Aswath Damodaran 1

Valuation: Packet 3
Real Options, Acquisition Valuation
and Value Enhancement
Aswath Damodaran
Updated: January 2012
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Real Options: Fact and Fantasy
Aswath Damodaran
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Underlying Theme: Searching for an Elusive Premium
!# Traditional discounted cashow 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 (exibility)
# 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 cashow value estimates.
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A bad investment
+100
-120
1/2
1/2
Today
Success
Failure
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Becomes a good one
+20
-20
1/3
2/3
+80
-100
2/3
1/3
STOP
Now
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Three Basic Questions
!# When is there a real option embedded in a decision or an asset?
!# When does that real option have signicant economic value?
!# Can that value be estimated using an option pricing model?
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When is there an option embedded in an action?
!# An option provides the holder with the right to buy or sell a specied
quantity of an underlying asset at a xed price (called a strike price or
an exercise price) at or before the expiration date of the option.
!# There has to be a clearly dened underlying asset whose value changes
over time in unpredictable ways.
!# The payoffs on this asset (real option) have to be contingent on an
specied event occurring within a nite period.
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Payoff Diagram on a Call
Price of underlying asset
Strike

Price
Net Payoff
on Call

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Payoff Diagram on Put Option
Price of underlying asset
Strike
Price

Net Payoff
On Put

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When does the option have signicant economic
value?
!# For an option to have signicant 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.
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Determinants of option value
!# Variables Relating to Underlying Asset
# Value of Underlying Asset; as this value increases, the right to buy at a xed price
(calls) will become more valuable and the right to sell at a xed 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 xed price becomes more (less)
valuable at a lower price.
# Life of the Option; both calls and puts benet from a longer life.
!# Level of Interest Rates; as rates increase, the right to buy (sell) at a xed price
in the future becomes more (less) valuable.
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When can you use option pricing models to value real
options?
!# The notion of a replicating portfolio that drives option pricing models
makes them most suited for valuing real options where
# The underlying asset is traded - this yield not only observable prices and volatility
as inputs to option pricing models but allows for the possibility of creating
replicating portfolios
# An active marketplace exists for the option itself.
# The cost of exercising the option is known with some degree of certainty.
!# When option pricing models are used to value real assets, we have to
accept the fact that
# The value estimates that emerge will be far more imprecise.
# The value can deviate much more dramatically from market price because of the
difculty of arbitrage.
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Creating a replicating portfolio
!# The objective in creating a replicating portfolio is to use a combination
of riskfree borrowing/lending and the underlying asset to create the
same cashows as the option being valued.
# Call = Borrowing + Buying ! of the Underlying Stock
# Put = Selling Short ! on Underlying Asset + Lending
# The number of shares bought or sold is called the option delta.
!# The principles of arbitrage then apply, and the value of the option has
to be equal to the value of the replicating portfolio.
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The Binomial Option Pricing Model
50
70
35
100
50
25
K = $ 40
t = 2
r = 11%
Option Details
Stock
Price
Call
60
10
0
50 D - 1.11 B = 10
25 D - 1.11 B = 0
D = 0.4, B = 9.01
Call = 0.4 * 35 - 9.01 = 4.99
Call = 4.99
100 D - 1.11 B = 60
50 D - 1.11 B = 10
D = 1, B = 36.04
Call = 1 * 70 - 36.04 = 33.96
Call = 33.96
70 D - 1.11 B = 33.96
35 D - 1.11 B = 4.99
D = 0.8278, B = 21.61
Call = 0.8278 * 50 - 21.61 = 19.42
Call = 19.42
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The Limiting Distributions.
!# As the time interval is shortened, the limiting distribution, as t -> 0,
can take one of two forms.
# If as t -> 0, price changes become smaller, the limiting distribution is the normal
distribution and the price process is a continuous one.
# If as t->0, price changes remain large, the limiting distribution is the poisson
distribution, i.e., a distribution that allows for price jumps.
!# The Black-Scholes model applies when the limiting distribution is
the normal distribution , and explicitly assumes that the price
process is continuous and that there are no jumps in asset prices.
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Black and Scholes
!# The version of the model presented by Black and Scholes was
designed to value European options, which were dividend-protected.
!# The value of a call option in the Black-Scholes model can be written
as a function of the following variables:
S = Current value of the underlying asset
K = Strike price of the option
t = Life to expiration of the option
r = Riskless interest rate corresponding to the life of the option
"
2
= Variance in the ln(value) of the underlying asset
Aswath Damodaran 17
The Black Scholes Model
Value of call = S N (d
1
) - K e
-rt
N(d
2
)
where,

# d
2
= d
1
- " "t
!# The replicating portfolio is embedded in the Black-Scholes model. To
replicate this call, you would need to
# Buy N(d1) shares of stock; N(d1) is called the option delta
# Borrow K e
-rt
N(d
2
)
d
1
=
ln
S
K
!
"
#
$
+ (r +
%
2
2
) t
% t
Aswath Damodaran 18
The Normal Distribution
d N(d) d N(d) d N(d)
-3.00 0.0013 -1.00 0.1587 1.05 0.8531
-2.95 0.0016 -0.95 0.1711 1.10 0.8643
-2.90 0.0019 -0.90 0.1841 1.15 0.8749
-2.85 0.0022 -0.85 0.1977 1.20 0.8849
-2.80 0.0026 -0.80 0.2119 1.25 0.8944
-2.75 0.0030 -0.75 0.2266 1.30 0.9032
-2.70 0.0035 -0.70 0.2420 1.35 0.9115
-2.65 0.0040 -0.65 0.2578 1.40 0.9192
-2.60 0.0047 -0.60 0.2743 1.45 0.9265
-2.55 0.0054 -0.55 0.2912 1.50 0.9332
-2.50 0.0062 -0.50 0.3085 1.55 0.9394
-2.45 0.0071 -0.45 0.3264 1.60 0.9452
-2.40 0.0082 -0.40 0.3446 1.65 0.9505
-2.35 0.0094 -0.35 0.3632 1.70 0.9554
-2.30 0.0107 -0.30 0.3821 1.75 0.9599
-2.25 0.0122 -0.25 0.4013 1.80 0.9641
-2.20 0.0139 -0.20 0.4207 1.85 0.9678
-2.15 0.0158 -0.15 0.4404 1.90 0.9713
-2.10 0.0179 -0.10 0.4602 1.95 0.9744
-2.05 0.0202 -0.05 0.4801 2.00 0.9772
-2.00 0.0228 0.00 0.5000 2.05 0.9798
-1.95 0.0256 0.05 0.5199 2.10 0.9821
-1.90 0.0287 0.10 0.5398 2.15 0.9842
-1.85 0.0322 0.15 0.5596 2.20 0.9861
-1.80 0.0359 0.20 0.5793 2.25 0.9878
-1.75 0.0401 0.25 0.5987 2.30 0.9893
-1.70 0.0446 0.30 0.6179 2.35 0.9906
-1.65 0.0495 0.35 0.6368 2.40 0.9918
-1.60 0.0548 0.40 0.6554 2.45 0.9929
-1.55 0.0606 0.45 0.6736 2.50 0.9938
-1.50 0.0668 0.50 0.6915 2.55 0.9946
-1.45 0.0735 0.55 0.7088 2.60 0.9953
-1.40 0.0808 0.60 0.7257 2.65 0.9960
-1.35 0.0885 0.65 0.7422 2.70 0.9965
-1.30 0.0968 0.70 0.7580 2.75 0.9970
-1.25 0.1056 0.75 0.7734 2.80 0.9974
-1.20 0.1151 0.80 0.7881 2.85 0.9978
-1.15 0.1251 0.85 0.8023 2.90 0.9981
-1.10 0.1357 0.90 0.8159 2.95 0.9984
-1.05 0.1469 0.95 0.8289 3.00 0.9987
-1.00 0.1587 1.00 0.8413
d
1
N(d
1
)
Aswath Damodaran 19
Adjusting for Dividends
!# If the dividend yield (y = dividends/ Current value of the asset) of the
underlying asset is expected to remain unchanged during the life of the
option, the Black-Scholes model can be modied to take dividends
into account.
C = S e
-yt
N(d
1
) - K e
-rt
N(d
2
)
where,



d
2
= d
1
- " "t
!# The value of a put can also be derived:
P = K e
-rt
(1-N(d
2
)) - S e
-yt
(1-N(d
1
))

d
1
=
ln
S
K
!
"
#
$
+ (r - y +
%
2
2
) t
% t
Aswath Damodaran 20
Choice of Option Pricing Models
!# Most practitioners who use option pricing models to value real options
argue for the binomial model over the Black-Scholes and justify this
choice by noting that
# Early exercise is the rule rather than the exception with real options
# Underlying asset values are generally discontinous.
!# If you can develop a binomial tree with outcomes at each node, it
looks a great deal like a decision tree from capital budgeting. The
question then becomes when and why the two approaches yield
different estimates of value.
Aswath Damodaran 21
The Decision Tree Alternative
!# Traditional decision tree analysis tends to use
# One cost of capital to discount cashows in each branch to the present
# Probabilities to compute an expected value
# These values will generally be different from option pricing model values
!# If you modied decision tree analysis to
# Use different discount rates at each node to reect where you are in the decision
tree (This is the Copeland solution) (or)
# Use the riskfree rate to discount cashows in each branch, estimate the
probabilities to estimate an expected value and adjust the expected value for the
market risk in the investment
Decision Trees could yield the same values as option pricing models
Aswath Damodaran 22
A decision tree valuation of a pharmaceutical company with
one drug in the FDA pipeline
Test
Abandon
Succeed
70%
Fail
30%
-$50
-$140.91
Types 1 & 2
Type 2
Type 1
Fail
10%
10%
30%
Develop
Abandon
Develop
Abandon
Develop
Abandon
Succeed
Succeed
Succeed
Fail
Fail
Fail
75%
25%
80%
20%
80%
20%
-$328.74
-$328.74
-$328.74
$585.62
-$328.74
-$97.43
-$366.30
-$366.30
$887.05
50%
$50.36
$93.37
$573.71
-$143.69
$402.75
Aswath Damodaran 23
Key Tests for Real Options
!# Is there an option embedded in this asset/ decision?
# Can you identify the underlying asset?
# Can you specify the contigency under which you will get payoff?
!# Is there exclusivity?
# If yes, there is option value.
# If no, there is none.
# If in between, you have to scale value.
!# Can you use an option pricing model to value the real option?
# Is the underlying asset traded?
# Can the option be bought and sold?
# Is the cost of exercising the option known and clear?
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Option Pricing Applications in Investment/Strategic
Analysis
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Options in Projects/Investments/Acquisitions
!# One of the limitations of traditional investment analysis is that it is
static and does not do a good job of capturing the options embedded in
investment.
# The rst of these options is the option to delay taking a investment, when a rm has
exclusive rights to it, until a later date.
# The second of these options is taking one investment may allow us to take
advantage of other opportunities (investments) in the future
# The last option that is embedded in projects is the option to abandon a investment,
if the cash ows do not measure up.
!# These options all add value to projects and may make a bad
investment (from traditional analysis) into a good one.
Aswath Damodaran 26
The Option to Delay
!# When a rm has exclusive rights to a project or product for a specic
period, it can delay taking this project or product until a later date.
!# A traditional investment analysis just answers the question of whether
the project is a good one if taken today.
!# Thus, the fact that a project does not pass muster today (because its
NPV is negative, or its IRR is less than its hurdle rate) does not mean
that the rights to this project are not valuable.
Aswath Damodaran 27
Valuing the Option to Delay a Project
Present Value of Expected
Cash Flows on Product
PV of Cash Flows
from Project
Initial Investment in
Project
Project has negative

