Real options..flexibility

Real Options and Interactions with Financial Flexibility
Author(s): Lenos Trigeorgis
Source: Financial Management , Autumn, 1993, Vol. 22, No. 3 (Autumn, 1993), pp. 202224
Published by: Wiley on behalf of the Financial Management Association International
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Topics in Real Options and Applications
Real Options and Interactions
With Financial Flexibility
Lenos Trigeorgis
Lenos Trigeorgis is an Assistant Professor of Finance at the Graduate School of Management,
Boston University, Boston, Massachusetts, and an Associate Professor of Finance
at the University of Cyprus, Nicosia, Cyprus.
0 Many academics and practicing managers now recog-
alization of cash flows will probably differ from what
nize that the net present value (NPV) rule and other dis-
management expected initially. As new information ar-
counted cash flow (DCF) approaches to capital budgeting
rives and uncertainty about market conditions and future
are inadequate in that they cannot properly capture
cash flows is gradually resolved, management may have
management's flexibility to adapt and revise later deci-
valuable flexibility to alter its operating strategy in order
sions in response to unexpected market developments.
to capitalize on favorable future opportunities or mitigate
losses. For example, management may be able to defer,
Traditional NPV makes implicit assumptions concerning
expand, contract, abandon, or otherwise alter a project at
an "expected scenario" of cash flows and presumes
different stages during its useful operating life.
management's passive commitment to a certain "operating
Management's flexibility to adapt its future actions in
strategy" (e.g., to initiate the project immediately, and
response to altered future market conditions expands an
operate it continuously at base scale until the end of its
investment opportunity's value by improving its upside
prespecified expected useful life).
potential while limiting downside losses relative to
In the actual marketplace, characterized by change,
management's initial expectations under passive manage-
uncertainty and competitive interactions, however, the re-
ment. The resulting asymmetry caused by managerial
adaptability calls for an "expanded NPV" rule reflecting
I would like to thank George M. Constantinides, Nalin Kulatilaka, Scott
both value components: the traditional (static or passive)
P. Mason, Stewart C. Myers, Martha A. Schary, Han Smit, two anony-
NPV of direct cash flows, and the option value of operating
mous reviewers, and the editor, James S. Ang, for useful comments on
and strategic adaptability. This does not mean that tradi-
earlier versions of parts of this work. The usual disclaimer applies.
202
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TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 203
tional NPV should be scrapped, but
Building
ratheron
should
the above
be seen
princip
as a crucial and necessary input
quently
to an extends
options-based,
the analysis
exin th
panded NPV analysis, i.e.,
leverage within a venture capital c
improvement in equityholders' v
Expanded (strategic) NPV = static (passive) NPV of expected cash flows
tional financial flexibility, noting
+ value of options from active management. (1)
with operating flexibility. The ben
venture
capitalhas
financing
in installm
An options approach to capital
budgeting
the poan option
to abandon
byof
the lende
tential to conceptualize and even
quantify
the value
revalue
atis
potentially
better te
options from active management.
Thislater
value
manifest as
other
issues
related
to
the
mix of
a collection of real (call or put) options embedded in
capital
financing
are also explored
capital investment opportunities,
having
as an underlying
paper operating
is organized
as follow
asset the gross project value ofThe
expected
cash
prehensive
literature
review
in Sec
flows. Many of these real options
occur naturally
(e.g.,
to
towhile
motivate
discussion
of
defer, contract, shut down or example
abandon),
others
may
presents
practical
principles
for
v
be planned and built-in at some extra cost (e.g., to expand
tions.
then
illustrates h
capacity or build growth options,
to Section
default III
when
investbe
extended
to
capture
interactions
ment is staged sequentially, or to switch between alterna-
The last
section
concludes
and
tive inputs or outputs). Exhibit ity.
I describes
briefly
the
most
sions.
common categories of encountered
real options, the types
of industries they are important in, and lists representative
authors that have analyzed them.1 A more comprehensive
I. A Review of the Real Options
review of the real options literature is given in the first
Literature
section.
Corporate
value creation
and competitive position
in
This paper has two main goals.
First,
it provides
a
markets
are critically
determined
by corporate
comprehensive overview of the different
existing
real
options
litera-
resource allocation
and theprinciples
evaluation of investment
ture and applications, and presents
practical
for opportunities.
The options.
field of capital budgeting
remained
quantifying the value of various
real
Second,
it stag-
nant for several
recent developments
takes a first step towards extending
the decades,
real until
options
litera- in real
options financial
provided the tools
and unlocked the The
possibilities
ture to recognize interactions with
flexibility.
to
revolutionize
the
field.
In
what
follows,
I
will
attempt to
comprehensive literature review traces the evolution of the
describe around
briefly some stages
in the development
and evoreal options revolution, organized
thematic
devellution
of
the
real
options
literature,
while
organizing
the
opments covering the early criticisms, conceptual ap-
presentation blocks,
around severalrisk-neutral
broad themes. This is not an
proaches, foundations and building
easy
task,
and
I
apologize
to
those
authors and readers
valuation and risk adjustment, analytic contributions
in who
may find my treatment
here
rather subjective and nonvaluing different options separately,
option
interactions,
exhaustive.
numerical techniques, competition and strategic options,
various applications, and future research directions. An
example is then used to conceptually
discussand
the basic
A. Symptoms, Diagnosis,
nature of the various real options
that
may Early
be embedded
Traditional
Medicine:
Critics,
in capital investments. Initially the
assuming
all-equity
financUnderinvestment
Problem,
and
ing, the paper presents principles useful for valuing both
Alternative Valuation Paradigms
upside-potential operating options, such as to defer an
The real options revolution arose in part as a response
investment or expand production, as well as various
to the dissatisfaction of corporate practitioners, strategists,
downside-protection options, such as to abandon for saland some academics with traditional capital budgeting
vage value or switch use (inputs/outputs), and abandon
techniques. Well before the development of real options,
project construction by defaulting on planned, staged fucorporate managers and strategists were grappling intuiture outlays.
tively with the elusive elements of managerial operating
flexibility and strategic interactions. Early critics (e.g.,
IParts of Exhibit 1 are adapted from Baldwin and Trigeorgis [8].
Dean [29], Hayes and Abernathy [35], and Hayes and
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204
FINANCIAL
Exhibit
1.
MANAGEMENT
Common
/
Real
AUTUMN
1993
Options
Category Description Important In Analyzed By
Option to defer Management holds a lease on (or All natural resource Tourinho [98];
an option to buy) valuable land extraction industries; Titman [97];
or resources. It can wait (x years) real estate development; McDonald & Siegel [76];
to see if output prices justify farming; paper products. Paddock, Siegel &
constructing a building or plant, Smith [83];
or developing a field. Ingersoll & Ross [44].
Time to build Staging investment as a series All R&D intensive Majd & Pindyck [68];
option (staged of outlays creates the option industries, especially Carr [22];
investment) to abandon the enterprise in pharmaceuticals; long- Trigeorgis [106].
midstream if new information is development capitalunfavorable. Each stage can be intensive projects, e.g.,
viewed as an option on the value large-scale construction or
of subsequent stages, and valued energy-generating plants;
as a compound option. start-up ventures.
