Relative Valuation. Aswath Damodaran. What is 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,
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Aswath Damodaran
“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”
Exportfolio manager
PE = Market Price per Share / Earnings per Share
is sometimes the average price for the 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
Median PE
Japan = 23.45
US = 23.21
Europe = 18.79
Em. Mkts = 16.18
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
E/P = 2.10% + 0.744 T.Bond Rate  0.327 (T.Bond RateT.Bill Rate) (2.44) (6.64) (1.34)
R squared = 51.35%
Dependent variable is: PE
R squared = 66.2% R squared (adjusted) = 63.1%
Variable Coefficient SE tratio 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
Predicted PE =
Time Period Value of extra 1% of growth Equity Risk Premium
January 2006 1.131 4.08%
January 2005 0.914 3.65%
January 2004 0.812 3.69%
July 2003 1.228 3.88%
January 2003 2.621 4.10%
July 2002 0.859 4.35%
January 2002 1.003 3.62%
July 2001 1.251 3.05%
January 2001 1.457 2.75%
July 2000 1.761 2.20%
January 2000 2.105 2.05%
Value/FCFF = (Market Value of Equity + Market Value of DebtCash)
EBIT (1t)  (Cap Ex  Deprecn)  Chg in WC
ö
5
(1.15)
ç
(1.15)
1

è
ø
5
V
(1.105)5
(1.15)
(1.05)
0
=
+
5
FCFF
.105

.15
(.10

.05)(1.105)
0
Illustration: Using Value/FCFF Approaches to value a firm: MCI Communications=
3
1
.
2
8
Free Cash Flow to the Firm
= EBIT (1t)  Net Cap Ex  Change in Working Capital
= 3356 (1  0.36) + 1100  2500  250 = $ 498 million
$ Value Correct Multiple
FCFF $498 31.28382355
EBIT (1t) $2,148 7.251163362
EBIT $ 3,356 4.640744552
EBITDA $4,456 3.49513885
1. The multiple can be computed even for firms that are reporting net losses, since earnings before interest, taxes and depreciation are usually positive.
2. For firms in certain industries, such as cellular, which require a substantial investment in infrastructure and long gestation periods, this multiple seems to be more appropriate than the price/earnings ratio.
3. In leveraged buyouts, where the key factor is cash generated by the firm prior to all discretionary expenditures, the EBITDA is the measure of cash flows from operations that can be used to support debt payment at least in the short term.
4. By looking at cashflows prior to capital expenditures, it may provide a better estimate of “optimal value”, especially if the capital expenditures are unwise or earn substandard returns.
5. By looking at the value of the firm and cashflows to the firm it allows for comparisons across firms with different financial leverage.
FCFF = EBIT (1t)  (Cex  Depr)  Working Capital
= (EBITDA  Depr) (1t)  (Cex  Depr)  Working Capital
= EBITDA (1t) + Depr (t)  Cex  Working Capital
Book Value of Equity
PBV = 0.81 + 5.32 (ROE) R2 = 46%
Total Revenues
PS = .39 + 0.6548 (Net Margin) R2 = 43.5%
PS = 81.36  7.54(Net Margin) R2 = 0.04
(0.49)
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.
(The cost of capital for Global Crossing is 13.80%)
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 VEBITDA Firms in sector have losses in early years and reported earnings can vary
depending on depreciation method
REITa P/CF Generally no cap ex investments
from equity earnings
Financial Services PBV Book value often marked to market
Retailing PS If leverage is similar across firms
VS If leverage is different
Aswath Damodaran
A bad investment………………….. Becomes a good one..
1. Learn at relatively low cost
2. Make better decisions based on learning
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
Net Payoff on
Extraction
Cost of Developing
Reserve
Value of estimated reserve of natural resource
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
Value of call = S N (d1)  K ert N(d2)
where,
PV of Cash Flows from Introducing the Drug Now = S = $ 3.422 billion
PV of Cost of Developing Drug for Commercial Use = K = $ 2.875 billion
Patent Life = t = 17 years Riskless Rate = r = 6.7% (17year T.Bond rate)
Variance in Expected Present Values =s2 = 0.224 (Industry average firm variance for biotech firms)
Expected Cost of Delay = y = 1/17 = 5.89%
d1 = 1.1362 N(d1) = 0.8720
d2 = 0.8512 N(d2) = 0.2076
Call Value= 3,422 exp(0.0589)(17) (0.8720)  2,875 (exp(0.067)(17) (0.2076)= $ 907 million
d1 = 1.0359 N(d1) = 0.8498
d2 = 0.2613 N(d2) = 0.6030
Value of oil company = Value of developed reserves (DCF valuation)
+ Value of undeveloped reserves (Valued as option)
Call Value= $ 234 Million
Debt Type Face Value Duration
Short term 935 0.50
10 year 2435 6.7
20 year 3555 12.6
Longer 1940 18.2
Total £8,865 mil 10.93 years
= (0.15)2 (0.41)2 + (0.85)2 (0.17)2 + 2 (0.15) (0.85)(0.5)(0.41)(0.17)= 0.0335
d1 = 0.8337 N(d1) = 0.2023
d2 = 1.4392 N(d2) = 0.0751