Valuation

Aswath Damodaran
http://www.damodaran.com
For the valuations in this presentation, go to 
Seminars/ Presentations

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 Some Initial Thoughts

" One hundred thousand lemmings cannot be wrong"

Graffiti

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 Misconceptions about Valuation

 Myth 1: A valuation is an objective search for “true” value

• Truth 1.1: All valuations are biased. The only questions are how much and in which
direction.
• Truth 1.2: The direction and magnitude of the bias in your valuation is directly
proportional to who pays you and how much you are paid.
 Myth 2.: A good valuation provides a precise estimate of value
• Truth 2.1: There are no precise valuations
• Truth 2.2: The payoff to valuation is greatest when valuation is least precise.
 Myth 3: . The more quantitative a model, the better the valuation
• Truth 3.1: One’s understanding of a valuation model is inversely proportional to
the number of inputs required for the model.
• Truth 3.2: Simpler valuation models do much better than complex ones.

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 Approaches to Valuation

 Discounted cashflow valuation, relates the value of an asset to the present

value of expected future cashflows on that asset.
 Relative valuation, estimates the value of an asset by looking at the pricing of
'comparable' assets relative to a common variable like earnings, cashflows,
book value or sales.
 Contingent claim valuation, uses option pricing models to measure the value
of assets that share option characteristics.

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 Discounted Cash Flow Valuation

 What is it: In discounted cash flow valuation, the value of an asset is the
present value of the expected cash flows on the asset.
 Philosophical Basis: Every asset has an intrinsic value that can be estimated,
based upon its characteristics in terms of cash flows, growth and risk.
 Information Needed: To use discounted cash flow valuation, you need
• to estimate the life of the asset
• to estimate the cash flows during the life of the asset
• to estimate the discount rate to apply to these cash flows to get present value
 Market Inefficiency: Markets are assumed to make mistakes in pricing assets
across time, and are assumed to correct themselves over time, as new
information comes out about assets.

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 Discounted Cashflow Valuation: Basis for Approach

CF1 CF2 CF3 CF4 CFn

Value of asset = + + + .....+
(1 + r)1 (1 + r) 2 (1 + r) 3 (1 + r) 4 (1 + r) n

where CFt is the expected cash flow in period t, r is the discount rate appropriate
given the riskiness of the cash flow and n is the life of the asset.
€ Proposition 1: For an asset to have value, the expected cash flows have to be
positive some time over the life of the asset.
Proposition 2: Assets that generate cash flows early in their life will be worth
more than assets that generate cash flows later; the latter may however
have greater growth and higher cash flows to compensate.

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 DCF Choices: Equity Valuation versus Firm Valuation
Firm Valuation: Value the entire business

Assets Liabilities
Existing Investments Fixed Claim on cash flows
Generate cashflows today Assets in Place Debt Little or No role in management
Includes long lived (fixed) and Fixed Maturity
short-lived(working Tax Deductible
capital) assets

Expected Value that will be Growth Assets Equity Residual Claim on cash flows
created by future investments Significant Role in management
Perpetual Lives

Equity valuation: Value just the

equity claim in the business

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 Equity Valuation

Figure 5.5: Equity Valuation

Assets Liabilities

Assets in Place Debt

Cash flows considered are
cashflows from assets,
after debt payments and
after making reinvestments
needed for future growth Discount rate reflects only the
Growth Assets Equity cost of raising equity financing

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

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 Firm Valuation

Figure 5.6: Firm Valuation

Assets Liabilities

Assets in Place Debt

Cash flows considered are
cashflows from assets, Discount rate reflects the cost
prior to any debt payments of raising both debt and equity
but after firm has financing, in proportion to their
reinvested to create growth use
assets Growth Assets Equity

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

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 Hyundai Heavy: Status Quo ($) Return on Capital
Reinvestment Rate 30%
50%
Current Cashflow to Firm Stable Growth
EBIT(1-t) : 1,269 Billion Won Expected Growth g = 5%; Beta = 1.20;
- Nt CpX 519 in EBIT (1-t) Country Premium= 0.8%
- Chg WC 135 .50*.30=.15 Cost of capital = 9.42%
= FCFF 615 15% ROC= 9.42%
Reinvestment Rate = 654/1269=51.5% Reinvestment Rate=g/ROC
Return on capital = 1269/3390 =37.45% =5/9.42 = 53.1%

Terminal Value5= 1258(.0942-.05) = 28,471

Wn Cashflows
Op. Assets 20,211
+ Cash: 3,612 Year 1 2 3 4 5 Term Yr
+ Non-0p 3,937 EBIT (1-t) 1,460 1,679 1,931 2,220 2,553 2,681
- Debt 186 - Reinvestment 730 839 965 1,110 1,277 1,423
=Equity 27,574 FCFF 730 839 965 1,110 1,277 =1,258
-Options 0
Value/Share 362.82
(362,820 Won/Sh) Discount at $ Cost of Capital (WACC) = 11.3% (.993) + 4.75% (0.007) = 11.26%

On June 1, 2008
Hyundai Heavy traded at
Cost of Equity Cost of Debt
Weights 350,000 Won/share.
11.30% (5%+0.8%+0.75%)(1-.275)
= 4.75% E = 99.3% D = 0.7%

Riskfree Rate:
Won Riskfree Rate= 5% Beta Mature market Country Equity Risk
+ 1.50 X premium + Lambda X Premium
4% 0.25 1.20%

Unlevered Beta for Firmʼs D/E Rel Equity

Sectors: 0.75 Ratio: 26.84% Country Default Mkt Vol
Spread X
0.8% 1.20
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 I. Estimating Discount Rates

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 Cost of Equity

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 A Riskfree Rate

For a rate to be riskfree in valuation, it has to be long term, default free and
currency matched (to the cash flows)
 Assume that you are valuing Hyundai Heavy Industries in Korean Won for a
US institutional investor. Which of the following rates would you use as a
riskfree rate?
 The rate on the US 10-year treasury bond (3.8%)
 The rate on the Korean (Won) 10-year government bond (5.8%)
 Other
How would your answer change if you were valuing Hyundai in US dollars for a
Korean institutional investor?

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 Riskfree Rates - Different Currencies

6.00%
A2
0.80%

5.00%
A1
AAA 0.25%
10-year Govenment bond rate

4.00% AAA

3.00%
5.00%
4.30% 4.30%
2.00% 3.80%
AAA

1.00% 1.70%

0.00%
Japan 10-year US T-bond $ German 10-Year Euro Greece 10-year Euro Korean 10-year Won

Riskfree Rate Default spread

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 Everyone uses historical premiums, but..

 The historical premium is the premium that stocks have historically earned
over riskless securities.
 Practitioners never seem to agree on the premium; it is sensitive to
• How far back you go in history…
• Whether you use T.bill rates or T.Bond rates
• Whether you use geometric or arithmetic averages.
 For instance, looking at the US:
Arithmetic average Geometric Average
Stocks - Stocks - Stocks - Stocks -
Historical Period T.Bills T.Bonds T.Bills T.Bonds
1928-2007 7.78% 6.42% 5.94% 4.79%
1967-2007 5.94% 4.33% 4.75% 3.50%
1997-2007 5.26% 2.68% 4.69% 2.34%

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 Assessing Country Risk Using Currency Ratings: Asia

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 Using Country Ratings to Estimate Equity Spreads

 Country ratings 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.
• One way to adjust the country spread upwards is to use information from the US
market. In the US, the equity risk premium has been roughly twice the default
spread on junk bonds.
• Another is to multiply the bond spread by the relative volatility of stock and bond
prices in that market. For example,
– Standard Deviation in KOSPI = 18%
– Standard Deviation in Korean government bond= 12%
– Adjusted Equity Spread = 0.80% (18/12) = 1.20%

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 From Country Risk Premiums to Corporate Risk premiums

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

country risk. In this case,
E(Return) = Riskfree Rate + Country ERP + Beta (US premium)
 Approach 2: Assume that a company’s exposure to country risk is similar to its
exposure to other market risk.
E(Return) = Riskfree Rate + Beta (US premium + Country ERP)
 Approach 3: Treat country risk as a separate risk factor and allow firms to
have different exposures to country risk (perhaps based upon the proportion of
their revenues come from non-domestic sales)
E(Return)=Riskfree Rate+ β (US premium) + λ (Country ERP)
Country ERP: Additional country equity risk premium

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 Estimating Company Exposure to Country Risk

 Different companies should be exposed to different degrees to country risk.

For instance, a Korean firm that generates the bulk of its revenues in Western
Europe and the US should be less exposed to country risk than one that
generates all its business within Korea.
 The factor “λ” measures the relative exposure of a firm to country risk. One
simplistic solution would be to do the following:
λ = % of revenues domesticallyfirm/ % of revenues domesticallyavg firm
Consider two firms – HyumdaI Heavy Industries and Megastudy, both Korean
companies. The former gets about 20% of its revenues in Korea and the latter
gets 100%. The average Korean firm gets about 80% of its revenues in Korea:
λHyundai = 20%/80% = 0.25
λMegastudy = 100%/80% = 1.25
 There are two implications
• A company’s risk exposure is determined by where it does business and not by
where it is located
• Firms might be able to actively manage their country risk exposures

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 Estimating E(Return) for Hyundai Heavy Industries

 Assume that the beta for Hyundai Heavy is 1.50, and that the riskfree rate used
is 5%. Also assume that the historical premium for the US (4.79%) is a
reasonable estimate of a mature market risk premium.
 Approach 1: Assume that every company in the country is equally exposed to
country risk. In this case,
E(Return) = 5% + 1.2% + 1.5 (4.79%) = 13.39%
 Approach 2: Assume that a company’s exposure to country risk is similar to its
exposure to other market risk.
E(Return) = 5% + 1.5 (4.79%+ 1.2%) = 13.99%
 Approach 3: Treat country risk as a separate risk factor and allow firms to
have different exposures to country risk (perhaps based upon the proportion of
their revenues come from non-domestic sales)
E(Return)= 5% + 1.5(4.79%) + 0.25 (1.2%) + 0.50 (2%) = 13.49%
Reflects revenues in Eastern Europe, China and the
Rest of Asia

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 An alternate view of ERP: Watch what I pay, not what I say..

 You can back out an equity risk premium from stock prices:

After year 5, we will assume that

earnings on the index will grow at
Between 2001 and 2007 Analysts expect earnings to grow 5% a year for the next 5 years. We 4.02%, the same rate as the entire
dividends and stock will assume that dividends & buybacks will keep pace.. economy (= riskfree rate).
buybacks averaged 4.02% Last year’s cashflow (59.03) growing at 5% a year
of the index each year.
61.98 65.08 68.33 71.75 75.34

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

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 Solving for the implied premium…

 If we know what investors paid for equities at the beginning of 2007 and we
can estimate the expected cash flows from equities, we can solve for the rate of
return that they expect to make (IRR):
61.98 65.08 68.33 71.75 75.34 75.35(1.0402)
1468.36 = + + + + +
(1+ r) (1+ r) 2 (1+ r) 3 (1+ r) 4 (1+ r) 5 (r − .0402)(1+ r) 5
 Expected Return on Stocks = 8.39%
 Implied Equity Risk Premium = Expected Return on Stocks - T.Bond Rate
€ =8.39% - 4.02% = 4.37%

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 Implied Premiums in the US

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 Implied Premium versus RiskFree Rate

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 Equity Risk Premiums and Bond Default Spreads

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 Which equity risk premium should you use for the US?