Option to alter If market conditions are more Natural resource Brennan & Schwartz [19];
operating scale favorable than expected, the firm industries such as McDonald & Siegel [75];
(e.g., to expand; can expand the scale of production mine operations; Trigeorgis & Mason [1 10];
to contract; or accelerate resource utilization. facilities planning Pindyck [84].
to shut down Conversely, if conditions are less and construction in
and restart) favorable than expected, it can cyclical industries;
reduce the scale of operations, fashion apparel;
In extreme cases, production may consumer goods;
temporarily halt and start up again, commercial real estate.
Option to abandon If market conditions decline Capital intensive Myers & Majd [82].
severely, management can abandon industries, such as
current operations permanently airlines and railroads;
and realize the resale value of financial services;
capital equipment and other new product introductions
assets in secondhand markets. in uncertain markets.
Option to switch If prices or demand change, Output shifts: Margrabe [69];
(e.g., outputs management can change the any good sought in small Kensinger [50];
or inputs) output mix of the facility batches or subject to Kulatilaka [55];
("product" flexibility). volatile demand, e.g., Kulatilaka &
Alternatively, the same outputs consumer electronics; Trigeorgis [63].
can be produced using toys; specialty paper;
different types of inputs machine parts; autos.
("process" flexibility). Input shifts:
all feedstock-dependent
facilities, e.g., oil;
electric power; chemicals;
crop switching; sourcing.
Growth options An early investment (e.g., R&D, All infrastructure-based Myers [80];
lease on undeveloped land or oil or strategic industries, Brealey & Myers [16];
reserves, strategic acquisition, especially high-tech, Kester [51], [52];
information network/infrastructure) R&D, or industries with Trigeorgis [100];
is a prerequisite or link in a chain multiple product generations Pindyck [84];
of interrelated projects, opening up or applications (e.g., Chung & Charoenwong 123].
future growth opportunities (e.g., computers, pharmaceuticals);
new generation product or process, multinational operations;
oil reserves, access to new market, strategic acquisitions.
strengthening of core capabilities).
Like interproject compound options.
Multiple Real-life projects often involve Real-life projects Brennan & Schwartz [19];
interacting a "collection" of various options, in most industries Trigeorgis [106];
options both upward-potential enhancing discussed above. Kulatilaka [58].
calls and downward-protection put
options present in combination.
Their combined option value may
differ from the sum of separate
option values, i.e., they interact.
They may also interact with
financial flexibility options.
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TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 205
Garvin [36]) recognized thatC.standard
discounted
Generic Medicine:
Foundations andcash
flow (DCF) criteria often undervalued
investment opporBuilding Blocks
tunities, leading to myopic decisions,
underinvestment
and
The quantitative
origins of real options,
of course,
eventual loss of competitive position,
because
derive from the
seminal workthey
of Black either
and Scholes [13]
ignored or did not properly value
important
strategic
conand Merton
[78] in pricing
financial options.
Cox, Ross,
siderations. Decision scientists further
maintained
that
the
and Rubinstein's [27] binomial approach enabled
a more
problem lay in the application
of the
wrong
simplified
valuation
of options valuation
in discrete-time. Margrabe
techniques altogether, proposing
instead
the
use of
simu[69] values
an option
to exchange
one risky
asset for
lation and decision tree analysis
(see
Hertz
and
Magee
another,
while
Stulz [94][38]
analyzes
options
on the maxi[67]) to capture the value of future
operating
flexibility
mum (or minimum)
of two risky
assets and Johnson [45]
associated with many projects.
Proponents
Hodder
extends
it to several risky(e.g.,
assets. These
papers have the
potentialhave
to help analyze
the generic
option
to switch
and Riggs [41] and Hodder [40])
argued
that
the
among
alternative
uses and related as
options
(e.g., abandon
problem arises from misuse of
DCF
techniques
comfor salvage
valuewhile
or switch among
alternative inputs or
monly applied in practice. Myers
[81],
confirming
outputs).
Geske various
[31] values a compound
option (i.e., an
that part of the problem results
from
misapplicaoption
to
acquire
another
option),
which,
in
principle, may
tions of the underlying theory, acknowledges that tradibe applied in valuing growth opportunities which become
tional DCF methods have inherent limitations when it
comes to valuing investments with significant operating or available only if earlier investments are undertaken. Carr
strategic options (e.g., in capturing the sequential inter- [22] combines the above two building blocks to value
sequential (compound) exchange options, involving an
option
to acquire a subsequent option to exchange the
that option pricing holds the best promise of valuing such
dependence among investments over time), suggesting
investments. Later, Trigeorgis and Mason [110] explain underlying asset for another risky alternative. Kulatilaka
that option valuation can be seen operationally as a special, [55] and [57] describes an equivalent dynamic program-
economically corrected version of decision tree analysis ming formulation for the option to switch among operating
modes. The above line of work has the potential, in printhat is better suited in valuing a variety of corporate operciple, to value investments with a series of investment
ating and strategic options, while Teisberg [95] provides a
practical comparative discussion of the DCF, decision outlays that can be switched to alternative states of opera-
tion, and particularly to eventually help value strategic
interproject dependencies.
analysis, and real option valuation paradigms. Baldwin
and Clark [5] discuss the importance of organizational
capabilities in strategic capital investment, while Baldwin
and Trigeorgis [8] propose remedying the underinvestment
problem and restoring competitiveness by developing spe-
cific adaptive capabilities viewed as an infrastructure for
acquiring and managing real options.
B. A New Direction: Conceptual Real
Options Approaches
D. Slightly Different Medicine: Risk-Neutral
Valuation and Risk Adjustment
The actual valuation of options in practice has been
greatly facilitated by Cox and Ross's [26] recognition that
an option can be replicated (or a "synthetic option" created) from an equivalent portfolio of traded securities.
Being independent of risk attitudes or capital market equilibrium considerations, such risk-neutral valuation enables
Building on Myers' [80] initial idea of thinking of present-value discounting, at the risk-free interest rate, of
discretionary investment opportunities as "growth op- expected future payoffs (with actual probabilities replaced
tions," Kester [51] conceptually discusses strategic and with risk-neutral ones), a fundamental characteristic of
competitive aspects of growth opportunities. Other gen- "arbitrage-free" price systems involving traded securities.
eral, conceptual real options frameworks are presented in Rubinstein [87] further showed that standard option pric-
Mason and Merton [71], Trigeorgis and Mason [110], ing formulas can be alternatively derived under risk averTrigeorgis [100], Brealey and Myers [16], and Kulatilaka sion, and that the existence of continuous trading opportuand Marcus [59], [60]. Mason and Merton [71], for exam- nities enabling a riskless hedge or risk neutrality are not
ple, provide a good discussion of many operating as wellreally necessary. Mason and Merton [71] and Kasanen and
as financing options, and integrate them in a project financ- Trigeorgis [48] maintain that real options may, in principle,
ing for a hypothetical, large-scale energy project.
be valued similar to financial options, even though they
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206
FINANCIAL
may
not
be
interested
would
be
MANAGEMENT
AUTUMN
1993
valuing offshore
petroleumin
leases, and
by Tourinho [98]
traded,
since
capital
bu
in
in valuing reserves of natural
resources. Ingersoll
and Rosspro
determining
what
the
worth if they
[44] reconsider
were
the decision
traded
to wait in light of
in
the benefithe m
contribution
The
/
portfolio)
perfectly
the cial
market
impact of a potential
value
future interestof
rate decline
a publ
on
to
existence
of
that
a project
traded
value. Majd and"twin
Pindyck [68] valuesecurity
the option to
hasdelay
the
sequential same
construction for risk
projects that take
charac
time to
build,with
or there is a maximum
at which investment can
correlated)
theratenontraded
r
proceed. Carr [22] and Trigeorgis
also deal
with
markets is sufficient
for [106]
real
optio
generally, Constantinides
valuing sequential or staged
[24],
(compound)
Cox,
investments.