NPV in this section
Project's NPV turns

positive in this section
Aswath Damodaran 28
Example 1: Valuing product patents as options
!# A product patent provides the rm with the right to develop the
product and market it.
!# It will do so only if the present value of the expected cash ows from
the product sales exceed the cost of development.
!# If this does not occur, the rm can shelve the patent and not incur any
further costs.
!# If I is the present value of the costs of developing the product, and V is
the present value of the expected cashows from development, the
payoffs from owning a product patent can be written as:
Payoff from owning a product patent = V - I if V> I
= 0 if V # I
Aswath Damodaran 29
Payoff on Product Option
Present Value of
cashows on product
Net Payoff to
introduction
Cost of product
introduction
Aswath Damodaran 30
Obtaining Inputs for Patent Valuation
Input Estimation Process
1. Value of the Underlying Asset Present Value of Cash Inflows from taking project
now
This will be noisy, but that adds value.
2. Variance in value of underlying asset Variance in cash flows of similar assets or firms
Variance in present value from capital budgeting
simulation.
3. Exercise Price on Option Option is exercised when investment is made.
Cost of making investment on the project ; assumed
to be constant in present value dollars.
4. Expiration of the Option Life of the patent
5. Dividend Yield Cost of delay
Each year of delay translates into one less year of
value-creating cashflows
Annual cost of delay =
1
n
Aswath Damodaran 31
Valuing a Product Patent: Avonex
!# Biogen, a bio-technology rm, has a patent on Avonex, a drug to treat
multiple sclerosis, for the next 17 years, and it plans to produce and
sell the drug by itself. The key inputs on the drug are as follows:
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% (17-year T.Bond rate)
Variance in Expected Present Values ="
2
= 0.224 (Industry average rm variance for
bio-tech rms)
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
Aswath Damodaran 32
The Optimal Time to Exercise
Patent value versus Net Present value
0
100
200
300
400
500
600
700
800
900
1000
17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Number of years left on patent
V
a
l
u
e
Value of patent as option Net present value of patent
Exercise the option here: Convert patent to commercial product
Aswath Damodaran 33
Valuing a rm with patents
!# The value of a rm with a substantial number of patents can be derived
using the option pricing model.
Value of Firm = Value of commercial products (using DCF value
+ Value of existing patents (using option pricing)
+ (Value of New patents that will be obtained in the
future Cost of obtaining these patents)
!# The last input measures the efciency of the rm in converting its
R&D into commercial products. If we assume that a rm earns its cost
of capital from research, this term will become zero.
!# If we use this approach, we should be careful not to double count and
allow for a high growth rate in cash ows (in the DCF valuation).
Aswath Damodaran 34
Value of Biogens existing products
# Biogen had two commercial products (a drug to treat Hepatitis B and
Intron) at the time of this valuation that it had licensed to other
pharmaceutical rms.
# The license fees on these products were expected to generate $ 50
million in after-tax cash ows each year for the next 12 years. To
value these cash ows, which were guaranteed contractually, the pre-
tax cost of debt of the guarantors was used:
Present Value of License Fees = $ 50 million (1 (1.07)
-12
)/.07
= $ 397.13 million
Aswath Damodaran 35
Value of Biogens Future R&D
# Biogen continued to fund research into new products, spending about
$ 100 million on R&D in the most recent year. These R&D expenses
were expected to grow 20% a year for the next 10 years, and 5%
thereafter.
# It was assumed that every dollar invested in research would create $
1.25 in value in patents (valued using the option pricing model
described above) for the next 10 years, and break even after that (i.e.,
generate $ 1 in patent value for every $ 1 invested in R&D).
# There was a signicant amount of risk associated with this component
and the cost of capital was estimated to be 15%.
Aswath Damodaran 36
Value of Future R&D
Yr Value of R&D Cost Excess Value Present Value
Patents (at 15%)
1 $ 150.00 $ 120.00 $ 30.00 $ 26.09
2 $ 180.00 $ 144.00 $ 36.00 $ 27.22
3 $ 216.00 $ 172.80 $ 43.20 $ 28.40
4 $ 259.20 $ 207.36 $ 51.84 $ 29.64
5 $ 311.04 $ 248.83 $ 62.21 $ 30.93
6 $ 373.25 $ 298.60 $ 74.65 $ 32.27
7 $ 447.90 $ 358.32 $ 89.58 $ 33.68
8 $ 537.48 $ 429.98 $ 107.50 $ 35.14
9 $ 644.97 $ 515.98 $ 128.99 $ 36.67
10 $ 773.97 $ 619.17 $ 154.79 $ 38.26
$ 318.30
Aswath Damodaran 37
Value of Biogen
!# The value of Biogen as a rm is the sum of all three components the
present value of cash ows from existing products, the value of
Avonex (as an option) and the value created by new research:
Value = Existing products + Existing Patents + Value: Future R&D
= $ 397.13 million + $ 907 million + $ 318.30 million
= $1622.43 million
!# Since Biogen had no debt outstanding, this value was divided by the
number of shares outstanding (35.50 million) to arrive at a value per
share:
Value per share = $ 1,622.43 million / 35.5 = $ 45.70
Aswath Damodaran 38
The Real Options Test: Patents and Technology
!# The Option Test:
# Underlying Asset: Product that would be generated by the patent
# Contingency:
If PV of CFs from development > Cost of development: PV - Cost
If PV of CFs from development < Cost of development: 0
!# The Exclusivity Test:
# Patents restrict competitors from developing similar products
# Patents do not restrict competitors from developing other products to treat the same
disease.
!# The Pricing Test
# Underlying Asset: Patents are not traded. Not only do you therefore have to estimate the present values and
volatilities yourself, you cannot construct replicating positions or do arbitrage.
# Option: Patents are bought and sold, though not as frequently as oil reserves or mines.
# Cost of Exercising the Option: This is the cost of converting the patent for commercial production. Here,
experience does help and drug rms can make fairly precise estimates of the cost.
!# Conclusion: You can estimate the value of the real option but the quality of your estimate will be a
direct function of the quality of your capital budgeting. It works best if you are valuing a publicly
traded rm that generates most of its value from one or a few patents - you can use the market value
of the rm and the variance in that value then in your option pricing model.
Aswath Damodaran 39
Example 2: Valuing Natural Resource Options
!# In a natural resource investment, the underlying asset is the resource
and the value of the asset is based upon two variables - the quantity of
the resource that is available in the investment and the price of the
resource.
!# In most such investments, there is a cost associated with developing
the resource, and the difference between the value of the asset
extracted and the cost of the development is the prot to the owner of
the resource.
!# Dening the cost of development as X, and the estimated value of the
resource as V, the potential payoffs on a natural resource option can be
written as follows:
Payoff on natural resource investment = V - X if V > X
= 0 if V# X
Aswath Damodaran 40
Payoff Diagram on Natural Resource Firms
Value of estimated reserve
of natural resource
Net Payoff on
Extraction
Cost of Developing
Reserve
Aswath Damodaran 41
Estimating Inputs for Natural Resource Options
Input Estimation Process
1. Value of Available Reserves of the Resource Expert estimates (Geologists for oil..); The
present value of the after-tax cash flows from
the resource are then estimated.
2. Cost of Developing Reserve (Strike Price) Past costs and the specifics of the investment
3. Time to Expiration Relinqushment Period: if asset has to be
relinquished at a point in time.
Time to exhaust inventory - based upon
inventory and capacity output.
4. Variance in value of underlying asset based upon variability of the price of the
resources and variability of available reserves.
5. Net Production Revenue (Dividend Yield) Net production revenue every year as percent
of market value.
6. Development Lag Calculate present value of reserve based upon
the lag.
Aswath Damodaran 42
Valuing an Oil Reserve
!# Consider an offshore oil property with an estimated oil reserve of 50
million barrels of oil, where the present value of the development cost
is $12 per barrel and the development lag is two years.
!# The rm has the rights to exploit this reserve for the next twenty years
and the marginal value per barrel of oil is $12 per barrel currently
(Price per barrel - marginal cost per barrel).
!# Once developed, the net production revenue each year will be 5% of
the value of the reserves.
!# The riskless rate is 8% and the variance in ln(oil prices) is 0.03.
Aswath Damodaran 43
Inputs to Option Pricing Model
!# Current Value of the asset = S = Value of the developed reserve
discounted back the length of the development lag at the dividend
yield = $12 * 50 /(1.05)
2
= $ 544.22
(If development is started today, the oil will not be available for sale until two years
from now. The estimated opportunity cost of this delay is the lost production
revenue over the delay period. Hence, the discounting of the reserve back at the
dividend yield)
!# Exercise Price = Present Value of development cost = $12 * 50 = $600
million
!# Time to expiration on the option = 20 years
!# Variance in the value of the underlying asset = 0.03
!# Riskless rate =8%
!# Dividend Yield = Net production revenue / Value of reserve = 5%
Aswath Damodaran 44
Valuing the Option
!# Based upon these inputs, the Black-Scholes model provides the
following value for the call:
d1 = 1.0359 N(d1) = 0.8498
d2 = 0.2613 N(d2) = 0.6030
!# Call Value= 544 .22 exp
(-0.05)(20)
(0.8498) -600 (exp
(-0.08)(20)
(0.6030)= $
97.08 million
!# This oil reserve, though not viable at current prices, still is a valuable
property because of its potential to create value if oil prices go up.
Aswath Damodaran 45
Extending the option pricing approach to value natural
resource rms
!# Since the assets owned by a natural resource rm can be viewed
primarily as options, the rm itself can be valued using option
pricing models.
!# The preferred approach would be to consider each option separately,
value it and cumulate the values of the options to get the rm value.
!# Since this information is likely to be difcult to obtain for large
natural resource rms, such as oil companies, which own hundreds of
such assets, a variant is to value the entire rm as one option.
!# A purist would probably disagree, arguing that valuing an option on a
portfolio of assets (as in this approach) will provide a lower value
than valuing a portfolio of options (which is what the natural
resource rm really own). Nevertheless, the value obtained from the
model still provides an interesting perspective on the determinants of
the value of natural resource rms.
Aswath Damodaran 46
Valuing Gulf Oil
!# Gulf Oil was the target of a takeover in early 1984 at $70 per share (It
had 165.30 million shares outstanding, and total debt of $9.9 billion).
# It had estimated reserves of 3038 million barrels of oil and the average cost of
developing these reserves was estimated to be $10 a barrel in present value dollars
(The development lag is approximately two years).
# The average relinquishment life of the reserves is 12 years.
# The price of oil was $22.38 per barrel, and the production cost, taxes and royalties
were estimated at $7 per barrel.
# The bond rate at the time of the analysis was 9.00%.
# Gulf was expected to have net production revenues each year of approximately 5%
of the value of the developed reserves. The variance in oil prices is 0.03.
Aswath Damodaran 47
Valuing Undeveloped Reserves
!# Inputs for valuing undeveloped reserves
# Value of underlying asset = Value of estimated reserves discounted back for period
of development lag= 3038 * ($ 22.38 - $7) / 1.05
2
= $42,380.44
# Exercise price = Estimated development cost of reserves = 3038 * $10 = $30,380
million
# Time to expiration = Average length of relinquishment option = 12 years
# Variance in value of asset = Variance in oil prices = 0.03
# Riskless interest rate = 9%
# Dividend yield = Net production revenue/ Value of developed reserves = 5%
!# Based upon these inputs, the Black-Scholes model provides the following
value for the call:
d1 = 1.6548 N(d1) = 0.9510
d2 = 1.0548 N(d2) = 0.8542
!# Call Value= 42,380.44 exp
(-0.05)(12)
(0.9510) -30,380 (exp
(-0.09)(12)
(0.8542)
= $ 13,306 million
Aswath Damodaran 48
Valuing Gulf Oil
!# In addition, Gulf Oil had free cashows to the rm from its oil and gas
production of $915 million from already developed reserves and these
cashows are likely to continue for ten years (the remaining lifetime of
developed reserves).
!# The present value of these developed reserves, discounted at the
weighted average cost of capital of 12.5%, yields:
# Value of already developed reserves = 915 (1 - 1.125
-10
)/.125 = $5065.83
!# Adding the value of the developed and undeveloped reserves
Value of undeveloped reserves = $ 13,306 million
Value of production in place = $ 5,066 million
Total value of rm = $ 18,372 million
Less Outstanding Debt = $ 9,900 million
Value of Equity = $ 8,472 million
Value per share = $ 8,472/165.3 = $51.25
Aswath Damodaran 49
Putting Natural Resource Options to the Test
!# The Option Test:
# Underlying Asset: Oil or gold in reserve
# Contingency: If value > Cost of development: Value - Dev Cost
If value < Cost of development: 0
!# The Exclusivity Test:
# Natural resource reserves are limited (at least for the short term)
# It takes time and resources to develop new reserves
!# The Option Pricing Test
# Underlying Asset: While the reserve or mine may not be traded, the commodity is.
If we assume that we know the quantity with a fair degree of certainty, you can
trade the underlying asset
# Option: Oil companies buy and sell reserves from each other regularly.
# Cost of Exercising the Option: This is the cost of developing a reserve. Given the
experience that commodity companies have with this, they can estimate this cost
with a fair degree of precision.
!# Real option pricing models work well with natural resource options.
Aswath Damodaran 50
The Option to Expand/Take Other Projects
!# Taking a project today may allow a rm to consider and take other
valuable projects in the future.
!# Thus, even though a project may have a negative NPV, it may be a
project worth taking if the option it provides the rm (to take other
projects in the future) provides a more-than-compensating value.
!# These are the options that rms often call strategic options and use
as a rationale for taking on negative NPV or even negative return
projects.
Aswath Damodaran 51
The Option to Expand
Present Value of Expected
Cash Flows on Expansion
PV of Cash Flows
from Expansion
Additional Investment
to Expand
Firm will not expand in

