Discounted Cash Flow Valuation: Many
a slip between the cup and the lip…
Aswath Damodaran
www.damodaran.com
Aswath Damodaran
1
Some Initial Thoughts
" One hundred thousand lemmings cannot be wrong"
Graffiti
Aswath Damodaran
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Misconceptions about Valuation

Myth 1: A valuation is an objective search for “true” value
•
•

Myth 2.: A good valuation provides a precise estimate of 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.
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
•
•
Aswath Damodaran
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.
3
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.
Aswath Damodaran
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Discounted Cash Flow Valuation



What is it: In discounted cash flow valuation, the value of an asset is the
present value of the expected cash flows on the asset.
Philosophical Basis: Every asset has an intrinsic value that can be estimated,
based upon its characteristics in terms of cash flows, growth and risk.
Information Needed: To use discounted cash flow valuation, you need
•
•
•

to estimate the life of the asset
to estimate the cash flows during the life of the asset
to estimate the discount rate to apply to these cash flows to get present value
Market Inefficiency: Markets are assumed to make mistakes in pricing assets
across time, and are assumed to correct themselves over time, as new
information comes out about assets.
Aswath Damodaran
5
DCF Choices: Equity Valuation versus Firm Valuation
Firm Valuation: Value the entire business
Assets
Existing Investments
Generate cashflows today
Includes long lived (fixed) and
short-lived(working
capital) assets
Expected Value that will be
created by future investments
Liabilities
Assets in Place
Debt
Growth Assets
Equity
Fixed Claim on cash flows
Little or No role in management
Fixed Maturity
Tax Deductible
Residual Claim on cash flows
Significant Role in management
Perpetual Lives
Equity valuation: Value just the
equity claim in the business
Aswath Damodaran
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Valuation with Infinite Life
DISCOUNTED CASHFLOW VALUATION
Expected Growth
Firm: Growth in
Operating Earnings
Equity: Growth in
Net Income/EPS
Cash flows
Firm: Pre-debt cash
flow
Equity: After debt
cash flows
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value
Value
Firm: Value of Firm
CF1
CF2
CF3
CF4
CF5
CFn
.........
Forever
Equity: Value of Equity
Length of Period of High Growth
Discount Rate
Firm:Cost of Capital
Equity: Cost of Equity
Aswath Damodaran
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DISCOUNTED CASHFLOW VALUATION
Cashflow to Firm
EBIT (1-t)
- (Cap Ex - Depr)
- Change in WC
= FCFF
Value of Operating Assets
+ Cash & Non-op Assets
= Value of Firm
- Value of Debt
= Value of Equity
+
Cost of Debt
(Riskfree Rate
+ Default Spread) (1-t)
Beta
- Measures market risk
Type of
Business
Aswath Damodaran
Firm is in stable growth:
Grows at constant rate
forever
Terminal Value= FCFF n+1 /(r-g n)
FCFF1
FCFF2
FCFF3
FCFF4
FCFF5
FCFFn
.........
Forever
Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))
Cost of Equity
Riskfree Rate :
- No default risk
- No reinvestment risk
- In same currency and
in same terms (real or
nominal as cash flows
Expected Growth
Reinvestment Rate
* Return on Capital
Operating
Leverage
X
Weights
Based on Market Value
Risk Premium
- Premium for average
risk investment
Financial
Leverage
Base Equity
Premium
Country Risk
Premium
8
Avg Reinvestment
rate = 25.08%
Embraer: Status Quo ($)
Reinvestment Rate
25.08%
Current Cashflow to Firm
EBIT(1-t) :
$ 404
- Nt CpX
23
- Chg WC
9
= FCFF
$ 372
Reinvestment Rate = 32/404= 7.9%
Return on Capital
21.85%
Stable Growth
g = 4.17%; Beta = 1.00;
Country Premium= 5%
Cost of capital = 8.76%
ROC= 8.76%; Tax rate=34%
Reinvestment Rate=g/ROC
=4.17/8.76= 47.62%
Expected Growth
in EBIT (1-t)
.2185*.2508=.0548
5.48 %
Terminal Value5= 288/(.0876-.0417) = 6272
$ Cashflows
Op. Assets $ 5,272
+ Cash:
795
- Debt
717
- Minor. Int.
12
=Equity
5,349
-Options
28
Value/Share $7.47
R$ 21.75
Year
EBIT(1-t)
- Reinvestment
= FCFF
1
426
107
319
3
474
119
355
4
500
126
374
Term Yr
549
- 261
= 288
5
527
132
395
Discount at$ Cost of Capital (WACC) = 10.52% (.84) + 6.05% (0.16) = 9.81%
Cost of Equity
10.52 %
Riskfree Rate :
$ Riskfree Rate= 4.17%
On October 6, 2003
Embraer Price = R$15.51
Cost of Debt
(4.17%+1%+4%)(1-.34)
= 6.05%
+
Beta
1.07
Unlevered Beta for
Sectors: 0.95
Aswath Damodaran
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449
113
336
X
Weights
E = 84% D = 16%
Mature market
premium
4%
Firm’s D/E
Ratio: 19%
+
Lambda
0.27
X
Country Equity Risk
Premium
7.67%
Country Default
Spread
6.01%
X
Rel Equity
Mkt Vol
1.28
9
Kristin’s Kandy: Status Quo
Current Cashflow to Firm
EBIT(1-t) :
300,000
- Nt CpX
100,000
- Chg WC
40,000
= FCFF
160,000
Reinvestment Rate = 46.67%
Return on Capital
13.64%
Reinvestment Rate
46.67%
Expected Growth
in EBIT (1-t)
.4667*.1364= .0636
6.36 %
Stable Growth
g = 4%; Beta =3.00;
ROC= 12.54%
Reinvestment Rate=31.90%
Terminal Value10= 289/(.1254-.04) = 3,403
Firm Value:
2,571
+ Cash
125
- Debt:
900
=Equity