Ing
plete
[28,
lemma
have
traded
by
or
not,
as
the
rate,
real
or
in
were
for its salvage
risk-neutral.
value seen as an American put option.
This
For
with
for
actual
examined, among others,
expected
by Margrabe [69], Kensinger
cash
no Baldwin
systematic
and Ruback [7] show that future
risk
price uncertainty
(e.g.,
creates aprecious
valuable switching option
that benefits shortcertain
metals
or
interest
underlying
actually
required
f
traded
[50], Kulatilaka [55],
assets
and Kulatilaka in
and Trigeorgis
equilibr
[63].
lived projects. or
Future investment
opportunities that are
certainty-equivalent
risk-neutral
capital
w
[75]
and by Brennan and Schwartz [19].
and Majd
subtracting
a Myers
risk
pre
[82]
analyze
the
option
to
permanently
abandon
a
project
market equilibrium), an
than
rate.
risk-free
the
restart operationsgrowth
was analyzed by McDonald
and Siegel
actual
rate
Options to switch use (i.e., outputs orcash
inputs) have flow
been
certainty-equivalent
rather
assets
be
capacity
priced
choice. The option
in
to temporarily
a world
shut down and
wit
(by
world
drilling
the
in
its
rate
discounting
adjusted
that
optionsany
to alter (i.e., contingent
expand or contract) operating scale orclai
can
appropriate
if
Harrison
and
Kreps
Trigeorgis and Mason [110]
and Pindyck
[84] examine [34
and
replacing
equivalent
be
4],
suggested
n
ra
rate
seen as corporate
(minus
growth options are
any
discussed in
divide
Myers
[80],is
Brealey
and Myers
[16], Kester [51]as
and [52],
asset
not
traded,
may
and Mason [110], Trigeorgis
[100], Pindyck
budgetingTrigeorgis
associated
options,
its
fall
of
and Chung
and Charoenwong [23].
below [84],
the
equilibrium
an
equivalent-risk
total
traded
fin
with the difference or "rate of return shortfall" necessi-
tating a dividend-like adjustment in option valuation (e.g.,
see McDonald and Siegel [74] and [75]). If the underlying
asset is traded in futures markets, though, this dividend-
(or convenience-yield-) like return shortfall or rate of
foregone earnings can be easily derived from the futures
prices of contracts with different maturities (see Brennan
and Schwartz [19]). In other cases, however, estimating
this return shortfall may require use of a market equilib-
rium model (e.g., see McDonald and Siegel [75]).
F. The Tablets Interact: Multiple Options
and Interdependencies
Despite its enormous theoretical contribution, the focus
of the earlier literature on valuing individual real options
(i.e., one type of option at a time) has nevertheless limited
its practical value. Real-life projects are often more com-
plex in that they involve a collection of multiple real
options whose values may interact. An early exception is
Brennan and Schwartz [19], who determine the combined
value of the options to shut down (and restart) a mine, and
E. A Tablet for Each Case: Valuing Each
Different Real Option Separately
to abandon it for salvage. They recognize that partial
irreversibility resulting from the costs of switching the
mine's operating state may create a persistence, inertia or
There came a series of papers which gave a boost to the hysteresis effect, making it long-term optimal to remain in
real options literature by focusing on valuing quantita- the same operating state even though short-term considertively - in many cases, deriving analytic, closed-form
solutions- one type after another of a variety of real
ations (i.e., current cash flows) may seem to favor immedi-
ate switching. Although hysteresis can be seen as a form
options, although each option was typically analyzed in of interaction between early and later decisions, Brennan
isolation. As summarized in Exhibit 1, the option to defer and Schwartz do not explicitly address the interactions
or initiate investment has been examined by McDonald among individual option values. Trigeorgis [106] focuses
and Siegel [76], by Paddock, Siegel, and Smith [83] in on the nature of real option interactions, pointing out, for
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TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 207
example, that the presence of
subsequent
options
can is ava
with
an analytic
solution
increase the value of the effective
underlying
asset for
second
category include
numeric
earlier options, while exerciseplicit
of prior
real options
may
or explicit
finite difference
alter (e.g., expand or contract) [17],
the underlying
asset
itself,
Brennan and
Schwartz
[18],
and hence the value of subsequent
it. Thus,of
the
[68].options
Finally,on
a number
analytic
combined value of a collection available:
of real options
differ
Geske may
and Johnson
[32
from the sum of separate option
values. Usinganalytic
a numerical
pound-option
polynom
analysis method suitable for valuing
complex
multi-option
proach;
Barone-Adesi
and Whal
investments (Trigeorgis [104]),quadratic
he presents
the valuationwhile o
approximation,
of options to defer, abandon, contract
or expand investproblem-specific
heuristic app
ment, and switch use in the context
of a generic
investment,
prehensive
review
of such numer
first with each option in isolation
and later
in combination.
in the
articles
by Geske and Sha
He shows, for example, that the
incremental
of an by Hu
[104],
as well asvalue
in a book
additional option, in the presence of other options, is
generally less than its value in isolation and declines as
H. The General Environm
and Strategic Options
more options are present. More generally, he identifies
situations where option interactions can be small or large
An important area that deserve
and negative as well as positive. Kulatilaka [58] subse-
where real options have the potent
quently examines the impact of interactions among three
difference, is that of competition
such options on their optimal exercise schedules. The
competitive advantages resulting f
recent recognition of real option interdependencies should
technologies, ownership of valua
subsequently enable a smoother transition from a theoretmanagerial capital, reputation or
ical stage to an application phase.
market power, empower compani
to grow through future profitable
G. The Bitter Pill: Numerical
Techniques
effectively
respond to
unexpected
In the more complex real-lifeties
option
as
in asituations,
changing such
technological,
business
environment.
A number
those involving multiple interacting
real
options, analytic
solutions may not exist and one
may not
even
be always and st
dressed
several
competitive
able to write down the set of partial
differential
equations
investment
early on.
