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Academy of Economic Studies, Bucharest
Doctoral School of Finance and Banking
Dissertation Thesis: July 2001
Supervisor: Professor Moisa Altar
Real Options- An Investment Valuation Method
Student: Oana Dămian
Real Options- An Investment Valuation Method
Introduction
1. Investment Projects Viewed as Real Options.
Real Option Analogy with Financial Options
2. Financial Options Models & Numerical Analysis
3. Case Study. Dynamic Network Technologies
Conclusions
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Introduction
Introduction
• Real options are options to buy, sell or exchange real assets
on possibly favorable terms.
• Most firms do not explicitly use the real option concept when
valuing investments. Nevertheless, firms do take into account
management flexibility (wait for further information, adapt the
project to new relevant information or even abandon the
project).
• Management has a number of options to exercise and avoid
future unfavorable developments or take advantage of the
favorable ones.
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1. Investment Projects Viewed as Real Options.
Real Option Analogy with Financial Options
Investment Projects Viewed as Real Options
” Similar to options on financial securities real
options involve discretionary decisions or rights , with
no obligations to acquire or exchange a asset for a
specified alternative price” - Trigeorgis [1996]
Def:
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1. Investment Projects Viewed as Real Options.
Real Option Analogy with Financial Options
Classifications:
Triantis [1999] mentions three
real option categories depending
on the project’s nature :
Trigeorgis [1996] basic types of real
options:
a) options to defer,
a) Options to grow
b) options to contract /expand
b) Contraction options
c) option to abandon for salvage value,
c) Flexibility Options
d) option to switch use.
Trigeorgis [1996] ranks real options depending on
exclusiveness of ownership into :
a) proprietary options
b) shared options
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1. Investment Projects Viewed as Real Options.
Real Option Analogy with Financial Options
Option to defer an investment
The option to defer is a call option on
the project gross present value. The
exercise price that has to be paid is
the project cost.
“Call elements”
exercise
price
(X)
- investment
costs
underlying
time
to expiry
(S)
project
- period
present
which
value
theofinvestment
is
valid
underlying
dividends(d)
volatility(σ)
- -(T-t)
value
lost
-gross
standard
to during
competitors,
deviation
cash
the
outflows
growth
oropportunity
rate
necessary
(percentage)
risk
riskinterest
rate
(r)
The
project
entire
value
should
of
neutral
thefree
project
adjustments
gross
present
value be equal to the value of
the call option together with the passive NPV:
Expanded NPV= option premium + NPV
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1. Investment Projects Viewed as Real Options.
Real Option Analogy with Financial Options
Options to defer and possible valuation methods
Type of call & some possible valuation methods
European call:
Black, Scholes & Merton [1973-75]
Numerical analysis
Trigeorgis [1990] model with jump
American call:
Real option
The management makes the decision to invest only at the end of
certain period. At the end of the period he can either not invest or
implement the project right away and start receiving the cash-flows.
Competitors entrance influence over the projects value can be taken
into account.
The management can make the decision to invest at any moment,
- no discontinuous dividends present: Black, Scholes & during a certain period. The moment he makes the decision to invest
Merton (1973-75)
the project is implemented and cash-flows start running right away.
- single dividend Roll, Geske & Whaley [1977-81]
Certain cash outflows (ex dividends paid to shareholders or value
Numerical analysis
lost to due to a competitor’s entry)
The management can make the decision to invest at the end of /
Other “calls”:
Numerical analysis:
during a certain period. The moment he makes the decision to invest
the project is implemented and cash-flows start running right away.
Certain cash outflows (ex dividends paid to shareholders or value lost
to due to a competitor entry) or certain cash inflows (ex. marketing,
advertising expenses) may occur.
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1. Investment Projects Viewed as Real Options.
Real Option Analogy with Financial Options
Real Option Analogy to Financial Options
Financial option valuation techniques can be used in valuing real
options .Yet, financial options models assumptions have to be met.