 Historical Risk Premium: When you use the historical risk premium, you are
assuming that premiums will revert back to a historical norm and that the time
period that you are using is the right norm.
 Current Implied Equity Risk premium: You are assuming that the market is
correct in the aggregate but makes mistakes on individual stocks. If you are
required to be market neutral, this is the premium you should use. (What
types of valuations require market neutrality?)
 Average Implied Equity Risk premium: The average implied equity risk
premium between 1960-2007 in the United States is about 4%. You are
assuming that the market is correct on average but not necessarily at a point in
time.

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 Implied Premium for KOSPI: May 30, 2008

 Level of the Index = 1825

 FCFE on the Index = 3.75% (Estimated FCFE for companies in index as % of
market value of equity)
 Other parameters
• Riskfree Rate = 5% (Won)
• Expected Growth (in Won)
– Next 5 years = 7.5% (Used expected growth rate in Earnings)
– After year 5 = 5%
 Solving for the expected return:
• Expected return on Equity = 9.39%
• Implied Equity premium = 9.39% - 5% = 4.39%
 Effect on valuation
• Hyundai’s value @ historical premium (4%) + country (1.2%) : 350,000 Wn /share
• Hyundai’s value @ implied premium: 352,000 Wn/ share

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 Estimating Beta

 The standard procedure for estimating 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 reflects the firm’s business mix over the period of the regression, not the current
mix
• It reflects the firm’s average financial leverage over the period rather than the
current leverage.

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 Beta Estimation: Amazon

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 Beta Estimation for Hyundai Heavy: The Index Effect

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 Determinants of Betas

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 Bottom-up Betas

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 Hyundai: Breaking down businesses

Value Unlevered
Business Revenues EV/Sales Value Weight beta
Shipbuilding 8341 3.23 26941 63.73% 1.60
Offshore &
Engineering 2563 1.97 5049 11.94% 1.44
Industrial plant 1200 1.55 1860 4.40% 1.29
Engine and
Machinery 2252 1.36 3063 7.24% 1.21
Electro Electric
System 1753 1.8 3155 7.46% 1.19
Construction
Equipment 1823 1.21 2206 5.22% 1.29
42274 100.00% 1.49

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 Bottom up Beta Estimates

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 Small Firm and Other Premiums

 It is common practice to add premiums on to the cost of equity for firm-

specific characteristics. For instance, many analysts add a small stock
premium of 3-3.5% (historical premium for small stocks over the market) to
the cost of equity for smaller companies.
 Adding arbitrary premiums to the cost of equity is always a dangerous
exercise. If small stocks are riskier than larger stocks, we need to specify the
reasons and try to quantify them rather than trust historical averages. (You
could argue that smaller companies are more likely to serve niche
(discretionary) markets or have higher operating leverage and adjust the beta
to reflect this tendency).

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 Is Beta an Adequate Measure of Risk for a Private Firm?

The owners of most private firms are not diversified. Beta measures the risk added
on to a diversified portfolio. Therefore, using beta to arrive at a cost of equity
for a private firm will
a) Under estimate the cost of equity for the private firm
b) Over estimate the cost of equity for the private firm
c) Could under or over estimate the cost of equity for the private firm

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 Total Risk versus Market Risk

 Adjust the beta to reflect total risk rather than market risk. This adjustment is a
relatively simple one, since the R squared of the regression measures the
proportion of the risk that is market risk.
Total Beta = Market Beta / Correlation of the sector with the market
 To estimate the beta for Kristin Kandy, we begin with the bottom-up
unlevered beta of food processing companies:
• Unlevered beta for publicly traded food processing companies = 0.78
• Average correlation of food processing companies with market = 0.333
• Unlevered total beta for Kristin Kandy = 0.78/0.333 = 2.34
• Debt to equity ratio for Kristin Kandy = 0.3/0.7 (assumed industry average)
• Total Beta = 2.34 ( 1- (1-.40)(30/70)) = 2.94
• Total Cost of Equity = 4.50% + 2.94 (4%) = 16.26%

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 When would you use this total risk measure?

 Under which of the following scenarios are you most likely to use the total
risk measure:
 when valuing a private firm for an initial public offering
 when valuing a private firm for sale to a publicly traded firm
 when valuing a private firm for sale to another private investor
 Assume that you own a private business. What does this tell you about the best
potential buyer for your business?

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 From Cost of Equity to Cost of Capital

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 What is debt?

 General Rule: Debt generally has the following characteristics:

• Commitment to make fixed payments in the future
• The fixed payments are tax deductible
• Failure to make the payments can lead to either default or loss of control of the firm
to the party to whom payments are due.
 As a consequence, debt should include
• Any interest-bearing liability, whether short term or long term.
• Any lease obligation, whether operating or capital.

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 Hyundai’s liabilities…

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 Estimating the Cost of Debt

 If the firm has bonds outstanding, and the bonds are traded, the yield to
maturity on a long-term, straight (no special features) bond can be used as the
interest rate.
 If the firm is rated, use the rating and a typical default spread on bonds with
that rating to estimate the cost of debt.
 If the firm is not rated,
• and it has recently borrowed long term from a bank, use the interest rate on the
borrowing or
• estimate a synthetic rating for the company, and use the synthetic rating to arrive at
a default spread and a cost of debt
 The cost of debt has to be estimated in the same currency as the cost of equity
and the cash flows in the valuation.

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 Estimating Synthetic Ratings

 The rating for a firm can be estimated using the financial characteristics of the
firm. In its simplest form, the rating can be estimated from the interest
coverage ratio
Interest Coverage Ratio = EBIT / Interest Expenses
 For Hyundai’s interest coverage ratio, we used the interest expenses and EBIT
from 2007.
Interest Coverage Ratio = 1751/ 11 = 153.60
 For Kristin Kandy, we used the interest expenses and EBIT from the most
recent financial year:
Interest Coverage Ratio = 500,000/ 85,000 = 5.88
 Amazon.com has negative operating income; this yields a negative interest
coverage ratio, which should suggest a D rating. We computed an average
interest coverage ratio of 2.82 over the next 5 years.

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 Interest Coverage Ratios, Ratings and Default Spreads

If Interest Coverage Ratio is Bond Rating Default Spread(1/00)`Spread(1/04) Spread (6/08)

> 8.50 (>12.50) AAA 0.20% 0.35% 0.75%
6.50 - 8.50 (9.5-12.5) AA 0.50% 0.50% 1.00%
5.50 - 6.50 (7.5-9.5) A+ 0.80% 0.70% 1.50%
4.25 - 5.50 (6-7.5) A 1.00% 0.85% 1.80%
3.00 - 4.25 (4.5-6) A– 1.25% 1.00% 2.00%
2.50 - 3.00 (3.5-4.5) BBB 1.50% 1.50% 2.25%
2.25 - 2.50 (3.5 -4) BB+ 1.75% 2.00% 3.00%
2.00 - 2.25 ((3-3.5) BB 2.00% 2.50% 3.50%
1.75 - 2.00 (2.5-3) B+ 2.50% 3.25% 4.75%
1.50 - 1.75 (2-2.5) B 3.25% 4.00% 6.50%
1.25 - 1.50 (1.5-2) B– 4.25% 6.00% 8.00%
0.80 - 1.25 (1.25-1.5) CCC 5.00% 8.00% 10.00%
0.65 - 0.80 (0.8-1.25) CC 6.00% 10.00% 11.50%
0.20 - 0.65 (0.5-0.8) C 7.50% 12.00% 12.70%
< 0.20 (<0.5) D 10.00% 20.00% 20.00%
For Hyundai and Kristin Kandy, I used the interest coverage ratio table for smaller/riskier firms (the
numbers in brackets) which yields a lower rating for the same interest coverage ratio.

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 Estimating the cost of debt for a firm

 The synthetic rating for Hyundai is AAA. Using the 2008 default spread of
0.75%, we estimate a cost of debt of 6.55% (using a riskfree rate of 5% and
adding in the country default spread of 0.80%):
Cost of debt = Riskfree rate + Country default spread + Company default spread
=5.00% + 0.80%+ 0.75% = 6.55%
 The synthetic rating for Kristin Kandy is A-. Using the 2004 default spread of
1.00% and a riskfree rate of 4.50%, we estimate a cost of debt of 5.50%.
Cost of debt = Riskfree rate + Default spread =4.50% + 1.00% = 5.50%
 The synthetic rating for Amazon.com in 2000 was BBB. The default spread
for BBB rated bond was 1.50% in 2000 and the treasury bond rate was 6.5%.
Cost of debt = Riskfree Rate + Default spread = 6.50% + 1.50% = 8.00%

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 Weights for the Cost of Capital Computation

 The weights used to compute the cost of capital should be the market value
weights for debt and equity.
 There is an element of circularity that is introduced into every valuation by
doing this, since the values that we attach to the firm and equity at the end of
the analysis are different from the values we gave them at the beginning.
 For private companies, neither the market value of equity nor the market value
of debt is observable. Rather than use book value weights, you should try
• Industry average debt ratios for publicly traded firms in the business
• Target debt ratio (if management has such a target)
• Estimated value of equity and debt from valuation (through an iterative process)

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 Estimating Cost of Capital: Amazon.com

 Equity
• Cost of Equity = 6.50% + 1.60 (4.00%) = 12.90%
• Market Value of Equity = $ 84/share* 340.79 mil shs = $ 28,626 mil (98.8%)
 Debt
• Cost of debt = 6.50% + 1.50% (default spread) = 8.00%
• Market Value of Debt = $ 349 mil (1.2%)
 Cost of Capital
Cost of Capital = 12.9 % (.988) + 8.00% (1- 0) (.012)) = 12.84%

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 Estimating Cost of Capital: Hyundai Heavy

 Equity
• Cost of Equity = 5% + 1.50 (4%) + 0.25 (1.20%) = 11.30%
• Market Value of Equity =27,740 billion Won (99.3%)
 Debt
• Pre-tax Cost of debt = 5% + 0.80% + 0.75%= 6.55%
• Market Value of Debt = 185.58 billion Won (0.7%)
 Cost of Capital
Cost of Capital = 11.30 % (.993) + 6.55% (1- .275) (0.007)) = 11.26%

The book value of equity at Hyundai Heavy is 5,492 billion Won

The book value of debt at Hyundai Heavy is 188 billion Won; Interest expense is
11.4 bil; Average maturity of debt = 3 years
Estimated market value of debt = 11.4 billion (PV of annuity, 3 years, 6.55%) + $
188 billion/1.06553 = 185.58 billion Won

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 Estimating Cost of Capital: Kristin Kandy

 Equity
• Cost of Equity = 4.50% + 2.94 (4%) = 16.26%
• Equity as percent of capital = 70%
 Debt
• Pre-tax Cost of debt = 4.50% + 1.00% = 5.50%
• Marginal tax rate = 40%
• Debt as percent of capital = 30% (Industry average)
 Cost of Capital
Cost of Capital = 16.26% (.70) + 5.50% (1-.40) (.30) = 12.37%

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 II. Estimating Cashflows and Growth

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 Defining Cashflow

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 From Reported to Actual Earnings

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 Dealing with Operating Lease Expenses

 Operating Lease Expenses are treated as operating expenses in computing

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

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 Operating Leases at The Gap in 2003