For example
describing the underlying stochastic
processes.
ability decis
[86] find
that inThe
sequential
to value such complex option
situations
has
been enworthwhile
to
undertake
investm
hanced, however, with various
numerical
analysis techwhen
early investment
can provid
niques, many of which take advantage
of benefits,
risk-neutral
ture project
especially w
valuation. Generally, there are
two types
of numerical
greater.
Baldwin
[3] finds that op
techniques for option valuation:
(i) those
that approximate
ment
for firms
with market power
the underlying stochastic processes
directly
and a
are
gensions may
require
positive
prem
erally more intuitive; and (ii) pensate
those approximating
for the loss inthe
value of f
resulting partial differential equations.
The undertaking
first category
results from
an invest
includes Monte Carlo simulation
used
by Boyle
[14], and
lyzes
options
to choose
capacity u
various lattice approaches certainty
such as when
Cox, investment
Ross, andis, agai
Rubinstein's [27] standard binomial
lattice
method,
and
considers
firm
entry and
exit deci
Trigeorgis' [104] log-transformed
binomial
method;
the
showing that in the presence
of su
latter are particularly well-suited
tonot
valuing
complex projmay
be long-term
optimal to
ects with multiple embedded
real prices
options,
a series
of
when
appear
attractive
in t
investment outlays, dividend-like
effects,Dixit's
as wellentry
as option
combines
and exit d
interactions. Boyle [15] shows how
lattice
frameworks
capacity
options
for the can
multinati
be extended to handle two state
variables,
whileKogut
Hull and
exchange
rates.
and Kula
White [43] suggest a control variate
technique
to location
improve
international
plant
option
computational efficiency when
a
similar
derivative
asset
reverting exchange rate volatilit
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208
FINANCIAL
Marks
[61]
flexibility
From
of
a
in
the
authors
Myers
tially
[16],
dealt
(e.g.,
supp
Myers
[81],
Kester [51]
tions
are currently
also and
rec
options
valuation
has been
ap
[110],
Trigeorgis
[100],
Breale
such
as
in
natural
resource
i
Trigeorgis and Kasanen [109]) have
and
leasing,
flexible
manufactu
competitive
and
strategic
options
For
sequential,
of
results
available
investments
due
ratherresource
than parallel,
implementati
resource
or products
commodity
pri
interrelated
consumer
when
l
durations,
resulting
in
high
from early product introductions (e.g.,
collection
ucts)
negotiations
with input
Applications
real Besides
options theoretical
perspective, develo
a num
regulation,
R&D,
new vent
example,
Kester [51]
develops
qu
investment
and strategy,
an
competitive
and strategic
aspects of
Early
applications
naturall
growth options, while Kester [52] prop
project
ing
1993
various
planned
a
AUTUMN
Mason
with
conceptually.
tively
firm's
explicit
and
/
the
bargaining
va
I. strategic
Cure for
All Kinds
examine
more
Trigeorgis
MANAGEMENT
shelf
and
mates.
and Schwar
needed
for Brennan
similar subsequent
nience
yield
derived
from
competitive advantage is
ero
space
when
commodity
value the
op
Kasanen
[109] also to
examine
sequ
a and
mine.
Paddock,
Siegel,
project interdependencies
synergies
as part
of
Trigeorgis
going
of
and
strategic
planning
Financial
embedded in undeveloped oil
and control process. In thi
empirical evidence that opti
Management, Kasanen [47] also deals w
DCF-based bids in valuing
problem of the interaction between cu
[101] values an actual mine
investments and future opportunities, using the r
major multinational compa
novel concept of a spawning matrix structure (capt
during construction, expan
the firm's ability to generate investment opportu
salvage. Bjerksund and Eke
across projects through feedback effects) to determ
field with options to defer
optimal mix of strategic and operating projects.
and Stangeland [79] value f
Trigeorgis [103] uses quantitative option pricing t
chastic inventories and pr
niques to examine early investment that may pre
[93] also discuss some appl
anticipated competitive entry, and to value the opt
the
strategic
defer
a
to
the
result
from
to
natural
resource
possibility
of tional
premature
project
termina
Brownian
motion
or
competitive
entry.
Further
dep
find that ignoring reversion
common assumption
of perfect
competi
uncertainty,
but may
over-
of
the
Kulatilaka
when
ming
impacted by random comp
Laughton and Jacoby [65] e
entry (Trigeorgis [102]). Ang and Dukas [2] incorp
of real options and long-t
both competitive and asymmetric
information, ar
mean-reversion price proce
that the time pattern of discounted
cash
flows also
m
be the case in certain
comm
due
investment
random
[62]
examine
howmore
the inves
options.
On the
appli
decisions of a firm will influence
the
production
experiences
with
Shell inde
a
of
and
competitors
generates
[91]
a
and
cost
combine
timing
Perotti
the
options
approach
donment
decision to
of inves
a refi
principles
from
game
cusses
problem
organization
competitors
menting
ble
basic
real
theory
and
formulatio
explore
various
investment
t
the process
of
adapting opt
In the based
area of
land
strategies in follow-up projects
on
the develo
reacti
trial
with
the market
price when
early inves
the timing
of developing
a
advantage.
In
this
issue,
Smit
and
A
growth option in a manufa
of
different
market
structures.
Su
[111],
Capozza
and Sick [21
the
value
of
vacant
land
sh
analysis with game theoretic tools
under
options
incorporating
promises
future
to
to
be
research.
an
based on
its best immediate
strategic
competitive
countera
building
now), but also
its
important
and challenging
directi
delayed and the land is con
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TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 209
use in the future. It may thus Bell
pay to
hold
vacant
[10]
andland
Kogut
and for
Kulatilak
its option value even in the presence
of currently
thriving
examine
entry, capacity,
and swit
real estate markets. Quigg [85A]
with
reports
multinational
empirical
operations
results
und
ity.valuation
Hiraki [39]
suggests
that the
indicating that option-based land
that
incorpo-
corporate
system ser
rates the option to wait to develop
land governance
provides better
structure
that
companies t
approximations of actual market
prices.
In aenables
different
rate [77]
real view
options.
context, McLaughlin and Taggart
the opportuother option
applications
nity cost of using excess capacityVarious
as the change
in the value
ranging
from
shipping
of the firm's options caused by
diverting
capacity
to an(Bjerks
environmental
pollution
and glob
alternative use. In leasing, Copeland
and Weston
[25], Lee,
dricks
[37]).
The
potential
Martin, and Senchack [66], McConnell and Schallheim for fu
seems
like
a growthoptions
option.
[73], and Trigeorgis [105] value
various
operating
embedded in leasing contracts.