1,796
Liq. Discount 12.5%
Equity value 1572
Year
EBIT (1-t)
- Reinvestment
=FCFF
1
$319
$149
$170
2
$339
$158
$181
3
$361
$168
$193
4
$384
$179
$205
5
$408
$191
$218
Term Yr
425
136
289
Discount atCost of Capital (WACC) = 16.26% (.70) + 3.30% (.30) = 12.37%
Cost of Debt
(4.5%+1.00)(1-.40)
= 3.30%
Cost of Equity
16.26%
Weights
E =70% D = 30%
Synthetic rating = ARiskfree Rate :
Riskfree rate = 4.50%
(10-year T.Bond rate)
Beta Correlation
0.98 0.33
/
+
Total Beta
2.94
Unlevered Beta for
Sectors: 0.82
Aswath Damodaran
X
Risk Premium
4.00%
Firm’s D/E
Ratio: 1.69%
Mature risk
premium
4%
Country Risk
Premium
0%
10
Discounted Cash Flow Valuation: High Growth with Negative Earnings
Current
Operating
Margin
Current
Revenue
EBIT
Reinvestment
Stable Growth
Sales Turnover
Ratio
Competitive
Advantages
Revenue
Growth
Expected
Operating
Margin
Tax Rate
- NOLs
Stable
Revenue
Growth
Stable
Stable
Operating Reinvestment
Margin
FCFF = Revenue* Op Margin (1-t) - Reinvestment
Value of Operating Assets
+ Cash & Non-op Assets
= Value of Firm
- Value of Debt
= Value of Equity
- Equity Options
= Value of Equity in Stock
Terminal Value= FCFF n+1 /(r-g n)
FCFF1
FCFF2
FCFF3
FCFF4
FCFF5
FCFFn
.........
Forever
Discount at WACC= Cost of Equity (Equity/(Debt + Equity)) + Cost of Debt (Debt/(Debt+ Equity))
Cost of Equity
Riskfree Rate :
- No default risk
- No reinvestment risk
- In same currency and
in same terms (real or
nominal as cash flows
+
Cost of Debt
(Riskfree Rate
+ Default Spread) (1-t)
Beta
- Measures market risk
Type of
Business
Aswath Damodaran
Operating
Leverage
X
Weights
Based on Market Value
Risk Premium
- Premium for average
risk investment
Financial
Leverage
Base Equity
Premium
Country Risk
Premium
11
Reinvestment:
Current
Revenue
$ 1,117
Cap ex inc ludes acquisitions
Working capital is 3% of revenues
Current
Margin:
-36.71%
Sales Turnover
Ratio: 3.00
EBIT
-410m
Value of Op Assets $ 14,910
+ Cash
$
26
= Value of Firm
$14,936
- Value of Debt
$ 349
= Value of Equity
$14,587
- Equity Options
$ 2,892
Value per share
$ 34.32
Revenues
EBIT
EBIT (1-t)
- Reinves tment
FCFF
Cos t of Equity
Cos t of Debt
AT cost of debt
Cos t of Capital
Expected
Margin:
-> 10.00%
9,774
$407
$407
$1,396
-$989
14,661
$1,038
$871
$1,629
-$758
5,585
-$94
-$94
$931
-$1,024
1
2
3
4
5
6
7
8
9
12.90%
8.00%
8.00%
12.84%
12.90%
8.00%
8.00%
12.84%
12.90%
8.00%
8.00%
12.84%
12.90%
8.00%
6.71%
12.83%
12.90%
8.00%
5.20%
12.81%
12.42%
7.80%
5.07%
12.13%
12.30%
7.75%
5.04%
11.96%
12.10%
7.67%
4.98%
11.69%
11.70%
7.50%
4.88%
11.15%
23,862
$2,212
$1,438
$1,601
-$163
28,729
$2,768
$1,799
$1,623
$177
Cost of Debt
6.5%+1.5%=8.0%
Tax rate = 0% -> 35%
Riskfree Rate :
T. Bond rate = 6.5%
Beta
1.60 -> 1.00
Internet/
Retail
Aswath Damodaran
19,059
$1,628
$1,058
$1,466
-$408
Operating
Leverage
X
Stable
Operating
Margin:
10.00%
33,211
$3,261
$2,119
$1,494
$625
36,798
$3,646
$2,370
$1,196
$1,174
Term. Year
$41,346
10.00%
35.00%
$2,688
$ 807
$1,881
39,006
$3,883
$2,524
$736
$1,788
10
10.50%
7.00%
4.55%
9.61%
Forever
Weights
Debt= 1.2% -> 15%
Amazon.com
January 2000
Stock Price = $ 84
Risk Premium
4%
Current
D/E: 1.21%
Stable
ROC=20%
Reinvest 30%
of EBIT(1-t)
Terminal Value= 1881/(.0961-.06)
=52,148
$2,793
-$373
-$373
$559
-$931
Cost of Equity
12.90%
+
Stable
Revenue
Growth: 6%
Competitive
Advantages
Revenue
Growth:
42%
NOL:
500 m
Stable Growth
Base Equity
Premium
Country Risk
Premium
12
I. Measure earnings right..
Firm’s
history
Comparable
Firms
Operating leases
- Convert into debt
- Adjust operating income
Normalize
Earnings
R&D Expenses
- Convert into asset
- Adjust operating income
Cleanse operating items of
- Financial Expenses
- Capital Expenses
- Non-recurring expenses
Measuring Earnings
Update
- Trailing Earnings
- Unofficial numbers
Aswath Damodaran
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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 pretax 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)
1
$899.00
2
$846.00
3
$738.00
4
$598.00
5
$477.00
6&7 $982.50 each year
Present Value (at 6%)
$848.11
$752.94
$619.64
$473.67
$356.44
$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

Aswath Damodaran
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The Collateral Effects of Treating Operating Leases as Debt
Conventional Accounting
Income Statement
EBIT& Leases = 1,990
- Op Leases
= 978
EBIT
= 1,012
Balance Sheet
Off balance sheet (Not shown as debt or as an
asset). Only the conventional debt of $1,970
million shows up on balance sheet
Cost of capital = 8.20%(7350/9320) + 4%
(1970/9320) = 7.31%
Cost of equity for The Gap = 8.20%
After-tax cost of debt = 4%
Market value of equity = 7350
Return on capital = 1012 (1-.35)/(3130+1970)
= 12.90%
Aswath Damodaran
Operating Leases Treated as Debt
Income Statement
EBIT& Leases = 1,990
- Deprecn: OL=
628
EBIT
= 1,362
Interest expense will rise to reflect the conversion
of operating leases as debt. Net income should
not change.
Balance Sheet
Asset
Liability
OL Ass et
4397
OL Debt 4397
Total debt = 4397 + 1970 = $6,367 million
Cost of capital = 8.20%(7350/13717) + 4%
(6367/13717) = 6.25%
Return on capital = 1362 (1-.35)/(3130+6367)
= 9.30%
15
Capitalizing R&D Expenses: SAP in 2004