this section
Expansion becomes
attractive in this section
Aswath Damodaran 52
An Example of an Expansion Option
!# Ambev is considering introducing a soft drink to the U.S. market. The
drink will initially be introduced only in the metropolitan areas of the
U.S. and the cost of this limited introduction is $ 500 million.
!# A nancial analysis of the cash ows from this investment suggests
that the present value of the cash ows from this investment to Ambev
will be only $ 400 million. Thus, by itself, the new investment has a
negative NPV of $ 100 million.
!# If the initial introduction works out well, Ambev could go ahead with
a full-scale introduction to the entire market with an additional
investment of $ 1 billion any time over the next 5 years. While the
current expectation is that the cash ows from having this investment
is only $ 750 million, there is considerable uncertainty about both the
potential for the drink, leading to signicant variance in this estimate.
Aswath Damodaran 53
Valuing the Expansion Option
!# Value of the Underlying Asset (S) = PV of Cash Flows from
Expansion to entire U.S. market, if done now =$ 750 Million
!# Strike Price (K) = Cost of Expansion into entire U.S market = $ 1000
Million
!# We estimate the standard deviation in the estimate of the project value
by using the annualized standard deviation in rm value of publicly
traded rms in the beverage markets, which is approximately 34.25%.
# Standard Deviation in Underlying Assets Value = 34.25%
!# Time to expiration = Period for which expansion option applies = 5
years
Call Value= $ 234 Million
Aswath Damodaran 54
Considering the Project with Expansion Option
!# NPV of Limited Introduction = $ 400 Million - $ 500 Million
= - $ 100 Million
!# Value of Option to Expand to full market= $ 234 Million
!# NPV of Project with option to expand
= - $ 100 million + $ 234 million
= $ 134 million
!# Invest in the project
Aswath Damodaran 55
Opportunities are not Options
An Exclusive Right to
Second Investment
A Zero competitive
advantage on Second Investment
100% of option value No option value
Increasing competitive advantage/ barriers to entry
Pharmaceutical
patents
Telecom
Licenses
Brand
Name
Technological
Edge
First-
Mover
Second Investment has
zero excess returns
Second investment
has large sustainable
excess return
Option has no value Option has high value
Is the first investment necessary for the second investment?
Pre-Requisit Not necessary
Aswath Damodaran 56
The Real Options Test for Expansion Options
!# The Options Test
# Underlying Asset: Expansion Project
# Contingency
If PV of CF from expansion > Expansion Cost: PV - Expansion Cost
If PV of CF from expansion < Expansion Cost: 0
!# The Exclusivity Test
# Barriers may range from strong (exclusive licenses granted by the government) to
weaker (brand name, knowledge of the market) to weakest (rst mover).
!# The Pricing Test
# Underlying Asset: As with patents, there is no trading in the underlying asset and
you have to estimate value and volatility.
# Option: Licenses are sometimes bought and sold, but more diffuse expansion
options are not.
# Cost of Exercising the Option: Not known with any precision and may itself evolve
over time as the market evolves.
!# Using option pricing models to value expansion options will not only yield
extremely noisy estimates, but may attach inappropriate premiums to
discounted cashow estimates.
Aswath Damodaran 57
Internet Firms as Options
!# Some analysts have justied the valuation of internet rms on the basis
that you are buying the option to expand into a very large market.
What do you think of this argument?
# Is there an option to expand embedded in these rms?
# Is it a valuable option?
Aswath Damodaran 58
The Option to Abandon
!# A rm may sometimes have the option to abandon a project, if the
cash ows do not measure up to expectations.
!# If abandoning the project allows the rm to save itself from further
losses, this option can make a project more valuable.
Present Value of Expected
Cash Flows on Project
PV of Cash Flows
from Project
Cost of Abandonment
Aswath Damodaran 59
Valuing the Option to Abandon
!# Airbus is considering a joint venture with Lear Aircraft to produce a
small commercial airplane (capable of carrying 40-50 passengers on
short haul ights)
# Airbus will have to invest $ 500 million for a 50% share of the venture
# Its share of the present value of expected cash ows is 480 million.
!# Lear Aircraft, which is eager to enter into the deal, offers to buy
Airbuss 50% share of the investment anytime over the next ve years
for $ 400 million, if Airbus decides to get out of the venture.
!# A simulation of the cash ows on this time share investment yields a
variance in the present value of the cash ows from being in the
partnership is 0.16.
!# The project has a life of 30 years.
Aswath Damodaran 60
Project with Option to Abandon
!# Value of the Underlying Asset (S) = PV of Cash Flows from Project
= $ 480 million
!# Strike Price (K) = Salvage Value from Abandonment = $ 400 million
!# Variance in Underlying Assets Value = 0.16
!# Time to expiration = Life of the Project =5 years
!# Dividend Yield = 1/Life of the Project = 1/30 = 0.033 (We are
assuming that the projects present value will drop by roughly 1/n
each year into the project)
!# Assume that the ve-year riskless rate is 6%. The value of the put
option can be estimated as follows:
Aswath Damodaran 61
Should Airbus enter into the joint venture?
!# Value of Put =Ke
-rt
(1-N(d2))- Se
-yt
(1-N(d1))
=400 (exp
(-0.06)(5)
(1-0.4624) - 480 exp
(-0.033)(5)
(1-0.7882)
= $ 73.23 million
!# The value of this abandonment option has to be added on to the net
present value of the project of -$ 20 million, yielding a total net
present value with the abandonment option of $ 53.23 million.
Aswath Damodaran 62
Implications for Investment Analysis/ Valuation
!# Having a option to abandon a project can make otherwise
unacceptable projects acceptable.
!# Other things remaining equal, you would attach more value to
companies with
# More cost exibility, that is, making more of the costs of the projects into variable
costs as opposed to xed costs.
# Fewer long-term contracts/obligations with employees and customers, since these
add to the cost of abandoning a project.
!# These actions will undoubtedly cost the rm some value, but this has
to be weighed off against the increase in the value of the abandonment
option.
Aswath Damodaran 63
Option Applications in the Financing Decision
Aswath Damodaran 64
Options in Capital Structure
!# The most direct applications of option pricing in capital structure
decisions is in the design of securities. In fact, most complex nancial
instruments can be broken down into some combination of a simple
bond/common stock and a variety of options.
# If these securities are to be issued to the public, and traded, the options have to be
priced.
# If these are non-traded instruments (bank loans, for instance), they still have to be
priced into the interest rate on the instrument.
!# The other application of option pricing is in valuing exibility. Often,
rms preserve debt capacity or hold back on issuing debt because they
want to maintain exibility.
Aswath Damodaran 65
The Value of Flexibility
!# Firms maintain excess debt capacity or larger cash balances than are
warranted by current needs, to meet unexpected future requirements.
!# While maintaining this nancing exibility has value to rms, it also
has a cost; the excess debt capacity implies that the rm is giving up
some value and has a higher cost of capital.
!# The value of exibility can be analyzed using the option pricing
framework; a rm maintains large cash balances and excess debt
capacity in order to have the option to take projects that might arise in
the future.
Aswath Damodaran 66
Value of Flexibility as an Option
!# Consider a rm that has expected reinvestment needs of X each year,
with a standard deviation in that value of "
X
. These external
reinvestments include both internal projects and acquisitions.
!# Assume that the rm is limited in its capacity to raise capital, for
internal or external reasons and that it can raise L from internal cash
ows and its normal access to capital markets.
!# Excess debt capacity becomes useful if external reinvestment needs
exceed the rms internal funds.
If X > L: Excess debt capacity can be used to cover the difference and
invest in projects
If X<L: Excess debt capacity remains unused (with an associated cost)