J. Other Sources the
and Future
Research
In the area of flexible manufacturing,
flexibility
Directions systems, flexible proprovided by flexible manufacturing
duction technology or other machinery
having
Other comprehensive
treatments multiple
of real options can be
uses has been analyzed from an
options
perspective
by [71] and
found
in the articles
by Mason and Merton
Kulatilaka [55], Triantis and Hodder
[99],
Aggarwal
Trigeorgis and
Mason [110],
a monograph[1],
by Sick [89],
Kulatilaka and Trigeorgis [63],
and review
Kamrad
an economics
article by and
Pindyck Ernst
[85], as well as in
[46], among others. In this issue,
Kulatilaka
[56]
values
the
a volume edited by Trigeorgis [107]
and a book
forthcomflexibility provided by an actual
dual-fuel
industrial
steam
ing from
MIT Press (Trigeorgis
[108]). The
Spring 1987
boiler that can switch between
alternative
energy
inputs
Issue
of the Midland Corporate
Finance
Journal and a
(natural gas and oil) as their relative
fluctuate,
and
1991 Special prices
Issue of Managerial
Finance (Vol.
17, No.
finds that the value of this flexibility
exceeds
the
2/3) have also beenfar
devoted
to real options
and capital
incremental cost over a rigid, single-fuel
alternative.
Baldbudgeting. In the present
issue of Financial
Management
win and Clark [6] study the flexibility
created
by
modular(Autumn 1993), the articles by Laughton and Jacoby [65],
ity in design that connects components
system
Smit and Ankum of
[91], a
andlarger
Kasanen [47]
are indicative of
through standard interfaces.
an active literature that is evolving in several new direcIn the area of government subsidies
and
regulation,
tions in modelling,
competition
and strategy, while the
Mason and Baldwin [70] value articles
government
subsidies
by Kemna [49] and
Kulatilaka [56] to
represent re-
large-scale energy projects as cent
put
options,
while
Teisberg
attempts
to implement
real options
valuation in actual
[96] provides an option valuation
analysis
of
investment
case applications.
Clearly,
an increased
attention to applichoices by a regulated firm. In
research
and development,
cation
and implementation
issues is the next stage in the
evolution
of real options.
Kolbe, Morris, and Teisberg [54]
discuss
option elements
embedded in R&D projects. Option
In addition
elements
to more actual
involved
case applications
in
and tackthe staging of start-up ventures
are discussed
in and
Sahlman
ling real-life
implementation issues
problems, fruitful
[88], Willner [112], and this article.
directions for
Strategic
future research,acquisitions
in both theory and practice,
include:
of other companies also often involve
a number of growth,
divestiture, and other flexibility
options,
discussed
by
(i) Focusing
more onas
investments
(such as in
R&D,
Smith and Triantis [102]. Other applications
of
options
pilot or market tests, or
excavations)
that canin
"genthe strategy area were discussed in
Section
earlier.
On
erate"
informationI.H.
and learning
(e.g., about
the
the empirical side, Kester [51] estimates
that
the value option
of
project's prospects)
by extending/adjusting
a firm's growth options is more than
half
the market
value
pricing
and risk-neutral
valuation with
Bayesian
of equity for many firms, even 70-80%
for more
volatile
analysis or alternative
(e.g., jump)
processes.
industries. Similarly, Pindyck
[84] in
also
suggests
that
(ii) Exploring
more depth
endogenous competitive
growth options represent more than
half
of
firm
value
if
counteractions and a variety of competitive/market
demand volatility exceeds 20%. In
foreign
investment,
structure and strategic issues using a combination
Baldwin [4] discusses various location,
timing
and
staging
of game-theoretic
industrial
organization
with opvaluation
tools.
options present when firms scan tion
the
global
marketplace.
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210
FINANCIAL
(iii)
MANAGEMENT
Modelling
better
/
AUTUMN
1993
the
various
strategic
A.
Example:
An Oil Extraction
and
Refinery Project
options.
(iv) Extending real options in an agency context rec-
A large oil company has a one-year lease to start drilling
ognizing that the potential (theoretical) value of
on undeveloped land with potential oil reserves. Initiating
real options may not be realized in practice if
the project may require certain exploration costs, to be
managers, in pursuing their own agenda (e.g., ex-
followed by construction of roads and other infrastructure
pansion or growth, rather than firm value maximi-
outlays, Il. This would be followed by outlays for the
zation), misuse their discretion and do not follow
construction of a new processing facility, I2. Extraction can
the optimal exercise policies implicit in option
valuation. This raises the need to design proper
begin only after construction is completed, i.e., cash flows
corrective incentive contracts by the firm (taking
lows the last outlay. During construction, if market condi-
also into account asymmetric information).
tions deteriorate, management can choose to forego any
(v) Recognizing better that real options may interact
not only among themselves but with financial flex-
are generated only during the "operating stage" that fol-
future planned outlays. Management may also choose to
reduce the scale of operation by c%, saving a portion of
ibility options as well, and understanding the re-
the last outlay, Ic, if the market is weak. The processing
sulting implications for the combined, interdepen-
plant can be designed upfront such that, if oil prices turn
dent corporate investment and financing decisions.
out higher than expected, the rate of production can be
In Section III, we take a first step toward recogniz-
enhanced by x% with a follow-up outlay ofl E. At any time,
ing such interactions among real and financial
management may salvage a portion of its investment by
flexibility options.
selling the plant and equipment for their salvage value or
(vi) On the practical side, applying real options to the
valuation of flexibility in related areas, such as in
competitive bidding, information technology or
other platform investments, energy and R&D
problems, international finance options, and so on.
(vii) Using real options to explain empirical phenomena
that are amenable to observation or statistical test-
ing, such as examining empirically whether managements of firms that are targets for acquisition
may sometimes turn down tender offers in part due
to the option to wait in anticipation of receiving
better future offers.
(viii) Conducting more field, survey, or empirical studies to test the conformity of theoretical real option
valuation and its implications with management's
intuition and experience, as well as with actual
price data when available.
switch them to an alternative use value, A. An associated
refinery plant - which may be designed to operate with
alternative sources of energy inputs - can convert crude
oil into a variety of refined products. This type of project
presents the following collection of real options:
(i) The option to defer investment. The lease enables
management to defer investment for up to one year
and benefit from the resolution of uncertainty
about oil prices during this period. Management
would invest II (i.e., exercise its option to extract
oil) only if oil prices increase sufficiently, but
would not commit to the project, saving the
planned outlays, if prices decline. Just before ex-
piration of the lease, the value creation will be
max(V - I1, 0). The option to defer is thus analogous to an American call option on the gross present value of the completed project's expected operating cash flows, V, with the exercise price being
equal to the required outlay, Ii. Since early invest-
II. Real Options: An Example and
Valuation Principles
ment implies sacrificing the option to wait, this
option value loss is like an additional investment
opportunity cost, justifying investment only if the
This section discusses conceptually the basic nature of
value of cash benefits, V, actually exceeds the
different real options through a comprehensive example,
initial outlay by a substantial premium. As noted
and then illustrates some practical principles for valuing
in Exhibit 1, the option to wait is particularly
such options. To facilitate our discussion of the various real
valuable in resource extraction industries, farming,
options that may be embedded in capital investments,
paper products, and real estate development due to
consider first the following example.
high uncertainties and long investment horizons.
