Academy of Economic Studies, Bucharest

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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 Damian
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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
Def 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
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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 projects nature
a) Options to grow b) Contraction options c)
Flexibility Options
Trigeorgis 1996 basic types of real options
a) options to defer, b) options to contract
/expand c) option to abandon for salvage value,
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 (S) - project gross present value
time to expiry (T-t) - period during which the
investment opportunity is valid
underlying volatility(s) - standard deviation of
the growth rate (percentage) of the project gross
present value
dividends(d) - value lost to competitors, cash
outflows or necessary risk neutral adjustments
risk- free interest rate (r)
The project entire value should 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
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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,
Lander1998 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 projects
value geometric Brownian motion dS?Sdt
?dz jump model Wilner 1995 dS?Sdt
(?-?)SdN dN1 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
risk-neutral 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
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

• Monte Carlo simulation
• Finite difference methods (implicit, explicit)
• 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) subscribers (growth rate)
July 2001 65 000(by July 2002) 2003 100
000 - 2004 200 000 100.00
2005 350 000 75.00 2006 600 000
71.00 2007 650 000
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
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3. Case study. DNT- Dynamic Network Technologies
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3. Case study. DNT- Dynamic Network Technologies
2. find the parameters of the stochastic process
the underlying follows
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.
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3. Case study. DNT- Dynamic Network Technologies
Expanded NPV -200 000 193 435.142625
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
19911996.
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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