted shares
Proceeds from opJon exercise
Value per share

Aswath Damodaran

= 2000
= 1000
= 1000
= 110
= 10 * 10 = 100
= (1000+ 100)/110 = $ 10
221

Problems with the treasury stock approach

222

The treasury stock approach fails to consider the

Jme premium on the opJons. In the example used,
we are assuming that an at the money opJon is
essenJally worth nothing.
The treasury stock approach also has problems with
out-of-the-money opJons. If considered, they can
increase the value of equity per share. If ignored,
they are treated as non-existent.

Aswath Damodaran

222

Dealing with opJons the right way

223

Step 1: Value the rm, using discounted cash ow or other

valuaJon models.
Step 2: Subtract out the value of the outstanding debt to arrive at
the value of equity. AlternaJvely, skip step 1 and esJmate the of
equity directly.
Step 3:Subtract out the market value (or esJmated market value)
of other equity claims:

Value of Warrants = Market Price per Warrant * Number of Warrants

: AlternaJvely esJmate the value using opJon pricing model
Value of Conversion OpJon = Market Value of ConverJble Bonds - Value
of Straight Debt PorJon of ConverJble Bonds
Value of employee OpJons: Value using the average exercise price and
maturity.

Step 4:Divide the remaining value of equity by the number of

shares outstanding to get value per share.

Aswath Damodaran

223

Valuing Equity OpJons issued by rms The

DiluJon Problem
224

OpJon pricing models can be used to value employee opJons

with four caveats

Employee opJons are long term, making the assumpJons about

constant variance and constant dividend yields much shakier,
Employee opJons result in stock diluJon, and
Employee opJons are open exercised before expiraJon, making it
dangerous to use European opJon pricing models.
Employee opJons cannot be exercised unJl the employee is vested.

These problems can be parJally alleviated by using an opJon

pricing model, allowing for ships in variance and early
exercise, and factoring in the diluJon eect. The resulJng
value can be adjusted for the probability that the employee
will not be vested.

Aswath Damodaran

224

Back to the numbers Inputs for OpJon

valuaJon
225

Stock Price = $ 10
Strike Price = $ 10
Maturity = 10 years
Standard deviaJon in stock price = 40%
Riskless Rate = 4%

Aswath Damodaran

225

Valuing the OpJons

226

Using a diluJon-adjusted Black Scholes model, we

arrive at the following inputs:
N (d1) = 0.8199
N (d2) = 0.3624
Value per call = $ 9.58 (0.8199) - $10 exp-(0.04) (10)

(0.3624) = $5.42

Dilution adjusted Stock price

Aswath Damodaran

226

Value of Equity to Value of Equity per share

227

Using the value per call of $5.42, we can now

esJmate the value of equity per share aper the
opJon grant:
Value of rm = 100 / (.08-.03)
Debt



= Equity


Value of opJons granted
= Value of Equity in stock
/ Number of shares outstanding
= Value per share

Aswath Damodaran

= 2000
= 1000
= 1000
= $ 54.2
= $945.8
/ 100
= $ 9.46
227

To tax adjust or not to tax adjust

228

In the example above, we have assumed that the

opJons do not provide any tax advantages. To the
extent that the exercise of the opJons creates tax
advantages, the actual cost of the opJons will be
lower by the tax savings.
One simple adjustment is to mulJply the value of
the opJons by (1- tax rate) to get an aper-tax opJon
cost.

Aswath Damodaran

228

OpJon grants in the future

229

Assume now that this rm intends to conJnue granJng

opJons each year to its top management as part of
compensaJon. These expected opJon grants will also
aect value.
The simplest mechanism for bringing in future opJon
grants into the analysis is to do the following:

EsJmate the value of opJons granted each year over the last
few years as a percent of revenues.
Forecast out the value of opJon grants as a percent of revenues
into future years, allowing for the fact that as revenues get
larger, opJon grants as a percent of revenues will become
smaller.
Consider this line item as part of operaJng expenses each year.
This will reduce the operaJng margin and cashow each year.

Aswath Damodaran

229

When opJons aect equity value per share the

most
230

OpJon grants aect value more

The lower the strike price is set relaJve to the stock price
The longer the term to maturity of the opJon
The more volaJle the stock price

The eect on value will be magnied if companies

are allowed to revisit opJon grants and reset the
exercise price if the stock price moves down.

Aswath Damodaran

230

NARRATIVE AND NUMBERS:

VALUATION AS A BRIDGE

Bridging the Gap

Favored Tools
- Accounting statements
- Excel spreadsheets
- Statistical Measures
- Pricing Data

Favored Tools
- Anecdotes
- Experience (own or others)
- Behavioral evidence

A Good Valuation
The Numbers People

Illusions/Delusions
1. Precision: Data is precise
2. Objectivity: Data has no bias
3. Control: Data can control reality

The Narrative People

Illusions/Delusions
1. Creativity cannot be quantified
2. If the story is good, the
investment will be.
3. Experience is the best teacher

232

Step 1: Create a narraJve

Every valuaJon starts with a narraJve, a story that you
see unfolding for your company in the future.
In developing this narraJve, you will be making
assessments of your company (its products, its
management), the market or markets that you see it
growing in, the compeJJon it faces and will face and the
macro environment in which it operates.
My narraDve for Uber: Uber will expand the car service
market moderately, primarily in urban environments, and
use its compeDDve advantages to get a signicant but not
dominant market share and maintain its prot margins.

233

Step 2: Check the narraJve against history,

economic rst principles & common sense
234

Aswath Damodaran

234

Step 3: Connect your narraJve to key

drivers of value
Total Market

Big market (China, Retailing, Autos)

narratives will show up as a big number here

X
Market Share

Networking and Winner-take-all narratives

show up as a high market share

=
Revenues (Sales)
Operating Expenses

Strong competitive edge narratives show up

as a combination of high market share and
high operating margin (operating income as %
of sales)

=
Operating Income
Taxes
=
After-tax Operating Income
-

Easy scaling (where companies can grow

quickly, easily and at low cost) narratives will
show up as low reinvestment given growth in
sales.

Reinvestment
=
After-tax Cash Flow
Adjust for time value & risk
Adjusted for operating risk
with a discount rate and
for failure with a
probability of failure.

Low risk narratives show up as a lower

discount rate or a lower probability of failure.

VALUE OF
OPERATING
ASSETS

235

Step 4: Value the company

236

Aswath Damodaran

236

Step 5: Keep the feedback loop

237

Aswath Damodaran

237

Step 6: Be ready to modify narraJve as

events unfold
238

Narra;ve Break/End

Narra;ve Shia

Narra;ve Change
(Expansion or Contrac;on)

Events, external (legal,

poliJcal or economic) or
internal (management,
compeJJve, default), that
can cause the narraJve to
break or end.

Improvement or
deterioraJon in iniJal
business model, changing
market size, market share
and/or protability.

Unexpected entry/success
in a new market or
unexpected exit/failure in
an exisJng market.

Your valuaJon esJmates

(cash ows, risk, growth &
value) are no longer
operaJve

Your valuaJon esJmates

will have to be modied to
reect the new data about
the company.

ValuaJon esJmates have

to be redone with new
overall market potenJal
and characterisJcs.

EsJmate a probability that Monte Carlo simulaJons or Real OpJons

it will occur &
scenario analysis
consequences
Aswath Damodaran

238

Aswath Damodaran

239

LET THE GAMES BEGIN TIME TO

VALUE COMPANIES..
Lets have some fun!

Equity Risk Premiums in ValuaJon

240

The equity risk premiums that I have used in the valuaJons that follow
reect my thinking (and how it has evolved) on the issue.

Pre-1998 valuaJons: In the valuaJons prior to 1998, I use a risk premium of 5.5%
for mature markets (close to both the historical and the implied premiums then)
Between 1998 and Sept 2008: In the valuaJons between 1998 and September
2008, I used a risk premium of 4% for mature markets, reecJng my belief that risk
premiums in mature markets do not change much and revert back to historical
norms (at least for implied premiums).
ValuaJons done in 2009: Aper the 2008 crisis and the jump in equity risk premiums
to 6.43% in January 2008, I have used a higher equity risk premium (5-6%) for the
next 5 years and will assume a reversion back to historical norms (4%) only aper
year 5.
In 2010, 2011 & 2012: In 2010, I reverted back to a mature market premium of
4.5%, reecJng the drop in equity risk premiums during 2009. In 2011, I used 5%,
reecJng again the change in implied premium over the year. In 2012 and 2013,
stayed with 6%, reverted to 5% in 2014 and will be using 5.75% in 2015.

Aswath Damodaran

240

Test 1: Is the firm paying

dividends like a stable growth
firm?
Dividend payout ratio is 73%
In trailing 12 months, through June
2008
Earnings per share = $3.17
Dividends per share = $2.32

Training Wheels valuation:

Con Ed in August 2008

Test 2: Is the stable growth rate

consistent with fundamentals?
Retention Ratio = 27%
ROE =Cost of equity = 7.7%
Expected growth = 2.1%

Growth rate forever = 2.1%

Value per share today= Expected Dividends per share next year / (Cost of equity - Growth rate)
= 2.32 (1.021)/ (.077 - ,021) = $42.30
Cost of Equity = 4.1% + 0.8 (4.5%) = 7.70%
Riskfree rate
4.10%
10-year T.Bond rate

Beta
0.80
Beta for regulated
power utilities

Equity Risk
Premium
4.5%
Implied Equity Risk
Premium - US
market in 8/2008

On August 12, 2008

Con Ed was trading at $
40.76.

Test 3: Is the firms risk and cost of equity consistent with a stable growith firm?
Beta of 0.80 is at lower end of the range of stable company betas: 0.8 -1.2

241

Why a stable growth dividend discount model?

1. Why stable growth: Company is a regulated utility, restricted from investing in new
growth markets. Growth is constrained by the fact that the population (and power
needs) of its customers in New York are growing at very low rates.
Growth rate forever = 2%
2. Why equity: Companys debt ratio has been stable at about 70% equity, 30% debt
for decades.
3. Why dividends: Company has paid out about 97% of its FCFE as dividends over
the last five years.

A break even growth rate to get to market

price
242

Con Ed: Value versus Growth Rate

$80.00
$70.00
$60.00
Break even point: Value = Price
Value per share

$50.00
$40.00
$30.00
$20.00
$10.00
$0.00
4.10%

Aswath Damodaran

3.10%

2.10%

1.10%

0.10%
-0.90%
Expected Growth rate

-1.90%

-2.90%

-3.90%

242

From DCF value to target price and returns

243

Assume that you believe that your valuaJon of Con Ed

($42.30) is a fair esJmate of the value, 7.70% is a
reasonable esJmate of Con Eds cost of equity and that
your expected dividends for next year (2.32*1.021) is a
fair esJmate, what is the expected stock price a year
from now (assuming that the market corrects its
mistake?)
If you bought the stock today at $40.76, what return can
you expect to make over the next year (assuming again
that the market corrects its mistake)?