R & D was assumed to have a 5-year life.
Year
R&D Expense
Unamortized portion
Current
1020.02
1.00
1020.02
-1
993.99
0.80
795.19
-2
909.39
0.60
545.63
-3
898.25
0.40
359.30
-4
969.38
0.20
193.88
-5
744.67
0.00
0.00
Value of research asset =
€ 2,914 million
Amortization of research asset in 2004
=
Increase in Operating Income = 1020 - 903 = € 117 million
Aswath Damodaran
Amortization this year
€ 198.80
€ 181.88
€ 179.65
€ 193.88
€ 148.93
€ 903 million
16
The Effect of Capitalizing R&D: SAP
Conventional Accounting
Income Statement
EBIT& R&D = 3045
- R&D
= 1020
EBIT
= 2025
EBIT (1-t)
= 1285 m
Balance Sheet
Off balance sheet asset. Book value of equity at
3,768 million Euros is understated because
biggest asset is off the books.
Capital Expenditures
Conventional net cap ex of 2 million Euros
Cash Flows
EBIT (1-t)
= 1285
- Net Cap Ex
=
2
FCFF
= 1283
Return on capital = 1285/(3768+530)
= 29.90%
Aswath Damodaran
R&D treated as capital expenditure
Income Statement
EBIT& R&D = 3045
- Amo rt: R&D = 903
EBIT
= 2142 (Increase of 117 m)
EBIT (1-t)
= 1359 m
Igno red tax benefit = (1020-903)(.3654) = 43
Adjusted EBIT (1-t) = 1359+43 = 1402 m
(Increase of 117 million)
Net Income will also increase by 117 million
Balance Sheet
Asset
Liability
R&D As set 2914 Book Equity +2914
Total Book Equity = 3768+2914= 6782 mil
Capital Expenditures
Net Cap ex = 2+ 1020 Π903 = 119 mil
Cash Flows
EBIT (1-t)
= 1402
- Net Cap Ex
=
119
FCFF
= 1283 m
Return on capital = 1402/(6782+530)
= 19.93%
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II. Get the big picture (not the accounting one) when it comes
to cap ex and working capital

Capital expenditures should include
•
•


Research and development expenses, once they have been re-categorized as capital
expenses.
Acquisitions of other firms, whether paid for with cash or stock.
Working capital should be defined not as the difference between current assets
and current liabilities but as the difference between non-cash current assets
and non-debt current liabilities.
On both items, start with what the company did in the most recent year but do
look at the company’s history and at industry averages.
Aswath Damodaran
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Acquisitions and Growth



If you want to count the growth from acquisitions, you have to count the cost
of acquisitions as part of capital expenditures. If you count the growth but not
the acquisitions, you will over value the company.
You have the alternative of completely ignoring acquisitions for both growth
and cap ex. If you do so, you are assuming that acquisitions are value neutral
(and that you pay a fair price on every acquisition).
The most difficult part of dealing with acquisitions is that they tend to be
volatile; in some cases, a firm may do an acquisition once every three or four
years. You have to normalize acquisition costs over multiple years.
Aswath Damodaran
19
III. Betas don’t come from regressions or services
Aswath Damodaran
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Determinants of Betas
Beta of Equity (Levered Beta)
Beta of Firm (Unlevered Beta)
Nature of product or
service offered by
company:
Other things remaining equal,
the more discretionary the
product or service, the higher
the beta.
Operating Leverage (Fixed
Costs as percent of total
costs):
Other things remaining equal
the greater the proportion of
the costs that are fixed, the
higher the beta of the
company.
Implications
1. Cyclical companies should
have higher betas than noncyclical companies.
2. Luxury goods firms should
have higher betas than basic
goods.
3. High priced goods/service
firms should have higher betas
than low prices goods/services
firms.
4. Growth firms should have
higher betas.
Implications
1. Firms with high infrastructure
needs and rigid cost structures
should have higher betas than
firms with flexible cost structures.
2. Smaller firms should have higher
betas than larger firms.
3. Young firms should have higher
betas than more mature firms.
Aswath Damodaran
Financial Leverage:
Other things remaining equal, the
greater the proportion of capital that
a firm raises from debt,the higher its
equity beta will be
Implciations
Highly levered firms should have highe betas
than firms with less debt.
Equity Beta (Levered beta) =
Unlev Beta (1 + (1- t) (Debt/Equity Ratio))
21
An alternative to regression betas…
Step 1: Find the business or businesses that your firm operates in.
Possible Refinements
Step 2: Find publicly traded firms in each of these businesses and
obtain their regression betas. Compute the simple average across
these regression betas to arrive at an average beta for these publicly
traded firms. Unlever this average beta using the average debt to
equity ratio across the publicly traded firms in the sample.
Unlevered beta for business = Average beta across publicly traded
firms/ (1 + (1- t) (Average D/E ratio across firms))
Step 3: Estimate how much value your firm derives from each of
the different businesses it is in.
Step 4: Compute a weighted average of the unlevered betas of the
different businesses (from step 2) using the weights from step 3.
Bottom-up Unlevered beta for your firm = Weighted average of the
unlevered betas of the individual business
Step 5: Compute a levered beta (equity beta) for your firm, using
the market debt to equity ratio for your firm.
Levered bottom-up beta = Unlevered beta (1+ (1-t) (Debt/Equity))
Aswath Damodaran
If you can, adjust this beta for differences
between your firm and the comparable
firms on operating leverage and product
characteristics.
While revenues or operating income
are often used as weights, it is better
to try to estimate the value of each
business.
If you expect the business mix of your
firm to change over time, you can
change the weights on a year-to-year
basis.
If you expect your debt to equity ratio to
change over time, the levered beta will
change over time.
22
Bottom-up Betas
Company
Comparable Companies
Unlevered
Levered Beta
Beta
Embraer
Global aerospace companies
0.95
0.80 (1 + (1-.34) (.19) = 1.07
Amazon (First 5 years)
Internet Retaile rs
1.58
1.58 (1- (1-0) (.0121) = 1.60
Amazon (After year 5)
Specialty Retailers
Kristin Kandy
Food Processing companies with market
1.00
0.78
0.78 ( 1+(1-.4) (30/70)) = 0.98
cap < $ 250 milli on
Aswath Damodaran
23
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
Aswath Damodaran
24
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:
•
•
•
•
•
•
Aswath Damodaran
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%
25
IV. And the past is not always a good indicator of the future
It is standard practice to use historical premiums as forward looking premiums. :
Arithmetic average Geometric Average
Stocks Stocks Stocks Historical Period
T.Bills
T.Bonds
T.Bills
Stocks T.Bonds
1928-2005
1964-2005
1994-2005
4.80%
3.21%
3.76%