 The Gap has conventional debt of about $ 1.97 billion on its balance sheet and
its pre-tax cost of debt is about 6%. Its operating 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 Operating Income = Stated OI + OL exp this year - Deprec’n
= $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

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 The Collateral Effects of Treating Operating Leases as Debt

C o nventional Accounting Operating Leases Treated as Debt

Income Statement Income Statement
EBIT& Leases = 1,990 EBIT& Leases = 1,990
- Op Leases = 978 - Deprecn: OL= 628
EBIT = 1,012 EBIT = 1,362
Interest expense will rise to reflect the conversion
of operating leases as debt. Net income should
not change.
Balance Sheet Balance Sheet
Off balance sheet (Not shown as debt or as an Asset Liability
asset). Only the conventional debt of $1,970 OL Asset 4397 OL Debt 4397
million shows up on balance sheet Total debt = 4397 + 1970 = $6,367 million

Cost of capital = 8.20%(7350/9320) + 4% Cost of capital = 8.20%(7350/13717) + 4%

(1970/9320) = 7.31% (6367/13717) = 6.25%
Cost of equity for The Gap = 8.20%
After-tax cost of debt = 4%
Market value of equity = 7350
Return on capital = 1012 (1-.35)/(3130+1970) Return on capital = 1362 (1-.35)/(3130+6367)
= 12.90% = 9.30%

Aswath Damodaran 59
 R&D Expenses: Operating or Capital Expenses

 Accounting standards require us to consider R&D as an operating 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 amortizable life for R&D (2 - 10 years)
• Collect past R&D expenses for as long as the amortizable life
• Sum up the unamortized R&D over the period. (Thus, if the amortizable life is 5
years, the research asset can be obtained by adding up 1/5th of the R&D expense
from five years ago, 2/5th of the R&D expense from four years ago...:

Aswath Damodaran 60
 Capitalizing R&D Expenses: Cisco in 1999

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

Year R&D Expense Unamortized portion Amortization this year
1999 (current) 1594.00 1.00 1594.00
1998 1026.00 0.80 820.80 $205.20
1997 698.00 0.60 418.80 $139.60
1996 399.00 0.40 159.60 $79.80
1995 211.00 0.20 42.20 $42.20
1994 89.00 0.00 0.00 $17.80
Total $ 3,035.40 $ 484.60
Value of research asset = $ 3,035.4 million
Amortization of research asset in 1998 = $ 484.6 million
Adjustment to Operating Income = $ 1,594 million - 484.6 million = 1,109.4 million

Aswath Damodaran 61
 The Effect of Capitalizing R&D

C o nventional Accounting R&D treated as capital expenditure

Income Statement Income Statement
EBIT& R&D = 5,049 EBIT& R&D = 5,049
- R&D = 1,594 - Amort: R&D = 485
EBIT = 3,455 EBIT = 4,564 (Increase of 1,109)
EBIT (1-t) = 2,246 EBIT (1-t) = 2,967
Ignored tax benefit = (1594-485)(.35) = 388
Adjusted EBIT (1-t) = 2967 + 388 = 3354
(Increase of $1,109 million)
Net Income will also increase by $1,109 million
Balance Sheet Balance Sheet
Off balance sheet asset. Book value of equity at Asset Liability
$11,722 million is understated because biggest R&D Asset 3035 Book Equity +3035
asset is off the books. Total Book Equity = 11722+3035 = 14757
Capital Expenditures Capital Expenditures
Conventional net cap ex of $98 million Net Cap ex = 98 + 1594 – 485 = 1206
Cash Flows Cash Flows
EBIT (1-t) = 2246 EBIT (1-t) = 3354
- Net Cap Ex = 98 - Net Cap Ex = 1206
FCFF = 2148 FCFF = 2148
Return on capital = 2246/11722 (no debt) Return on capital = 3354/14757
= 19.16% = 22.78%

Aswath Damodaran 62
 What tax rate?

 The tax rate that you should use in computing the after-tax operating income
should be
 The effective tax rate in the financial 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 after-tax cost of debt using the
same tax rate

Aswath Damodaran 63
 Capital expenditures should include

 Research and development expenses, once they have been re-categorized as

capital expenses. The adjusted net cap ex will be
Adjusted Net Capital Expenditures = Net Capital Expenditures + Current year’s R&D
expenses - Amortization of Research Asset
 Acquisitions of other firms, since these are like capital expenditures. The
adjusted net cap ex will be
Adjusted Net Cap Ex = Net Capital Expenditures + Acquisitions of other firms -
Amortization of such acquisitions
Two caveats:
1. Most firms do not do acquisitions every year. Hence, a normalized measure of
acquisitions (looking at an average over time) should be used
2. The best place to find acquisitions is in the statement of cash flows, usually
categorized under other investment activities

Aswath Damodaran 64
 Cisco’s Net Capital Expenditures in 1999

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

- Depreciation (from statement of CF) = $ 486 mil
Net Cap Ex (from statement of CF) = $ 98 mil
+ R & D expense = $ 1,594 mil
- Amortization of R&D = $ 485 mil
+ Acquisitions = $ 2,516 mil
Adjusted Net Capital Expenditures = $3,723 mil

(Amortization was included in the depreciation number)

Aswath Damodaran 65
 Working Capital Investments

 In accounting terms, the working capital is the difference between current

assets (inventory, cash and accounts receivable) and current liabilities
(accounts payables, short term debt and debt due within the next year)
 A cleaner definition of working capital from a cash flow perspective is the
difference between non-cash current assets (inventory and accounts
receivable) and non-debt current liabilities (accounts payable)
 Any investment in this measure of working capital ties up cash. Therefore, any
increases (decreases) in working capital will reduce (increase) cash flows in
that period.
 When forecasting future growth, it is important to forecast the effects of such
growth on working capital needs, and building these effects into the cash
flows.

Aswath Damodaran 66
 Dealing with Negative or Abnormally Low Earnings

Aswath Damodaran 67
 Normalizing Earnings: Amazon

Year Revenues Operating Margin EBIT

Tr12m $1,117 -36.71% -$410
1 $2,793 -13.35% -$373
2 $5,585 -1.68% -$94
3 $9,774 4.16% $407
4 $14,661 7.08% $1,038
5 $19,059 8.54% $1,628
6 $23,862 9.27% $2,212
7 $28,729 9.64% $2,768
8 $33,211 9.82% $3,261
9 $36,798 9.91% $3,646
10 $39,006 9.95% $3,883
TY(11) $41,346 10.00% $4,135 Industry Average

Aswath Damodaran 68
 Estimating FCFF: Hyundai Heavy Industries

 EBIT = 1,751 billion Won

 Tax rate = 27.5%
 Net Capital expenditures =Cap Ex - Depreciation = 911 – 392 = 519 billion W
 Change in Working Capital = - 135 billion Won
Estimating FCFF
Current EBIT * (1 - tax rate) = 1751 (1-.275) = 1,269 billion Won
- (Capital Spending - Depreciation) 519 billion Won
- Change in Working Capital 135 billion Won
Current FCFF 615 billion Won
Reinvestment in 2007 = 519 +135 = 654 billion Won
Reinvestment rate = 654/1269 = 51.52%

Aswath Damodaran 69
 Estimating FCFF: Amazon.com

 EBIT (Trailing 1999) = -$ 410 million

 Tax rate used = 0% (Assumed Effective = Marginal)
 Capital spending (Trailing 1999) = $ 243 million
 Depreciation (Trailing 1999) = $ 31 million
 Non-cash Working capital Change (1999) = - 80 million
 Estimating FCFF (1999)
Current EBIT * (1 - tax rate) = - 410 (1-0) = - $410 million
- (Capital Spending - Depreciation) = $212 million
- Change in Working Capital = -$ 80 million
Current FCFF = - $542 million

Aswath Damodaran 70
 Growth in Earnings

 Look at the past

• The historical growth in earnings per share is usually a good starting point for
growth estimation
 Look at what others are estimating
• Analysts estimate growth in earnings per share for many firms. It is useful to know
what their estimates are.
 Look at fundamentals
• Ultimately, all growth in earnings can be traced to two fundamentals - how much
the firm is investing in new projects, and what returns these projects are making for
the firm.

Aswath Damodaran 71
 Fundamental Growth when Returns are stable

Aswath Damodaran 72
 Measuring Return on Capital (Equity)

Aswath Damodaran 73
 Expected Growth Estimate: Hyundai Heavy

Reinevestment in 2007 Invested Capital in 2006

EBIT (1-t) in 2007: Net Cap Ex = 519 EBIT (1-t) in year 2007 BV of Debt 187
1,269 million Chg in WC = 135 1,269 million + BV of Equity 4479
Total = 654 - Cash 1276
Invested Capital = 3390

Reinvestment Rate = Reinvestment/ EBIT (1-t) X Return on Capital = EBIT (1-t)/ Invested Capital = 19.3%
= 654/1269 = 51/5% =1269/3390 = 37.45%

Normalized Values

Average reinvestment rate over last 5 years X Lower return on capital reflecting increasing scale = 15%
50% 30%

Aswath Damodaran 74
 Fundamental Growth when return on equity (capital) is
changing

 When the return on equity or capital is changing, there will be a second

component to growth, positive if the return is increasing and negative if the
return is decreasing. If ROCt is the return on capital in period t and ROCt+1 is
the return on capital in period t+1, the expected growth rate in operating
income will be:
Expected Growth Rate = ROCt+1 * Reinvestment rate
+(ROCt+1 – ROCt) / ROCt
 For example, assume that you have a firm that is generating a return on capital
of 8% on its existing assets and expects to increase this return to 10% next
year. The efficiency growth for this firm is
Efficiency growth = (10% -8%)/ 8% = 25%
Thus, if this firm has a reinvestment rate of 50% and makes a 10% return on
capital on its new investments as well, its total growth next year will be 30%
Growth rate = .50 * 10% + 25% = 30%
The key difference is that growth from new investments is sustainable whereas
returns from efficiency are short term (or transitory).
Aswath Damodaran 75
 Revenue Growth and Operating Margins

 With negative operating income and a negative return on capital, the

fundamental growth equation is of little use for Amazon.com
 For Amazon, the effect of reinvestment shows up in revenue growth rates and
changes in expected operating margins:
Expected Revenue Growth in $ = Reinvestment (in $ terms) * (Sales/ Capital)
 The effect on expected margins is more subtle. Amazon’s reinvestments
(especially in acquisitions) may help create barriers to entry and other
competitive advantages that will ultimately translate into high operating
margins and high profits.

Aswath Damodaran 76
 Growth in Revenues, Earnings and Reinvestment: Amazon

Year Revenue Chg in Reinvestment Chg Rev/ Chg Reinvestment ROC

Growth Revenue
1 150.00% $1,676 $559 3.00 -76.62%
2 100.00% $2,793 $931 3.00 -8.96%
3 75.00% $4,189 $1,396 3.00 20.59%
4 50.00% $4,887 $1,629 3.00 25.82%
5 30.00% $4,398 $1,466 3.00 21.16%
6 25.20% $4,803 $1,601 3.00 22.23%
7 20.40% $4,868 $1,623 3.00 22.30%
8 15.60% $4,482 $1,494 3.00 21.87%
9 10.80% $3,587 $1,196 3.00 21.19%
10 6.00% $2,208 $736 3.00 20.39%
Assume that firm can earn high returns because of established economies of scale.