Aswath Damodaran

243

Current Cashflow to Firm

EBIT(1-t)= 5344 (1-.35)= 3474
- Nt CpX=
350
- Chg WC
691
= FCFF
2433
Reinvestment Rate = 1041/3474
=29.97%
Return on capital = 25.19%

3M: A Pre-crisis valuation

Reinvestment Rate
30%

Expected Growth in
EBIT (1-t)
.30*.25=.075
7.5%

Value/Share $ 83.55

Year
EBIT (1-t)
- Reinvestment
= FCFF

1
$3,734
$1,120
$2,614

3
$4,279
$1,312
$2,967

Cost of Debt
(3.72%+.75%)(1-.35)
= 2.91%

Beta
1.15

Unlevered Beta for

Sectors: 1.09

244

2
$4,014
$1,204
$2,810

4
$4,485
$1,435
$3,049

5
$4,619
$1,540 ,
$3,079

Term Yr
$4,758
$2,113
$2,645

Cost of capital = 8.32% (0.92) + 2.91% (0.08) = 7.88%

Cost of Equity
8.32%

Riskfree Rate:
Riskfree rate = 3.72%

Stable Growth
g = 3%; Beta = 1.10;
Debt Ratio= 20%; Tax rate=35%
Cost of capital = 6.76%
ROC= 6.76%;
Reinvestment Rate=3/6.76=44%

Terminal Value5= 2645/(.0676-.03) = 70,409

First 5 years
Op. Assets 60607
+ Cash:
3253
- Debt
4920
=Equity
58400

Return on Capital
25%

Aswath Damodaran

Weights
E = 92% D = 8%

Risk Premium
4%

D/E=8.8%

On September 12,
2008, 3M was
trading at $70/share

Lowered base operating income by 10%

3M: Post-crisis valuation
Reduced growth
Current Cashflow to Firm
Reinvestment Rate rate to 5%
EBIT(1-t)= 4810 (1-.35)= 3,180
25%
Expected Growth in
- Nt CpX=
350
EBIT (1-t)
- Chg WC
691
.25*.20=.05
= FCFF
2139
5%
Reinvestment Rate = 1041/3180
=33%
Return on capital = 23.06%

Value/Share $ 60.53

Cost of Equity
10.86%

Riskfree Rate:
Riskfree rate = 3.96%

Year
EBIT (1-t)
- Reinvestment
= FCFF

1
$3,339
$835
$2,504

2
$3,506
$877
$2,630

3
$3,667
$1,025
$2,642

4
$3,807
$1,288
$2,519

5
$3,921
$1,558
$2,363

Term Yr
$4,038
$1,604
$2,434

Cost of capital = 10.86% (0.92) + 3.55% (0.08) = 10.27%

Higher default spread for next 5 years

Cost of Debt
(3.96%+.1.5%)(1-.35)
= 3.55%

Beta
1.15

Unlevered Beta for

Sectors: 1.09

245

Return on Capital
20%

Terminal Value5= 2434/(.0755-.03) = 53,481

First 5 years
Op. Assets 43,975
+ Cash:
3253
- Debt
4920
=Equity
42308

Did not increase debt

ratio in stable growth
to 20%
Stable Growth
g = 3%; Beta = 1.00;; ERP =4%
Debt Ratio= 8%; Tax rate=35%
Cost of capital = 7.55%
ROC= 7.55%;
Reinvestment Rate=3/7.55=40%

Aswath Damodaran

Weights
E = 92% D = 8%

On October 16, 2008,

MMM was trading at
$57/share.

Increased risk premium to 6% for next 5 years

Risk Premium
6%
X

D/E=8.8%

From a Company to the Market: Valuing the S&P 500: Dividend Discount Model in January 2015
Rationale for model
Why dividends? Because it is the only tangible cash flow, right?
Why 2-stage? Because the expected growth rate in near term is higher than stable growth rate.
Expected Growth
Analyst estimate for
growth over next 5
years = 5.58%

Dividends
$ Dividends in trailing 12
months = 38.57

Terminal Value= DPS in year 6/ (r-g)

= (50.59*1.0217)/(.0728-.0217) = 1010.91

Dividends
40.72

g = Riskfree rate = 2.17%

Assume that earnings on the index will
grow at same rate as economy.

42.99

45.39

47.92

50.59

.........
Forever

Value of Equity per

share = PV of
Dividends &
Terminal value at
7.94% = 895.14

Discount at Cost of Equity

On January 1, 2015, the
S&P 500 index was
trading at 2058.90.
Cost of Equity
2.17% + 1.00 (5.11%) = 7.28%

Riskfree Rate:
Treasury bond rate
2.17%

246

Beta
1.00

S&P 500 is a good reflection of

overall market

Risk Premium
5.11%
Set at the average ERP over
the last decade

From a Company to the Market: Valuing the S&P 500: Augmented Dividend Discount Model in January 2015
Rationale for model
Why augmented dividends? Because companies are increasing returning cash in the form of stock buybacks
Why 2-stage? Because the expected growth rate in near term is higher than stable growth rate.
Expected Growth
Analyst estimate for
growth over next 5
years = 5.58%

Dividends
$ Dividends + $ Buybacks in
trailing 12 months = 100.50

Terminal Value= Augmented Dividends in year 6/ (r-g)

= (131.81*1.0217)/(.0728-.0217) = 2633.97

Dividends
106.10

g = Riskfree rate = 2.17%

Assume that earnings on the index will
grow at same rate as economy.

112.01

118.26

128.45

131.81
.........
Forever

Value of Equity per

share = PV of
Dividends &
Terminal value at
7.28% = 2332.34

Discount at Cost of Equity

On January 1, 2015, the
S&P 500 index was
trading at 2058.90
Cost of Equity
2.17% + 1.00 (5.11%) = 7.28%

Riskfree Rate:
Treasury bond rate
2.17%

Beta
1.00

S&P 500 is a good reflection of

overall market

247

Risk Premium
5.11%
Set at the average ERP over
the last decade

Valuing the S&P 500: Augmented Dividends and Fundamental Growth January 2015
Rationale for model
Why augmented dividends? Because companies are increasing returning cash in the form of stock buybacks
Why 2-stage? Why not?
ROE = 16.03%
Dividends
$ Dividends + $ Buybacks in
trailing 12 months = 100.50

Retention Ratio = 12.42%

Expected Growth
ROE * Retention Ratio
= .1603*.1242 = 1.99%

Terminal Value= Augmented Dividends in year 6/ (r-g)

= (110.90*1.0217)/(.0728-.0217) = 2216.06

Dividends
102.50

g = Riskfree rate = 2.17%

Assume that earnings on the index will
grow at same rate as economy.

104.54

106.62

108.74

110.90

.........
Forever

Value of Equity per

share = PV of
Dividends &
Terminal value at
7.28% = 1992.11

Discount at Cost of Equity

On January 1, 2015, the
S&P 500 index was
trading at 2058.90
Cost of Equity
2.17% + 1.00 (5.11%) = 7.28%

Riskfree Rate:
Treasury bond rate
2.17%

Beta
1.00

S&P 500 is a good reflection of

overall market

248

Aswath Damodaran

Risk Premium
5.11%
Set at the average ERP over
the last decade

Aswath Damodaran

249

THE DARK SIDE OF VALUATION:

VALUING DIFFICULT-TO-VALUE
COMPANIES
Anyone can value a money-making stable company..

The fundamental determinants of value

250

What are the

cashflows from
existing assets?
- Equity: Cashflows
after debt payments
- Firm: Cashflows
before debt payments

Aswath Damodaran

What is the value added by growth assets?

Equity: Growth in equity earnings/ cashflows
Firm: Growth in operating earnings/
cashflows

How risky are the cash flows from both

existing assets and growth assets?
Equity: Risk in equity in the company
Firm: Risk in the firms operations

When will the firm

become a mature
fiirm, and what are
the potential
roadblocks?

250

The Dark Side of ValuaJon

251

Valuing stable, money making companies with

consistent and clear accounJng statements, a long and
stable history and lots of comparable rms is easy to do.
The true test of your valuaJon skills is when you have to
value dicult companies. In parJcular, the challenges
are greatest when valuing:
Young companies, early in the life cycle, in young businesses
Companies that dont t the accounJng mold
Companies that face substanJal truncaJon risk (default or
naJonalizaJon risk)

Aswath Damodaran

251

Dicult to value companies

252

Across the life cycle:

Across markets

Young, growth rms: Limited history, small revenues in conjuncJon with big operaJng losses
and a propensity for failure make these companies tough to value.
Mature companies in transiJon: When mature companies change or are forced to change,
history may have to be abandoned and parameters have to be reesJmated.
Declining and Distressed rms: A long but irrelevant history, declining markets, high debt loads
and the likelihood of distress make them troublesome.
Emerging market companies are open dicult to value because of the way they are
structured, their exposure to country risk and poor corporate governance.

Across sectors

Financial service rms: Opacity of nancial statements and diculJes in esJmaJng basic
inputs leave us trusJng managers to tell us whats going on.
Commodity and cyclical rms: Dependence of the underlying commodity prices or overall
economic growth make these valuaJons suscepJble to macro factors.
Firms with intangible assets: AccounJng principles are lep to the wayside on these rms.

Aswath Damodaran

252

I. The challenge with young companies

253

Making judgments on revenues/ profits difficult becaue

you cannot draw on history. If you have no product/
service, it is difficult to gauge market potential or
profitability. The company;s entire value lies in future
growth but you have little to base your estimate on.
Cash flows from existing
What is the value added by growth
assets non-existent or
assets?
negative.
What are the cashflows
from existing assets?
How risky are the cash flows from both
Different claims on existing assets and growth assets?
cash flows can
affect value of
Limited historical data on earnings,
equity at each
and no market prices for securities
stage.
makes it difficult to assess risk.
What is the value of
equity in the firm?

Aswath Damodaran

When will the firm

become a mature
fiirm, and what are
the potential
roadblocks?
Will the firm will make it
through the gauntlet of market
demand and competition.
Even if it does, assessing
when it will become mature is
difficult because there is so
little to go on.

253

Upping the ante.. Young companies in young

businesses
254

When valuing a business, we generally draw on three sources of informaJon

The rms current nancial statement

n How much did the rm sell?
n How much did it earn?
The rms nancial history, usually summarized in its nancial statements.
n How fast have the rms revenues and earnings grown over Jme?
n What can we learn about cost structure and protability from these trends?
n SuscepJbility to macro-economic factors (recessions and cyclical rms)
The industry and comparable rm data
n What happens to rms as they mature? (Margins.. Revenue growth Reinvestment
needs Risk)

It is when valuing these companies that you nd yourself tempted by the dark
side, where

Paradigm ships happen

New metrics are invented
The story dominates and the numbers lag

Aswath Damodaran

254

Sales to capital ratio and

expected margin are retail
industry average numbers

9a. Amazon in January 2000

Current
Revenue
$ 1,117

From previous
years
NOL:
500 m

Current
Margin:
-36.71%

Sales Turnover
Ratio: 3.00

EBIT
-410m

- Value of Debt
= Value of Equity
- Equity Options
Value per share

$ 349
$14,587
$ 2,892
$ 34.32 Cost of Equity

All existing options valued

as options, using current
stock price of $84.