A set of assumptions under which realoptions can be “financial option based” valued, Lander[1998]:
1) there is only one real option modeled and valued at a time
2) there is only one source of uncertainty
3) there is an approximation for the process governing the value of the
underlying
4) “markets are complete, the firm is risk-neutral or risk is fully diversifiable” and
adjustments can be made in order to get to work into a risk- neutral world
5) cash outflows/inflows (ex. dividends) are known and constant, can be
determined from market prices or are a proportion of the value of the underlying
6) costs are known & there are no foregone earnings
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1. Investment Projects Viewed as Real Options.
Real Options Analogy with Financial Options
1) Assumptions regarding the project’s value
geometric Brownian motion: dS=Sdt +dz
jump model Wilner [1995]: dS=Sdt +(-)SdN
dN=1 w.p. dt or 0 w.p. 1-dt
a mix of jump and geometric Brownian motion: Trigeorgis [1996]
dS=(-d)Sdt +(k-1)dN+dz
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1. Investment Projects Viewed as Real Options.
Real Options Analogy with Financial Options
2) Assumptions regarding asset tradability and riskneutral valuation
• Any derivative on an asset that could be ”something as far
removed from financial markets as the temperature from the center
of New Orleans “ can be valued in a risk neutral world - Hull [2000]
• When converting into a risk neutral world a dividend like
adjustment has to be made. The dividend equals the difference
between the return of a similar traded asset and the nontraded
asset return.
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1. Investment Projects Viewed as Real Options.
Real Options Analogy with Financial Options
3) Assumptions regarding interactions among multiple
real options embedded in a project

r ( T  t )
ce
E[c T - t ]
Cox, Ingersoll & Ross [1985].
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2. Financial option models & numerical analysis
Financial options models
Black, Scholes & Merton (1973) - analytical valuation of
European options
Roll, Geske & Whaley(1977-79-81) – analytical valuation for
American call option on a dividend paying underlying
Margrabe(1978) – analytical valuation for an option to
exchange one asset for another
Wilner [1995] , Trigeorgis [1996]- analytical valuation for
models with jumps
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2. Financial option models & numerical analysis
Numerical analysis
1. Monte Carlo simulation
2. Finite difference methods (implicit, explicit)
3. Lattice approach: binomial trees, trinomial trees,
log-transformed binomial trees for valuing complex
multi-option investments Trigeorgis [1991]
Kulatilaka [1988] , Trigeorgis [1996] general method for valuing
options with multiple “options” (operating modes)
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3. Case study. DNT- Dynamic Network Technologies
DNT is one of the top 3 Internet Service Providers in Romania.
Recently DNT has merged with Astral TV, a cable TV company. At the
end of March
2001 Astral TV registered
approximately 700 000
subscribers.
Situation: starting from 2003, DNT is interested in introducing a new
residential telephony service that uses voice over IP.
Problem:
What is the value of the project today ?
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3. Case study. DNT- Dynamic Network Technologies
Input data:
- the product : software package & data transmission services ( cost of
acquiring a new subscriber 200 USD, monthly fee/subscriber 12 USD,
variable monthly costs/subscriber 7 USD, negligible fixed costs).
- if the project were taken up today
Year
subscribers
July 2001
65 000(by July 2002)
- product development scenario: cost 200 mil USD
Year
subscribers (at year end)
July 2001
65 000(by July 2002)
2003
100 000
2004
200 000
2005
350 000
2006
600 000
2007
650 000
subscribers (growth rate)
100.00%
75.00%
71.00%
8.33%
- WACC:(1-tax)rborrow =(1-25%)*12%
-interest rate, time to expiry, proprietary option
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3. Case study. DNT- Dynamic Network Technologies
Assumptions:
1 risk neutrality adjustments for the nontraded asset are not needed
2 until 2003 the number of subscribers at the beginning is assumed to
follow a geometric Brownian motion
3 The embedded option is a proprietary one
4 once a subscriber has bought the product it is assumed that he dose
not give it up. A constant sum of discounted cash flows can be
calculated per subscriber
5 the month to month growth rates of the number of subscribers
remain the same (but are not equal to each other) under all possible
states of nature, once the project has been undertaken
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3. Case study. DNT- Dynamic Network Technologies
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3. Case study. DNT- Dynamic Network Technologies
Steps followed :
1. model the option underlying, the discounted present value of future
cash-flows
2. find the parameters of the stochastic process the underlying follows
3. calculate expanded NPV and comment on it.