7.83%
5.52%
8.80%
5.95%
4.29%
7.07%
6.47%
4.08%
5.15%
An alternative is to back out the premium from market prices:
In 2005, dividends & stock
buybacks were 3.34% of
the index, generating
41.63.in cashflows
Analyst estimate of growth in net income for S&P 500 over next 5
years = 8%
44.96
48.56
52.44
56.64
After year 5, we will assume that
earnings on the index will grow at
4.39%, the same rate as the entire
economy
61.17
January 1, 2006
S&P 500 is at 1248.24

Implied Equity risk premium = Expected return on stocks - Treasury bond rate = 8.47%-4.39% = 4.08%
Aswath Damodaran
26
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970
1969
1968
1967
1966
1965
1964
1963
1962
1961
1960
0.00%
27
Aswath Damodaran
4.00%
3.00%
Implied Premium
Implied Premiums in the US
Implied Premium for US Equity Market
7.00%
6.00%
5.00%
2.00%
1.00%
Year
Implied Premium for Brazil - February 2006

Using the Bovespa as our measure of Brazilian equity, we estimated the
following:
•
•
•
•
•

Level of index = 38364
FCFE for stocks in index in 2005 = 4.73% of index level
Expected growth rate (in US $) in earnings & FCFE for next 5 years = 10.00%
Growth rate beyond year 5 = 4.50%
Risk free rate= 4.50%
Solving for the level of the index, we get
•
•
Aswath Damodaran
Expected return on Brazilian stocks = 10.73%
Implied equity risk premium for Brazil = 10.73% - 4.50% = 6.23%
28
V. There is a downside to globalization…


Emerging markets offer growth opportunities but they are also riskier. If we
want to count the growth, we have to also consider the risk.
Consider, for example, Brazil as a country. There are two simple assessments
of country risk that we can use for it • A country rating from S&P, Moody’s or IBCA and an associated default
spread for that rating.
• The default spread between a dollar denominated bond issued by the
Brazilian government and the treasury bond rate.
Aswath Damodaran
29
A blended approach…


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.
Another is to multiply the bond default spread by the relative volatility of
stock and bond prices in that market. Using this approach in 2003:
•
Country risk premium = Default spread on country bond* Country Equity / Country Bond
– Standard Deviation in Bovespa (Equity) = 29.24%
– Standard Deviation in Brazil C-Bond = 24.15%
– Default spread on C-Bond = 6.50%
•

Country Risk Premium for Brazil = 6.50% (29.24%/24.15%) = 7.87%
Using the same approach in 2006 would yield a much lower country
risk premium:
• Country risk premium = 2.00% (27.15%/15.56%) = 3.49%
Aswath Damodaran
30
VI. And it is not just emerging market companies that are
exposed to this risk..

If we 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+ b (US premium) + l (Country ERP)

The easiest and most accessible data is on revenues. Most companies break their
revenues down by region. One simplistic solution would be to do the following:
l = % of revenues domesticallyfirm/ % of revenues domesticallyavg firm
Consider, for instance, Embraer, Embratel and Ambev, all of which are incorporated and
traded in Brazil. Embraer gets 3% of its revenues from Brazil, Embratel gets almost all
of its revenues in Brazil and Ambev gets about 92% of its revenues in Brazil. The
average Brazilian company gets about 77% of its revenues in Brazil:

•
•
•

LambdaEmbraer = 3%/ 77% = .04
LambdaEmbratel = 100%/77% = 1.30
LambdaAmbev = 92%/77% = 1.19
There are two implications
•
•
Aswath Damodaran
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
31
Estimating Lambdas: Earnings Approach
Figure 2: EPS changes versus Country Risk: Embraer and Embratel
1.5
1
Quarterly EPS
0.5
0
Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3
1998 1998 1998 1998 1999 1999 1999 1999 2000 2000 2000 2000 2001 2001 2001 2001 2002 2002 2002 2002 2003 2003 2003
-0.5
-1
-1.5
-2
Quarter
Aswath Damodaran
32
Estimating Lambdas: Stock Returns versus C-Bond Returns
ReturnEmbraer = 0.0195 + 0.2681 ReturnC Bond
ReturnAmbev = 0.0290+ 0.4136 ReturnC Bond
ReturnVale = 0.02169 + 0.3760.ReturnC Bond
ReturnEmbratel = -0.0308 + 2.0030 ReturnC Bond
ReturnPetrobras= -0.0308 + 0.6600 ReturnC Bond
Embraer versus C Bond: 2000-2003
Embratel versus C Bond: 2000-2003
40
100
80
60
Return on Embratel
Return on Embraer
20
0
-20
40
20
0
-20
-40
-40
-60
-60
-30
-80
-20
-10
0
Return on C-Bond
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10
20
-30
-20
-10
0
10
20
Return on C-Bond
33
VII. Discount rates can (and often should) change over
time…