Riskfree Rate:
T. Bond rate = 6.5%

9,774
$407
$407
$1,396
-$989

14,661
$1,038
$871
$1,629
-$758

19,059
$1,628
$1,058
$1,466
-$408

12.90%
8.00%
8.00%
12.84%

12.90%
8.00%
8.00%
12.84%

12.90%
8.00%
6.71%
12.83%

12.90%
8.00%
5.20%
12.81%

12.42%
7.80%
5.07%
12.13%

12.30%
7.75%
5.04%
11.96%

12.10%
7.67%
4.98%
11.69%

11.70%
7.50%
4.88%
11.15%

23,862
$2,212
$1,438
$1,601
-$163

28,729
$2,768
$1,799
$1,623
$177

Cost of Debt
6.5%+1.5%=8.0%
Tax rate = 0% -> 35%

Dot.com retailers for firrst 5 years

Convetional retailers after year 5
Beta
X
+ 1.60 -> 1.00

Operating
Leverage

Stable
ROC=20%
Reinvest 30%
of EBIT(1-t)

Terminal Value= 1881/(.0961-.06)

=52,148

5,585
-$94
-$94
$931
-$1,024

Used average
interest coverage
ratio over next 5
years to get BBB
rating.

Internet/
Retail

Aswath Damodaran

Expected
Margin:
-> 10.00%

$2,793
-$373
-$373
$559
-$931

12.90%
Cost of Debt
8.00%
AT cost of debt 8.00%
Cost of Capital 12.84%

Cost of Equity
12.90%

255

Competitive
Advantages

Revenue
Growth:
42%

Revenues
Value of Op Assets $ 14,910 EBIT
(1-t)
+ Cash
$
26 EBIT
- Reinvestment
= Value of Firm
$14,936 FCFF

Stable Growth
Stable
Stable
Operating
Revenue
Margin:
Growth: 6%
10.00%

33,211
$3,261
$2,119
$1,494
$625

36,798
$3,646
$2,370
$1,196
$1,174

39,006
$3,883
$2,524
$736
$1,788

Term. Year
$41,346
10.00%
35.00%
$2,688
$ 807
$1,881

10
10.50%
7.00%
4.55%
9.61%

Weights
Debt= 1.2% -> 15%

Forever

Amazon was
trading at $84 in
January 2000.

Pushed debt ratio

to retail industry
average of 15%.
Risk Premium
4%

Current
D/E: 1.21%

Base Equity
Premium

Country Risk
Premium

Lesson 1: Dont trust regression betas.

256

Aswath Damodaran

256

Lesson 2: Work backwards and keep it simple

257

Year
Tr12m
1
2
3
4
5
6
7
8
9
10
TY(11)

Revenues
$1,117
$2,793
$5,585
$9,774
$14,661
$19,059
$23,862
$28,729
$33,211
$36,798
$39,006
$41,346

Aswath Damodaran

OperaJng Margin
-36.71%

-13.35%

-1.68%

4.16%

7.08%

8.54%

9.27%

9.64%

9.82%

9.91%

9.95%

10.00%

EBIT
-$410
-$373
-$94
$407
$1,038
$1,628
$2,212
$2,768
$3,261
$3,646
$3,883
$4,135

257

Lesson 3: Scaling up is hard to do

258

Aswath Damodaran

258

Lesson 4: Dont forget to pay for growth and

check your reinvestment
259

Year
1
2
3
4
5
6
7
8
9
10

Rev growth
150.00%
100.00%
75.00%
50.00%
30.00%
25.20%
20.40%
15.60%
10.80%
6.00%

Aswath Damodaran

Chg in Rev
$1,676
$2,793
$4,189
$4,887
$4,398
$4,803
$4,868
$4,482
$3,587
$2,208

Reinv S/Cap ROC

$559 3.00 -76.62%
$931 3.00 -8.96%
$1,396 3.00 20.59%
$1,629 3.00 25.82%
$1,466 3.00 21.16%
$1,601 3.00 22.23%
$1,623 3.00 22.30%
$1,494 3.00 21.87%
$1,196 3.00 21.19%
$736 3.00 20.39%
259

Lesson 5: And dont worry about diluJon It is

already factored in
260

With young growth companies, it is almost a given that the number

of shares outstanding will increase over Jme for two reasons:

To grow, the company will have to issue new shares either to raise cash to
take projects or to oer to target company stockholders in acquisiJons
Many young, growth companies also oer opJons to managers as
compensaJon and these opJons will get exercised, if the company is
successful.

In DCF valuaJon, both eects are already incorporated into the

value per share, even though we use the current number of shares
in esJmaJng value per share

The need for new equity issues is captured in negaJve cash ows in the
earlier years. The present value of these negaJve cash ows will drag
down the current value of equity and this is the eect of future diluJon.
The opJons are valued and neRed out against the current value. Using an
opJon pricing model allows you to incorporate the expected likelihood
that they will be exercised and the price at which they will be exercised.

Aswath Damodaran

260

Lesson 6: There are always scenarios where the

market price can be jusJed
261

30%
35%
40%
45%
50%
55%
60%

$
$
$
$
$
$
$

Aswath Damodaran

6%
(1.94)
1.41
6.10
12.59
21.47
33.47
49.53

$
$
$
$
$
$
$

8%
2.95
8.37
15.93
26.34
40.50
59.60
85.10

$
$
$
$
$
$
$

10%
7.84
15.33
25.74
40.05
59.52
85.72
120.66

$
$
$
$
$
$
$

12%
12.71
22.27
35.54
53.77
78.53
111.84
156.22

$
$
$
$
$
$
$

14%
17.57
29.21
45.34
67.48
97.54
137.95
191.77

261

Lesson 7: You will be wrong 100% of the Jme

and it really is not (always) your fault
262

No maRer how careful you are in ge}ng your inputs and

how well structured your model is, your esJmate of
value will change both as new informaJon comes out
about the company, the business and the economy.
As informaJon comes out, you will have to adjust and
adapt your model to reect the informaJon. Rather than
be defensive about the resulJng changes in value,
recognize that this is the essence of risk.
A test: If your valuaJons are unbiased, you should nd
yourself increasing esJmated values as open as you are
decreasing values. In other words, there should be equal
doses of good and bad news aecJng valuaJons (at
least over Jme).

Aswath Damodaran

262

Reinvestment:

9b. Amazon in January 2001

Current
Revenue
$ 2,465

Cap ex includes acquisitions

Working capital is 3% of revenues

Current
Margin:
-34.60%

Sales Turnover
Ratio: 3.02
EBIT
-853m

Revenue
Growth:
25.41%

NOL:
1,289 m

Value of Op Assets $ 8,789

+ Cash & Non-op $ 1,263
= Value of Firm
$10,052
- Value of Debt
$ 1,879
= Value of Equity
$ 8,173
- Equity Options
$ 845
Value per share
$ 20.83

Competitiv
e
Advantages
Expected
Margin:
-> 9.32%

2
$6,471
-$107
-$107
$714
-$822
2

3
$9,059
$347
$347
$857
-$510
3

4
$11,777
$774
$774
$900
-$126
4

5
$14,132
$1,123
$1,017
$780
$237
5

6
$16,534
$1,428
$928
$796
$132
6

7
$18,849
$1,692
$1,100
$766
$333
7

8
$20,922
$1,914
$1,244
$687
$558
8

9
$22,596
$2,087
$1,356
$554
$802
9

10
$23,726
$2,201
$1,431
$374
$1,057
10

Debt Ratio
Beta
Cost of Equity
AT cost of debt
Cost of Capital

27.27%
2.18
13.81%
10.00%
12.77%

27.27%
2.18
13.81%
10.00%
12.77%

27.27%
2.18
13.81%
10.00%
12.77%

27.27%
2.18
13.81%
9.06%
12.52%

24.81%
1.96
12.95%
6.11%
11.25%

24.20%
1.75
12.09%
6.01%
10.62%

23.18%
1.53
11.22%
5.85%
9.98%

21.13%
1.32
10.36%
5.53%
9.34%

15.00%
1.10
9.50%
4.55%
8.76%

27.27%
2.18
13.81%
10.00%
12.77%

Cost of Debt
6.5%+3.5%=10.0%
Tax rate = 0% -> 35%

Riskfree Rate:
T. Bond rate = 5.1%

+
Aswath Damodaran

Beta
2.18-> 1.10

Internet/
Retail

Operating
Leverage

Term. Year
$24,912
$2,302
$1,509
$ 445
$1,064

Forever

Weights
Debt= 27.3% -> 15%

Amazon.com
January 2001
Stock price = $14

Risk Premium
4%

Current
D/E: 37.5%

Stable
ROC=16.94%
Reinvest 29.5%
of EBIT(1-t)

Terminal Value= 1064/(.0876-.05)

=$ 28,310

1
Revenues
$4,314
EBIT
-$545
EBIT(1-t)
-$545
- Reinvestment $612
FCFF
-$1,157
1

Cost of Equity
13.81%

263

Stable Growth
Stable
Stable
Operating
Revenue
Margin:
Growth: 5%
9.32%

Base Equity
Premium

Country Risk
Premium

And the market is open more wrong.

264
Amazon: Value and Price

$90.00
$80.00

$70.00

$60.00

$50.00
Value per share
Price per share

$40.00

$30.00
$20.00

$10.00

$0.00
2000

2001

2002

2003

Time of analysis

Aswath Damodaran

264

II. Mature Companies in transiJon..

265

Mature companies are generally the easiest group to

value. They have long, established histories that can be
mined for inputs. They have investment policies that are
set and capital structures that are stable, thus making
valuaJon more grounded in past data.
However, this stability in the numbers can mask real
problems at the company. The company may be set in a
process, where it invests more or less than it should and
does not have the right nancing mix. In eect, the
policies are consistent, stable and bad.
If you expect these companies to change or as is more
open the case to have change thrust upon them,

Aswath Damodaran

265

The perils of valuing mature companies

266

Figure 7.1: Estimation Issues - Mature Companies

Lots of historical data
on earnings and
cashflows. Key
questions remain if
these numbers are
volatile over time or if
the existing assets are
not being efficiently
utilized.

Growth is usually not very high, but firms may still be

generating healthy returns on investments, relative to
cost of funding. Questions include how long they can
generate these excess returns and with what growth
rate in operations. Restructuring can change both
inputs dramatically and some firms maintain high
growth through acquisitions.
What is the value added by growth
assets?