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3. Case study. DNT- Dynamic Network Technologies
1. model the option underlying, the discounted present value of future cash-flows
D  200  5
1
1
 wacc
12
1e
 498.738823 USD
D  discounted cash flows per subscriber
w  ln( 1  WACC )  ln( 1.09)  8,6177696%
N( t ) 
k
1  ae  ( t  2000)
k  763.8987 a  151.21399
(k, a)  (x, y) 0  x  300, 500  y  800 
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3. Case study. DNT- Dynamic Network Technologies
DCF  e  w ( N 2003D  ( N
2003&
  N 2003 )De
12
 e  w ( N 2003D  N 2003(icg
2003&
48
 e  w N 2003D(1   (icg
i 1
2003&
w
1
12  ...  ( N
  icg 2003 )De
12
i  icg
i 1 )e
2003&
12
12
DCF  N 2003 2 975.92527 USD
icg  cumulated growth indice for th e
w
w
2003&
48  N
47 )De
2003&
12
12
1
12  ...  N
2003(icg
2003&
w
47
12 )
48  icg
47 )De
2003&
12
12
w
48
12 )
i
12 )
number of subscriber s
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3. Case study. DNT- Dynamic Network Technologies
2. find the parameters of the stochastic process the underlying follows
Situations
Growth rate for the next 1.5 years
most likely value
28% ( 18.66% per year)
10 out of 100 cases
Growth rate between 24% and 30%
50 out of 100 cases
Growth rate between 10% and 45%
60 out of 100 cases
Growth rate between 7% and 48%
90 out of 100 cases
Growth rate between -12% and 70%
Subjective values
The underlying growth rate has an approximated 28% mean and 25%
volatility normal distribution on a 1.5 years basis. On 1 year basis the
mean is 18.666% and approximately 20 %volatility.
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3. Case study. DNT- Dynamic Network Technologies
3. calculate expanded NPV and comment on it.
X - exercise
price
S- NPV today
T-t - time to
exercise
σ
d
r
Initial cost 200 000 thousands USD
N2001½
x2975.92527=65x2975.92527=193
435.1426 thousands USD
1.5 years
approximately 20 %
The dividend should stand for risk neutral
adjustments and/or account for cash-flows lost
to competitors. Cash flows lost to competitors
can be considered 0 (proprietary option). No
risk neutral adjustments are made.
6.75 per year
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3. Case study. DNT- Dynamic Network Technologies
Expanded NPV
= -200 000 + 193 435.1426+25 275.50036
= 18 710.64296 thousands USD
The Greeks
- delta,
-vega,
- theta,
-rho.
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3. Case study. DNT- Dynamic Network Technologies
Further research to be made in order to better account for the following:
1. other embedded real options should be considered
2. the growth path chosen,
3.in real life the cash flows per subscriber do change in time and should
be closer to a market value rather than the number of subscribers is,
4 competition.
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Conclusions
Conclusions
One of the two objectives of the paper has been to shortly present the real
options concept, the analogies with financial options and how real options
can actually be priced.
The conclusion is that once a real option has been found, a model has to be
chosen and then make the required adjustments so as the model assumptions
are fulfilled. The most permissive way (as far as the assumptions are
concerned) to value a real option seems to be, up to now, the method of
Kulatilaka [1988] and Trigeorgis [1991&1996].
The second objective of the paper has been attempting to value an Internet
telephony project using the real options concept. The project has been valued as
an option to defer. The expanded net present value has been calculated yet,
results have been obtained under a number of powerful assumptions.
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