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and
TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 211
planned
investment outlays (Ic). This
flexibility
to
(ii) The option to default during
construction
(or
the
time-to-build option). In most real-life
projects,
the
mitigate loss is analogous
to a put option
on part
required investment is not incurred
(c%) of the base-scale
asproject,
a single
with exercise price
upfront outlay. The actual staging
capital
equal toof
the potential
cost investsavings (Ic), giving
ment as a series of outlays over
time
valumax(Ic
- cV, 0). creates
The option to contract,
just as
able options to "default" at any
given
(e.g.,
the option
to expand,stage
may be particularly
valuable
after exploration if the reserves
prices
turn
in the or
case ofoil
new product
introductions
in uncer-
out very low). Thus, each stage
(e.g.,
tain markets.
The optionbuilding
to contract may also be
necessary infrastructure) can important,
be viewed
an opfor example,as
in choosing
among techtion on the value of subsequentnologies
stages
by
incurring
or plants with a different construction to
the installment cost outlay (e.g.,
II)costrequired
maintenance
mix, where it may to
be preferable
proceed to the next stage, and
can
therefore
be costs
to build a plant with lower initial construction
valued similar to compound options.
This
option
and higher maintenance expenditures in is
order to
valuable in all R&D intensive
industries,
espeacquire
the flexibility to contract
operations by
cially pharmaceuticals, in highly
uncertain,
longcutting down
on maintenance if market
conditions
development capital intensiveturn
industries,
such as
out unfavorable.
energy-generating plants or large-scale construc(v) The option to shut down (and restart) operations.
tion, and in venture capital.
In real life, the plant does not have to operate (i.e.,
(iii) The option to expand. If oil prices
or
market
extract oil) in
eachother
and every period
automatically.
conditions turn out more favorable
than
In fact, if oil
prices areexpected,
such that cash revenues are
management can actually accelerate
rate
not sufficientthe
to cover
variableor
operating (e.g.,
expand the scale of production
(by x%)
by
incurmaintenance)
costs, it
might
be better not to operring a follow-up cost outlay (IE).
This is
similar
to
ate temporarily,
especially
if the costs
of switching
a call option to acquire an additional
part
(x%)
of
between the operating and idle modes are rela-
the base-scale project, paying tively
IE as
exercise
price. operations
small.
If prices rise sufficiently,
The investment opportunity can
with
the
option
toyear can be
start again. Thus, operation in each
expand can be viewed as the
base-scale
project
seen
as a call option to acquire
that year's cash
plus a call option on future investment,
i.e.,
V costs
+ of operrevenues (C) by paying the
variable
max(xV - IE, 0). Given an initial design choice,
ating (Iv) as exercise price, i.e., max(C - Iv, 0).2
management may deliberately Options
favor
a more
expento alter
the operating
scale (i.e., expand,
sive technology for the built-in flexibility to excontract, or shut down) are typically found in natpand production if and when it becomes desirable.
ural resource industries, such as mine operations,
As discussed further below, the option to expand
facilities planning and construction in cyclical inmay also be of strategic importance, especially if
dustries, fashion apparel, consumer goods, and
it enables the firm to capitalize
on future
growth
commercial
real estate.
opportunities. As noted, when the firm buys vacant
(vi) The option to abandon for salvage value. If oil
undeveloped land, or when it builds a small plant
prices suffer a sustainable decline or the operation
in a new geographic location (domestic or overdoes poorly for some other reason, management
seas) to position itself to take advantage of a develdoes not have to continue incurring the fixed costs.
oping large market, it essentially installs an expanInstead, management
may have
a valuable option
sion/growth option. This option,
which will
be
exercised only if future market developments turn
management
has an option to obtain project value V (net
out favorable, can make a 2Alternatively,
seemingly
unprofitable
of fixed costs,
IF) minus variable costsworth
(Iv), or shut down and receive
(based on static NPV) base-case
investment
project value minus that year's foregone cash revenue (C), i.e., max(V -
undertaking.
(iv) The option to contract. If market conditions are
weaker than originally expected, management can
operate below capacity or even reduce the scale of
operations (by c%), thereby saving part of the
IV, V - C) - IF = (V - IF) - min(lv, C). The latter expression implies that
the option not to operate enables management to acquire project value
(net of fixed costs) by paying the minimum of variable costs (if the project
does well and management decides to operate) or the cash revenues (that
would be sacrificed if the project does poorly and it chooses not to
operate).
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212
FINANCIAL
to
MANAGEMENT
abandon
for
its
capital
American
As
1993
and
other
assets
in
ics, toys
or pharmaceuticals,
where product differ-
noted,
put
AUTUMN
project
permanently
among alternative
"outputs," is more valuable in in e
industries
such as the
automobiles,resale
consumer electron-valu
value
(i.e.,
equipment
markets).
with
the
salvage
/
seco
this
can
be
entiation and option
diversity are important
and/or prod-
val
option
on iscurrent
uct demand
volatile. In such cases, project
it may be
exercise
price
the
or
best
worthwhilesalvage
to install a more costly
flexible
capac-
alt
use value (A), entitling
management
to
ity to acquire the
ability to alter product mix or
+ max(A - V, 0) or
max(V,
Natural
production
scale in responseA).
to changing
market
demands.
general-purpose capital
assets would
V
higher
salvage
and (viii)
option
abandonment
v
Corporate growth
options. As noted, another verassets.
Valuable
abandonm
sion of the earlier option to expand of considerable
special-purpose
tions
tries,
are
generally
such
services,
as
as
in
well
found
in capital
intensi
strategic importance
are corporate growth
options
airlines
railroads,
that set the and
path of future
opportunities. Suppose, in
as inin new
product
introduc
the above example,
that the proposed
refinery
uncertain markets.
facility is based on a new, technologically superior
(vii) The option to switch use (i.e., inputs or outputs).
"process" for oil refinement developed and tested
Suppose the associated oil refinery operation can
internally on a pilot plant basis. Although the pro-
be designed to use alternative forms of energy
posed facility in isolation may appear unattractive,
inputs (e.g., fuel oil, gas, or electricity) to convert
it could be only the first in a series of similar
crude oil into a variety of output products (e.g.,
facilities if the process is successfully developed
gasoline, lubricants, or polyester). This would pro-
and commercialized, and may even lead to entirely
vide valuable built-in flexibility to switch from the
new oil by-products. More generally, many early
current input to the cheapest future input, or from
investments (e.g., R&D, a lease on undeveloped
the current output to the most profitable future
land or a tract with potential oil reserves, a strategic
product mix, as the relative prices of the inputs or
acquisition, or an information technology net-
outputs fluctuate over time. In fact, the firm should
work) can be seen as prerequisites or links in a
be willing to pay a certain positive premium for
chain of interrelated projects. The value of these
such a flexible technology over a rigid alternative
projects may derive not so much from their ex-
that confers no choice or less choice. Indeed, if the
pected directly measurable cash flows, but rather
firm can in this way develop extra uses for its assets
from unlocking future growth opportunities (e.g.,
over its competitors, it may be at a significant
a new-generation product or process, oil reserves,
advantage. Generally, "process" flexibility can be
access to a new or expanding market, strengthen-
achieved not only via technology (e.g., by building
ing of the firm's core capabilities or strategic posi-
a flexible facility that can switch among alternative
tioning). An opportunity to invest in a first-gener-
energy "inputs"), but also by maintaining relation-
ation high-tech product, for example, is analogous
ships with a variety of suppliers, changing the mix
to an option on options (an interproject compound
as their relative prices change. Subcontracting pol-
option). Despite a seemingly negative NPV, the
icies may allow further flexibility to contract the
infrastructure, experience, and potential by-
scale of future operations at a low cost in case of
products generated during the development of the
unfavorable market developments. As noted, a
multinational oil company may similarly locate
first-generation product may serve as springboards
production facilities in various countries in order
ture generations of that product, or even for gener-
for developing lower-cost or improved-quality fu-
to acquire the flexibility to shift production to the
ating new applications into other areas. But unless
lowest-cost producing facilities, as the relative
the firm makes that initial investment, subsequent
costs, other local market conditions, or exchange
generations or other applications would not even
rates change over time. Process flexibility is valu-
be feasible. The infrastructure and experience
able in feedstock-dependent facilities, such as oil,
gained can be proprietary and can place the firm at
electric power, chemicals, and crop switching.