Aswath Damodaran 77
 III. The Tail that wags the dog…
Terminal Value

Aswath Damodaran 78
 Getting Closure in Valuation

 A publicly traded firm potentially has an infinite life. The value is therefore the
present value of cash flows forever. CF
t=∞ t
Value = ∑ t
t = 1 (1+ r)

 Since we cannot estimate cash flows forever, we estimate cash flows for a
“growth period” and then estimate a terminal value, to capture the value at the
end of the period:
t = N CFt Terminal Value
Value = ∑ +
t (1 + r)N
t = 1 (1 + r)

Aswath Damodaran 79
 Ways of Estimating Terminal Value

Aswath Damodaran 80
 Stable Growth and Terminal Value

 When a firm’s cash flows grow at a “constant” rate forever, the present value
of those cash flows can be written as:
Value = Expected Cash Flow Next Period / (r - g)
where,
r = Discount rate (Cost of Equity or Cost of Capital)
g = Expected growth rate
 This “constant” growth rate is called a stable growth rate and cannot be higher
than the growth rate of the economy in which the firm operates.
 While companies can maintain high growth rates for extended periods, they
will all approach “stable growth” at some point in time.

Aswath Damodaran 81
 1. How high can the stable growth rate be?

 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
firms, the growth rate of the latter will probably be lower than the growth rate of the
economy.
• The stable growth rate can be negative. The terminal value will be lower and you
are assuming that your firm will disappear over time.
• If you use nominal cashflows and discount rates, the growth rate should be nominal
in the currency in which the valuation is denominated.
 One simple proxy for the nominal growth rate of the economy is the riskfree
rate.
• Riskfree rate = Expected inflation + Expected Real Interest Rate
• Nominal growth rate in economy = Expected Inflation + Expected Real Growth

Aswath Damodaran 82
 2. When will the firm reach stable growth?

 Size of the firm

• Success usually makes a firm larger. As firms become larger, it becomes much
more difficult for them to maintain high growth rates
 Current growth rate
• While past growth is not always a reliable indicator of future growth, there is a
correlation between current growth and future growth. Thus, a firm growing at 30%
currently probably has higher growth and a longer expected growth period than one
growing 10% a year now.
 Barriers to entry and differential advantages
• Ultimately, high growth comes from high project returns, which, in turn, comes
from barriers to entry and differential advantages.
• The question of how long growth will last and how high it will be can therefore be
framed as a question about what the barriers to entry are, how long they will stay up
and how strong they will remain.

Aswath Damodaran 83
 3. What else should change in stable growth?

 In stable growth, firms should have the characteristics of other stable growth
firms. In particular,
• The risk of the firm, as measured by beta and ratings, should reflect that of a stable
growth firm.
– Beta should move towards one
– The cost of debt should reflect the safety of stable firms (BBB or higher)
• The debt ratio of the firm might increase to reflect the larger and more stable
earnings of these firms.
– The debt ratio of the firm might moved to the optimal or an industry average
– If the managers of the firm are deeply averse to debt, this may never happen
• The return on capital generated on investments should move to sustainable levels,
relative to both the sector and the company’s own cost of capital.

Aswath Damodaran 84
 4. What excess returns will you generate in stable growth and
why does it matter?

 Strange though this may seem, the terminal value is not as much a function of
stable growth as it is a function of what you assume about excess returns in
stable growth.
 The key connecting link is the reinvestment rate that you have in stable
growth, which is a function of your return on capital:
Reinvestment Rate = Stable growth rate/ Stable ROC
The terminal value can be written in terms of ROC as follows:
Terminal Value = EBITn+1 (1-t) (1 – g/ ROC)/ (Cost of capital – g)
 In the scenario where you assume that a firm earns a return on capital equal to
its cost of capital in stable growth, the terminal value will not change as the
growth rate changes.
 If you assume that your firm will earn positive (negative) excess returns in
perpetuity, the terminal value will increase (decrease) as the stable growth rate
increases.

Aswath Damodaran 85
 Hyundai and Amazon.com: Stable Growth Inputs

High Growth Stable Growth

 Hyundai Heavy
• Beta 1.50 1.20
• Debt Ratio 0.7% 10%
• Return on Capital 30% 9.42%
• Cost of Capital 11.26% 9.42%
• Expected Growth Rate 15% 5%
• Reinvestment Rate 50% 5%/9.42% = 53.1%
 Amazon.com
• Beta 1.60 1.00
• Debt Ratio 1.20% 15%
• Return on Capital Negative 20%
• Expected Growth Rate NMF 6%
• Reinvestment Rate >100% 6%/20% = 30%

Aswath Damodaran 86
 Hyundai: Terminal Value and Growth

Growth Reinvestment Terminal

Rate Rate FCFF value
0% 0.00% ￦2,681 ￦28,471
1% 10.62% ￦2,396 ￦28,471
2% 21.24% ￦2,112 ￦28,471
3% 31.86% ￦1,827 ￦28,471
4% 42.48% ￦1,542 ￦28,471
5% 53.10% ￦1,258 ￦28,471

As growth increases, value does not change. Why?

Under what conditions will value increase as growth increases?
Under what conditions will value decrease as growth increases?

Aswath Damodaran 87
 Value Enhancement: Back to Basics

Aswath Damodaran 88
 Price Enhancement versus Value Enhancement

Aswath Damodaran 89
 The Paths to Value Creation

 Using the DCF framework, there are four basic ways in which the value of a
firm can be enhanced:
• The cash flows from existing assets to the firm can be increased, by either
– increasing after-tax earnings from assets in place or
– reducing reinvestment needs (net capital expenditures or working capital)
• The expected growth rate in these cash flows can be increased by either
– Increasing the rate of reinvestment in the firm
– Improving the return on capital on those reinvestments
• The length of the high growth period can be extended to allow for more years of
high growth.
• The cost of capital can be reduced by
– Reducing the operating risk in investments/assets
– Changing the financial mix
– Changing the financing composition

Aswath Damodaran 90
 Value Creation 1: Increase Cash Flows from Assets in Place

Aswath Damodaran 91
 Value Creation 2: Increase Expected Growth

Price Leader versus Volume Leader Strategies

Return on Capital = Operating Margin * Capital Turnover Ratio

Aswath Damodaran 92
 Value Creating Growth… Evaluating the Alternatives..

Aswath Damodaran 93
 III. Building Competitive Advantages: Increase length of the
growth period

Aswath Damodaran 94
 Value Creation 4: Reduce Cost of Capital

Aswath Damodaran 95
 Hyundai’s Optimal Financing Mix

Interest
Debt Cost of Bond rate on Cost of Debt Firm
Ratio Beta Equity Rating debt Tax Rate (after-tax) WACC Value (G)
0% 1.49 11.27% AAA 6.55% 27.50% 4.75% 11.27% $26,470
10% 1.61 11.77% A 7.60% 27.50% 5.51% 11.15% $27,021
20% 1.76 12.41% B 12.30% 27.50% 8.92% 11.71% $24,648
30% 1.96 13.23% CC 17.30% 27.04% 12.62% 13.05% $20,313
40% 2.30 14.66% C 18.50% 18.90% 15.00% 14.80% $16,437
50% 2.76 16.59% C 18.50% 15.12% 15.70% 16.15% $14,278
60% 3.47 19.57% D 19.80% 11.74% 17.48% 18.31% $11,727
70% 4.63 24.43% D 19.80% 10.06% 17.81% 19.79% $10,414
80% 6.94 34.14% D 19.80% 8.80% 18.06% 21.27% $9,340
90% 13.88 63.28% D 19.80% 7.83% 18.25% 22.75% $8,445

Aswath Damodaran 96
 IV. Loose Ends in Valuation: From
firm value to value of equity per
share

Aswath Damodaran 97
 But what comes next?

Aswath Damodaran 98
 1. An Exercise in Cash Valuation

Company A Company B Company C

Enterprise Value $ 1 billion $ 1 billion $ 1 billion
Cash $ 100 mil $ 100 mil $ 100 mil
Return on Capital 10% 5% 22%
Cost of Capital 10% 10% 12%
Trades in US US Indonesia

Aswath Damodaran 99
 Cash: Discount or Premium?

Aswath Damodaran 100

 Cash and Trouble?
Cash/
Company Name Primary Industry ROIC Value
Able C&C Co. Ltd. Personal Products 0.49% 38.74%
Varo Vision Co Ltd - 0.85% 76.99%
Raygen Co. Ltd. Semiconductors 1.12% 38.39%
Kodicom Co. Ltd. Consumer Electronics 2.62% 53.35%
Kukyoung Glass Industries Building Products 3.10% 38.75%
DASAN Networks Inc. Communications Equipment 3.45% 49.05%
Tellord Co. Ltd. - 6.89% 45.47%
FRTEK Co. Ltd Communications Equipment 6.98% 45.51%
Ilsung Construction Co., Ltd. Construction and Engineering 7.29% 89.49%
H&T Co., Ltd. Computer Storage and Peripherals 7.76% 42.92%
Feelingk Co. Ltd. Internet Software and Services 8.38% 46.79%
Duck Yang Industry Co. Ltd. Auto Parts and Equipment 8.84% 92.63%
Sewoo Global Co. Ltd. Commodity Chemicals 9.23% 43.88%
D&T, Inc. IT Consulting and Other Services 9.51% 39.31%

Aswath Damodaran 101

 2. Dealing with Holdings in Other firms

 Holdings in other firms can be categorized into

• Minority passive holdings, in which case only the dividend from the holdings is
shown in the balance sheet
• Minority active holdings, in which case the share of equity income is shown in the
income statements
• Majority active holdings, in which case the financial statements are consolidated.
 We tend to be sloppy in practice in dealing with cross holdings. After valuing
the operating assets of a firm, using consolidated statements, it is common to
add on the balance sheet value of minority holdings (which are in book value
terms) and subtract out the minority interests (again in book value terms),
representing the portion of the consolidated company that does not belong to
the parent company.

Aswath Damodaran 102

 How to value holdings in other firms.. In a perfect world..

 In a perfect world, we would strip the parent company from its subsidiaries
and value each one separately. The value of the combined firm will be
• Value of parent company + Proportion of value of each subsidiary
 To do this right, you will need to be provided detailed information on each
subsidiary to estimated cash flows and discount rates.

Aswath Damodaran 103

 Two compromise solutions…

 The market value solution: When the subsidiaries are publicly traded, you
could use their traded market capitalizations to estimate the values of the cross
holdings. You do risk carrying into your valuation any mistakes that the
market may be making in valuation.
 The relative value solution: When there are too many cross holdings to value
separately or when there is insufficient information provided on cross
holdings, you can convert the book values of holdings that you have on the
balance sheet (for both minority holdings and minority interests in majority
holdings) by using the average price to book value ratio of the sector in which
the subsidiaries operate.