The inputs into the cost of capital - the cost of equity (beta), the cost of debt
(default risk) and the debt ratio - can change over time. For younger firms,
they should change over time.
At the minimum, they should change when you get to your terminal year to
inputs that better reflect a mature firm.
Aswath Damodaran
34
Amazon: Shifting Cost of Capital
Amazon: Evolving Cost of Capital
14.00%
16.00%
14.00%
12.00%
12.00%
10.00%
8.00%
8.00%
6.00%
Debt Ratio
Cost of capital
10.00%
6.00%
4.00%
4.00%
2.00%
2.00%
0.00%
0.00%
Current
1
2
3
4
5
6
7
8
9
10
Terminal
Year of forecast
Cost of Equity
Aswath Damodaran
After-tax cost of debt
Debt Ratio
Cost of Capital
35
VIII. Growth has to be earned (not endowed or estimated)
Expected Growth
Net Income
Retention Ratio=
1 - Dividends/Net
Income
X
Operating Income
Return on Equity
Net Income/Book Value of
Equity
Reinvestment
Rate = (Net Cap
Ex + Chg in
WC/EBIT(1-t)
Adjust EBIT for
a. Extraordinary or one-time expenses or income
b. Operating leases and R&D
c. Cyclicality in earnings (Normalize)
d. Acquisition Debris (Goodwill amortization etc.)
ROC =
X
Return on Capital =
EBIT(1-t)/Book Value of
Capital
Use a marginal tax rate
to be safe. A high ROC
created by paying low
effective taxes is not
sustainable
EBIT ( 1- tax rate)
Book Value of Equity + Book value of debt - Cash
Adjust book equity for
1. Capitalized R&D
2. Acquisition Debris (Goodwill)
Adjust book value of debt for
a. Capitalized operating leases
Use end of prior year numbers or average over the year
but be consistent in your application
Aswath Damodaran
36
But you can get a bonus from using existing assets more
efficiently…


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, a company whose return on capital increases from 5% to 7.5% in
a year will report an earnings growth rate of 50%, even with no new
investment. If it happens over 5 years, there will be approximately 10% higher
growth each for those five years.
Aswath Damodaran
37
And if margins are changing, start with revenues… and keep
your life simple
Year
Tr12m
1
2
3
4
5
6
7
8
9
10
TY(11)
Aswath Damodaran
Revenues
Growth
$1,117
$2,793
150%
$5,585
100%
$9,774
75%
$14,66150% 7.08%
$19,05930% 8.54%
$23,86225.2%
$28,72920.4%
$33,211 15.6%
$36,79810.8%
$39,0066% 9.95%
$41,346
10.00%
Operating Margin
-36.71%
-13.35%
-1.68%
4.16%
$1,038
$1,628
9.27%
9.64%
9.82%
9.91%
$3,883
$4,135
EBIT
-$410
-$373
-$94
$407
$2,212
$2,768
$3,261
$3,646
38
IX. All good things come to an end..And the terminal value is
not an ATM…
This tax rate locks in
forever. Does it make
sense to use an
effective tax rate?
Terminal Valuen =
Are you reinvesting enough to
sustain your stable growth rate?
Check
Reinv Rate = g/ ROC
EBIT n+1 (1 - tax rate) (1 - Reinvestment Rate)
Cost of capital - Expected growth rate
This is a mature company.
It’s cost of capital should
reflect that.
Aswath Damodaran
This growth rate should be
less than the nominlnal
growth rate of the economy
39
Growth, Reinvestment and Terminal Value: Back to Embraer
Growth Rate
0%
1%
2%
3%
4%
Reinvestment Rate
0.00%
11.42%
22.84%
34.26%
45.68%
FCFF
$549.28
$486.55
$423.82
$361.10
$298.37
Terminal value
$6,272.38
$6,272.38
$6,272.38
$6,272.38
$6,272.38
Return on capital = 8.76%
Reinvestment Rate = g/8.76%
Aswath Damodaran
40
X. The loose ends matter…
Value of Operating Assets
Since this is a discounted cashflow valuation, should there be a real option
premium?
+ Cash and Marketable
Securities
Operating versus Non-opeating cash
Should cash be discounted for earning a low return?
+ Value of Cross Holdings
How do you value cross holdings in other companies?
What if the cross holdings are in private businesses?
+ Value of Other Assets
What about other valuable assets?
How do you consider under utlilized assets?
Should you discount this value for opacity or complexity?
How about a premium for synergy?
What about a premium for intangibles (brand name)?
Value of Firm
- Value of Debt
What should be counted in debt?
Should you subtract book or market value of debt?
What about other obligations (pension fund and health care?
What about contingent liabilities?
What about minority interests?
= Value of Equity
Should there be a premium/discount for control?
Should there be a discount for distress
- Value of Equity Options
What equity options should be valued here (vested versus non-vested)?
How do you value equity options?
= Value of Common Stock
Should you divide by primary or diluted shares?
/ Number of shares
= Value per share
Aswath Damodaran
Should there be a discount for illiquidity/ marketability?
Should there be a discount for minority interests?
41
1a. The Value of Cash


The simplest and most direct way of dealing with cash and marketable
securities is to keep it out of the valuation - the cash flows should be before
interest income from cash and securities, and the discount rate should not be
contaminated by the inclusion of cash. (Use betas of the operating assets alone
to estimate the cost of equity).
Once the operating assets have been valued, you should add back the value of
cash and marketable securities.
Aswath Damodaran
42
How much cash is too much cash?
Cash as % of Firm Value: July 2000
1200
1000
800
600
400
200
0
0-1%
Aswath Damodaran
1-2%
2-5%
5-10%
10-15%
15-20%
20-25%
25-30%
>30%
43
Should you ever discount cash for its low returns?