a competitive advantage, which may even rein-
"Product" flexibility, enabling the firm to switch
force itself if learning cost curve effects are pres-
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TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 213
what
we assume throughout that the value
ent. Growth options are found In
in
allfollows,
infrastructure-
based or strategic industries,
of theespecially
project (i.e., the value,
in highin millions of dollars, in each
year, t,multiple
of its subsequent
expected cash flows appropriately
tech, R&D, or industries with
product
back to that year), Vt, and its twin security price
generations or applications discounted
(e.g., semiconductors,
(e.g.,in
a twin
oil stock price in $ per
share, or simply the
computers, pharmaceuticals),
multinational
operations, and in strategic acquisitions.
price of oil in $ per barrel), St, move through time as
follows:
In a more general context, such operating and strategic
adaptability represented by corporate real options can
(324,be
64.88)
achieved at various stages during the value chain, from
(180, 36) suppliers
switching the factor input mix among various
and subcontracting practices, to rapid
product
design21.6)
(e.g.,
(100,
20) (108,
computer-aided design) and modularity in design, to shift(60, 12)
ing production among various products rapidly
and cost-
efficiently in a flexible manufacturing system. The next
(36, 7.2)
section illustrates, through simple numerical examples,
Year
0
Year
1
Year
2
basic practical principles for valuing several of the above
real options. For expositional simplicity,
we will subseFor example,
the pair
quently ignore any return shortfall
or gross
other dividend-like
rent
project value
effects (see Section I.D. above of
for$20
appropriate
adjusta barrel
(or
ments).
Under
traditional
project
value
project's
B. Principles of Valuing Various Real
Options
cash
using
twin
generic investment opportunity (e.g., similar to the above
=
Note
oil extraction project). Specifically, suppose we are faced
exactly
with an opportunity to invest I0 = $104 (in millions) in an
oil
oil project whose (gross) value in each period will either
0o
fluctuations: a year later, the project will have an expected
oil price moves up (C+ = 180) or $60 if it moves down (C-
In
= 60).4 There is an equal probability (q = 0.5) that the price
104,
the
the
=
of oil, or generally of a "twin security" that is traded in the
financial markets and has the same risk characteristics (i.e.,
based
on
unable
to
because
is perfectly correlated) with the real project under consid-
eration (such as the stock price of a similar operating
unlevered oil company). Both the project and its twin
security (or oil prices) have an expected rate of return (or
initial
lies
in
count
is r= 8%.
are
3Trigeorgis
based
cally
and
valuation
corrected,
open-market
4All
project
"millions"
Mason
can
be
[110]
seen
not
version
of
opportunities
values
are
use
a
similar
decision
tree
event
The
in
a
such
example
as
of
com
real
claims
to
show
valuation
a
i
symmetri
vary
risk-neutral
N
captu
discretio
future
contingent
operationally
1
negative
Nevertheless,
using
=
valuation
rates
NP
manag
decision.
the
th
analysis
their
on
the
claims
discount rate) of k = 20%, while the risk-free interest rate
its
I0
properly
of
pendence
gr
to
subtract
of
DCF
(or
this
-
absence
v
i.e.,
project's
V0
traditional
of oil will move up or down in any year. Let S be the price
that
After
NPV
value (from subsequent cash flows) of $180 (million) if the
rate,
proportional
price).
=
ob
the
security
discount
move up by 80% or down by 40%, depending on oil price
be
end-of-period
priate
100.
$20
(passive
would
flows),
project's
Consider, as in Trigeorgis and Mason [110],3 valuing a
a
(V
o
special,
analysis
to5As
trade
and borrow.
noted,
the basic
(DTA)
idea
pr
thou
is
tha
tha
equity
by purchasing
a specified
hereafter
assumed
to be in millions
of
subsequently
and financing
dropped).
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the
purchase
in
pa
214
FINANCIAL
MANAGEMENT
tion can be obtained in our actual risk-averse world as in
/
AUTUMN
1993
kinds of both upside-potential op
a "risk-neutral" world in which the current value of anyexpand, and downside-protection
contingent claim could be obtained from its expecteddon for salvage or default durin
future values - with expectations taken over the risk-neu-hance the value of the opportunit
tral probabilities, p, imputed from the twin security's (orof equity or NPV) in the above g
oil) prices - discounted at the riskless rate, r. In such a standard assumption of all-equi
risk-neutral world, the current (beginning of the period) here is on basic practical princip
value of the project (or of equityholders' claim), E, is given of operating option at a time.
by:
1. The Option to Defer Invest
The company has a one-year le
E = pE + (1(1 +r)
- p)E-
prietary right to defer undertakin
ing the oil) for a year, thus benef
where
of uncertainty about oil prices ov
(1 + r)S - S
p
(S+ - S-)
undertaking the project immedi
-(3)
(of- 4), the opportunity to invest
a positive worth since managemen
prices and project value rise suff
The probability, p, can be estimated from the price dynam-
obligation to invest under unf
ics of the twin security (or of oil prices):
Since the option to wait is analo
project value, V, with an exerci
(1.08 x 20)- 12 = 0.4.
36- 12
quired outlay next year, 11 = 11
E+= max(V+ - 1,, 0) = max(180 Note that the value for p = 0.4 is distinct from the actual
probability, q = 0.5, and can be used to determine "cerE = max(V - 11, 0) = max(60
tainty-equivalent" values (or expected cash flows) which
can be properly discounted at the risk-free rate. For The
exam- project's total value (i.e.,
ple,
includes the value of the option
(3) is:
Vo
pC+
+ (1 -(1
p)C=
0.4 r)
x1801.08
+100.
0.6 x 60 100. (4(4)
+
pE + (1 - p)E 0.4 x 67.68 + 0.6 x 0
+ r)
1.08
E0(1=
25.07.