Aswath Damodaran 67
What happens when you make the investment?
!# If the investment earns excess returns, the rms value will increase
by the present value of these excess returns over time. If we assume
that the excess return each year is constant and perpetual, the present
value of the excess returns that would be earned can be written as:
Value of investment = (ROC - Cost of capital)/ Cost of capital
!# The value of the investments that you can take because you have
excess debt capacity becomes the payoff to maintaining excess debt
capacity.
If X > L: [(ROC - Cost of capital)/ Cost of capital] New investments
If X<L: 0
Aswath Damodaran 68
The Value of Flexibility
Actual
Reinvestment
Needs
Expected
(Normal)
Reinvestment
Needs that can
be financed
without
flexibility
Cost of Maintaining Financing Flexibility
Use financing flexibility
to take unanticipated
investments (acquisitions)
Payoff: (S-K)*Excess Return/WACC
Excess Return/WACC = PV of excess returns in perpetutity
Aswath Damodaran 69
Disneys Optimal Debt Ratio
Debt Ratio Cost of Equity Cost of Debt Cost of Capital
0.00% 13.00% 4.61% 13.00%
10.00% 13.43% 4.61% 12.55%
Current:18% 13.85% 4.80% 12.22%
20.00% 13.96% 4.99% 12.17%
30.00% 14.65% 5.28% 11.84%
40.00% 15.56% 5.76% 11.64%
50.00% 16.85% 6.56% 11.70%
60.00% 18.77% 7.68% 12.11%
70.00% 21.97% 7.68% 11.97%
80.00% 28.95% 7.97% 12.17%
90.00% 52.14% 9.42% 13.69%

Aswath Damodaran 70
Inputs to Option Valuation Model- Disney
Model
input
Estimated as In general For Disney
S Expected annual
reinvestment needs (as
% of rm value)
Measures
magnitude of
reinvestment
needs
Average of
Reinvestment/
Value over last
5 years = 5.3%
"
2
Variance in annual
reinvestment needs
Measures how
much volatility
there is in
investment
needs.
Variance over
last 5 years in
ln(Reinvestment
/Value) =0.375
K (Internal + Normal
access to external
funds)/ Value
Measures the
capital
constraint
Average over
last 5 years =
4.8%
T 1 year Measures an
annual value for
exibility
T =1
Aswath Damodaran 71
Valuing Flexibility at Disney
The value of an option with these characteristics is 1.6092%. You can
consider this the value of the option to take a project, but the overall
value of exibility will still depend upon the quality of the projects
taken. In other words, the value of the option to take a project is zero if
the project has zero net present value.
!# Disney earns 18.69% on its projects has a cost of capital of 12.22%.
The excess return (annually) is 6.47%. Assuming that they can
continue to generate these excess returns in perpetuity:
Value of Flexibility (annual)= 1.6092%(.0647/.1222) = 0.85 % of value
!# Disneys cost of capital at its optimal debt ratio is 11.64%. The cost it
incurs to maintain exibility is therefore 0.58% annually
(12.22%-11.64%). It therefore pays to maintain exibility.
Aswath Damodaran 72
Determinants of the Value of Flexibility
!# Capital Constraints (External and Internal): The greater the capacity to
raise funds, either internally or externally, the less the value of
exibility.
# 1.1: Firms with signicant internal operating cash ows should value exibility
less than rms with small or negative operating cash ows.
# 1.2: Firms with easy access to nancial markets should have a lower value for
exibility than rms without that access.
!# Unpredictability of reinvestment needs: The more unpredictable the
reinvestment needs of a rm, the greater the value of exibility.
!# Capacity to earn excess returns: The greater the capacity to earn excess
returns, the greater the value of exibility.
# 1.3: Firms that do not have the capacity to earn or sustain excess returns get no
value from exibility.
Aswath Damodaran 73
Option Pricing Applications in Valuation
Equity Value in Deeply Troubled Firms
Value of Undeveloped Reserves for Natural Resource Firm
Value of Patent/License
Aswath Damodaran 74
Option Pricing Applications in Equity Valuation
!# Equity in a troubled rm (i.e. a rm with high leverage, negative
earnings and a signicant chance of bankruptcy) can be viewed as a
call option, which is the option to liquidate the rm.
!# Natural resource companies, where the undeveloped reserves can be
viewed as options on the natural resource.
!# Start-up rms or high growth rms which derive the bulk of their
value from the rights to a product or a service (eg. a patent)
Aswath Damodaran 75
Valuing Equity as an option
!# The equity in a rm is a residual claim, i.e., equity holders lay claim
to all cashows left over after other nancial claim-holders (debt,
preferred stock etc.) have been satised.
!# If a rm is liquidated, the same principle applies, with equity investors
receiving whatever is left over in the rm after all outstanding debts
and other nancial claims are paid off.
!# The principle of limited liability, however, protects equity investors
in publicly traded rms if the value of the rm is less than the value of
the outstanding debt, and they cannot lose more than their investment
in the rm.
Aswath Damodaran 76
Equity as a call option
!# The payoff to equity investors, on liquidation, can therefore be written
as:
Payoff to equity on liquidation = V - D if V > D
= 0 if V # D
where,
V = Value of the rm
D = Face Value of the outstanding debt and other external claims
!# A call option, with a strike price of K, on an asset with a current value
of S, has the following payoffs:
Payoff on exercise = S - K if S > K
= 0 if S # K
Aswath Damodaran 77
Payoff Diagram for Liquidation Option
Value of firm
Net Payoff
on Equity
Face Value
of Debt
Aswath Damodaran 78
Application to valuation: A simple example
!# Assume that you have a rm whose assets are currently valued at $100
million and that the standard deviation in this asset value is 40%.
!# Further, assume that the face value of debt is $80 million (It is zero
coupon debt with 10 years left to maturity).
!# If the ten-year treasury bond rate is 10%,
# how much is the equity worth?
# What should the interest rate on debt be?
Aswath Damodaran 79
Model Parameters
!# Value of the underlying asset = S = Value of the rm = $ 100 million
!# Exercise price = K = Face Value of outstanding debt = $ 80 million
!# Life of the option = t = Life of zero-coupon debt = 10 years
!# Variance in the value of the underlying asset = "
2
= Variance in rm
value = 0.16
!# Riskless rate = r = Treasury bond rate corresponding to option life =
10%
Aswath Damodaran 80
Valuing Equity as a Call Option
!# Based upon these inputs, the Black-Scholes model provides the
following value for the call:
# d1 = 1.5994 N(d1) = 0.9451
# d2 = 0.3345 N(d2) = 0.6310
!# Value of the call = 100 (0.9451) - 80 exp
(-0.10)(10)
(0.6310) = $75.94
million
!# Value of the outstanding debt = $100 - $75.94 = $24.06 million
!# Interest rate on debt = ($ 80 / $24.06)
1/10
-1 = 12.77%
Aswath Damodaran 81
I. The Effect of Catastrophic Drops in Value
!# Assume now that a catastrophe wipes out half the value of this rm
(the value drops to $ 50 million), while the face value of the debt
remains at $ 80 million. What will happen to the equity value of this
rm?
"# It will drop in value to $ 25.94 million [ $ 50 million - market value of
debt from previous page]
"# It will be worth nothing since debt outstanding > Firm Value
"# It will be worth more than $ 25.94 million
Aswath Damodaran 82
Valuing Equity in the Troubled Firm
!# Value of the underlying asset = S = Value of the rm = $ 50 million
!# Exercise price = K = Face Value of outstanding debt = $ 80 million
!# Life of the option = t = Life of zero-coupon debt = 10 years
!# Variance in the value of the underlying asset = "
2
= Variance in rm
value = 0.16
!# Riskless rate = r = Treasury bond rate corresponding to option life =
10%
Aswath Damodaran 83
The Value of Equity as an Option
!# Based upon these inputs, the Black-Scholes model provides the
following value for the call:
# d1 = 1.0515 N(d1) = 0.8534
# d2 = -0.2135 N(d2) = 0.4155
!# Value of the call = 50 (0.8534) - 80 exp
(-0.10)(10)
(0.4155) = $30.44
million
!# Value of the bond= $50 - $30.44 = $19.56 million
!# The equity in this rm drops by, because of the option characteristics
of equity.
!# This might explain why stock in rms, which are in Chapter 11 and
essentially bankrupt, still has value.
Aswath Damodaran 84
Equity value persists ..
Value of Equity as Firm Value Changes
0
10
20
30
40
50
60
70
80
100 90 80 70 60 50 40 30 20 10
Value of Firm ($ 80 Face Value of Debt)
V
a
l
u
e

o
f

E
q
u
i
t
y
Aswath Damodaran 85
II. The conict between stockholders and bondholders
!# Consider again the rm described in the earlier example , with a value
of assets of $100 million, a face value of zero-coupon ten-year debt of
$80 million, a standard deviation in the value of the rm of 40%. The
equity and debt in this rm were valued as follows:
# Value of Equity = $75.94 million
# Value of Debt = $24.06 million
# Value of Firm == $100 million
!# Now assume that the stockholders have the opportunity to take a
project with a negative net present value of -$2 million, but assume
that this project is a very risky project that will push up the standard
deviation in rm value to 50%. Would you invest in this project?
a)# Yes
b)# No
Aswath Damodaran 86
Valuing Equity after the Project
!# Value of the underlying asset = S = Value of the rm = $ 100 million -
$2 million = $ 98 million (The value of the rm is lowered because of
the negative net present value project)
!# Exercise price = K = Face Value of outstanding debt = $ 80 million
!# Life of the option = t = Life of zero-coupon debt = 10 years
!# Variance in the value of the underlying asset = "
2
= Variance in rm
value = 0.25
!# Riskless rate = r = Treasury bond rate corresponding to option life =
10%
Aswath Damodaran 87
Option Valuation
!# Option Pricing Results for Equity and Debt Value
# Value of Equity = $77.71
# Value of Debt = $20.29
# Value of Firm = $98.00
!# The value of equity rises from $75.94 million to $ 77.71 million ,
even though the rm value declines by $2 million. The increase in
equity value comes at the expense of bondholders, who nd their
wealth decline from $24.06 million to $20.19 million.
Aswath Damodaran 88
Effects of an Acquisition
!# Assume that you are the manager of a rm and that you buy another
rm, with a fair market value of $ 150 million, for exactly $ 150
million. In an efcient market, the stock price of your rm will
"# Increase
"# Decrease
"# Remain Unchanged
Aswath Damodaran 89
Effects on equity of a conglomerate merger
!# You are provided information on two rms, which operate in unrelated
businesses and hope to merge.
Firm A Firm B
Value of the rm $100 million $ 150 million
Face Value of Debt (10 yr zeros) $ 80 million $ 50 million
Maturity of debt 10 years 10 years
Std. Dev. in value 40 % 50 %
Correlation between cashows 0.4
The ten-year bond rate is 10%.
!# The variance in the value of the rm after the acquisition can be calculated as
follows:
Variance in combined rm value = w
1
2
"
1
2
+ w
2
2
"
2
2
+ 2 w
1
w
2
$
12
"
1
"
2