Aswath Damodaran 104

 Hyundai’s Cross Holdings

Cross holding % of Total MarketValue of Book P/Book

holding Cap holding Value (Sector)
Hyundai Merchant
Marine 17.60% 4806.00 845.86
Public Hyundai Motors 3.46% 17540.00 606.88
Hyundai Elevator 2.16% 688.00 14.86
Hyundai Corp 0.36% 602.00 2.17
Others ? ? 84.20

Hyundai Oil Bank 19.87% 1825.77 362.78 329.80 1.10

Hyundai Samho 94.92% 2026.23 1923.30 1068.50 1.80
Private Hyundai Finance 67.49% 143.75 97.02 88.20 1.10
Value of Cross
holdings 3937.07

Aswath Damodaran 105

 3. Other Assets that have not been counted yet..

 Unutilized assets: If you have assets or property that are not being utilized
(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 firm.
 Overfunded pension plans: If you have a defined benefit plan and your assets
exceed your expected liabilities, you could consider the over funding with two
caveats:
• Collective bargaining agreements may prevent you from laying claim to these
excess assets.
• There are tax consequences. Often, withdrawals from pension plans get taxed at
much higher rates.
Do not double count an asset. If you count the income from an asset in your cashflows,
you cannot count the market value of the asset in your value.

Aswath Damodaran 106

 4. A Discount for Complexity:
An Experiment

Company A Company B
Operating Income $ 1 billion $ 1 billion
Tax rate 40% 40%
ROIC 10% 10%
Expected Growth 5% 5%
Cost of capital 8% 8%
Business Mix Single Business Multiple Businesses
Holdings Simple Complex
Accounting Transparent Opaque
 Which firm would you value more highly?

Aswath Damodaran 107

 Measuring Complexity: Volume of Data in Financial
Statements

Company Number of pages in last 10Q Number of pages in last 10K

General Electric 65 410
Microsoft 63 218
Wal-mart 38 244
Exxon Mobil 86 332
Pfizer 171 460
Citigroup 252 1026
Intel 69 215
AIG 164 720
Johnson & Johnson 63 218
IBM 85 353

Aswath Damodaran 108

 Measuring Complexity: A Complexity Score
Item Factors Follow-up Question Answer Weighting factor Gerdau Score GE Score
Operating Income 1. Multiple Businesses Number of businesses (with more than 10% of
revenues) = 1 2.00 2 30
2. One-time income and expenses
Percent of operating income = 10% 10.00 1 0.8
3. Income from unspecified sources
Percent of operating income = 0% 10.00 0 1.2
4. Items in income statement that are volatile
Percent of operating income = 15% 5.00 0.75 1
Tax Rate 1. Income from multiple locales
Percent of revenues from non-domestic locales = 70% 3.00 2.1 1.8
2. Different tax and reporting books
Yes or No No Yes=3 0 3
3. Headquarters in tax havens
Yes or No No Yes=3 0 0
4. Volatile effective tax rate
Yes or No Yes Yes=2 2 0
Capital Expenditures 1. Volatile capital expenditures
Yes or No Yes Yes=2 2 2
2. Frequent and large acquisitions
Yes or No Yes Yes=4 4 4
3. Stock payment for acquisitions and
investments Yes or No No Yes=4 0 4
Working capital 1. Unspecified current assets and current
liabilities Yes or No No Yes=3 0 0
2. Volatile working capital items
Yes or No Yes Yes=2 2 2
Expected Growth rate 1. Off-balance sheet assets and liabilities
(operating leases and R&D)
Yes or No No Yes=3 0 3
2. Substantial stock buybacks
Yes or No No Yes=3 0 3
3. Changing return on capital over time
Is your return on capital volatile? Yes Yes=5 5 5
4. Unsustainably high return
Is your firm's ROC much higher than industry average? No Yes=5 0 0
Cost of capital 1. Multiple businesses
Number of businesses (more than 10% of revenues) = 1 1.00 1 20
2. Operations in emerging markets
Percent of revenues= 50% 5.00 2.5 2.5
3. Is the debt market traded?
Yes or No No No=2 2 0
4. Does the company have a rating?
Yes or No Yes No=2 0 0
5. Does the company have off-balance sheet
debt? Yes or No No Yes=5 0 5
No-operating assets Minority holdings as percent of book assets
Minority holdings as percent of book assets 0% 20.00 0 0.8
Firm to Equity value Consolidation of subsidiaries
Minority interest as percent of book value of equity 63% 20.00 12.6 1.2
Per share value Shares with different voting rights
Does the firm have shares with different voting rights? Yes Yes = 10 10 0
Equity options outstanding
Options outstanding as percent of shares 0% 10.00 0 0.25
Complexity Score = 48.95 90.55
Aswath Damodaran 109
 Hyundai: An Enigma wrapped in a Mystery

Aswath Damodaran 110

 Dealing with Complexity

In Discounted Cashflow Valuation

 The Aggressive Analyst: Trust the firm to tell the truth and value the firm
based upon the firm’s statements about their value.
 The Conservative Analyst: Don’t value what you cannot see.
 The Compromise: Adjust the value for complexity
• Adjust cash flows for complexity
• Adjust the discount rate for complexity
• Adjust the expected growth rate/ length of growth period
• Value the firm and then discount value for complexity
In relative valuation
In a relative valuation, you may be able to assess the price that the market is charging for
complexity:
With the hundred largest market cap firms, for instance:
PBV = 0.65 + 15.31 ROE – 0.55 Beta + 3.04 Expected growth rate – 0.003 # Pages in 10K

Aswath Damodaran 111

 5. The Value of Synergy

 Synergy can be valued. In fact, if you want to pay for it, it should be valued.
 To value synergy, you need to answer two questions:
(a) What form is the synergy expected to take? Will it reduce costs as a percentage of
sales and increase profit margins (as is the case when there are economies of scale)?
Will it increase future growth (as is the case when there is increased market
power)? )
(b) When can the synergy be reasonably expected to start affecting cashflows?
(Will the gains from synergy show up instantaneously after the takeover? If it will
take time, when can the gains be expected to start showing up? )
 If you cannot answer these questions, you need to go back to the drawing
board…

Aswath Damodaran 112

 Sources of Synergy

Aswath Damodaran 113

 Valuing Synergy

(1) the firms involved in the merger are valued independently, by discounting
expected cash flows to each firm at the weighted average cost of capital for
that firm.
(2) the value of the combined firm, with no synergy, is obtained by adding the
values obtained for each firm in the first step.
(3) The effects of synergy are built into expected growth rates and cashflows,
and the combined firm is re-valued with synergy.
Value of Synergy = Value of the combined firm, with synergy - Value of the
combined firm, without synergy

Aswath Damodaran 114

 Valuing Synergy: P&G + Gillette

P&G Gillette Piglet: No Synergy Piglet: Synergy

Free Cashflow to Equity $5,864.74 $1,547.50 $7,412.24 $7,569.73 Annual operating expenses reduced by $250 million
Growth rate for first 5 years 12% 10% 11.58% 12.50% Slighly higher growth rate
Growth rate after five years 4% 4% 4.00% 4.00%
Beta 0.90 0.80 0.88 0.88
Cost of Equity 7.90% 7.50% 7.81% 7.81% Value of synergy
Value of Equity $221,292 $59,878 $281,170 $298,355 $17,185

Aswath Damodaran 115

 6. Brand name, great management, superb product …Are we
short changing the intangibles?

 There is often a temptation to add on premiums for intangibles. Among them

are
• Brand name
• Great management
• Loyal workforce
• Technological prowess
 There are two potential dangers:
• For some assets, the value may already be in your value and adding a premium will
be double counting.
• For other assets, the value may be ignored but incorporating it will not be easy.

Aswath Damodaran 116

 Categorizing Intangibles

Independent and Cash flow Not independent and cash flow No cash flows now but potential
generating intangibles generating to the firm for cashflows in future
Examples Copyrights, trademarks, licenses, Brand names, Quality and Morale Undeveloped patents, operating or
franchises, professional practices of work force, Technological financial flexibility (to expand into
(medical, dental) expertise, Corporate reputation new products/markets or abandon
existing ones)
Valuation approach Estimate expected cashflows from • C ompare DCF value of firm Option valuation
the product or service and discount with intangible with firm • V a lue the undeveloped patent
back at appropriate discount rate. without (if you can find one) as an option to develop the
• A ssume that all excess returns underlying product.
of firm are due to intangible. • V a lue expansion options as call
• C ompare multiples at which options
firm trades to sector averages. • V a lue abandonment options as
put options.
Challenges • L ife is usually finite and With multiple intangibles (brand • Need exclusivity.
terminal value may be small. name and reputation for service), it • D i f f icult to replicate and
• C a s hflows and value may be becomes difficult to break down arbitrage (making option
person dependent (for individual components. pricing models dicey)
professional practices)

Aswath Damodaran 117

 Valuing Brand Name

Coca Cola With Cott Margins

Current Revenues = $21,962.00 $21,962.00
Length of high-growth period 10 10
Reinvestment Rate = 50% 50%
Operating Margin (after-tax) 15.57% 5.28%
Sales/Capital (Turnover ratio) 1.34 1.34
Return on capital (after-tax) 20.84% 7.06%
Growth rate during period (g) = 10.42% 3.53%
Cost of Capital during period = 7.65% 7.65%
Stable Growth Period
Growth rate in steady state = 4.00% 4.00%
Return on capital = 7.65% 7.65%
Reinvestment Rate = 52.28% 52.28%
Cost of Capital = 7.65% 7.65%
Value of Firm = $79,611.25 $15,371.24

Aswath Damodaran 118

 7. Be circumspect about defining debt for cost of capital
purposes…

 General Rule: Debt generally has the following characteristics:

• Commitment to make fixed payments in the future
• The fixed payments are tax deductible
• Failure to make the payments can lead to either default or loss of control of the firm
to the party to whom payments are due.
 Defined as such, debt should include
• All interest bearing liabilities, short term as well as long term
• All leases, operating as well as capital
 Debt should not include
• Accounts payable or supplier credit

Aswath Damodaran 119

 Book Value or Market Value

 For some firms that are in financial trouble, the book value of debt can be
substantially higher than the market value of debt. Analysts worry that
subtracting out the market value of debt in this case can yield too high a value
for equity.
 A discounted cashflow valuation is designed to value a going concern. In a
going concern, it is the market value of debt that should count, even if it is
much lower than book value.
 In a liquidation valuation, you can subtract out the book value of debt from the
liquidation value of the assets.
Converting book debt into market debt,,,,,

Aswath Damodaran 120

 But you should consider other potential liabilities when
getting to equity value

 If you have under funded pension fund or health care plans, you should
consider the under funding at this stage in getting to the value of equity.
• If you do so, you should not double count by also including a cash flow line item
reflecting cash you would need to set aside to meet the unfunded obligation.
• You should not be counting these items as debt in your cost of capital
calculations….
 If you have contingent liabilities - for example, a potential liability from a
lawsuit that has not been decided - you should consider the expected value of
these contingent liabilities
• Value of contingent liability = Probability that the liability will occur * Expected
value of liability

Aswath Damodaran 121

 8. The Value of Control

 The value of the control premium that will be paid to acquire a block of equity
will depend upon two factors -
• Probability that control of firm will change: This refers to the probability that
incumbent management will be replaced. this can be either through acquisition or
through existing stockholders exercising their muscle.
• Value of Gaining Control of the Company: The value of gaining control of a
company arises from two sources - the increase in value that can be wrought by
changes in the way the company is managed and run, and the side benefits and
perquisites of being in control
Value of Gaining Control = Present Value (Value of Company with change in control -
Value of company without change in control) + Side Benefits of Control