What are the cashflows

from existing assets?

Equity claims can

vary in voting
rights and
dividends.

How risky are the cash flows from both

existing assets and growth assets?
Operating risk should be stable, but
the firm can change its financial
leverage This can affect both the
cost of equtiy and capital.

When will the firm

become a mature
fiirm, and what are
the potential
roadblocks?
Maintaining excess returns or
high growth for any length of
time is difficult to do for a
mature firm.

What is the value of

equity in the firm?

Aswath Damodaran

266

Hormel Foods: The Value of Control Changing

Hormel Foods sells packaged meat and other food products and has been in existence as a publicly traded company for almost 80 years.
In 2008, the firm reported after-tax operating income of $315 million, reflecting a compounded growth of 5% over the previous 5 years.
The Status Quo
Run by existing management, with conservative reinvestment policies (reinvestment rate = 14.34% and debt ratio = 10.4%.
Anemic growth rate and short growth period, due to reinvestment policy
Low debt ratio affects cost of capital

Probability of management change = 10%

Expected value =$31.91 (.90) + $37.80 (.10) = $32.50

New and better management

More aggressive reinvestment which increases the reinvestment rate (to 40%) and tlength of growth (to 5 years), and higher debt ratio (20%).
Operating Restructuring 1
Financial restructuring 2
Expected growth rate = ROC * Reinvestment Rate
Cost of capital = Cost of equity (1-Debt ratio) + Cost of debt (Debt ratio)
Expected growth rae (status quo) = 14.34% * 19.14% = 2.75%
Status quo = 7.33% (1-.104) + 3.60% (1-.40) (.104) = 6.79%
Expected growth rate (optimal) = 14.00% * 40% = 5.60%
Optimal = 7.75% (1-.20) + 3.60% (1-.40) (.20) = 6.63%
ROC drops, reinvestment rises and growth goes up.
Cost of equity rises but cost of capital drops.

267

Aswath Damodaran

Lesson 1: Cost cu}ng and increased eciency are easier

accomplished on paper than in pracJce and require
commitment
268

Aswath Damodaran

268

Lesson 2: Increasing growth is not always a value

creaJng opJon.. And it may destroy value at Jmes..
269

Excess Return (ROC minus Cost of Capital) for rms with market capitalizaDon> $50
million: Global in 2014
45.00%
40.00%
35.00%
30.00%

<-5%

25.00%

-5% - 0%
0 -5%

20.00%

5 -10%
15.00%

>10%

10.00%
5.00%
0.00%
Australia, NZ and Developed Europe Emerging Markets
Canada

Aswath Damodaran

Japan

United States

Global

269

Lesson 3: Financial leverage is a double-edged

sword..
270
Exhibit 7.1: Optimal Financing Mix: Hormel Foods in January 2009
As debt ratio increases, equity
becomes riskier.(higher beta)
and cost of equity goes up.
1

As firm borrows more money,

its ratings drop and cost of
2
debt rises

Current Cost
of Capital

Debt ratio is percent of overall

market value of firm that comes
from debt financing.

Aswath Damodaran

Optimal: Cost of
capital lowest
between 20 and
30%.

At debt ratios > 80%, firm does not have enough

operating income to cover interest expenses. Tax
rate goes down to reflect lost tax benefits.
3

As cost of capital drops,

firm value rises (as
operating cash flows
remain unchanged)

270

III. Dealing with decline and distress

271

Historial data often

Growth can be negative, as firm sheds assets and
reflects flat or declining shrinks. As less profitable assets are shed, the firms
revenues and falling
remaining assets may improve in quality.
margins. Investments
often earn less than the What is the value added by growth
assets?
cost of capital.
What are the cashflows
from existing assets?
Underfunded pension
obligations and
litigation claims can
lower value of equity.
Liquidation
preferences can affect
value of equity
What is the value of
equity in the firm?

Aswath Damodaran

How risky are the cash flows from both

existing assets and growth assets?
Depending upon the risk of the
assets being divested and the use of
the proceeds from the divestuture (to
pay dividends or retire debt), the risk
in both the firm and its equity can
change.

When will the firm

become a mature
fiirm, and what are
the potential
roadblocks?

There is a real chance,

especially with high financial
leverage, that the firm will not
make it. If it is expected to
survive as a going concern, it
will be as a much smaller
entity.

271

a. Dealing with Decline

272

In decline, rms open see declining revenues and lower margins,

translaJng in negaJve expected growth over Jme.
If these rms are run by good managers, they will not ght decline.
Instead, they will adapt to it and shut down or sell investments
that do not generate the cost of capital. This can translate into
negaJve net capital expenditures (depreciaJon exceeds cap ex),
declining working capital and an overall negaJve reinvestment
rate. The best case scenario is that the rm can shed its bad assets,
make itself a much smaller and healthier rm and then seRle into
long-term stable growth.
As an investor, your worst case scenario is that these rms are run
by managers in denial who conJnue to expand the rm by making
bad investments (that generate lower returns than the cost of
capital). These rms may be able to grow revenues and operaJng
income but will destroy value along the way.

Aswath Damodaran

272

11. Sears Holdings: Status Quo

Current Cashflow to Firm
EBIT(1-t) :
1,183
- Nt CpX
-18
- Chg WC
- 67
= FCFF
1,268
Reinvestment Rate = -75/1183
=-7.19%
Return on capital = 4.99%

Reinvestment Rate
-30.00%

Return on Capital
5%

Expected Growth
in EBIT (1-t)
-.30*..05=-0.015
-1.5%

Stable Growth
g = 2%; Beta = 1.00;
Country Premium= 0%
Cost of capital = 7.13%
ROC= 7.13%; Tax rate=38%
Reinvestment Rate=28.05%
Terminal Value4= 868/(.0713-.02) = 16,921

Op. Assets 17,634

+ Cash:
1,622
- Debt
7,726
=Equity
11,528
-Options
5
Value/Share $87.29

EBIT (1-t)
- Reinvestment
FCFF

1
$1,165
($349)
$1,514

2
$1,147
($344)
$1,492

3
$1,130
($339)
$1,469

4
$1,113
($334)
$1,447

Term Yr
$1,206
$ 339
$ 868

Discount at Cost of Capital (WACC) = 9.58% (.566) + 4.80% (0.434) = 7.50%

Cost of Equity
9.58%

Riskfree Rate
Riskfree rate = 4.09%

273

Aswath Damodaran

Cost of Debt
(4.09%+3,65%)(1-.38)
= 4.80%

Beta
1.22

Unlevered Beta for

Sectors: 0.77

Weights
E = 56.6% D = 43.4%

Risk Premium
4.00%

Firms D/E
Ratio: 93.1%

Mature risk
premium
4%

Country
Equity Prem
0%

On July 23, 2008,

Sears was trading at
$76.25 a share.

b. Dealing with the downside of Distress

274

A DCF valuaJon values a rm as a going concern. If there is a signicant

likelihood of the rm failing before it reaches stable growth and if the
assets will then be sold for a value less than the present value of the
expected cashows (a distress sale value), DCF valuaJons will overstate
the value of the rm.
Value of Equity= DCF value of equity (1 - Probability of distress) + Distress
sale value of equity (Probability of distress)
There are three ways in which we can esJmate the probability of distress:

Use the bond raJng to esJmate the cumulaJve probability of distress over 10 years
EsJmate the probability of distress with a probit
EsJmate the probability of distress by looking at market value of bonds..

The distress sale value of equity is usually best esJmated as a percent of

book value (and this value will be lower if the economy is doing badly and
there are other rms in the same business also in distress).

Aswath Damodaran

274

Reinvestment:
Current
Revenue
$ 4,390

Extended
reinvestment
break, due ot
investment in
past

EBIT
$ 209m

Value of Op Assets
+ Cash & Non-op
= Value of Firm
- Value of Debt
= Value of Equity

$ 9,793
$ 3,040
$12,833
$ 7,565
$ 5,268

Value per share

$ 8.12

Industry
average
Expected
Margin:
-> 17%

$4,434
5.81%
$258
26.0%
$191
-$19
$210
1

$4,523
6.86%
$310
26.0%
$229
-$11
$241
2

$5,427
7.90%
$429
26.0%
$317
$0
$317
3

$6,513
8.95%
$583
26.0%
$431
$22
$410
4

$7,815
10%
$782
26.0%
$578
$58
$520
5

$8,206
11.40%
$935
28.4%
$670
$67
$603
6

$8,616
12.80%
$1,103
30.8%
$763
$153
$611
7

$9,047
14.20%
$1,285
33.2%
$858
$215
$644
8

$9,499 $9,974
15.60% 17%
$1,482 $1,696
35.6% 38.00%
$954
$1,051
$286
$350
$668
$701
9
10

Beta
Cost of equity
Cost of debt
Debtl ratio
Cost of capital

3.14
21.82%
9%
73.50%
9.88%

3.14
21.82%
9%
73.50%
9.88%

3.14
21.82%
9%
73.50%
9.88%

3.14
21.82%
9%
73.50%
9.88%

3.14
21.82%
9%
73.50%
9.88%

2.75
19.50%
8.70%
68.80%
9.79%

2.36
17.17%
8.40%
64.10%
9.50%

1.97
14.85%
8.10%
59.40%
9.01%

1.59
12.52%
7.80%
54.70%
8.32%

Cost of Debt
3%+6%= 9%
9% (1-.38)=5.58%

Riskfree Rate:
T. Bond rate = 3%

+
Aswath Damodaran

Beta
3.14-> 1.20

Casino
1.15

1.20
10.20%
7.50%
50.00%
7.43%

Term. Year
$10,273
17%
$ 1,746
38%
$1,083
$ 325
$758

Forever

Weights
Debt= 73.5% ->50%

Las Vegas Sands

Feburary 2009
Trading @ $4.25

Risk Premium
6%

Current
D/E: 277%

Stable
ROC=10%
Reinvest 30%
of EBIT(1-t)

Terminal Value= 758(.0743-.03)

=$ 17,129

Revenues
Oper margin
EBIT
Tax rate
EBIT * (1 - t)
- Reinvestment
FCFF

Cost of Equity
21.82%

275

Stable Growth
Stable
Stable
Operating
Revenue
Margin:
Growth: 3%
17%

Capital expenditures include cost of

new casinos and working capital

Current
Margin:
4.76%

Base Equity
Premium

Country Risk
Premium

AdjusJng the value of LVS for distress..