= (0.4)
2
(0.16) + (0.6)
2
(0.25) + 2 (0.4) (0.6) (0.4) (0.4) (0.5)
= 0.154
Aswath Damodaran 90
Valuing the Combined Firm
!# The values of equity and debt in the individual rms and the combined rm
can then be estimated using the option pricing model:
Firm A Firm B Combined rm
Value of equity in the rm $75.94 $134.47 $ 207.43
Value of debt in the rm $24.06 $ 15.53 $ 42.57
Value of the rm $100.00 $150.00 $ 250.00
!# The combined value of the equity prior to the merger is $ 210.41 million and it
declines to $207.43 million after.
!# The wealth of the bondholders increases by an equal amount.
!# There is a transfer of wealth from stockholders to bondholders, as a
consequence of the merger. Thus, conglomerate mergers that are not followed
by increases in leverage are likely to see this redistribution of wealth occur
across claim holders in the rm.
Aswath Damodaran 91
Obtaining option pricing inputs - Some real world
problems
!# The examples that have been used to illustrate the use of option
pricing theory to value equity have made some simplifying
assumptions. Among them are the following:
(1) There were only two claim holders in the rm - debt and equity.
(2) There is only one issue of debt outstanding and it can be retired at face value.
(3) The debt has a zero coupon and no special features (convertibility, put clauses etc.)
(4) The value of the rm and the variance in that value can be estimated.
Aswath Damodaran 92
Real World Approaches to Valuing Equity in Troubled
Firms: Getting Inputs
Input Estimation Process
Value of the Firm Cumulate market values of equity and debt (or)
Value the assets in place using FCFF and WACC (or)
Use cumulated market value of assets, if traded.
Variance in Firm Value If stocks and bonds are traded,
!
2
firm
= w
e
2
!
e
2
+ w
d
2
!
d
2
+ 2 w
e
w
d
"
ed
!
e
!
d
where !
e
2
= variance in the stock price
w
e
= MV weight of Equity
!
d
2
= the variance in the bond price w
d
= MV weight of debt
If not traded, use variances of similarly rated bonds.
Use average firm value variance from the industry in which
company operates.
Value of the Debt If the debt is short term, you can use only the face or book value
of the debt.
If the debt is long term and coupon bearing, add the cumulated
nominal value of these coupons to the face value of the debt.
Maturity of the Debt Face value weighted duration of bonds outstanding (or)
If not available, use weighted maturity
Aswath Damodaran 93
Valuing Equity as an option - Eurotunnel in early 1998
!# Eurotunnel has been a nancial disaster since its opening
# In 1997, Eurotunnel had earnings before interest and taxes of -56 million and net
income of -685 million
# At the end of 1997, its book value of equity was -117 million
!# It had 8,865 million in face value of debt outstanding
# The weighted average duration of this debt was 10.93 years
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
Aswath Damodaran 94
The Basic DCF Valuation
!# The value of the rm estimated using projected cashows to the rm,
discounted at the weighted average cost of capital was 2,312 million.
!# This was based upon the following assumptions
# Revenues will grow 5% a year in perpetuity.
# The COGS which is currently 85% of revenues will drop to 65% of revenues in yr
5 and stay at that level.
# Capital spending and depreciation will grow 5% a year in perpetuity.
# There are no working capital requirements.
# The debt ratio, which is currently 95.35%, will drop to 70% after year 5. The cost
of debt is 10% in high growth period and 8% after that.
# The beta for the stock will be 1.10 for the next ve years, and drop to 0.8 after the
next 5 years.
# The long term bond rate is 6%.
Aswath Damodaran 95
Other Inputs
!# The stock has been traded on the London Exchange, and the
annualized std deviation based upon ln (prices) is 41%.
!# There are Eurotunnel bonds, that have been traded; the annualized std
deviation in ln(price) for the bonds is 17%.
# The correlation between stock price and bond price changes has been 0.5. The
proportion of debt in the capital structure during the period (1992-1996) was 85%.
# Annualized variance in rm value
= (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
!# The 15-year bond rate is 6%. (I used a bond with a duration of roughly
11 years to match the life of my option)
Aswath Damodaran 96
Valuing Eurotunnel Equity and Debt
!# Inputs to Model
# Value of the underlying asset = S = Value of the rm = 2,312 million
# Exercise price = K = Face Value of outstanding debt = 8,865 million
# Life of the option = t = Weighted average duration of debt = 10.93 years
# Variance in the value of the underlying asset = "
2
= Variance in rm value =
0.0335
# Riskless rate = r = Treasury bond rate corresponding to option life = 6%
!# Based upon these inputs, the Black-Scholes model provides the following
value for the call:
d1 = -0.8337 N(d1) = 0.2023
d2 = -1.4392 N(d2) = 0.0751
!# Value of the call = 2312 (0.2023) - 8,865 exp
(-0.06)(10.93)
(0.0751) = 122
million
!# Appropriate interest rate on debt = (8865/2190)
(1/10.93)
-1= 13.65%
Aswath Damodaran 97
In Closing
!# There are real options everywhere.
!# Most of them have no signicant economic value because there is no
exclusivity associated with using them.
!# When options have signicant economic value, the inputs needed to
value them in a binomial model can be used in more traditional
approaches (decision trees) to yield equivalent value.
!# The real value from real options lies in
# Recognizing that building in exibility and escape hatches into large decisions has
value
# Insights we get on understanding how and why companies behave the way they do
in investment analysis and capital structure choices.
Aswath Damodaran 98
Aswath Damodaran 99
Acquirers Anonymous: Seven Steps back to Sobriety
Aswath Damodaran
Aswath Damodaran 100
Acquisitions are great for target companies but not
always for acquiring company stockholders
Aswath Damodaran 101
And the long-term follow up is not positive either..
o# Managers often argue that the market is unable to see the long term
benets of mergers that they can see at the time of the deal. If they are
right, mergers should create long term benets to acquiring rms.
o# The evidence does not support this hypothesis:
o# McKinsey and Co. has examined acquisition programs at companies on
o# Did the return on capital invested in acquisitions exceed the cost of capital?
o# Did the acquisitions help the parent companies outperform the competition?
Half of all programs failed one test, and a quarter failed both.
o# Synergy is elusive. KPMG in a more recent study of global acquisitions concludes
that most mergers (>80%) fail - the merged companies do worse than their peer
group.
o# A large number of acquisitions that are reversed within fairly short time periods.
About 20% of the acquisitions made between 1982 and 1986 were divested by
1988. In studies that have tracked acquisitions for longer time periods (ten years or
more) the divestiture rate of acquisitions rises to almost 50%.
Aswath Damodaran 102
A scary thought The disease is spreading
Indian rms acquiring US targets 1999 - 2005
Indian Acquirers: Returns around acquisition announcements
Aswath Damodaran 103
Growing through acquisitions seems to be a losers
game
!# Firms that grow through acquisitions have generally had far more
trouble creating value than rms that grow through internal
investments.
!# In general, acquiring rms tend to
# Pay too much for target rms
# Over estimate the value of synergy and control
# Have a difcult time delivering the promised benets
!# Worse still, there seems to be very little learning built into the process.
The same mistakes are made over and over again, often by the same
rms with the same advisors.
!# Conclusion: There is something structurally wrong with the process
for acquisitions which is feeding into the mistakes.
Aswath Damodaran 104
The seven sins in acquisitions
1.# Risk Transference: Attributing acquiring company risk characteristics
to the target rm.
2.# Debt subsidies: Subsiding target rm stockholders for the strengths of
the acquiring rm.
3.# Auto-pilot Control: The 20% control premium and other myth
4.# Elusive Synergy: Misidentifying and mis-valuing synergy.
5.# Its all relative: Transaction multiples, exit multiples
6.# Verdict rst, trial afterwards: Price rst, valuation to follow
7.# Its not my fault: Holding no one responsible for delivering results.
Aswath Damodaran 105
Testing sheet
Test Passed/Failed Rationalization
Risk transference
Debt subsidies
Control premium
The value of synergy
Comparables and Exit
Multiples
Bias
A successful
acquisition strategy
Aswath Damodaran 106
Lets start with a target rm
!# The target rm has the following income statement:
Revenues 100
-# Operating Expenses 80
= Operating Income 20
-# Taxes 8
= After-tax OI 12
!# Assume that this rm will generate this operating income forever (with
no growth) and that the cost of equity for this rm is 20%. The rm
has no debt outstanding. What is the value of this rm?
Aswath Damodaran 107
Test 1: Risk Transference
!# Assume that as an acquiring rm, you are in a much safer business and
have a cost of equity of 10%. What is the value of the target rm to
you?

Aswath Damodaran 108
Lesson 1: Dont transfer your risk characteristics to the
target rm
!# The cost of equity used for an investment should reect the risk of the
investment and not the risk characteristics of the investor who raised
the funds.
!# Risky businesses cannot become safe just because the buyer of these
businesses is in a safe business.
Aswath Damodaran 109
Test 2: Cheap debt?
!# Assume as an acquirer that you have access to cheap debt (at 4%) and
that you plan to fund half the acquisition with debt. How much would
you be willing to pay for the target rm?
Aswath Damodaran 110
Lesson 2: Render unto the target rm that which is the
target rms but not a penny more..
!# As an acquiring rm, it is entirely possible that you can borrow much
more than the target rm can on its own and at a much lower rate. If
you build these characteristics into the valuation of the target rm, you
are essentially transferring wealth from your rms stockholder to the
target rms stockholders.
!# When valuing a target rm, use a cost of capital that reects the debt
capacity and the cost of debt that would apply to the rm.
Aswath Damodaran 111
Test 3: Control Premiums
!# Assume that you are now told that it is conventional to pay a 20%
premium for control in acquisitions (backed up by Mergerstat). How
much would you be willing to pay for the target rm?
!# Would your answer change if I told you that you can run the target
rm better and that if you do, you will be able to generate a 30% pre-
tax operating margin (rather than the 20% margin that is currently
being earned).
!# What if the target rm were perfectly run?
Aswath Damodaran 112
Lesson 3: Beware of rules of thumb
!# Valuation is cluttered with rules of thumb. After painstakingly valuing
a target rm, using your best estimates, you will be often be told that
# It is common practice to add arbitrary premiums for brand name, quality of
management, control etc
# These premiums will be often be backed up by data, studies and services. What
they will not reveal is the enormous sampling bias in the studies and the standard
errors in the estimates.
# If you have done your valuation right, those premiums should already be
incorporated in your estimated value. Paying a premium will be double counting.
Aswath Damodaran 113
Test 4: Synergy.
!# Assume that you are told that the combined rm will be less risky than
the two individual rms and that it should have a lower cost of capital
(and a higher value). Is this likely?
!# Assume now that you are told that there are potential growth and cost
savings synergies in the acquisition. Would that increase the value of
the target rm?

!# Should you pay this as a premium?