Aswath Damodaran 122

 Hyundai Heavy: Status Quo ($) Return on Capital
Reinvestment Rate 30%
50%
Current Cashflow to Firm Stable Growth
EBIT(1-t) : 1,269 Billion Won Expected Growth g = 5%; Beta = 1.20;
- Nt CpX 519 in EBIT (1-t) Country Premium= 0.8%
- Chg WC 135 .50*.30=.15 Cost of capital = 9.42%
= FCFF 615 15% ROC= 9.42%
Reinvestment Rate = 654/1269=51.5% Reinvestment Rate=g/ROC
Return on capital = 1269/3390 =37.45% =5/9.42 = 53.1%

Terminal Value5= 1258(.0942-.05) = 28,471

Wn Cashflows
Op. Assets 20,211
+ Cash: 3,612 Year 1 2 3 4 5 Term Yr
+ Non-0p 3,937 EBIT (1-t) 1,460 1,679 1,931 2,220 2,553 2,681
- Debt 186 - Reinvestment 730 839 965 1,110 1,277 1,423
=Equity 27,574 FCFF 730 839 965 1,110 1,277 =1,258
-Options 0
Value/Share 362.82
(362,820 Won/Sh) Discount at $ Cost of Capital (WACC) = 11.3% (.993) + 4.75% (0.007) = 11.26%

On June 1, 2008
Hyundai Heavy traded at
Cost of Equity Cost of Debt
Weights 350,000 Won/share.
11.30% (5%+0.8%+0.75%)(1-.275)
= 4.75% E = 99.3% D = 0.7%

Riskfree Rate:
Won Riskfree Rate= 5% Beta Mature market Country Equity Risk
+ 1.50 X premium + Lambda X Premium
4% 0.25 1.20%

Unlevered Beta for Firmʼs D/E Rel Equity

Sectors: 0.75 Ratio: 26.84% Country Default Mkt Vol
Spread X
0.8% 1.20
Aswath Damodaran 123
 Hyundai Heavy: Restructured($) Return on Capital
Reinvestment Rate 30%
50%
Current Cashflow to Firm Stable Growth
EBIT(1-t) : 1,269 Billion Won Expected Growth g = 5%; Beta = 1.20;
- Nt CpX 519 in EBIT (1-t) Country Premium= 0.8%
- Chg WC 135 .50*.30=.15 Cost of capital = 9.42%
= FCFF 615 15% ROC= 9.42%
Reinvestment Rate = 654/1269=51.5% Reinvestment Rate=g/ROC
Return on capital = 1269/3390 =37.45% =5/9.42 = 53.1%

Terminal Value5= 1932(.0942-.05) = 43,732

Wn Cashflows
Op. Assets 23,112
+ Cash: 3,612 Year 1 2 3 4 5 6 7 8 9 10 Term Yr
+ Non-0p 3,937 EBIT (1-t) 1,460 1,679 1,931 2,220 2,553 2,885 3,203 3,491 3,735 3,922 4,118
- Debt 186 - Reinvestment 730 839 965 1,110 1,277 1,461 1,641 1,810 1,960 2,082 2,186
=Equity 30,481 FCFF 730 839 965 1,110 1,277 1,425 1,562 1,681 1,775 1,840 =1,932
-Options 0
Value/Share 401.06
(401,060 Won/Sh) Discount at $ Cost of Capital (WACC) = 11.3% (.9) + 4.75% (0.1) = 11.16%

On June 1, 2008
Hyundai Heavy traded at
Cost of Equity Cost of Debt
Weights 350,000 Won/share.
11.74% (5%+0.8%+1.8%)(1-.275)
= 5.51% E = 90% D = 10%

Riskfree Rate:
Won Riskfree Rate= 5% Beta Mature market Country Equity Risk
+ 1.61 X premium + Lambda X Premium
4% 0.25 1.20%

Unlevered Beta for Firmʼs D/E Rel Equity

Sectors: 0.75 Ratio: 26.84% Country Default Mkt Vol
Spread X
0.8% 1.20

Aswath Damodaran 124

 The Value of Control in a publicly traded firm..

 If the value of a firm run optimally is significantly higher than the value of the
firm with the status quo (or incumbent management), you can write the value
that you should be willing to pay as:
Value of control = Value of firm optimally run - Value of firm with status quo
Value of control at Hyundai Heavy= 401 Won per share – 362 Won per share = 39
Won per share
 Implications:
• In an acquisition, this is the most that you would be willing to pay as a premium
(assuming no other synergy)
• As a stockholder, you will be willing to pay a value between 362 and 401 Wn,
depending upon your views on whether control will change.
• If there are voting and non-voting shares, the difference in prices between the two
should reflect the value of control.

Aswath Damodaran 125

 Minority and Majority interests in a private firm

 When you get a controlling interest in a private firm (generally >51%, but
could be less…), you would be willing to pay the appropriate proportion of the
optimal value of the firm.
 When you buy a minority interest in a firm, you will be willing to pay the
appropriate fraction of the status quo value of the firm.
 For badly managed firms, there can be a significant difference in value
between 51% of a firm and 49% of the same firm. This is the minority
discount.
 If you own a private firm and you are trying to get a private equity or venture
capital investor to invest in your firm, it may be in your best interests to offer
them a share of control in the firm even though they may have well below
51%.

Aswath Damodaran 126

 9. Distress and the Going Concern Assumption

 Traditional valuation techniques are built on the assumption of a going

concern, i.e., a firm that has continuing operations and there is no significant
threat to these operations.
• In discounted cashflow valuation, this going concern assumption finds its place
most prominently in the terminal value calculation, which usually is based upon an
infinite life and ever-growing cashflows.
• In relative valuation, this going concern assumption often shows up implicitly
because a firm is valued based upon how other firms - most of which are healthy -
are priced by the market today.
 When there is a significant likelihood that a firm will not survive the
immediate future (next few years), traditional valuation models may yield an
over-optimistic estimate of value.

Aswath Damodaran 127

Aswath Damodaran 128
 Valuing Global Crossing with Distress

 Probability of distress
• Price of 8 year,
t= 8 12% πbond issued
120(1− by Global
) t 1000(1− π Crossing
)8 = $ 653
653 = ∑ Distress
t
+ Distress
8
t=1 (1.05) (1.05)

• Probability of distress = 13.53% a year

•€ Cumulative probability of survival over 10 years = (1- .1353)10 = 23.37%
 Distress sale value of equity
• Book value of capital = $14,531 million
• Distress sale value = 15% of book value = .15*14531 = $2,180 million
• Book value of debt = $7,647 million
• Distress sale value of equity = $ 0
 Distress adjusted value of equity
• Value of Global Crossing = $3.22 (.2337) + $0.00 (.7663) = $0.75

Aswath Damodaran 129

 10. Equity to Employees: Effect on Value

 In recent years, firms have turned to giving employees (and especially top
managers) equity option packages as part of compensation. These options are
usually
• Long term
• At-the-money when issued
• On volatile stocks
 Are they worth money? And if yes, who is paying for them?
 Two key issues with employee options:
• How do options granted in the past affect equity value per share today?
• How do expected future option grants affect equity value today?

Aswath Damodaran 130

 Equity Options and Value

 Options outstanding
• Step 1: List all options outstanding, with maturity, exercise price and vesting status.
• Step 2: Value the options, taking into account dilution, vesting and early exercise
considerations
• Step 3: Subtract from the value of equity and divide by the actual number of shares
outstanding (not diluted or partially diluted).
 Expected future option and restricted stock issues
• Step 1: Forecast value of options that will be granted each year as percent of
revenues that year. (As firm gets larger, this should decrease)
• Step 2: Treat as operating expense and reduce operating income and cash flows
• Step 3: Take present value of cashflows to value operations or equity.

Aswath Damodaran 131

 11. Analyzing the Effect of Illiquidity on Value

 Investments which are less liquid should trade for less than otherwise similar
investments which are more liquid.
 The size of the illiquidity discount should depend upon
• Type of Assets owned by the Firm: The more liquid the assets owned by the firm,
the lower should be the liquidity discount for the firm
• Size of the Firm: The larger the firm, the smaller should be size of the liquidity
discount.
• Health of the Firm: Stock in healthier firms should sell for a smaller discount than
stock in troubled firms.
• Cash Flow Generating Capacity: Securities in firms which are generating large
amounts of cash from operations should sell for a smaller discounts than securities
in firms which do not generate large cash flows.
• Size of the Block: The liquidity discount should increase with the size of the
portion of the firm being sold.

Aswath Damodaran 132

 Illiquidity Discount: Restricted Stock Studies

 Restricted securities are securities issued by a company, but not registered

with the SEC, that can be sold through private placements to investors, but
cannot be resold in the open market for a two-year holding period, and limited
amounts can be sold after that. Studies of restricted stock over time have
concluded that the discount is between 25 and 35%. Many practitioners use
this as the illiquidity discount for all private firms.
 A more nuanced used of restricted stock studies is to relate the discount to
fundamental characteristics of the company - level of revenues, health of the
company etc.. And to adjust the discount for any firm to reflect its
characteristics:
• The discount will be smaller for larger firms
• The discount will be smaller for healthier firms

Aswath Damodaran 133

 Illiquidity Discounts from Bid-Ask Spreads

 Using data from the end of 2000, for instance, we regressed the bid-ask spread
against annual revenues, a dummy variable for positive earnings (DERN: 0 if
negative and 1 if positive), cash as a percent of firm value and trading volume.
Spread = 0.145 – 0.0022 ln (Annual Revenues) -0.015 (DERN) – 0.016 (Cash/
Firm Value) – 0.11 ($ Monthly trading volume/ Firm Value)
 We could substitute in the revenues of Kristin Kandy ($5 million), the fact that
it has positive earnings and the cash as a percent of revenues held by the firm
(8%):
Spread = 0.145 – 0.0022 ln (Annual Revenues) -0.015 (DERN) – 0.016 (Cash/
Firm Value) – 0.11 ($ Monthly trading volume/ Firm Value)
= 0.145 – 0.0022 ln (5) -0.015 (1) – 0.016 (.08) – 0.11 (0) = .12.52%
 Based on this approach, we would estimate an illiquidity discount of 12.52%
for Kristin Kandy.

Aswath Damodaran 134

 V. Value, Price and Information:
Closing the Deal

Aswath Damodaran 135

Aswath Damodaran 136
 Amazon.com: Break Even at $84?

6% 8% 10% 12% 14%

30% $ (1.94) $ 2.95 $ 7.84 $ 12.71 $ 17.57
35% $ 1.41 $ 8.37 $ 15.33 $ 22.27 $ 29.21
40% $ 6.10 $ 15.93 $ 25.74 $ 35.54 $ 45.34
45% $ 12.59 $ 26.34 $ 40.05 $ 53.77 $ 67.48
50% $ 21.47 $ 40.50 $ 59.52 $ 78.53 $ 97.54
55% $ 33.47 $ 59.60 $ 85.72 $ 111.84 $ 137.95
60% $ 49.53 $ 85.10 $ 120.66 $ 156.22 $ 191.77

Aswath Damodaran 137

Aswath Damodaran 138
 Amazon over time…

Aswath Damodaran 139

 Relative Valuation
Aswath Damodaran

Aswath Damodaran 140

 The Essence of relative valuation?

 In relative valuation, the value of an asset is compared to the values assessed

by the market for similar or comparable assets.
 To do relative valuation then,
• we need to identify comparable assets and obtain market values for these assets
• convert these market values into standardized values, since the absolute prices
cannot be compared This process of standardizing creates price multiples.
• compare the standardized value or multiple for the asset being analyzed to the
standardized values for comparable asset, controlling for any differences between
the firms that might affect the multiple, to judge whether the asset is under or over
valued

Aswath Damodaran 141

 Relative valuation is pervasive…

 Most asset valuations are relative.