276

In February 2009, LVS was rated B+ by S&P. Historically, 28.25% of B+

rated bonds default within 10 years. LVS has a 6.375% bond, maturing in
February 2015 (7 years), trading at $529. If we discount the expected cash
ows on the bond at the riskfree rate, we can back out the probability of
distress from the bond price:
t =7

63.75(1 Distress )t 1000(1 Distress )7

529 =
+
t
(1.03)
(1.03)7
t =1

If LVS is becomes distressed:

Solving for the probability of bankruptcy, we get:

Distress = Annual probability of default = 13.54%
CumulaJve probability of surviving 10 years = (1 - .1354)10 = 23.34%

CumulaJve probability
of distress over 10 years = 1 - .2334 = .7666 or 76.66%
Expected distress sale proceeds = $2,769 million < Face value of debt
Expected equity value/share = $0.00

Expected value per share = $8.12 (1 - .7666) + $0.00 (.7666) = $1.92

Aswath Damodaran

276

IV. Emerging Market Companies

277

Estimation Issues - Emerging Market Companies

Big shifts in economic
environment (inflation,
itnerest rates) can affect
Growth rates for a company will be affected heavily be
operating earnings history.
growth rate and political developments in the country
Poor corporate
in which it operates.
governance and weak
accounting standards can What is the value added by growth
lead to lack of
assets?
transparency on earnings.
When will the firm
What are the cashflows
become a mature
from existing assets?
fiirm, and what are
the potential
How risky are the cash flows from both
roadblocks?
Cross holdings can existing assets and growth assets?
affect value of
Even if the companys risk is stable,
Economic crises can put
equity
there can be significant changes in
many companies at risk.
country risk over time.
Government actions
What is the value of
(nationalization) can affect
equity in the firm?
long term value.

Aswath Damodaran

277

Lesson 1: Country risk has to be incorporated

but with a scalpel, not a bludgeon
278

Emerging market companies are undoubtedly exposed

to addiJonal country risk because they are incorporated
in countries that are more exposed to poliJcal and
economic risk.
Not all emerging market companies are equally exposed
to country risk and many developed markets have
emerging market risk exposure because of their
operaJons.
You can use either the weighted country risk premium,
with the weights reecJng the countries you get your
revenues from or the lambda approach (which may
incorporate more than revenues) to capture country risk
exposure.

Aswath Damodaran

278

Avg Reinvestment
rate =40%

A $ Valuation of Embraer

Current Cashflow to Firm

EBIT(1-t) :
$ 434
- Nt CpX
- 11
- Chg WC
178
= FCFF
$ 267
Reinvestment Rate = 167/289= 56%
Effective tax rate = 19.5%

Reinvestment Rate
40%

Return on Capital
18.1%

Expected Growth in
EBIT (1-t)
.40*.181=.072
7.2%

Terminal Value5= 254(.0738-.038) = 8,371

$ Cashflows
Op. Assets $ 6,239
+ Cash:
3,068
- Debt
2,070
- Minor. Int.
177
=Equity
7,059
-Options
4
Value/Share $9.53
R$ 15.72

Year
EBIT (1-t)
- Reinvestment
FCFF

3
$535
$214
$321

4
$574
$229
$344

Term Yr
524
270
= 254

5
$615
$246
$369

On May 22, 2008

Embraer Price = R$ 17.2

Cost of Debt
(3.8%+1.7%+1.1%)(1-.34)
= 4.36%

Beta
0.88

Unlevered Beta for

Sectors: 0.75

279

2
$499
$200
$299

Discount at $ Cost of Capital (WACC) = 8.31% (.788) + 4.36% (0.212) = 7.47%

Cost of Equity
8.31%

Riskfree Rate:
US$ Riskfree Rate=
3.8%

1
$465
$186
$279

Stable Growth
g = 3.8%; Beta = 1.00;
Country Premium= 1.5%
Cost of capital = 7.38%
ROC= 7.38%; Tax rate=34%
Reinvestment Rate=g/ROC
=3.8/7.38 = 51.47%

Aswath Damodaran

Weights
E = 78.8% D = 21.2%

Mature market
premium
4%
Firms D/E
Ratio: 26.84%

Lambda
0.27

Country Equity Risk

Premium
3.66%

Country Default
Spread
2.2%

Rel Equity
Mkt Vol
1.64

Lesson 2: Currency should not maRer

280

You can value any company in any currency. Thus, you

can value a Brazilian company in nominal reais, US
dollars or Swiss Francs.
For your valuaJon to stay invariant and consistent, your
cash ows and discount rates have to be in the same
currency. Thus, if you are using a high inaJon currency,
both your growth rates and discount rates will be much
higher.
For your cash ows to be consistent, you have to use
expected exchange rates that reect purchasing power
parity (the higher inaJon currency has to depreciate by
the inaJon dierenJal each year).

Aswath Damodaran

280

Lesson 3: The corporate governance drag

281

a.
b.

Stockholders in Asian, LaJn American and many European

companies have liRle or no power over the managers of the
rm. In many cases, insiders own voJng shares and control
the rm and the potenJal for conict of interests is huge.
This weak corporate governance is open a reason for given
for using higher discount rates or discounJng the esJmated
value for these companies.
Would you discount the value that you esJmate for an
emerging market company to allow for this absence of
stockholder power?
Yes
No.

Aswath Damodaran

281

6a. Tube Investments: Status Quo (in Rs)

Current Cashflow to Firm
Reinvestment Rate
EBIT(1-t) :
4,425
60%
- Nt CpX
843
- Chg WC
4,150
= FCFF
- 568
Reinvestment Rate =112.82%

Return on Capital
9.20%
Stable Growth
g = 5%; Beta = 1.00;
Debt ratio = 44.2%
Country Premium= 3%
ROC= 9.22%
Reinvestment Rate=54.35%

Expected Growth
in EBIT (1-t)
.60*.092-= .0552
5.52%

Terminal Value5= 2775/(.1478-.05) = 28,378

Firm Value:
+ Cash:
- Debt:
=Equity
-Options
Value/Share
Rs61.57

19,578
13,653
18,073
15,158
0

EBIT(1-t)
- Reinvestment
FCFF

$4,928
$2,957
$1,971

$5,200
$3,120
$2,080

$5,487
$3,292
$2,195

$5,790
$3,474
$2,316

Term Yr
6,079
3,304
2,775

Discount at Cost of Capital (WACC) = 22.8% (.558) + 9.45% (0.442) = 16.90%

Cost of Equity
22.80%

Riskfree Rate:
Rs riskfree rate = 12%

282

$4,670
$2,802
$1,868

Aswath Damodaran

Cost of Debt
(12%+1.50%)(1-.30)
= 9.45%

Beta
1.17

Unlevered Beta for

Sectors: 0.75

Weights
E = 55.8% D = 44.2%

Risk Premium
9.23%

Firms D/E
Ratio: 79%

Mature risk
premium
4%

Country Risk
Premium
5.23%

In 2000, the stock was

trading at 102
Rupees/share.

Company earns
higher returns on new
projects

6b. Tube Investments: Higher Marginal Return(in Rs)

Current Cashflow to Firm
Reinvestment Rate
EBIT(1-t) :
4,425
60%
- Nt CpX
843
- Chg WC
4,150
= FCFF
- 568
Reinvestment Rate =112.82%

Expected Growth
in EBIT (1-t)
.60*.122-= .0732
7.32%

Existing assets continue

to generate negative
excess returns.
Firm Value: 25,185
+ Cash:
13,653
- Debt:
18,073
=Equity
20,765
-Options
0
Value/Share 84.34

Return on Capital
12.20%
Stable Growth
g = 5%; Beta = 1.00;
Debt ratio = 44.2%
Country Premium= 3%
ROC=12.2%
Reinvestment Rate= 40.98%
Terminal Value5= 3904/(.1478-.05) = 39.921

EBIT(1-t)
- Reinvestment
FCFF

$4,749
$2,850
$1,900

$5,097
$3,058
$2,039

$5,470
$3,282
$2,188

$5,871
$3,522
$2,348

$6,300
$3,780
$2,520

Discount at Cost of Capital (WACC) = 22.8% (.558) + 9.45% (0.442) = 16.90%

Cost of Equity
22.80%

Riskfree Rate:
Rs riskfree rate = 12%

Cost of Debt
(12%+1.50%)(1-.30)
= 9.45%

Beta
1.17

Unlevered Beta for

Sectors: 0.75

283

Aswath Damodaran

Weights
E = 55.8% D = 44.2%

Risk Premium
9.23%

Firms D/E
Ratio: 79%

Mature risk
premium
4%

Country Risk
Premium
5.23%

Term Yr
6,615
2,711
3,904

Return on Capital
12.20%

6c.Tube Investments: Higher Average Return

Current Cashflow to Firm
Reinvestment Rate
EBIT(1-t) :
4,425
60%
- Nt CpX
843
- Chg WC
4,150
= FCFF
- 568
Reinvestment Rate =112.82%

Expected Growth
60*.122 +
.0581 = .1313
13.13%

Improvement on existing assets

{ (1+(.122-.092)/.092) 1/5-1}
Stable Growth
g = 5%; Beta = 1.00;
Debt ratio = 44.2%
Country Premium= 3%
ROC=12.2%
Reinvestment Rate= 40.98%

5.81%

Terminal Value5= 5081/(.1478-.05) = 51,956

Firm Value: 31,829
+ Cash:
13,653
- Debt:
18,073
=Equity
27,409
-Options
0
Value/Share 111.3

EBIT(1-t)
- Reinvestment
FCFF

$5,006
$3,004
$2,003

$5,664
$3,398
$2,265

$6,407
$3,844
$2,563

$7,248
$4,349
$2,899

$8,200
$4,920
$3,280

Discount at Cost of Capital (WACC) = 22.8% (.558) + 9.45% (0.442) = 16.90%

Cost of Equity
22.80%

Riskfree Rate:
Rsl riskfree rate = 12%

284

Aswath Damodaran

Cost of Debt
(12%+1.50%)(1-.30)
= 9.45%

Beta
1.17

Unlevered Beta for

Sectors: 0.75

Weights
E = 55.8% D = 44.2%

Risk Premium
9.23%

Firms D/E
Ratio: 79%

Mature risk
premium
4%

Country Risk
Premium
5.23%

Term Yr
8,610
3,529
5,081

Lesson 4: Watch out for cross holdings

285

Emerging market companies are more prone to having

cross holdings that companies in developed markets.
This is parJally the result of history (since many of the
larger public companies used to be family owned
businesses unJl a few decades ago) and partly because
those who run these companies value control (and use
cross holdings to preserve this control).
In many emerging market companies, the real process of
valuaJon begins when you have nished your DCF
valuaJon, since the cross holdings (which can be
numerous) have to be valued, open with minimal
informaJon.