There are some analysts who argue that companies with a lot of cash on their
balance sheets should be penalized by having the excess cash discounted to
reflect the fact that it earns a low return.
•
•


Excess cash is usually defined as holding cash that is greater than what the firm
needs for operations.
A low return is defined as a return lower than what the firm earns on its non-cash
investments.
This is the wrong reason for discounting cash. If the cash is invested in
riskless securities, it should earn a low rate of return. As long as the return is
high enough, given the riskless nature of the investment, cash does not destroy
value.
There is a right reason, though, that may apply to some companies…
Aswath Damodaran
44
Cash: Discount or Premium?
Market Value of $ 1 in cash:
Estimates obtained by regressing Enterprise Value against Cash
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Mature firms, Negative excess returns
Aswath Damodaran
All firms
High Growth firms, High Excess Returns
45
1b. Dealing with Holdings in Other firms

Holdings in other firms can be categorized into
•
•
•
Aswath Damodaran
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.
46
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
47
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
48
2. 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
49
3. A Discount for Complexity:
An Experiment
Company A
Operating Income $ 1 billion
Tax rate
40%
ROIC
10%
Expected Growth 5%
Cost of capital
8%
Business Mix
Single Business
Holdings
Simple
Accounting
Transparent
 Which firm would you value more highly?
Aswath Damodaran
Company B
$ 1 billion
40%
10%
5%
8%
Multiple Businesses
Complex
Opaque
50
Sources of Complexity

Accounting Standards
•
•
•

Nature and mix of businesses
•
•

Multiple businesses (Eg. GE)
Multiple countries (Eg. Coca Cola)
Structuring of businesses
•
•

Inconsistency in applying accounting principles (Operating leases, R&D etc.)
Fuzzy Accounting Standards (One-time charges, hidden assets)
Unintended Consequences of Increased Disclosure
Cross Holdings (The Japanese Curse)
Creative Holding Structures (Enronitis)
Financing Choices
•
•
Aswath Damodaran
Growth of Hybrids
New Securities (Playing the Ratings Game)
51
Reasons for Complexity

Control
•
•

Complex holding structures were designed to make it more difficult for outsiders
(which includes investors) to know how much a firm is worth, how much it is
making and what assets it holds.
Multiple classes of shares and financing choices also make it more likely that
incumbents can retain control in the event of a challenge.
Tax Benefits
•
Complex tax law begets complex business mixes and holding structures.
– Different tax rates for different locales and different transactions
– Tax credits

Deceit
Aswath Damodaran
52
Measuring Complexity: Volume of Data in Financial
Statements
Company
Gene ral Electric
Mic rosoft
Wal-mart
Exxon Mobil
Pfiz er
Citi group
Intel
AIG
John son & John son
IBM
Aswath Damodaran
Number of pages in last 10Q
65
63
38
86
171
252
69
164
63
85
Number of pages in last 10K
410
218
244
332
460
1026
215
720
218
353
53
Measuring Complexity: A Complexity Score
Item
Factors
Operating Income 1. Multiple Businesses
2. One-time income and expenses
Answer
2
20%
Complexity score
4
1
Percent of operating income =
15%
0.75
1. Income from mu ltiple locales
Percent of operating income =
Percent of revenues from n on-domestic locales =
5%
100%
0.25
3
2. Different tax and reporting books
3. Headquarters in tax havens
4. Volatile effective tax rate
Yes or No
Yes or No
Yes
Yes
3
3
Yes or No
Yes or No
Yes or No
Yes or No
Yes
Yes
Yes
Yes
2
2
4
4
Yes or No
Yes or No
Yes
Yes
3
2
Yes
Yes
Yes
3
3
5
Yes
2
5
2
3. Income from u nspecified sources
4. Items in income statement that are volatile
Tax Rate
Capital
Expenditures
1. Volatile capital expenditures
2. Frequent and large acquisitions
Working capital
3. Stock payment for acquisitions and investments
1. Unspecified current assets and current liabilities
2. Volatile working capital items
Follow-up Question
Numb er of businesses (with mo re than 10% of revenues) =
Percent of operating income =
Expected Growth 1. Off-balance sheet assets and liabilities (operating
rate
leases and R&D)
Yes or No
2. Substantial stock buybacks
Yes or No
3. Changing return on capital over time
Is your return on capital volatile?
4. Unsustainably high return
Is your firm's ROC much higher than industry average?
Cost of capital
1. Multiple businesses
Numb er of businesses (more than 10% of revenues) =
2. Operations in eme rging markets
3. Is the debt market traded?
Percent of revenues=
Yes or No
30%
Yes
1.5
0
4. Does the company have a rating?
5. Does the company have off-balance sheet debt?
Yes or No
Yes
0
Yes or No
No
Complexity Score =
Aswath Damodaran
0
51.5
54
Dealing with Complexity



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
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
55
4. 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
56
A procedure for 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
57
Sources of Synergy
Synergy is created when two firms are combined and can be
either financial or operating
Operating Synergy accrues to the combined firm as
Strategic Advantages
Higher returns on
new investments
More new
Investments
Higher ROC
Higher Reinvestment
Higher Growth
Rate
Higher Growth Rate
Aswath Damodaran
Economies of Scale
More sustainable
excess returns
Cost Savings in
current operations
Longer Growth
Period
Higher Margin
Financial Synergy
Tax Benefits
Lower taxes on
earnings due to
- higher
depreciaiton
- operating loss
carryforwards
Added Debt
Capacity
Higher debt
raito and lower
cost of capital
Diversification?
May reduce
cost of equity
for private or
closely held
firm
Higher Baseyear EBIT
58
J.P. Morgan’s estimate of total synergies in Labatt/Ambev
Merger
Aswath Damodaran
59
Who gets the benefits of synergy?
Total Synergy = $ 2 billion
Premium paid to
Labatt Stockholders
= $7.3 billion - $6.85
billion = $ 450 million
Aswath Damodaran
Voting Shares
in Ambev
Non-voting
Shares in Ambev
$1.55 billion to be shared?
60
5. 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
61
Categorizing Intangibles
Examples
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
Copyrights, trademarks, li censes,
Brand names, Quali ty and Morale
Undeveloped patents, operating or
franchises, professional practices
of work force, Technological
financial flexibili ty (to expand into
(medical, dental)
expertise, Corporate reputation
new products/markets or abandon
existing ones)
Valuation approach
Estim ate expected cashflows from

Compare DCF value of firm
Option valuation
the product or service and discount
with intangible with firm

back at appropriate discount rate.
without (if you can find one)
as an option to develop the
Assume that all excess returns
underlyi ng product.

of firm are due to intangible.