Aswath Damodaran 114
The Value 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 Financial Synergy
Higher returns on
new investments
More new
Investments
Cost Savings in
current operations
Tax Benefits
Added Debt
Capacity
Diversification?
Higher ROC
Higher Growth
Rate
Higher Reinvestment
Higher Growth Rate
Higher Margin
Higher Base-
year EBIT
Strategic Advantages Economies of Scale
Longer Growth
Period
More sustainable
excess returns
Lower taxes on
earnings due to
- higher
depreciaiton
- operating loss
carryforwards
Higher debt
raito and lower
cost of capital
May reduce
cost of equity
for private or
closely held
firm
Aswath Damodaran 115
Valuing Synergy
(1) the rms involved in the merger are valued independently, by
discounting expected cash ows to each rm at the weighted average
cost of capital for that rm.
(2) the value of the combined rm, with no synergy, is obtained by
adding the values obtained for each rm in the rst step.
(3) The effects of synergy are built into expected growth rates and
cashows, and the combined rm is re-valued with synergy.
Value of Synergy = Value of the combined rm, with synergy - Value of
the combined rm, without synergy
Aswath Damodaran 116
Synergy: Example 1
The illusion of lower risk
!# When we estimate the cost of equity for a publicly traded rm, we
focus only on the risk that cannot be diversied away in that rm
(which is the rationale for using beta or betas to estimate the cost of
equity).
!# When two rms merge, it is true that the combined rm may be less
risky than the two rms individually, but the risk that is reduced is
rm specied risk. By denition, market risk is risk that cannot be
diversied away and the beta of the combined rm will always be a
weighted average of the betas of the two rms in the merger.
!# When does it make sense to merge to reduce total risk?
Aswath Damodaran 117
Synergy - Example 2
Higher growth and cost savings
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 118
Synergy: Example 3
Tax Benets?
!# Assume that you are Best Buys, the electronics retailer, and that you
would like to enter the hardware component of the market. You have
been approached by investment bankers for Zenith, which while still a
recognized brand name, is on its last legs nancially. The rm has net
operating losses of $ 2 billion. If your tax rate is 36%, estimate the tax
benets from this acquisition.
!# If Best Buys had only $500 million in taxable income, how would you
compute the tax benets?
!# If the market value of Zenith is $800 million, would you pay this tax
benet as a premium on the market value?
Aswath Damodaran 119
Synergy: Example 4
Asset Write-up
!# One of the earliest leveraged buyouts was done on Congoleum Inc., a
diversied rm in ship building, ooring and automotive accessories,
in 1979 by the rm's own management.
# After the takeover, estimated to cost $400 million, the rm would be allowed to
write up its assets to reect their new market values, and claim depreciation on the
new values.
# The estimated change in depreciation and the present value effect of this
depreciation, discounted at the rm's cost of capital of 14.5% is shown below:
Aswath Damodaran 120
Congoleums Tax Benets
Year Deprec'n Deprec'n Change in Tax Savings PV
before after Deprec'n
1980 $8.00 $35.51 $27.51 $13.20 $11.53
1981 $8.80 $36.26 $27.46 $13.18 $10.05
1982 $9.68 $37.07 $27.39 $13.15 $8.76
1983 $10.65 $37.95 $27.30 $13.10 $7.62
1984 $11.71 $21.23 $9.52 $4.57 $2.32
1985 $12.65 $17.50 $4.85 $2.33 $1.03
1986 $13.66 $16.00 $2.34 $1.12 $0.43
1987 $14.75 $14.75 $0.00 $0.00 $0.00
1988 $15.94 $15.94 $0.00 $0.00 $0.00
1989 $17.21 $17.21 $0.00 $0.00 $0.00
1980-89 $123.05 $249.42 $126.37 $60.66 $41.76
Aswath Damodaran 121
Lesson 4: Dont pay for buzz words
!# Through time, acquirers have always found ways of justifying paying
for premiums over estimated value by using buzz words - synergy in
the 1980s, strategic considerations in the 1990s and real options in this
decade.
!# While all of these can have value, the onus should be on those pushing
for the acquisitions to show that they do and not on those pushing
against them to show that they do not.