Aswath Damodaran

285

8. The Tata Group April 2010

reinvestment rate
Tata Chemicals: April 2010 Average
from 2007-09: 56.5%
Current Cashflow to Firm
Reinvestment Rate
EBIT(1-t) :
Rs 5,833
56.5%
Expected Growth
- Nt CpX
Rs 5,832
in EBIT (1-t)
- Chg WC
Rs 4,229
.565*.1035=0.0585
= FCFF
- Rs 4,228
5.85%
Reinv Rate = (5832+4229)/5833 =
172.50%
Tax rate = 31.5%
Return on capital = 10.35%
Op. Assets Rs 57,128
+ Cash:
6,388
+ Other NO
56,454
- Debt
32,374
=Equity
87,597
Value/Share Rs 372

Year
EBIT (1-t)
- Reinvestment
FCFF

Rs Cashflows
1
2
INR 6,174 INR 6,535
INR 3,488 INR 3,692
INR 2,685 INR 2,842

Return on Capital
10.35%

Stable Growth
g = 5%; Beta = 1.00
Country Premium= 3%
Tax rate = 33.99%
Cost of capital = 9.78%
ROC= 9.78%;
Reinvestment Rate=g/ROC
=5/ 9.78= 51.14%

Average reinvestment rate

from 2005-09: 179.59%;
without acquisitions: 70%

Tata Motors: April 2010

Current Cashflow to Firm

Reinvestment Rate
EBIT(1-t) :
Rs 20,116
70%
- Nt CpX
Rs 31,590
- Chg WC
Rs 2,732
= FCFF
- Rs 14,205
Reinv Rate = (31590+2732)/20116 =
170.61%; Tax rate = 21.00%
Return on capital = 17.16%

Terminal Value5= 3831/(.0978-.05) = Rs 80,187

3
INR 6,917
INR 3,908
INR 3,008

4
INR 7,321
INR 4,137
INR 3,184

5
INR 7,749
INR 4,379
INR 3,370

7841
4010
3831

Return on Capital
17.16%

Terminal Value5= 26412/(.1039-.05) = Rs 489,813

Rs Cashflows
Op. Assets Rs231,914
+ Cash:
11418
+ Other NO 140576
- Debt
109198
=Equity
274,710

Year
EBIT (1-t)
- Reinvestment
FCFF

1
22533
15773
6760

2
25240
17668
7572

3
28272
19790
8482

Stable Growth
g = 5%; Beta = 1.00
Country Premium= 3%
Cost of capital = 10.39%
Tax rate = 33.99%
ROC= 12%;
Reinvestment Rate=g/ROC
=5/ 12= 41.67%

Expected Growth
from new inv.
.70*.1716=0.1201

4
31668
22168
9500

5
35472
24830
10642

6
39236
25242
13994

7
42848
25138
17711

8
46192
24482
21710

9
49150
23264
25886

10
51607
21503
30104

45278
18866
26412

Value/Share Rs 665

Discount at $ Cost of Capital (WACC) = 13.82% (.695) + 6.6% (0.305) = 11.62%

Cost of Equity
13.82%

Riskfree Rate:
Rs Riskfree Rate= 5%

Cost of Debt
(5%+ 2%+3)(1-.3399)
= 6.6%

Beta
1.21

Unlevered Beta for

Sectors: 0.95

Weights
E = 69.5% D = 30.5%

Mature market
premium
4.5%

Firms D/E
Ratio: 42%

Lambda
0.75

On April 1, 2010
Tata Chemicals price = Rs 314

Country Equity Risk

Premium
4.50%

Country Default
Spread
3%

Discount at $ Cost of Capital (WACC) = 14.00% (.747) + 8.09% (0.253) = 12.50%

Growth declines to 5%
and cost of capital
moves to stable period
level.
Cost of Equity
Cost of Debt
Weights
14.00%
(5%+ 4.25%+3)(1-.3399)
On
April 1, 2010
E
=
74.7%
D
=
25.3%
= 8.09%
Tata Motors price = Rs 781

Riskfree Rate:
Rs Riskfree Rate= 5%

Beta
1.20

Unlevered Beta for

Sectors: 1.04

Rel Equity
Mkt Vol
1.50

Mature market
premium
4.5%

Firms D/E
Ratio: 33%

Current Cashflow to Firm

EBIT(1-t) :
Rs 43,420
- Nt CpX
Rs 5,611
- Chg WC
Rs 6,130
= FCFF
Rs 31,679
Reinv Rate = (56111+6130)/43420=
27.04%; Tax rate = 15.55%
Return on capital = 40.63%

Reinvestment Rate
56.73%

Return on Capital
40.63%

Expected Growth
from new inv.
5673*.4063=0.2305

Year
EBIT (1-t)
- Reinvestment
FCFF

1
53429
30308
23120

2
65744
37294
28450

3
80897
45890
35007

4
99544
56468
43076

5
122488
69483
53005

Rel Equity
Mkt Vol
1.50

Stable Growth
g = 5%; Beta = 1.00
Country Premium= 3%
Cost of capital = 9.52%
Tax rate = 33.99%
ROC= 15%;
Reinvestment Rate=g/ROC
=5/ 15= 33.33%

Terminal Value5= 118655/(.0952-.05) = 2,625,649

Rs Cashflows
Op. Assets 1,355,361
+ Cash:
3,188
+ Other NO
66,140
- Debt
505
=Equity
1,424,185

Country Equity Risk

Premium
4.50%

Country Default
Spread
3%

Average reinvestment rate

from 2005--2009 =56.73%%

TCS: April 2010

Lambda
0.80

6
146299
76145
70154

7
169458
80271
89187

8
190165
81183
108983

9
206538
78509
128029

10
216865
72288
144577

177982
59327
118655

Discount at Rs Cost of Capital (WACC) = 10.63% (.999) + 5.61% (0.001) = 10.62%

Cost of Equity
10.63%

Riskfree Rate:
Rs Riskfree Rate= 5%

Cost of Debt
(5%+ 0.5%+3)(1-.3399)
= 5.61%

Beta
1.05

Unlevered Beta for

Sectors: 1.05

286

Aswath Damodaran

Growth declines to 5%
and cost of capital
moves to stable period
level.

Weights
E = 99.9% D = 0.1%

Mature market
premium
4.5%
Firms D/E
Ratio: 0.1%

Lambda
0.20

On April 1, 2010
TCS price = Rs 841

Country Equity Risk

Premium
4.50%

Country Default
Spread
3%

Rel Equity
Mkt Vol
1.50

Tata Companies: Value Breakdown

287

100.00%

5.32%

1.62%

2.97%

0.22%
4.64%

36.62%

80.00%

47.45%
47.06%

60.00%

% of value from cash

95.13%

% of value from holdings

% of value from operating assets

40.00%
60.41%
47.62%

50.94%

20.00%

0.00%
Tata Chemicals

Aswath Damodaran

Tata Steel

Tata Motors

TCS

287

Lesson 5: TruncaJon risk can come in many

forms
288

Natural disasters: Small companies in some economies

are much exposed to natural disasters (hurricanes,
earthquakes), without the means to hedge against that
risk (with insurance or derivaJve products).
Terrorism risk: Companies in some countries that are
unstable or in the grips of civil war are exposed to
damage or destrucJon.
NaJonalizaJon risk: While less common than it used to
be, there are countries where businesses may be
naJonalized, with owners receiving less than fair value
as compensaJon.

Aswath Damodaran

288

Dealing with truncaJon risk..

289

Assume that you are valuing Gazprom, the Russian oil

company and have esJmated a value of US $180 billion
for the operaJng assets. The rm has $30 billion in debt
outstanding. What is the value of equity in the rm?
Now assume that the rm has 15 billion shares
outstanding. EsJmate the value of equity per share.
The Russian government owns 42% of the outstanding
shares. Would that change your esJmate of value of
equity per share?

Aswath Damodaran

289

V. Valuing Financial Service Companies

290

Existing assets are

usually financial
assets or loans, often
marked to market.
Earnings do not
provide much
information on
underlying risk.

Defining capital expenditures and working capital is a

challenge.Growth can be strongly influenced by
regulatory limits and constraints. Both the amount of
new investments and the returns on these investments
can change with regulatory changes.
What is the value added by growth
assets?

What are the cashflows

from existing assets?

Preferred stock is a
significant source of
capital.
What is the value of
equity in the firm?

Aswath Damodaran

How risky are the cash flows from both

existing assets and growth assets?
For financial service firms, debt is
raw material rather than a source of
capital. It is not only tough to define
but if defined broadly can result in
high financial leverage, magnifying
the impact of small operating risk
changes on equity risk.

When will the firm

become a mature
fiirm, and what are
the potential
roadblocks?
In addition to all the normal
constraints, financial service
firms also have to worry about
maintaining capital ratios that
are acceptable ot regulators. If
they do not, they can be taken
over and shut down.

290

2a. ABN AMRO - December 2003

Rationale for model

Why dividends? Because FCFE cannot be estimated
Why 2-stage? Because the expected growth rate in near term is higher than stable growth rate.
Retention
Ratio =
51.35%

Dividends
EPS =
1.85 Eur
* Payout Ratio 48.65%
DPS = 0.90 Eur

ROE = 16%
Expected Growth
51.35% *
16% = 8.22%

g =4%: ROE = 8.35%(=Cost of equity)

Beta = 1.00
Payout = (1- 4/8.35) = .521

Terminal Value= EPS6*Payout/(r-g)

= (2.86*.521)/(.0835-.04) = 34.20
EPS 2.00 Eur
DPS 0.97 Eur

2.17 Eur
1.05 Eur

Value of Equity per

share = PV of
Dividends &
Terminal value at
8.15% = 27.62
Euros

2.34Eur
1.14 Eur

2.54 Eur
1.23 Eur

2.75 Eur
1.34 Eur
.........
Forever

Discount at Cost of Equity

In December 2003, Amro
was trading at 18.55 Euros
per share
Cost of Equity
4.95% + 0.95 (4%) = 8.15%

Riskfree Rate:
Long term bond rate in
Euros
4.35%

291

Aswath Damodaran

Beta
0.95

Average beta for European banks =

0.95

Risk Premium
4%

Mature Market
4%

Country Risk
0%

Left return on equity at 2008

levels. well below 16% in
2007 and 20% in 2004-2006.

2b. Goldman Sachs: August 2008

Rationale for model

Why dividends? Because FCFE cannot be estimated
Why 3-stage? Because the firm is behaving (reinvesting, growing) like a firm with potential.
Retention
Ratio =
91.65%

Dividends
EPS =
$16.77 *
Payout Ratio 8.35%
DPS =$1.40
(Updated numbers for 2008
financial year ending 11/08)

ROE = 13.19%
Expected Growth in
first 5 years =
91.65%*13.19% =
12.09%

g =4%: ROE = 10%(>Cost of equity)

Beta = 1.20
Payout = (1- 4/10) = .60 or 60%

Terminal Value= EPS10*Payout/(r-g)

= (42.03*1.04*.6)/(.095-.04) = 476.86
Year

Value of Equity per

share = PV of
Dividends &
Terminal value =
$222.49

EPS
Payout ratio
DPS

1
$18.80
8.35%
$1.57

2
$21.07
8.35%
$1.76

3
$23.62
8.35%
$1.97

4
$26.47
8.35%
$2.21

5
$29.67
8.35%
$2.48

6
$32.78
18.68%
$6.12

7
$35.68
29.01%
$10.35

8
$38.26
39.34%
$15.05

9
$40.41
49.67%
$20.07

10
$42.03
60.00%
$25.22

Discount at Cost of Equity

Between years 6-10, as growth drops
to 4%, payout ratio increases and cost
of equity decreases.