 Most equity valuations on Wall Street are relative valuations.
• Almost 85% of equity research reports are based upon a multiple and comparables.
• More than 50% of all acquisition valuations are based upon multiples
• Rules of thumb based on multiples are not only common but are often the basis for
final valuation judgments.
 While there are more discounted cashflow valuations in consulting and
corporate finance, they are often relative valuations masquerading as
discounted cash flow valuations.
• The objective in many discounted cashflow valuations is to back into a number that
has been obtained by using a multiple.
• The terminal value in a significant number of discounted cashflow valuations is
estimated using a multiple.

Aswath Damodaran 142

 The Reasons for the allure…

“If you think I’m crazy, you should see the guy who lives across the hall”
Jerry Seinfeld talking about Kramer in a Seinfeld episode

“ A little inaccuracy sometimes saves tons of explanation”

H.H. Munro

“ If you are going to screw up, make sure that you have lots of company”
Ex-portfolio manager

Aswath Damodaran 143

 The Market Imperative….

 Relative valuation is much more likely to reflect market perceptions and

moods than discounted cash flow valuation. This can be an advantage when it
is important that the price reflect these perceptions as is the case when
• the objective is to sell a security at that price today (as in the case of an IPO)
• investing on “momentum” based strategies
 With relative valuation, there will always be a significant proportion of
securities that are under valued and over valued.
 Since portfolio managers are judged based upon how they perform on a
relative basis (to the market and other money managers), relative valuation is
more tailored to their needs
 Relative valuation generally requires less information than discounted cash
flow valuation (especially when multiples are used as screens)

Aswath Damodaran 144

 The Four Steps to Deconstructing Multiples

 Define the multiple

• In use, the same multiple can be defined in different ways by different users. When
comparing and using multiples, estimated by someone else, it is critical that we
understand how the multiples have been estimated
 Describe the multiple
• Too many people who use a multiple have no idea what its cross sectional
distribution is. If you do not know what the cross sectional distribution of a
multiple is, it is difficult to look at a number and pass judgment on whether it is too
high or low.
 Analyze the multiple
• It is critical that we understand the fundamentals that drive each multiple, and the
nature of the relationship between the multiple and each variable.
 Apply the multiple
• Defining the comparable universe and controlling for differences is far more
difficult in practice than it is in theory.

Aswath Damodaran 145

 Definitional Tests

 Is the multiple consistently defined?

• Proposition 1: Both the value (the numerator) and the standardizing variable
( the denominator) should be to the same claimholders in the firm. In other
words, the value of equity should be divided by equity earnings or equity book
value, and firm value should be divided by firm earnings or book value.
 Is the multiple uniformly estimated?
• The variables used in defining the multiple should be estimated uniformly across
assets in the “comparable firm” list.
• If earnings-based multiples are used, the accounting rules to measure earnings
should be applied consistently across assets. The same rule applies with book-value
based multiples.

Aswath Damodaran 146

 Example 1: Price Earnings Ratio: Definition

PE = Market Price per Share / Earnings per Share

 There are a number of variants on the basic PE ratio in use. They are based
upon how the price and the earnings are defined.
 Price: is usually the current price
is sometimes the average price for the year
 EPS: earnings per share in most recent financial year
earnings per share in trailing 12 months (Trailing PE)
forecasted earnings per share next year (Forward PE)
forecasted earnings per share in future year

Aswath Damodaran 147

 Example 2: Enterprise Value /EBITDA Multiple

 The enterprise value to EBITDA multiple is obtained by netting cash out

against debt to arrive at enterprise value and dividing by EBITDA.
Enterprise Value Market Value of Equity + Market Value of Debt - Cash
=
EBITDA Earnings before Interest, Taxes and Depreciation

 Why do we net out cash from firm value?

 What happens if a firm has cross holdings which are categorized as:
• Minority interests?
• Majority active interests?

Aswath Damodaran 148

 Descriptive Tests

 What is the average and standard deviation for this multiple, across the
universe (market)?
 What is the median for this multiple?
• The median for this multiple is often a more reliable comparison point.
 How large are the outliers to the distribution, and how do we deal with the
outliers?
• Throwing out the outliers may seem like an obvious solution, but if the outliers all
lie on one side of the distribution (they usually are large positive numbers), this can
lead to a biased estimate.
 Are there cases where the multiple cannot be estimated? Will ignoring these
cases lead to a biased estimate of the multiple?
 How has this multiple changed over time?

Aswath Damodaran 149

 Looking at the distribution…

Aswath Damodaran 150

 PE: Deciphering the Distribution

Aswath Damodaran 151

 PE Ratios in Korea…

Aswath Damodaran 152

 And 8 times EBITDA is not cheap

Aswath Damodaran 153

 Analytical Tests

 What are the fundamentals that determine and drive these multiples?
• Proposition 2: Embedded in every multiple are all of the variables that drive every
discounted cash flow valuation - growth, risk and cash flow patterns.
• In fact, using a simple discounted cash flow model and basic algebra should yield
the fundamentals that drive a multiple
 How do changes in these fundamentals change the multiple?
• The relationship between a fundamental (like growth) and a multiple (such as PE)
is seldom linear. For example, if firm A has twice the growth rate of firm B, it will
generally not trade at twice its PE ratio
• Proposition 3: It is impossible to properly compare firms on a multiple, if we
do not know the nature of the relationship between fundamentals and the
multiple.

Aswath Damodaran 154

 PE Ratio: Understanding the Fundamentals

 To understand the fundamentals, start with a basic equity discounted cash flow
model.
 With the dividend discount model,
DPS 1
P0 =
r − gn

 Dividing both sides by the current earnings per share,

P0 Payout Ratio * (1 + g n )
= PE =
EPS0 r-gn

 If this had been a FCFE Model,

FCFE1
P0 =
r − gn
P0 (FCFE/Earnings) * (1+ g n )
= PE =
EPS0 r-g n

Aswath Damodaran 155

€
 Using the Fundamental Model to Estimate PE For a High
Growth Firm

 The price-earnings ratio for a high growth firm can also be related to
fundamentals. In the special case of the two-stage dividend discount model,
this relationship can be made explicit fairly simply:
 (1+ g)n 
EPS0 * Payout Ratio *(1+ g)* 1 −
 (1+ r) n  EPS0 * Payout Ratio n *(1+ g)n *(1+ g n )
P0 = +
r-g (r -g n )(1+ r)n

• For a firm that does not pay what it can afford to in dividends, substitute FCFE/
Earnings for the payout ratio.
 Dividing both sides by the earnings per share:
 (1 + g)n 
Payout Ratio * (1 + g) *  1 −
P0  (1+ r) n  Payout Ratio n *(1+ g) n * (1 + gn )
= +
EPS0 r -g (r - g n )(1+ r) n

Aswath Damodaran 156

 A Simple Example

 Assume that you have been asked to estimate the PE ratio for a firm which has
the following characteristics:
Variable High Growth Phase Stable Growth Phase
Expected Growth Rate 25% 8%
Payout Ratio 20% 50%
Beta 1.00 1.00
Number of years 5 years Forever after year 5
 Riskfree rate = T.Bond Rate = 6%
 Required rate of return = 6% + 1(5.5%)= 11.5%

 (1.25) 5 
0.2 * (1.25) * 1− 5 5
 (1.115)  0.5 * (1.25) * (1.08)
PE = + = 28.75
(.115 - .25) (.115 - .08) (1.115) 5

€
Aswath Damodaran 157
 a. PE and Growth: Firm grows at x% for 5 years, 8%
thereafter

Aswath Damodaran 158

 b. PE and Risk: A Follow up Example

Aswath Damodaran 159

 Comparisons of PE across time: PE Ratio for the S&P 500

Aswath Damodaran 160

 Is low (high) PE cheap (expensive)?

 A market strategist argues that stocks are over priced because the PE ratio
today is too high relative to the average PE ratio across time. Do you agree?
 Yes
 No
 If you do not agree, what factors might explain the higher PE ratio today?

Aswath Damodaran 161

 E/P Ratios , T.Bond Rates and Term Structure

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 Regression Results

 There is a strong positive relationship between E/P ratios and T.Bond rates, as
evidenced by the correlation of 0.70 between the two variables.,
 In addition, there is evidence that the term structure also affects the PE ratio.
 In the following regression, using 1960-2007 data, we regress E/P ratios
against the level of T.Bond rates and a term structure variable (T.Bond - T.Bill
rate)
E/P = 2.19% + 0.734 T.Bond Rate - 0.335 (T.Bond Rate-T.Bill Rate)
(2.70) (6.80) (-1.41)
R squared = 51.23%

Aswath Damodaran 163

 The Determinants of Multiples…

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 Application Tests

 Given the firm that we are valuing, what is a “comparable” firm?

• While traditional analysis is built on the premise that firms in the same sector are
comparable firms, valuation theory would suggest that a comparable firm is one
which is similar to the one being analyzed in terms of fundamentals.
• Proposition 4: There is no reason why a firm cannot be compared with another
firm in a very different business, if the two firms have the same risk, growth
and cash flow characteristics.
 Given the comparable firms, how do we adjust for differences across firms on
the fundamentals?
• Proposition 5: It is impossible to find an exactly identical firm to the one you
are valuing.

Aswath Damodaran 165

 I. Comparing PE Ratios across a Sector: PE

Company Name PE Growth

PT Indosat ADR 7.8 0.06
Telebras ADR 8.9 0.075
Telecom Corporation of New Zealand ADR 11.2 0.11
Telecom Argentina Stet - France Telecom SA ADR B 12.5 0.08
Hellenic Telecommunication Organization SA ADR 12.8 0.12
Telecomunicaciones de Chile ADR 16.6 0.08
Swisscom AG ADR 18.3 0.11
Asia Satellite Telecom Holdings ADR 19.6 0.16
Portugal Telecom SA ADR 20.8 0.13
Telefonos de Mexico ADR L 21.1 0.14
Matav RT ADR 21.5 0.22
Telstra ADR 21.7 0.12
Gilat Communications 22.7 0.31
Deutsche Telekom AG ADR 24.6 0.11
British Telecommunications PLC ADR 25.7 0.07
Tele Danmark AS ADR 27 0.09
Telekomunikasi Indonesia ADR 28.4 0.32
Cable & Wireless PLC ADR 29.8 0.14
APT Satellite Holdings ADR 31 0.33
Telefonica SA ADR 32.5 0.18
Royal KPN NV ADR 35.7 0.13
Telecom Italia SPA ADR 42.2 0.14
Nippon Telegraph & Telephone ADR 44.3 0.2
France Telecom SA ADR 45.2 0.19
Korea Telecom ADR 71.3 0.44

Aswath Damodaran 166

 PE, Growth and Risk

Dependent variable is: PE

R squared = 66.2% R squared (adjusted) = 63.1%

Variable Coefficient SE t-ratio prob

Constant 13.1151 3.471 3.78 0.0010
Growth rate 121.223 19.27 6.29 ≤ 0.0001
Emerging Market -13.8531 3.606 -3.84 0.0009
Emerging Market is a dummy: 1 if emerging market
0 if not

Aswath Damodaran 167

 Is Telebras under valued?