Aswath Damodaran 122
Test 5: Comparables and Exit Multiples
!# Now assume that you are told that an analysis of other acquisitions reveals that acquirers
have been willing to pay 5 times EBIT.. Given that your target rm has EBIT of $ 20
million, would you be willing to pay $ 100 million for the acquisition?
!# What if I estimate the terminal value using an exit multiple of 5 times EBIT?
!# As an additional input, your investment banker tells you that the acquisition is accretive.
(Your PE ratio is 20 whereas the PE ratio of the target is only 10 Therefore, you will
get a jump in earnings per share after the acquisition)
Aswath Damodaran 123
Biased samples = Poor results
!# Biased samples yield biased results. Basing what you pay on what
other acquirers have paid is a recipe for disaster. After all, we know
that acquirer, on average, pay too much for acquisitions. By matching
their prices, we risk replicating their mistakes.
!# Even when we use the pricing metrics of other rms in the sector, we
may be basing the prices we pay on rms that are not truly
comparable.
!# When we use exit multiples, we are assuming that what the market is
paying for comparable companies today is what it will continue to pay
in the future.
Aswath Damodaran 124
Lesson 5: Dont be a lemming
!# All too often, acquisitions are justied by using one of the following
two arguments:
# Every one else in your sector is doing acquisitions. You have to do the same to
survive.
# The value of a target rm is based upon what others have paid on acquisitions,
which may be much higher than what your estimate of value for the rm is.
!# With the right set of comparable rms (selected to back up your story),
you can justify almost any price.
!# And EPS accretion is a meaningless measure. After all, buying an
company with a PE lower than yours will lead mathematically to EPS
accretion.
Aswath Damodaran 125
Test 6: The CEO really wants to do this
!# Now assume that you know that the CEO of the acquiring rm really,
really wants to do this acquisition and that the investment bankers on
both sides have produced fairness opinions that indicate that the rm is
worth $ 100 million. Would you be willing to go along?
Aswath Damodaran 126
Lesson 6: Dont let egos or investment bankers get the
better of common sense
!# If you dene your objective in a bidding war as winning the auction at
any cost, you will win. But beware the winners curse!
!# The premiums paid on acquisitions often have nothing to do with
synergy, control or strategic considerations (though they may be
provided as the reasons). They may just reect the egos of the CEOs
of the acquiring rms.
Aswath Damodaran 127
Test 7: Is it hopeless?
!# The odds seem to be clearly weighted against success in acquisitions.
If you were to create a strategy to grow, based upon acquisitions,
which of the following offers your best chance of success?
This Or this
Sole Bidder Bidding War
Public target Private target
Pay with cash Pay with stock
Small target Large target
Cost synergies Growth synergies
Aswath Damodaran 128
Better to lose a bidding war than to win one
Returns in the 40 months before & after bidding war
Source: Malmendier, Moretti & Peters (2011)
Aswath Damodaran 129
You are better off buying small rather than large
targets with cash rather than stock
Aswath Damodaran 130
And focusing on private rms and subsidiaries, rather
than public rms
Aswath Damodaran 131
Growth vs Cost Synergies
Aswath Damodaran 132
Synergy: Odds of success
!# Studies that have focused on synergies have concluded that you are far
more likely to deliver cost synergies than growth synergies.
!# Synergies that are concrete and planned for at the time of the merger
are more likely to be delivered than fuzzy synergies.
!# Synergy is much more likely to show up when someone is held
responsible for delivering the synergy.
!# You are more likely to get a share of the synergy gains in an
acquisition when you are a single bidder than if you are one of
multiple bidders.
Aswath Damodaran 133
Lesson 7: For acquisitions to create value, you have to
stay disciplined..
!# If you have a successful acquisition strategy, stay focused on that
strategy. Dont let size or hubris drive you to expand the strategy.
!# Realistic plans for delivering synergy and control have to be put in
place before the merger is completed. By realistic, we have to mean
that the magnitude of the benets have to be reachable and not pipe
dreams and that the time frame should reect the reality that it takes a
while for two organizations to work as one.
!# The best thing to do in a bidding war is to drop out.
!# Someone (preferably the person pushing hardest for the merger)
should be held to account for delivering the benets.
!# The compensation for investment bankers and others involved in the
deal should be tied to how well the deal works rather than for getting
the deal done.
Aswath Damodaran 134
Value Enhancement and the Expected Value of Control:
Back to Basics
Aswath Damodaran 135
Price Enhancement versus Value Enhancement
Aswath Damodaran 136
The Paths to Value Creation
!# Using the DCF framework, there are four basic ways in which the value of a rm can be
enhanced:
# The cash ows from existing assets to the rm 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 ows can be increased by either
# Increasing the rate of reinvestment in the rm
# 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 nancial mix
# Changing the nancing composition
Aswath Damodaran 137
Value Creation 1: Increase Cash Flows from Assets in
Place
Revenues
* Operating Margin
= EBIT
- Tax Rate * EBIT
= EBIT (1-t)
+ Depreciation
- Capital Expenditures
- Chg in Working Capital
= FCFF
Divest assets that
have negative EBIT
More efficient
operations and
cost cuttting:
Higher Margins
Reduce tax rate
- moving income to lower tax locales
- transfer pricing
- risk management
Live off past over-
investment
Better inventory
management and
tighter credit policies
Aswath Damodaran 138
Value Creation 2: Increase Expected Growth
Reinvestment Rate
* Return on Capital
= Expected Growth Rate
Reinvest more in
projects
Do acquisitions
Increase operating
margins
Increase capital turnover ratio
Price Leader versus Volume Leader Strategies
Return on Capital = Operating Margin * Capital Turnover Ratio
Aswath Damodaran 139
Value Creating Growth Evaluating the Alternatives..
Aswath Damodaran 140
III. Building Competitive Advantages: Increase length of
the growth period
Increase length of growth period
Build on existing
competitive
advantages
Find new
competitive
advantages
Brand
name
Legal
Protection
Switching
Costs
Cost
advantages
Aswath Damodaran 141
Value Creation 4: Reduce Cost of Capital
Cost of Equity (E/(D+E) + Pre-tax Cost of Debt (D./(D+E)) = Cost of Capital
Change financing mix
Make product or service
less discretionary to
customers
Reduce operating
leverage
Match debt to
assets, reducing
default risk
Changing
product
characteristics
More
effective
advertising
Outsourcing Flexible wage contracts &
cost structure
Swaps Derivatives Hybrids
Aswath Damodaran 142
Current Cashflow to Firm
EBIT(1-t) : 1414
- Nt CpX 831
- Chg WC - 19
= FCFF 602
Reinvestment Rate = 812/1414
=57.42%
Expected Growth
in EBIT (1-t)
.5742*.1993=.1144
11.44%
Stable Growth
g = 3.41%; Beta = 1.00;
Debt Ratio= 20%
Cost of capital = 6.62%
ROC= 6.62%; Tax rate=35%
Reinvestment Rate=51.54%
Terminal Value
10
= 1717/(.0662-.0341) = 53546
Cost of Equity
8.77%
Cost of Debt
(3.41%+..35%)(1-.3654)
= 2.39%
Weights
E = 98.6% D = 1.4%
Cost of Capital (WACC) = 8.77% (0.986) + 2.39% (0.014) = 8.68%
Op. Assets 31,615
+ Cash: 3,018
- Debt 558
- Pension Lian 305
- Minor. Int. 55
=Equity 34,656
-Options 180
Value/Share106.12
Riskfree Rate:
Euro riskfree rate = 3.41%
+
Beta
1.26
X
Risk Premium
4.25%
Unlevered Beta for
Sectors: 1.25
Mature risk
premium
4%
Country
Equity Prem
0.25%
SAP: Status Quo
Reinvestment Rate
57.42%
Return on Capital
19.93%
Term Yr
5451
3543
1826
1717
Avg Reinvestment
rate = 36.94%
On May 5, 2005,
SAP was trading at
122 Euros/share
First 5 years
Growth decreases
gradually to 3.41%
Debt ratio increases to 20%
Beta decreases to 1.00
Year 1 2 3 4 5 6 7 8 9 10
EBIT 2,483 2,767 3,083 3,436 3,829 4,206 4,552 4,854 5,097 5,271
EBIT(1-t) 1,576 1,756 1,957 2,181 2,430 2,669 2,889 3,080 3,235 3,345
- Reinvestm 905 1,008 1,124 1,252 1,395 1,501 1,591 1,660 1,705 1,724
= FCFF 671 748 833 929 1,035 1,168 1,298 1,420 1,530 1,621
Aswath Damodaran 143
SAP : Optimal Capital Structure
Debt Ratio Beta Cost of Equity Bond Rating Interest rate on debt Tax Rate Cost of Debt (after-tax) WACC Firm Value (G)
0% 1.25 8.72% AAA 3.76% 36.54% 2.39% 8.72% $39,088
10% 1.34 9.09% AAA 3.76% 36.54% 2.39% 8.42% $41,480
20% 1.45 9.56% A 4.26% 36.54% 2.70% 8.19% $43,567
30% 1.59 10.16% A- 4.41% 36.54% 2.80% 7.95% $45,900
40% 1.78 10.96% CCC 11.41% 36.54% 7.24% 9.47% $34,043
50% 2.22 12.85% C 15.41% 22.08% 12.01% 12.43% $22,444
60% 2.78 15.21% C 15.41% 18.40% 12.58% 13.63% $19,650
70% 3.70 19.15% C 15.41% 15.77% 12.98% 14.83% $17,444
80% 5.55 27.01% C 15.41% 13.80% 13.28% 16.03% $15,658
90% 11.11 50.62% C 15.41% 12.26% 13.52% 17.23% $14,181
Aswath Damodaran 144
Current Cashflow to Firm
EBIT(1-t) : 1414
- Nt CpX 831
- Chg WC - 19
= FCFF 602
Reinvestment Rate = 812/1414
=57.42%
Expected Growth
in EBIT (1-t)
.70*.1993=.1144
13.99%
Stable Growth
g = 3.41%; Beta = 1.00;
Debt Ratio= 30%
Cost of capital = 6.27%
ROC= 6.27%; Tax rate=35%
Reinvestment Rate=54.38%
Terminal Value
10
= 1898/(.0627-.0341) = 66367
Cost of Equity
10.57%
Cost of Debt
(3.41%+1.00%)(1-.3654)
= 2.80%
Weights
E = 70% D = 30%
Cost of Capital (WACC) = 10.57% (0.70) + 2.80% (0.30) = 8.24%
Op. Assets 38045
+ Cash: 3,018
- Debt 558
- Pension Lian 305
- Minor. Int. 55
=Equity 40157
-Options 180
Value/Share 126.51
Riskfree Rate:
Euro riskfree rate = 3.41%
+
Beta
1.59
X
Risk Premium
4.50%
Unlevered Beta for
Sectors: 1.25
Mature risk
premium
4%
Country
Equity Prem
0.5%
SAP: Restructured
Reinvestment Rate
70%
Return on Capital
19.93%
Term Yr
6402
4161
2263
1898
Avg Reinvestment
rate = 36.94%
On May 5, 2005,
SAP was trading at
122 Euros/share
First 5 years
Growth decreases
gradually to 3.41%
Year 1 2 3 4 5 6 7 8 9 10
EBIT 2,543 2,898 3,304 3,766 4,293 4,802 5,271 5,673 5,987 6,191
EBIT(1-t) 1,614 1,839 2,097 2,390 2,724 3,047 3,345 3,600 3,799 3,929
- Reinvest 1,130 1,288 1,468 1,673 1,907 2,011 2,074 2,089 2,052 1,965
= FCFF 484 552 629 717 817 1,036 1,271 1,512 1,747 1,963
Reinvest more in Reinvest more in
emerging markets emerging markets
Use more debt financing. Use more debt financing.
Aswath Damodaran 145
Current Cashflow to Firm
EBIT(1-t) : 163
- Nt CpX 39
- Chg WC 4
= FCFF 120
Reinvestment Rate = 43/163
=26.46%
Expected Growth
in EBIT (1-t)
.2645*.0406=.0107
1.07%
Stable Growth
g = 3%; Beta = 1.00;
Cost of capital = 6.76%
ROC= 6.76%; Tax rate=35%
Reinvestment Rate=44.37%
Terminal Value
5
= 104/(.0676-.03) = 2714
Cost of Equity
8.50%
Cost of Debt
(4.10%+2%)(1-.35)
= 3.97%
Weights
E = 48.6% D = 51.4%
Discount atCost of Capital (WACC) = 8.50% (.486) + 3.97% (0.514) = 6.17%
Op. Assets 2,472
+ Cash: 330
- Debt 1847
=Equity 955
-Options 0
Value/Share $ 5.13
Riskfree Rate:
Riskfree rate = 4.10%
+
Beta
1.10
X
Risk Premium
4%
Unlevered Beta for
Sectors: 0.80
Firm!s D/E
Ratio: 21.35%
Mature risk
premium
4%
Country
Equity Prem
0%
Blockbuster: Status Quo
Reinvestment Rate
26.46%
Return on Capital
4.06%
Term Yr
184
82
102
1 2 3 4 5
EBIT (1-t) $165 $167 $169 $173 $178
- Reinvestment $44 $44 $51 $64 $79
FCFF $121 $123 $118 $109 $99
Aswath Damodaran 146
Current Cashflow to Firm
EBIT(1-t) : 249
- Nt CpX 39
- Chg WC 4
= FCFF 206
Reinvestment Rate = 43/249
=17.32%
Expected Growth
in EBIT (1-t)
.1732*.0620=.0107
1.07%
Stable Growth
g = 3%; Beta = 1.00;
Cost of capital = 6.76%
ROC= 6.76%; Tax rate=35%
Reinvestment Rate=44.37%
Terminal Value
5
= 156/(.0676-.03) = 4145
Cost of Equity
8.50%
Cost of Debt
(4.10%+2%)(1-.35)
= 3.97%
Weights
E = 48.6% D = 51.4%
Discount atCost of Capital (WACC) = 8.50% (.486) + 3.97% (0.514) = 6.17%
Op. Assets 3,840
+ Cash: 330
- Debt 1847
=Equity 2323
-Options 0
Value/Share $ 12.47
Riskfree Rate:
Riskfree rate = 4.10%
+
Beta
1.10
X
Risk Premium
4%
Unlevered Beta for
Sectors: 0.80
Firm!s D/E
Ratio: 21.35%
Mature risk
premium
4%
Country
Equity Prem
0%
Blockbuster: Restructured
Reinvestment Rate
17.32%
Return on Capital
6.20%
Term Yr
280
124
156
1 2 3 4 5
EBIT (1-t) $252 $255 $258 $264 $272
- Reinvestment $44 $44 $59 $89 $121
FCFF $208 $211 $200 $176 $151
Aswath Damodaran 147
The Expected Value of Control
The Value of Control
Probability that you can change the
management of the firm
Change in firm value from changing
management
X
Takeover
Restrictions
Voting Rules &
Rights
Access to
Funds
Size of
company
Value of the
firm run
optimally
Value of the
firm run status
quo
-
Aswath Damodaran 148
The Probability of Changing Control Factors to
consider
!# Institutional Factors
# Capital restrictions: In markets where it is difcult to raise funding for hostile
acquisitions, management change will be less likely.
# State Restrictions: Some markets restrict hostile acquisitions for parochial, political,
social (loss of jobs) and economic reasons (prevent monopolies).
# Inertia and Conicts of Interest: Institutions may tilt to incumbents.
# Presence of activist investors, who are willing to challenge incumbents..
!# Firm-specic factors
# Anti-takeover amendments: They more difcult for a hostile acquirer to acquire the
company or dissident stockholders to change management.
# Voting Rights: Shares with disproportionate voting rights held by insiders.
# Corporate Holding Structures: Cross holdings and Pyramid structures allow insiders
with small holdings to control large numbers of rms.
# Large Stockholders as managers: A large stockholder (usually the founder) is also
the incumbent manager of the rm.
Aswath Damodaran 149
Why the probability of management changing shifts
over time.
!# Corporate governance rules can change over time, as new laws are
passed. If the change gives stockholders more power, the likelihood of
management changing will increase.
!# Activist investing ebbs and ows with market movements (activist
investors are more visible in down markets) and often in response to
scandals.
!# Events such as hostile acquisitions can make investors reassess the
likelihood of change by reminding them of the power that they do
possess.
Aswath Damodaran 150
Estimating the Probability of Change
!# You can estimate the probability of management changes by using historical
data (on companies where change has occurred) and statistical techniques such
as probits or logits.
!# Empirically, the following seem to be related to the probability of
management change:
# Stock price and earnings performance, with forced turnover more likely in rms
that have performed poorly relative to their peer group and to expectations.
# Structure of the board, with forced CEO changes more likely to occur when the
board is small, is composed of outsiders and when the CEO is not also the chairman
of the board of directors.
# Ownership structure; forced CEO changes are more common in companies with
high institutional and low insider holdings. They also seem to occur more
frequently in rms that are more dependent upon equity markets for new capital.
# Industry structure, with CEOs more likely to be replaced in competitive industries.
Aswath Damodaran 151
Manifestations of the Value of Control
!# Hostile acquisitions: In hostile acquisitions which are motivated by control,
the control premium should reect the change in value that will come from
changing management.
!# Valuing publicly traded rms: The market price for every publicly traded rm
should incorporate an expected value of control, as a function of the value of
control and the probability of control changing.
Market value = Status quo value + (Optimal value Status quo value)* Probability of
management changing
!# Voting and non-voting shares: The premium (if any) that you would pay for a
voting share should increase with the expected value of control.
!# Minority Discounts in private companies: The minority discount (attached to
buying less than a controlling stake) in a private business should be increase
with the expected value of control.
Aswath Damodaran 152
1. Hostile Acquisition: Example
!# In a hostile acquisition, you can ensure management change after you
take over the rm. Consequently, you would be willing to pay up to
the optimal value.
!# As an example, Blockbuster was trading at $9.50 per share in July
2005. The optimal value per share that we estimated as $ 12.47 per
share. Assuming that this is a reasonable estimate, you would be
willing to pay up to $2.97 as a premium in acquiring the shares.
!# Issues to ponder:
# Would you automatically pay $2.97 as a premium per share? Why or why not?
# What would your premium per share be if change will take three years to
implement?
Aswath Damodaran 153
2. Market prices of Publicly Traded Companies: An
example
!# The market price per share at the time of the valuation (May 2005)
was roughly $9.50.
Expected value per share = Status Quo Value + Probability of control changing *
(Optimal Value Status Quo Value)
$ 9.50 = $ 5.13 + Probability of control changing ($12.47 - $5.13)
!# The market is attaching a probability of 59.5% that management
policies can be changed. This was after Icahns successful challenge
of management. Prior to his arriving, the market price per share was
$8.20, yielding a probability of only 41.8% of management changing.