Forever

In August 2008, Goldman

was trading at $ 169/share.

Cost of Equity
4.10% + 1.40 (4.5%) = 10.4%

Riskfree Rate:
Treasury bond rate
4.10%

Beta
1.40

Average beta for inveestment

banks= 1.40

292

Aswath Damodaran

Risk Premium
4.5%
Impled Equity Risk
premium in 8/08
Mature Market
4.5%

Country Risk
0%

Lesson 1: Financial service companies are

opaque
293

With nancial service rms, we enter into a FausJan bargain.

They tell us very liRle about the quality of their assets (loans,
for a bank, for instance are not broken down by default risk
status) but we accept that in return for assets being marked
to market (by accountants who presumably have access to
the informaJon that we dont have).
In addiJon, esJmaJng cash ows for a nancial service rm
is dicult to do. So, we trust nancial service rms to pay out
their cash ows as dividends. Hence, the use of the dividend
discount model.
During Jmes of crises or when you dont trust banks to pay
out what they can aord to in dividends, using the dividend
discount model may not give you a reliable value.

Aswath Damodaran

293

2c. Wells Fargo: Valuation on October 7, 2008

Rationale for model

Why dividends? Because FCFE cannot be estimated
Why 2-stage? Because the expected growth rate in near term is higher than stable growth rate.

Return on
equity: 17.56%

Retention
Ratio =
45.37%

Dividends (Trailing 12
months)
EPS =
$2.16 *
Payout Ratio 54.63%
DPS =
$1.18

Assuming that Wells will have to increase its

capital base by about 30% to reflect tighter
regulatory concerns. (.1756/1.3 =.135
ROE = 13.5%

Expected Growth
45.37% *
13.5% = 6.13%

g =3%: ROE = 7.6%(=Cost of equity)

Beta = 1.00: ERP = 4%
Payout = (1- 3/7.6) = .60.55%

Terminal Value= EPS6*Payout/(r-g)

= ($3.00*.6055)/(.076-.03) = $39.41
EPS $ 2.29
DPS $1.25

$2.43
$1.33

$2.58
$1.41

Value of Equity per

share = PV of
Dividends &
Terminal value at
9.6% = $30.29

$2.74
$1.50

$2.91
$1.59

.........
Forever

Discount at Cost of Equity

In October 2008, Wells
Fargo was trading at $33
per share
Cost of Equity
3.60% + 1.20 (5%) = 9.60%

Riskfree Rate:
Long term treasury bond
rate
3.60%

294

Aswath Damodaran

Beta
1.20

Average beta for US Banks over

last year: 1.20

Risk Premium
5%
Updated in October 2008

Mature Market
5%

Country Risk
0%

Lesson 2: For nancial service companies, book

value maRers
295

The book value of assets and equity is mostly irrelevant when valuing
non-nancial service companies. Aper all, the book value of equity is a
historical gure and can be nonsensical. (The book value of equity can be
negaJve and is so for more than a 1000 publicly traded US companies)
With nancial service rms, book value of equity is relevant for two
reasons:

Since nancial service rms mark to market, the book value is more likely to reect
what the rms own right now (rather than a historical value)
The regulatory capital raJos are based on book equity. Thus, a bank with negaJve
or even low book equity will be shut down by the regulators.

From a valuaJon perspecJve, it therefore makes sense to pay heed to

book value. In fact, you can argue that reinvestment for a bank is the
amount that it needs to add to book equity to sustain its growth
ambiJons and safety requirements:

FCFE = Net Income Reinvestment in regulatory capital (book equity)

Aswath Damodaran

295

FCFE for a bank

296

To esJmate the FCFE for a bank, we redene reinvestment as investment

in regulatory capital. Since any dividends paid deplete equity capital and
retained earnings increase that capital, the FCFE is:

FCFEBank= Net Income Increase in Regulatory Capital (Book Equity)

Deutsche Bank: FCFE

Aswath Damodaran

296

297

Aswath Damodaran

VI. Valuing Companies with intangible assets

298

If capital expenditures are miscategorized as

operating expenses, it becomes very difficult to
assess how much a firm is reinvesting for future
growth and how well its investments are doing.
What is the value added by growth
assets?
What are the cashflows
from existing assets?
The capital
expenditures
associated with
acquiring intangible
assets (technology,
himan capital) are
mis-categorized as
operating expenses,
leading to inccorect
accounting earnings
and measures of
capital invested.

Aswath Damodaran

How risky are the cash flows from both

existing assets and growth assets?
It ican be more difficult to borrow
against intangible assets than it is
against tangible assets. The risk in
operations can change depending
upon how stable the intangbiel asset
is.

When will the firm

become a mature
fiirm, and what are
the potential
roadblocks?
Intangbile assets such as
brand name and customer
loyalty can last for very long
periods or dissipate
overnight.

298

Lesson 1: AccounJng rules are cluRered with

inconsistencies
299

If we start with accounJng rst principles, capital expenditures are

expenditures designed to create benets over many periods. They
should not be used to reduce operaJng income in the period that
they are made, but should be depreciated/amorJzed over their
life. They should show up as assets on the balance sheet.
AccounJng is consistent in its treatment of cap ex with
manufacturing rms, but is inconsistent with rms that do not t
the mold.

With pharmaceuJcal and technology rms, R&D is the ulJmate cap ex but
is treated as an operaJng expense.
With consulJng rms and other rms dependent on human capital,
recruiJng and training expenses are your long term investments that are
treated as operaJng expenses.
With brand name consumer product companies, a porJon of the
adverJsing expense is to build up brand name and is the real capital
expenditure. It is treated as an operaJng expense.

Aswath Damodaran

299

Exhibit 11.1: Converting R&D expenses to R&D assets - Amgen

Step 1: Ddetermining an amortizable life for R & D expenses. 1
How long will it take, on an expected basis, for research to pay off at Amgen? Given the length of the approval process for new
drugs by the Food and Drugs Administration, we will assume that this amortizable life is 10 years.
Step 2: Capitalize historical R&D exoense
2

4
Current years R&D expense = Cap ex = $3,030 million
R&D amortization = Depreciation = $ 1,694 million
Unamortized R&D = Capital invested (R&D) = $13,284 million

Step 3: Restate earnings, book value and return numbers

300

Aswath Damodaran

Cap Ex = Acc net Cap Ex(255) +

Acquisitions (3975) + R&D (2216)
Current Cashflow to Firm
EBIT(1-t)= :7336(1-.28)= 6058
- Nt CpX=
6443
- Chg WC
37
= FCFF
- 423
Reinvestment Rate = 6480/6058
=106.98%
Return on capital = 16.71%

10. Amgen: Status Quo

Reinvestment Rate
60%

First 5 years
Op. Assets 94214
+ Cash:
1283
- Debt
8272
=Equity
87226
-Options
479
Value/Share $ 74.33

Year
EBIT
EBIT (1-t)
- Reinvestment
= FCFF

1
$9,221
$6,639
$3,983
$2,656

2
$10,106
$7,276
$4,366
$2,911

3
$11,076
$7,975
$4,785
$3,190

Return on Capital
16%

Expected Growth
in EBIT (1-t)
.60*.16=.096
9.6%

Growth decreases
Terminal Value10 = 7300/(.0808-.04) = 179,099
gradually to 4%
4
5
6
7
8
9
10
Term Yr
$12,140 $13,305 $14,433 $15,496 $16,463 $17,306 $17,998
18718
$8,741 $9,580 $10,392 $11,157 $11,853 $12,460 $12,958
12167
$5,244 $5,748 $5,820 $5,802 $5,690 $5,482 $5,183
4867
$3,496 $3,832 $4,573 $5,355 $6,164 $6,978 $7,775
7300

Cost of Capital (WACC) = 11.7% (0.90) + 3.66% (0.10) = 10.90%

Cost of Equity
11.70%

Riskfree Rate:
Riskfree rate = 4.78%

301

Aswath Damodaran

Cost of Debt
(4.78%+..85%)(1-.35)
= 3.66%

Beta
1.73

Unlevered Beta for

Sectors: 1.59

Stable Growth
g = 4%; Beta = 1.10;
Debt Ratio= 20%; Tax rate=35%
Cost of capital = 8.08%
ROC= 10.00%;
Reinvestment Rate=4/10=40%

Weights
E = 90% D = 10%

Risk Premium
4%

D/E=11.06%

Debt ratio increases to 20%

Beta decreases to 1.10

On May 1,2007,
Amgen was trading
at $ 55/share

Lesson 2: And xing those inconsistencies can

alter your view of a company and aect its value
302

Aswath Damodaran

302

VII. Valuing cyclical and commodity companies

303

Company growth often comes from movements in the

economic cycle, for cyclical firms, or commodity prices,
for commodity companies.

What is the value added by growth

assets?
What are the cashflows
from existing assets?
Historial revenue and
earnings data are
volatile, as the
economic cycle and
commodity prices
change.

Aswath Damodaran

How risky are the cash flows from both

existing assets and growth assets?
Primary risk is from the economy for
cyclical firms and from commodity
price movements for commodity
companies. These risks can stay
dormant for long periods of apparent
prosperity.

When will the firm

become a mature
fiirm, and what are
the potential
roadblocks?
For commodity companies, the
fact that there are only finite
amounts of the commodity may
put a limit on growth forever.
For cyclical firms, there is the
peril that the next recession
may put an end to the firm.