Compare multiples at which
firm trades to sector averages.
Value the undeveloped patent
Value expansion options as call
options

Value abandonment options as
put options.
Chall enges


Lif e is usua lly finite and
With multiple intangibles (brand

Need exclusivity.
termi nal value may be small .
name and reputation for service), it

Diffi cult to repli cate and
Cashflows and value may be
becomes diffi cult to break down
arbitrage (making o ption
person dependent (for
individual components.
pricing models dicey)
professional practices)
Aswath Damodaran
62
Valuing Brand Name
Current Revenues =
Length of high-growth period
Reinvestment Rate =
Operating Margin (after-tax)
Sales/Capital (Turnover ratio)
Return on capital (after-tax)
Growth rate during period (g) =
Cost of Capital during period =
Stable Growth Period
Growth rate in steady state =
Return on capital =
Reinvestment Rate =
Cost of Capital =
Value of Firm =
Aswath Damodaran
Coca Cola
$21,962.00
10
50%
15.57%
1.34
20.84%
10.42%
7.65%
With Cott Margins
$21,962.00
10
50%
5.28%
1.34
7.06%
3.53%
7.65%
4.00%
7.65%
52.28%
7.65%
$79,611.25
4.00%
7.65%
52.28%
7.65%
$15,371.24
63
6. Defining Debt

General Rule: Debt generally has the following characteristics:
•
•
•

Defined as such, debt should include
•
•

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.
All interest bearing liabilities, short term as well as long term
All leases, operating as well as capital
Debt should not include
•
Aswath Damodaran
Accounts payable or supplier credit
64
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
65
But you should consider other potential liabilities

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
•
Aswath Damodaran
Value of contingent liability = Probability that the liability will occur * Expected
value of liability
66
7. 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
67
I. Ways of Increasing Cash Flows from Assets in Place
More efficient
operations and
cost cuttting:
Higher Margins
Revenues
* Operating Margin
= EBIT
Divest assets that
have negative EBIT
- Tax Rate * EBIT
= EBIT (1-t)
Reduce tax rate
- moving income to lower tax locales
- transfer pricing
- risk management
Aswath Damodaran
+ Depreciation
- Capital Expenditures
- Chg in Working Capital
= FCFF
Live off past overinvestment
Better inventory
management and
tighter credit policies
68
II. Value Enhancement through Growth
Reinvest more in
projects
Increase operating
margins
Do acquisitions
Reinvestment Rate
* Return on Capital
Increase capital turnover ratio
= Expected Growth Rate
Aswath Damodaran
69
III. Building Competitive Advantages: Increase length of the
growth period
Increase length of growth period
Build on existing
competitive
advantages
Brand
name
Aswath Damodaran
Legal
Protection
Find new
competitive
advantages
Switching
Costs
Cost
advantages
70
IV. Reducing Cost of Capital
Outsourcing
Flexible wage contracts &
cost structure
Reduce operating
leverage
Change financing mix
Cost of Equity (E/(D+E) + Pre-tax Cost of Debt (D./(D+E)) = Cost of Capital
Make product or service
less discretionary to
customers
Changing
product
characteristics
Aswath Damodaran
More
effective
advertising
Match debt to
assets, reducing
default risk
Swaps
Derivatives
Hybrids
71
Embraer : Optimal Capital Structure
Debt Ratio
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Aswath Damodaran
Beta
0.95
1.02
1.11
1.22
1.37
1.58
1.89
2.42
3.48
6.95
Cost of Equity
10.05%
10.32%
10.67%
11.12%
11.72%
12.56%
13.81%
15.90%
20.14%
34.05%
Bond Rating
AAA
AAA
AA
A
AB
CCC
CC
CC
CC
Interest rate on debt
8.92%
8.92%
9.17%
9.97%
10.17%
14.67%
18.17%
19.67%
19.67%
19.67%
Tax Rate
34.00%
34.00%
34.00%
34.00%
34.00%
34.00%
34.00%
34.00%
33.63%
29.90%
Cost of Debt (after-tax)
5.89%
5.89%
6.05%
6.58%
6.71%
9.68%
11.99%
12.98%
13.05%
13.79%
WACC
10.05%
9.88%
9.75%
9.76%
9.72%
11.12%
12.72%
13.86%
14.47%
15.81%
Firm Value (G)
$3,577
$3,639
$3,690
$3,686
$3,703
$3,218
$2,799
$2,562
$2,450
$2,236
72
Embraer: Restructured ($)
Reinvestment Rate
40.00%
Current Cashflow to Firm
EBIT(1-t) :
$ 404
- Nt CpX
23
- Chg WC
9
= FCFF
$ 372
Reinvestment Rate = 32/404= 7.9%
Return on Capital
20%
Stable Growth
g = 4.17%; Beta = 1.00;
Country Premium= 5%
Cost of capital = 7.87%
ROC= 7.87%; Tax rate=34%
Reinvestment Rate=g/ROC
=4.17/7.87= 52.99%
Expected Growth
in EBIT (1-t)
.40*.20=.08
8.00 %
Terminal Value5= 291/(.0876-.0417) = 7855
$ Cashflows
Op. Assets $ 6,096
+ Cash:
795
- Debt
717
- Minor. Int.
12
=Equity
6,196
-Options
28
Value/Share $8.66
R$ 25.21
Year
EBIT(1-t)
- Reinvestment
= FCFF
1
436
174
262
3
509
204
305
4
549
219
330
Term Yr
618
- 327
= 291
5
593
237
356
Discount at$ Cost of Capital (WACC) = 11.72% (.60) + 6.71% (0.40) = 9.72%
Cost of Equity
11.72 %
Riskfree Rate :
$ Riskfree Rate= 4.17%
On October 6, 2003
Embraer Price = R$15
Cost of Debt
(4.17%+2%+4%)(1-.34)
= 6.71%
+
Beta
1.37
Unlevered Beta for
Sectors: 0.95
Aswath Damodaran
2
471
188
283
X
Weights
E = 60% D = 40%
Mature market
premium
4%
Firm’s D/E
Ratio: 19%
+
Lambda
0.27
X
Country Equity Risk
Premium
7.67%
Country Default
Spread
6.01%
X
Rel Equity
Mkt Vol
1.28
73
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 Embraer = 25.21 Reais per share - 21.75 Reais per share = 3.46
Reais per share