 Predicted PE = 13.12 + 121.22 (.075) - 13.85 (1) = 8.35

 At an actual price to earnings ratio of 8.9, Telebras is slightly overvalued.

Aswath Damodaran 168

 II. Price to Book vs ROE: Korean Consumer Electronics
Stocks in June 2008

Aswath Damodaran 169

 A Risk Adjusted Version?

Most overvalued

Most undervalued

Aswath Damodaran 170

 III. Value/EBITDA Multiple: Trucking Companies

Aswath Damodaran 171

 A Test on EBITDA

 Ryder System looks very cheap on a Value/EBITDA multiple basis, relative to

the rest of the sector. What explanation (other than misvaluation) might there
be for this difference?

Aswath Damodaran 172

 IV. A Case Study: Internet Stocks in early 2000

Aswath Damodaran 173

 PS Ratios and Margins are not highly correlated

 Regressing PS ratios against current margins yields the following

PS = 81.36 - 7.54(Net Margin) R2 = 0.04
(0.49)
 This is not surprising. These firms are priced based upon expected margins,
rather than current margins.

Aswath Damodaran 174

 Solution 1: Use proxies for survival and growth: Amazon in
early 2000

 Hypothesizing that firms with higher revenue growth and higher cash balances
should have a greater chance of surviving and becoming profitable, we ran the
following regression: (The level of revenues was used to control for size)
PS = 30.61 - 2.77 ln(Rev) + 6.42 (Rev Growth) + 5.11 (Cash/Rev)
(0.66) (2.63) (3.49)
R squared = 31.8%
Predicted PS = 30.61 - 2.77(7.1039) + 6.42(1.9946) + 5.11 (.3069) = 30.42
Actual PS = 25.63
Stock is undervalued, relative to other internet stocks.

Aswath Damodaran 175

 Solution 2: Use forward multiples

 Global Crossing lost $1.9 billion in 2001 and is expected to continue to lose money for
the next 3 years. In a discounted cashflow valuation (see notes on DCF valuation) of
Global Crossing, we estimated an expected EBITDA for Global Crossing in five years of
$ 1,371 million.
 The average enterprise value/ EBITDA multiple for healthy telecomm firms is 7.2
currently.
 Applying this multiple to Global Crossing’s EBITDA in year 5, yields a value in year 5
of
• Enterprise Value in year 5 = 1371 * 7.2 = $9,871 million
• Enterprise Value today = $ 9,871 million/ 1.1385 = $5,172 million
(The cost of capital for Global Crossing is 13.80%)
• The probability that Global Crossing will not make it as a going concern is 77%.
• Expected Enterprise value today = 0.23 (5172) = $1,190 million

Aswath Damodaran 176

 Comparisons to the entire market: Why not?

 In contrast to the 'comparable firm' approach, the information in the entire

cross-section of firms can be used to predict PE ratios.
 The simplest way of summarizing this information is with a multiple
regression, with the PE ratio as the dependent variable, and proxies for risk,
growth and payout forming the independent variables.

Aswath Damodaran 177

 PE versus Expected EPS Growth: January 2008

Aswath Damodaran 178

 PE Ratio: Standard Regression for US stocks - January 2008

Aswath Damodaran 179

 Fundamentals hold in every market: PE regressions across
markets…
Region Regression R squared

Europe PE = 14.15 – 2.62 Beta + 7.50 Payout + 29.06 17.9%

Expected growth rate

Japan PE = 13.55 – 1.25 Beta + 26.05 Payout + 11.87 18.4%

Expected growth rate
Emerging PE = 5.63 + 11.35 Beta + 2.71 Payout + 92.72 13.9%
Markets Expected growth rate

Aswath Damodaran 180

 Market Regressions: Korean Market in 2008

Multiple Regression R squared

PBV PBV = 1.28 + 34.1 ROE +0.51 Beta 46.5%

EV/Sales EV/Sales = 1.72 -0.72 Beta + 176.9 Operating 16.0%

Margin
Price/Sales PS = 1.27 – 1.71 Beta + 91.5 Net Profit Margin 12.0%

Aswath Damodaran 181

 Relative Valuation: Some closing propositions

 Proposition 1: In a relative valuation, all that you are concluding is that a stock
is under or over valued, relative to your comparable group.
• Your relative valuation judgment can be right and your stock can be hopelessly
over valued at the same time.
 Proposition 2: In asset valuation, there are no similar assets. Every asset is
unique.
• If you don’t control for fundamental differences in risk, cashflows and growth
across firms when comparing how they are priced, your valuation conclusions will
reflect your flawed judgments rather than market misvaluations.

Aswath Damodaran 182

 Choosing Between the Multiples

 As presented in this section, there are dozens of multiples that can be

potentially used to value an individual firm.
 In addition, relative valuation can be relative to a sector (or comparable firms)
or to the entire market (using the regressions, for instance)
 Since there can be only one final estimate of value, there are three choices at
this stage:
• Use a simple average of the valuations obtained using a number of different
multiples
• Use a weighted average of the valuations obtained using a nmber of different
multiples
• Choose one of the multiples and base your valuation on that multiple

Aswath Damodaran 183

 Picking one Multiple

 This is usually the best way to approach this issue. While a range of values can
be obtained from a number of multiples, the “best estimate” value is obtained
using one multiple.
 The multiple that is used can be chosen in one of two ways:
• Use the multiple that best fits your objective. Thus, if you want the company to be
undervalued, you pick the multiple that yields the highest value.
• Use the multiple that has the highest R-squared in the sector when regressed against
fundamentals. Thus, if you have tried PE, PBV, PS, etc. and run regressions of
these multiples against fundamentals, use the multiple that works best at explaining
differences across firms in that sector.
• Use the multiple that seems to make the most sense for that sector, given how value
is measured and created.

Aswath Damodaran 184

 A More Intuitive Approach

 Managers in every sector tend to focus on specific variables when analyzing

strategy and performance. The multiple used will generally reflect this focus.
Consider three examples.
• In retailing: The focus is usually on same store sales (turnover) and profit margins.
Not surprisingly, the revenue multiple is most common in this sector.
• In financial services: The emphasis is usually on return on equity. Book Equity is
often viewed as a scarce resource, since capital ratios are based upon it. Price to
book ratios dominate.
• In technology: Growth is usually the dominant theme. PEG ratios were invented in
this sector.

Aswath Damodaran 185

 In Practice…

 As a general rule of thumb, the following table provides a way of picking a

multiple for a sector
Sector Multiple Used Rationale
Cyclical Manufacturing PE, Relative PE Often with normalized earnings
High Tech, High Growth PEG Big differences in growth across
firms
High Growth/No Earnings PS, VS Assume future margins will be good
Heavy Infrastructure EV/EBITDA Losses/ Big depreciation charges
Financial Services PBV Book value often marked to market
Retailing PS If leverage is similar across firms
VS If leverage is different

Aswath Damodaran 186

 Reviewing: The Four Steps to Understanding Multiples

 Define the multiple

• Check for consistency
• Make sure that they are estimated uniformly
 Describe the multiple
• Multiples have skewed distributions: The averages are seldom good indicators of
typical multiples
• Check for bias, if the multiple cannot be estimated
 Analyze the multiple
• Identify the companion variable that drives the multiple
• Examine the nature of the relationship
 Apply the multiple

Aswath Damodaran 187

 Real Options: Fact and Fantasy
Aswath Damodaran

Aswath Damodaran 188

 Underlying Theme: Searching for an Elusive Premium

 Traditional discounted cashflow models under estimate the value of

investments, where there are options embedded in the investments to
• Delay or defer making the investment (delay)
• Adjust or alter production schedules as price changes (flexibility)
• Expand into new markets or products at later stages in the process, based upon
observing favorable outcomes at the early stages (expansion)
• Stop production or abandon investments if the outcomes are unfavorable at early
stages (abandonment)
 Put another way, real option advocates believe that you should be paying a
premium on discounted cashflow value estimates.

Aswath Damodaran 189

 A Real Option Premium

 In the last few years, there are some who have argued that discounted cashflow
valuations under valued some companies and that a real option premium
should be tacked on to DCF valuations. To understanding its moorings,
compare the two trees below:
A bad investment………………….. Becomes a good one..

1. Learn at relatively low cost

2. Make better decisions based on learning

Aswath Damodaran 190

 Three Basic Questions

 When is there a real option embedded in a decision or an asset?

 When does that real option have significant economic value?
 Can that value be estimated using an option pricing model?

Aswath Damodaran 191

 When is there an option embedded in an action?

 An option provides the holder with the right to buy or sell a specified quantity
of an underlying asset at a fixed price (called a strike price or an exercise
price) at or before the expiration date of the option.
 There has to be a clearly defined underlying asset whose value changes over
time in unpredictable ways.
 The payoffs on this asset (real option) have to be contingent on an specified
event occurring within a finite period.

Aswath Damodaran 192

 Payoff Diagram on a Call

Net Payoff
on Call

Strike
Price

Price of underlying asset

Aswath Damodaran 193

 Example 1: Product Patent as an Option

PV of Cash Flows
from Project

Initial Investment in
Project

Present Value of Expected

Cash Flows on Product
Project's NPV turns
Project has negative positive in this section
NPV in this section

Aswath Damodaran 194

 Example 2: Undeveloped Oil Reserve as an option

Net Payoff on
Extraction

Cost of Developing
Reserve

Value of estimated reserve

of natural resource

Aswath Damodaran 195

 Example 3: Expansion of existing project as an option

PV of Cash Flows
from Expansion

Additional Investment
to Expand

Present Value of Expected

Cash Flows on Expansion
Expansion becomes
Firm will not expand in attractive in this section
this section

Aswath Damodaran 196

 When does the option have significant economic value?

 For an option to have significant economic value, there has to be a restriction

on competition in the event of the contingency. In a perfectly competitive
product market, no contingency, no matter how positive, will generate positive
net present value.
 At the limit, real options are most valuable when you have exclusivity - you
and only you can take advantage of the contingency. They become less
valuable as the barriers to competition become less steep.

Aswath Damodaran 197

 Exclusivity: Putting Real Options to the Test

 Product Options: Patent on a drug

• Patents restrict competitors from developing similar products
• Patents do not restrict competitors from developing other products to treat the same
disease.
 Natural Resource options: An undeveloped oil reserve or gold mine.
• Natural resource reserves are limited.
• It takes time and resources to develop new reserves
 Growth Options: Expansion into a new product or market
• Barriers may range from strong (exclusive licenses granted by the government - as
in telecom businesses) to weaker (brand name, knowledge of the market) to
weakest (first mover).

Aswath Damodaran 198

 Determinants of option value

 Variables Relating to Underlying Asset

• Value of Underlying Asset; as this value increases, the right to buy at a fixed price
(calls) will become more valuable and the right to sell at a fixed price (puts) will
become less valuable.
• Variance in that value; as the variance increases, both calls and puts will become
more valuable because all options have limited downside and depend upon price
volatility for upside.
• Expected dividends on the asset, which are likely to reduce the price appreciation
component of the asset, reducing the value of calls and increasing the value of puts.
 Variables Relating to Option
• Strike Price of Options; the right to buy (sell) at a fixed price becomes more (less)
valuable at a lower price.
• Life of the Option; both calls and puts benefit from a longer life.
 Level of Interest Rates; as rates increase, the right to buy (sell) at a fixed price
in the future becomes more (less) valuable.

Aswath Damodaran 199