Value of Equity Value per s hare
Status Quo $ 955 million $ 5.13 per share
Optimally mana ged $2,323 million $12.47 per share

Aswath Damodaran 154
Value of stock in a publicly traded rm
!# When a rm is badly managed, the market still assesses the probability that it
will be run better in the future and attaches a value of control to the stock price
today:
!# With voting shares and non-voting shares, a disproportionate share of the
value of control will go to the voting shares. In the extreme scenario where
non-voting shares are completely unprotected:
!
Value per share =
Status Quo Value + Probability of control change (Optimal - Status Quo Value)
Number of shares outstanding
!
Value per non - voting share =
Status Quo Value
# Voting Shares + # Non - voting shares
!
Value per voting share = Value of non - voting share +
Probability of control change (Optimal - Status Quo Value)
# Voting Shares
Aswath Damodaran 155
3. Voting and Non-voting Shares: An Example
!# To value voting and non-voting shares, we will consider Embraer, the
Brazilian aerospace company. As is typical of most Brazilian companies, the
company has common (voting) shares and preferred (non-voting shares).
# Status Quo Value = 12.5 billion $R for the equity;
# Optimal Value = 14.7 billion $R, assuming that the rm would be more aggressive
both in its use of debt and in its reinvestment policy.
!# There are 242.5 million voting shares and 476.7 non-voting shares in the
company and the probability of management change is relatively low.
Assuming a probability of 20% that management will change, we estimated
the value per non-voting and voting share:
# Value per non-voting share = Status Quo Value/ (# voting shares + # non-voting
shares) = 12,500/(242.5+476.7) = 17.38 $R/ share
# Value per voting share = Status Quo value/sh + Probability of management change
* (Optimal value Status Quo Value) = 17.38 + 0.2* (14,700-12,500)/242.5 =
19.19 $R/share
!# With our assumptions, the voting shares should trade at a premium of 10.4%
over the non-voting shares.
Aswath Damodaran 156
4. Minority Discount: An example
!# Assume that you are valuing Kristin Kandy, a privately owned candy
business for sale in a private transaction. You have estimated a value
of $ 1.6 million for the equity in this rm, assuming that the existing
management of the rm continues into the future and a value of $ 2
million for the equity with new and more creative management in
place.
# Value of 51% of the rm = 51% of optimal value = 0.51* $ 2 million = $1.02
million
# Value of 49% of the rm = 49% of status quo value = 0.49 * $1.6 million =
$784,000
!# Note that a 2% difference in ownership translates into a large
difference in value because one stake ensures control and the other
does not.
Aswath Damodaran 157
To conclude
!# The value of control in a rm should lie in being able to run that rm
differently and better. Consequently, the value of control should be greater in
poorly performing rms, where the primary reason for the poor performance is
the management.
!# The market value of every rm reects the expected value of control, which is
the product of the probability of management changing and the effect on value
of that change. This has far ranging implications. In acquisitions, the
premiums paid should reect how much the price already reects the expected
value of control; in a market that already reects a high value for expected
control, the premiums should be smaller.
!# With companies with voting and non-voting shares, the premium on voting
shares should reect the expected value of control. If the probability of control
changing is small and/or the value of changing management is small (because
the company is well run), the expected value of control should be small and so
should the voting stock premium.
!# In private company valuation, the discount applied to minority blocks should
be a reection of the value of control.
Aswath Damodaran 158
Alternative Approaches to Value Enhancement
!# Maximize a variable that is correlated with the value of the rm. There
are several choices for such a variable. It could be
# an accounting variable, such as earnings or return on investment
# a marketing variable, such as market share
# a cash ow variable, such as cash ow return on investment (CFROI)
# a risk-adjusted cash ow variable, such as Economic Value Added (EVA)
!# The advantages of using these variables are that they
# Are often simpler and easier to use than DCF value.
!# The disadvantage is that the
# Simplicity comes at a cost; these variables are not perfectly correlated with DCF
value.
Aswath Damodaran 159
Economic Value Added (EVA) and CFROI
!# The Economic Value Added (EVA) is a measure of surplus value
created on an investment.
# Dene the return on capital (ROC) to be the true cash ow return on capital
earned on an investment.
# Dene the cost of capital as the weighted average of the costs of the different
nancing instruments used to nance the investment.
EVA = (Return on Capital - Cost of Capital) (Capital Invested in Project)
!# The CFROI is a measure of the cash ow return made on capital
CFROI = (Adjusted EBIT (1-t) + Depreciation & Other Non-cash
Charges) / Capital Invested

Aswath Damodaran 160
The bottom line
!# The value of a rm is not going to change just because you use a
different metric for value. All approaches that are discounted cash ow
approaches should yield the same value for a business, if they make
consistent assumptions.
!# If there are differences in value from using different approaches, they
must be attributable to differences in assumptions, either explicit or
implicit, behind the valuation.
Aswath Damodaran 161
A Simple Illustration
!# Assume that you have a rm with a book value value of capital of $
100 million, on which it expects to generate a return on capital of 15%
in perpetuity with a cost of capital of 10%.
!# This rm is expected to make additional investments of $ 10 million at
the beginning of each year for the next 5 years. These investments are
also expected to generate 15% as return on capital in perpetuity, with a
cost of capital of 10%.
!# After year 5, assume that
# The earnings will grow 5% a year in perpetuity.
# The rm will keep reinvesting back into the business but the return on capital on
these new investments will be equal to the cost of capital (10%).
Aswath Damodaran 162
Firm Value using EVA Approach
Capital Invested in Assets in Place = $ 100
EVA from Assets in Place = (.15 .10) (100)/.10 = $ 50
+ PV of EVA from New Investments in Year 1 = [(.15 - .10)(10)/.10] = $ 5
+ PV of EVA from New Investments in Year 2 = [(.15 - .10)(10)/.10]/1.1 = $ 4.55
+ PV of EVA from New Investments in Year 3 = [(.15 - .10)(10)/.10]/1.1
2
= $ 4.13
+ PV of EVA from New Investments in Year 4 = [(.15 - .10)(10)/.10]/1.1
3
= $ 3.76
+ PV of EVA from New Investments in Year 5 = [(.15 - .10)(10)/.10]/1.1
4
= $ 3.42
Value of Firm = $ 170.85
Aswath Damodaran 163
Firm Value using DCF Valuation: Estimating FCFF
Base
Year
1 2 3 4 5 Term.
Year
EBIT (1-t) : Assets in Place $ 15.00 $ 15.00 $ 15.00 $ 15.00 $ 15.00 $ 15.00
EBIT(1-t) :Investments- Yr 1 $ 1.50 $ 1.50 $ 1.50 $ 1.50 $ 1.50
EBIT(1-t) :Investments- Yr 2 $ 1.50 $ 1.50 $ 1.50 $ 1.50
EBIT(1-t): Investments -Yr 3 $ 1.50 $ 1.50 $ 1.50
EBIT(1-t): Investments -Yr 4 $ 1.50 $ 1.50
EBIT(1-t): Investments- Yr 5 $ 1.50
Total EBIT(1-t) $ 16.50 $ 18.00 $ 19.50 $ 21.00 $ 22.50 $ 23.63
- Net Capital Expenditures $10.00 $ 10.00 $ 10.00 $ 10.00 $ 10.00 $ 11.25 $ 11.81
FCFF $ 6.50 $ 8.00 $ 9.50 $ 11.00 $ 11.25 $ 11.81
After year 5, the reinvestment rate is 50% = g/ ROC
Aswath Damodaran 164
Firm Value: Present Value of FCFF
Year 0 1 2 3 4 5 Term Year
FCFF $ 6.50 $ 8.00 $ 9.50 $ 11.00 $ 11.25 $ 11.81
PV of FCFF ($10) $ 5.91 $ 6.61 $ 7.14 $ 7.51 $ 6.99
Terminal Value $ 236.25
PV of Terminal Value $ 146.69
Value of Firm
$170.85
Aswath Damodaran 165
Implications
!# Growth, by itself, does not create value. It is growth, with investment
in excess return projects, that creates value.
# The growth of 5% a year after year 5 creates no additional value.
!# The market value added (MVA), which is dened to be the excess
of market value over capital invested is a function of tthe excess value
created.
# In the example above, the market value of $ 170.85 million exceeds the book value
of $ 100 million, because the return on capital is 5% higher than the cost of capital.
Aswath Damodaran 166
Year-by-year EVA Changes
!# Firms are often evaluated based upon year-to-year changes in EVA
rather than the present value of EVA over time.
!# The advantage of this comparison is that it is simple and does not
require the making of forecasts about future earnings potential.
!# Another advantage is that it can be broken down by any unit - person,
division etc., as long as one is willing to assign capital and allocate
earnings across these same units.
!# While it is simpler than DCF valuation, using year-by-year EVA
changes comes at a cost. In particular, it is entirely possible that a rm
which focuses on increasing EVA on a year-to-year basis may end up
being less valuable.
Aswath Damodaran 167
Gaming the system: Delivering high current EVA while
destroying value
!# The Growth trade off game: Managers may give up valuable growth
opportunities in the future to deliver higher EVA in the current year.
!# The Risk game: Managers may be able to deliver a higher dollar EVA
but in riskier businesses. The value of the business is the present value
of EVA over time and the risk effect may dominate the increased
EVA.
!# The capital invested game: The key to delivering positive EVA is to
make investments that do not show up as part of capital invested. That
way, your operating income will increase while capital invested will
decrease.
Aswath Damodaran 168
Delivering a high EVA may not translate into higher
stock prices
!# The relationship between EVA and Market Value Changes is more
complicated than the one between EVA and Firm Value.
!# The market value of a rm reects not only the Expected EVA of
Assets in Place but also the Expected EVA from Future Projects
!# To the extent that the actual economic value added is smaller than the
expected EVA the market value can decrease even though the EVA is
higher.
Aswath Damodaran 169
High EVA companies do not earn excess returns
Aswath Damodaran 170
Increases in EVA do not create excess returns
Aswath Damodaran 171
Implications of Findings
!# This does not imply that increasing EVA is bad from a corporate
nance standpoint. In fact, given a choice between delivering a
below-expectation EVA and no EVA at all, the rm should deliver
the below-expectation EVA.
!# It does suggest that the correlation between increasing year-to-year
EVA and market value will be weaker for rms with high anticipated
growth (and excess returns) than for rms with low or no anticipated
growth.
!# It does suggest also that investment strategiesbased upon EVA have
to be carefully constructed, especially for rms where there is an
expectation built into prices of high surplus returns.
Aswath Damodaran 172
When focusing on year-to-year EVA changes has least
side effects
1. Most or all of the assets of the rm are already in place; i.e, very little
or none of the value of the rm is expected to come from future
growth.
# [This minimizes the risk that increases in current EVA come at the expense of
future EVA]
2. The leverage is stable and the cost of capital cannot be altered easily by
the investment decisions made by the rm.
# [This minimizes the risk that the higher EVA is accompanied by an increase in the
cost of capital]
3. The rm is in a sector where investors anticipate little or not surplus
returns; i.e., rms in this sector are expected to earn their cost of
capital.
# [This minimizes the risk that the increase in EVA is less than what the market
expected it to be, leading to a drop in the market price.]
Aswath Damodaran 173
When focusing on year-to-year EVA changes can be
dangerous
1. High growth rms, where the bulk of the value can be attributed to
future growth.
2. Firms where neither the leverage not the risk prole of the rm is
stable, and can be changed by actions taken by the rm.
3. Firms where the current market value has imputed in it expectations of
signicant surplus value or excess return projects in the future.
Note that all of these problems can be avoided if we restate the objective as
maximizing the present value of EVA over time. If we do so, however, some of the
perceived advantages of EVA - its simplicity and observability - disappear.
Aswath Damodaran 174
The Bottom line
!# Value creation is hard work. There are no short cuts.
!# Investment banks/Consultants/Experts who claim to have short cuts
and metrics that allow for easy value creation are holding back on hard
truths.
!# Value creation does not happen in nance departments of businesses.
Every employee has a role to play.