Implications:
•
•
•
Aswath Damodaran
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 21.75 and 25.21,
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.
74
Minority Discounts and Voting Shares


Assume that a firm has a value of $ 100 million run by incumbent managers and $ 150
million run optimally.
Proposition 1: The market price will reflect the expected value of control
•
•
The firm has 10 million voting shares outstanding.
Since the potential for changing management is created by this offering, the value per share
will fall between $10 and $15, depending upon the probability that is attached to the
management change. Thus, if the probability of the management change is 60%, the value per
share will be $13.00.
Value/Share = (150*.6+100*.4)/10 = $13

Proposition 2: If you have shares with different voting rights, the voting shares will get
a disproportionate share of the value of control…

Proposition 3: The value of a minority interest (49%) of a private business will be
significantly lower then the value of a majority stake in the same business if control has
value.
Aswath Damodaran
75
8. 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
76
Current
Revenue
$ 3,804
Current
Margin:
-49.82%
Stable Growth
Cap ex growth slows
and net cap ex
decreases
EBIT
-1895m
Revenue
Growth:
13.33%
NOL:
2,076m
Stable
Revenue
Growth: 5%
EBITDA/Sales
-> 30%
Stable
EBITDA/
Sales
30%
Stable
ROC=7.36%
Reinvest
67.93%
Terminal Value= 677(.0736-.05)
=$ 28,683
Value of Op Assets $ 5,530
+ Cash & Non-op
$ 2,260
= Value of Firm
$ 7,790
- Value of Debt
$ 4,923
= Value of Equity
$ 2867
- Equity Options
$
14
Value per share
$ 3.22
Revenues
EBITDA
EBIT
EBIT (1-t)
+ Depreciation
- Cap Ex
- Chg WC
FCFF
$3,804
($95)
($1,675)
($1,675)
$1,580
$3,431
$0
($3,526)
1
$5,326
$0
($1,738)
($1,738)
$1,738
$1,716
$46
($1,761)
2
$6,923
$346
($1,565)
($1,565)
$1,911
$1,201
$48
($903)
3
$8,308
$831
($1,272)
($1,272)
$2,102
$1,261
$42
($472)
4
$9,139
$1,371
$320
$320
$1,051
$1,324
$25
$22
5
$10,053 $11,058 $11,942 $12,659 $13,292
$1,809 $2,322 $2,508 $3,038 $3,589
$1,074 $1,550 $1,697 $2,186 $2,694
$1,074 $1,550 $1,697 $2,186 $2,276
$736
$773
$811
$852
$894
$1,390 $1,460 $1,533 $1,609 $1,690
$27
$30
$27
$21
$19
$392
$832
$949
$1,407 $1,461
6
7
8
9
10
Beta
Cos t of Equity
Cos t of Debt
Debt Ratio
Cos t of Capital
3.00
16.80%
12.80%
74.91%
13.80%
3.00
16.80%
12.80%
74.91%
13.80%
3.00
16.80%
12.80%
74.91%
13.80%
3.00
16.80%
12.80%
74.91%
13.80%
3.00
16.80%
12.80%
74.91%
13.80%
2.60
15.20%
11.84%
67.93%
12.92%
Cost of Equity
16.80%
Cost of Debt
4.8%+8.0%=12.8%
Tax rate = 0% -> 35%
Riskfree Rate :
T. Bond rate = 4.8%
+
Beta
3.00> 1.10
Internet/
Retail
Aswath Damodaran
2.20
13.60%
10.88%
60.95%
11.94%
Operating
Leverage
X
1.80
12.00%
9.92%
53.96%
10.88%
1.40
10.40%
8.96%
46.98%
9.72%
Forever
1.00
8.80%
6.76%
40.00%
7.98%
Weights
Debt= 74.91% -> 40%
Global Crossing
November 2001
Stock price = $1.86
Risk Premium
4%
Current
D/E: 441%
Term. Year
$13,902
$ 4,187
$ 3,248
$ 2,111
$ 939
$ 2,353
$ 20
$ 677
Base Equity
Premium
Country Risk
Premium
77
Valuing Global Crossing with Distress


Probability of distress
•
Price of 8 year,t=12%
bond issued by
Global Crossing =8 $ 653
8
t
•
•
Probability of distress = 13.53% a year
Cumulative probability of survival over 10 years = (1- .1353)10 = 23.37%

Distress sale value of equity
•
•
•
•

120(1  Distress) 1000(1   Distress)

t
(1.05)
(1.05) 8
t=1
653 = 
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
•
Aswath Damodaran
Value of Global Crossing = $3.22 (.2337) + $0.00 (.7663) = $0.75
78
9. 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:
•
•
Aswath Damodaran
How do options granted in the past affect equity value per share today?
How do expected future option grants affect equity value today?
79
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 accoutning 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
•
•
•
Aswath Damodaran
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.
80
10. 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
•
•
•
•
•
Aswath Damodaran
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.
81
Empirical Evidence on Illiquidity Discounts: Restricted
Stock

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. Restricted securities trade at significant
discounts on publicly traded shares in the same company.
•
•
•
Aswath Damodaran
Maher examined restricted stock purchases made by four mutual funds in the
period 1969-73 and concluded that they traded an average discount of 35.43% on
publicly traded stock in the same companies.
Moroney reported a mean discount of 35% for acquisitions of 146 restricted stock
issues by 10 investment companies, using data from 1970.
In a recent study of this phenomenon, Silber finds that the median discount for
restricted stock is 33.75%.
82
An Alternate Approach to the Illiquidity Discount: Bid Ask
Spread


The bid ask spread is the difference between the price at which you can buy a
security and the price at which you can sell it, at the same point. In other
words, it is the illiqudity discount on a publicly traded stock.
Studies have tied the bid-ask spread to
•
•
•

the size of the firm
the trading volume on the stock
the degree
Regressing the bid-ask spread against variables that can be measured for a
private firm (such as revenues, cash flow generating capacity, type of assets,
variance in operating income) and are also available for publicly traded firms
offers promise.
Aswath Damodaran
83
A Bid-Ask Spread Regression
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)

You could plug in the values for a private firm into this regression (with zero trading
volume) and estimate the spread for the firm.

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
84
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Aswath Damodaran
85