303

Valuing a Cyclical Company - Toyota in Early 2009

Year
Revenues
Operating Income
EBITDA
Operating Margin
FY1 1992
10,163,380
218,511
218,511
2.15%
FY1 1993
10,210,750
181,897
181,897
1.78%
FY1 1994
9,362,732
136,226
136,226
1.45%
FY1 1995
8,120,975
255,719
255,719
3.15%
FY1 1996
10,718,740
348,069
348,069
3.25%
FY1 1997
12,243,830
665,110
665,110
5.43%
FY1 1998
11,678,400
779,800
1,382,950
6.68%
FY1 1999
12,749,010
774,947
1,415,997
6.08%
FY1 2000
12,879,560
775,982
1,430,982
6.02%
FY1 2001
13,424,420
870,131
1,542,631
6.48%
FY1 2002
15,106,300
1,123,475
1,822,975
7.44%
FY1 2003
16,054,290
1,363,680
2,101,780
8.49%
FY1 2004
17,294,760
1,666,894
2,454,994
9.64%
FY1 2005
18,551,530
1,672,187
2,447,987
9.01%
FY1 2006
21,036,910
1,878,342
2,769,742
8.93%
FY1 2007
23,948,090
2,238,683
3,185,683
9.35%
FY1 2008
26,289,240
2,270,375
3,312,775
8.64%
FY 2009 (Estimate)
22,661,325
267,904
1,310,304
1.18%
1,306,867
7.33%

Normalized Earnings 1
As a cyclical company, Toyotas earnings have been volatile and 2009 earnings reflect the
troubled global economy. We will assume that when economic growth returns, the
operating margin for Toyota will revert back to the historical average.
Normalized Operating Income = Revenues in 2009 * Average Operating Margin (98--09)
= 22661 * .0733 =1660.7 billion yen

Value of operating assets =

304

In early 2009, Toyota Motors had the

highest market share in the sector.
However, the global economic
recession in 2008-09 had pulled
earnings down.
Normalized Return on capital and
2
Reinvestment
Once earnings bounce back to normal, we
assume that Toyota will be able to earn a
return on capital equal to its cost of capital
(5.09%). This is a sector, where earning
excess returns has proved to be difficult
even for the best of firms.
To sustain a 1.5% growth rate, the
reinvestment rate has to be:
Reinvestment rate = 1.5%/5.09%
= 29.46%
Operating Assets
+ Cash
+ Non-operating assets
- Debt
- Minority Interests
Value of Equity
/ No of shares
Value per share

1660.7 (1.015) (1- .407) (1- .2946)

= 19,640 billion
(.0509 - .015)

Normalized Cost of capital

3
The cost of capital is computed using the average beta of
automobile companies (1.10), and Toyotas cost of debt (3.25%)
and debt ratio (52.9% debt ratio. We use the Japanese marginal
Damodaran
tax Aswath
rate of 40.7%
for computing both the after-tax cost of debt
and the after-tax operating income
Cost of capital = 8.65% (.471) + 3.25% (1-.407) (.529) = 5.09%

Stable Growth 4
Once earnings are normalized, we
assume that Toyota, as the largest
market-share company, will be able
to maintain only stable growth
(1.5% in Yen terms)

19,640
2,288
6,845
11,862
583
/3,448
4735

Valuing a commodity company - Exxon in Early 2009

Historical data: Exxon Operating Income vs Oil
Price

Regressing Exxons operating income against the oil price per barrel
from 1985-2008:
Operating Income = -6,395 + 911.32 (Average Oil Price) R2 = 90.2%
(2.95) (14.59)
Exxon Mobil's operating income increases about $9.11 billion for every
$ 10 increase in the price per barrel of oil and 90% of the variation in
Exxon's earnings over time comes from movements in oil prices.

Estiimate normalized income based on current oil price 1

At the time of the valuation, the oil price was $ 45 a barrel. Exxons
operating income based on thisi price is
Normalized Operating Income = -6,395 +
911.32 ($45) = $34,614

Exxons cost of capital 4

Exxon has been a predominantly equtiy funded company, and is
explected to remain so, with a deb ratio of onlly 2.85%: Its cost of
equity is 8.35% (based on a beta of 0.90) and its pre-tax cost of debt
is 3.75% (given AAA rating). The marginal tax rate is 38%.
Aswath
Damodaran
305
Cost of capital
= 8.35%
(.9715) + 3.75% (1-.38) (.0285) = 8.18%.

Estimate return on capital and reinvestment rate

based on normalized income 2
This%operating%income%translates%into%a%return%on%capital%
of%approximately%21%%and%a%reinvestment%rate%of%9.52%,%
based%upon%a%2%%growth%rate.%%
Reinvestment%Rate%=%g/%ROC%=%2/21%%=%9.52%

Expected growth in operating income 3

Since Exxon Mobile is the largest oil company in the world, we
will assume an expected growth of only 2% in perpetuity.

Lesson 1: With macro companies, it is easy to

get lost in macro assumpJons
306

With cyclical and commodity companies, it is undeniable that

the value you arrive at will be aected by your views on the
economy or the price of the commodity.
Consequently, you will feel the urge to take a stand on these
macro variables and build them into your valuaJon. Doing so,
though, will create valuaJons that are jointly impacted by
your views on macro variables and your views on the
company, and it is dicult to separate the two.
The best (though not easiest) thing to do is to separate your
macro views from your micro views. Use current market
based numbers for your valuaJon, but then provide a
separate assessment of what you think about those market
numbers.

Aswath Damodaran

306

Lesson 2: Use probabilisJc tools to assess value

as a funcJon of macro variables
307

If there is a key macro variable aecJng the value of your

company that you are uncertain about (and who is not), why
not quanJfy the uncertainty in a distribuJon (rather than a
single price) and use that distribuJon in your valuaJon.
That is exactly what you do in a Monte Carlo simulaJon,
where you allow one or more variables to be distribuJons
and compute a distribuJon of values for the company.
With a simulaJon, you get not only everything you would get
in a standard valuaJon (an esJmated value for your
company) but you will get addiJonal output (on the variaJon
in that value and the likelihood that your rm is under or
over valued)

Aswath Damodaran

307

Exxon Mobil ValuaJon: SimulaJon

308

Aswath Damodaran

308

Aswath Damodaran

VALUE, PRICE AND

INFORMATION:
CLOSING THE DEAL
Value versus Price

309

Are you valuing or pricing?

310

Tools for intrinsic analysis

- Discounted Cashflow Valuation (DCF)
- Intrinsic multiples
- Book value based approaches
- Excess Return Models

Value of cashflows,
adjusted for time
and risk

INTRINSIC
VALUE

Drivers of intrinsic value

- Cashflows from existing assets
- Growth in cash flows
- Quality of Growth

Aswath Damodaran

Value

Tools for pricing

- Multiples and comparables
- Charting and technical indicators
- Pseudo DCF

Tools for "the gap"

- Behavioral finance
- Price catalysts

THE GAP
Is there one?
Will it close?

Price

Drivers of "the gap"

- Information
- Liquidity
- Corporate governance

PRICE

Drivers of price
- Market moods & momentum
- Surface stories about fundamentals

310

Three views of the gap

311

View of the gap

Investment Strategies

The Ecient
Marketer

The gaps between price and value, if

they do occur, are random.

Index funds

The value
extremist

You view pricers as dileRantes who

Buy and hold stocks
will move on to fad and fad.
where value < price
Eventually, the price will converge on
value.

The pricing
extremist

Value is only in the heads of the

eggheads. Even if it exists (and it is
quesJonable), price may never
converge on value.

Aswath Damodaran

(1) Look for mispriced

securiJes.
(2) Get ahead of ships in
demand/momentum.

311

The pricers dilemma..

312

No anchor: If you do not believe in intrinsic value and make

no aRempt to esJmate it, you have no moorings when you
invest. You will therefore be pushed back and forth as the
price moves from high to low. In other words, everything
becomes relaJve and you can lose perspecJve.
ReacJve: Without a core measure of value, your investment
strategy will open be reacJve rather than proacJve.
Crowds are ckle and tough to get a read on: The key to
being successful as a pricer is to be able to read the crowd
mood and to detect ships in that mood early in the process.
By their nature, crowds are tough to read and almost
impossible to model systemaJcally.

Aswath Damodaran

312

The valuers dilemma and ways of dealing with

it
313

Uncertainty about the magnitude of the gap:

Margin of safety: Many value investors swear by the noJon of the

margin of safety as protecJon against risk/uncertainty.
Collect more informaJon: CollecJng more informaJon about the
company is viewed as one way to make your investment less risky.
Ask what if quesJons: Doing scenario analysis or what if analysis gives
you a sense of whether you should invest.
Confront uncertainty: Face up to the uncertainty, bring it into the
analysis and deal with the consequences.

Uncertainty about gap closing: This is tougher and you can

reduce your exposure to it by

Lengthening your Jme horizon

Providing or looking for a catalyst that will cause the gap to close.

Aswath Damodaran

313

OpJon 1: Margin of Safety

314

The margin of safety (MOS) is a buer that you build into

your investment decisions to protect yourself from
investment mistakes. Thus, if your margin of safety is 30%,
you will buy a stock only if the price is more than 30% below
its intrinsic value.
While value investors use the margin of safety as a shield
against risk, keep in mind that:

MOS comes into play at the end of the investment process, not at the
beginning.
MOS does not subsJtute for risk assessment and intrinsic valuaJon,
but augments them.
The MOS cannot and should not be a xed number, but should be
reecJve of the uncertainty in the assessment of intrinsic value.
Being too conservaJve can be damaging to your long term investment
prospects. Too high a MOS can hurt you as an investor.

Aswath Damodaran

314

Option 2: Collect more information/ Do

your homework
315

There is a widely held view among value investors that they are not
as exposed to risk as the rest of the market, because they do their
homework, poring over nancial statements or using raJos to
screen for risky stocks. Put simply, they are assuming that the
more they know about an investment, the less risky it becomes.
That may be true from some peripheral risks and a few rm
specic risks, but it denitely is not for the macro risks. You cannot
make a cyclical company less cyclical by studying it more or take
the naJonalizaJon risk out of Venezuelan company by doing more
research.
ImplicaDon 1: The need for diversicaJon does not decrease just because
you are a value investor who picks stocks with much research and care.
ImplicaDon 2: There is a law of diminishing returns to informaJon. At a point,
addiJonal informaJon will only serve to distract you.

Aswath Damodaran

315

Option 3: Build What-if analyses

316

A valuaJon is a funcJon of the inputs you feed into the

valuaJon. To the degree that you are pessimisJc or opJmisJc
on any of the inputs, your valuaJon will reect it.
There are three ways in which you can do what-if analyses

Best-case, Worst-case analyses, where you set all the inputs at their
most opJmisJc and most pessimisJc levels
Plausible scenarios: Here, you dene what you feel are the most
plausible scenarios (allowing for the interacJon across variables) and
value the company under these scenarios
SensiJvity to specic inputs: Change specic and key inputs to see the
eect on value, or look at the impact of a large event (FDA approval
for a drug company, loss in a lawsuit for a tobacco company) on value.

ProposiDon 1: As a general rule, what-if analyses will

yield large ranges for value, with the actual price
somewhere within the range.

Aswath Damodaran

316

Option 4: Confront uncertainty

Simulations The Amgen valuation
317

Correlation =0.4

Aswath Damodaran

317

The Simulated Values of Amgen:

What do I do with this output?
318

Aswath Damodaran

318

Strategies for managing the risk in the closing

of the gap
319

The karmic approach: In this one, you buy (sell short) under
(over) valued companies and sit back and wait for the gap to
close. You are implicitly assuming that given Jme, the market
will see the error of its ways and x that error.
The catalyst approach: For the gap to close, the price has to
converge on value. For that convergence to occur, there
usually has to be a catalyst.

If you are an acJvist investor, you may be the catalyst yourself. In fact,
your act of buying the stock may be a sucient signal for the market
to reassess the price.
If you are not, you have to look for other catalysts. Here are some to
watch for: a new CEO or management team, a blockbuster new
product or an acquisiJon bid where the rm is targeted.

Aswath Damodaran

319

A closing thought
320

Aswath Damodaran

320