(6)
In what follows, we assume that if any part of the required
investment outlay (having present value of $104 million)
From Equation (1), the value of t
is not going to be spent immediately but in future installvided by the lease itself is thus gi
ments, that amount is placed in an escrow account earning
the riskless interest rate.7 We
nextto
illustrate
how various
Option
defer = expanded
NPV - passiv
which, incidentally, is equal to
riskless interest rate, r. This ability toproject's
construct agross
"synthetic"
claim or an
value.8
equivalent/replicating portfolio (from the "twin security" and riskless
bonds) based on no-arbitrage equilibrium principles enables the solution
8The above example confirms that CCA
for the current value of the equity claim to be independent of the actual
decision tree analysis (DTA), with the key
probabilities (in this case, 0.5) or investors' risk attitudes (the twin
are transformed so as to allow the use of a
security's expected rate of return or discount rate, k = 0.20).
however, that the DCF/DTA value of waiti
6This confirms the gross project value,
V0 = 100,
obtained earlier
using
by CCA.
The DCF/DTA
approach
in this c
traditional DCF with the actual probability
= 0.5)
the risk-adjusted
of the (q
option
ifand
it discounts
at the constan
discount rate (k = 0.20).
comparable in risk to the "naked" (passiv
7This assumption is intended to make the analysis somewhat more
realistic and invariant to the cost structure make-up, and is not at all
+ _k)
EO- qE+ + (1
(1 - q)E0.5 x 1.20
67.68 + 0.5 x 0 _ 28.20
crucial to the analysis.
E + k) 1.28.20 .
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TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 215
relative prices of inputs,
outputs or the plant resale value
2. The Option to Expand (Growth
Option)
in a secondhand
fluctuate, equityholders
Once the project is undertaken,
any market
necessary
infra- may find
preferable is
to abandon
the current project's
use by switchstructure is completed and theit plant
operating,
manage-
ment may have the option to accelerate
thea more
rate
or expand
ing to a cheaper input,
profitable
output, or simply
the scale of production by, say,sell
50%
(x =assets
0.50)
by
incurring
the plant's
to the
secondhand
market. Let the
a follow-up investment outlay
of value
IE in
= its
40,
project's
best provided
alternative use, A,oil
(or the salvage
prices and general market conditions
turn
better
than
value for which
it can out
be exchanged)
fluctuate
over time
originally expected. Thus, in
year 1 management can
as:
choose either to maintain the base scale operation (i.e.,
230.4
receive project value, V, at no extra cost) or expand by 50%
the scale and project value by incurring the extra outlay.
144
That is, the original investment opportunity is seen as the
initial-scale project plus a call option
on a 115.2
future opportu90
nity, or E = V + max(xV - IE, 0) = max(V, (1+ x)V - IE):
72
E+ = max(V+, 1.5V+ - IE) = max(180, 270 - 40) = 230
57.6
i.e., expand;
Year
E = max(V , 1.5V - IE) = max(60, 90 - 40) = 60 (8)
Note
use
opportunity (including the value of the option to expand if
Year
that
value
i.e., maintain base scale. The value of the investment
(Vo
rate
becomes:
so
of
+ -Io0=
r) 1.08
Eo = (I
P +)
18 - 104 = 14.5, (9)
it
switch
=
=
to
is
100)
-
cu
below
the
(20%);
it
market
abandon
the
down
(e.g.,
in
ne
ke
pr
mana
year
and thus the value of the option to expand is:
Option to expand = 14.5 - (- 4) = 18.5, (10)
or 18.5% of the gross project value.
of V1equityholders
= 60 for a can
higher
useofvalue
Thus,
choosealternative
the maximum
the
of A1 = 72).9
project's value in its present use, V, or its value in the best
alternative use, A, i.e., E = max(V, A):
3. Options to Abandon for Salvage Value or
E+ = max(Vf, A+)= max(180, 144) = 180 = V+,
Switch Use
In terms of downside protection, management has the
i.e., continue;
option to abandon the oil extraction project at any time in
exchange for its salvage value or value in its best alterna-
tive use, if oil prices suffer a sustainable decline. The
associated oil refinery plant also can use alternative energy
E = max(V-, A) = max(60, 72) = 72 = A , (11)
inputs and has the flexibility to convert crude oil into a
variety of products. As market conditions change and the
i.e., switch use. The value of the investment (including the
option to abandon early or switch use) is then:
Again, the error in the traditional DTA approach arises from the use of a
single (or constant) risk-adjusted discount rate. Asymmetric claims on an
9We assume here for simplicity that the project's value in its current use
asset do not have the same riskiness (and hence expected rate of return)
and in its best alternative use (or salvage value) are perfectly positively
as the underlying asset itself. CCA corrects for this error by transforming
correlated. Of course, the option to switch use would be even more
the probabilities.
valuable the lower the correlation between V and A.
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t
otherw
immediately
moves
use
2
project's
90)
use
if
optimal
if
Year
return
that
but
1
the
(Ao
switched
market conditions turn out better than expected) then
pE+ + (1 - p)E- 0.4 x 230 + 0.6 x 60
0
1
216
FINANCIAL
pE+
+
E0
I0
(1 +=
r)
(1
MANAGEMENT
-
p)E-
/
AUTUMN
1993
and the option to abandon by defaulting during c
tion is:
0.4 x 180+0.6 x 72
=-1.08104 = +2.67 (12)
Option to abandon by defaulting = -1.33 - (- 4) = 2
so that the project with the option to switch use is now
or about three percent of project value. This va
desirable. The value of the option itself is:
course dependent on the staged cost schedule.
For(13)
simplicity, the above examples were based
Option to switch use = 2.67 - (- 4) = 6.67,
one-period risk-neutral backward valuation pro
This procedure can be easily extended to a discret
or almost seven percent of the project's gross value. This
period setting with any number of stages. Starting
value is clearly dependent on the schedule of
salvage or
terminal values, the process would move backw
alternative use values.
culating option values one step earlier (using th
4. The Option to Default (on Planned Staged
Cost Installments) During Construction
Even during the construction phase, management may
abandon a project to save any subsequent investment out-
down values obtained in the preceding step), and
two-period extension is illustrated in the next se
the number of steps increases, the discrete-time
naturally approaches its continuous Black-Schol
equivalent (with appropriate adjustments), when
lays, if the coming required investment exceeds the value ists.
from continuing the project (including any future options).
In the next section, we turn to various financial flexibilSuppose that the investment (of $104 present value) necity options, starting with equityholders' option to default
essary to implement the oil extraction project can be staged
on debt payments deriving from limited liability. A similar
as a series of "installments": Io = $44 out of the $104
allocated amount will need to be paid out immediately (in
year 0) as a start-up cost for infrastructure, with the $60
balance placed in an escrow account (earning the risk-free
rate) planned to be paid as a II = $64.8 follow-up outlay
financial abandonment option held by the lender can be
created through staged financing. Interactions among such
financial flexibility and the earlier operating options are
explored.
for constructing the processing plant in year 1. Next year
management will then pay the investment cost "installment" as planned only in return for a higher project value
Ill. Interactions With Financial Flexibility
from continuing, else it will forego the investment and
receive nothing. Thus, the option to default when investment is staged sequentially during construction translates
into E = max(V - II, 0):
A. Equityholders' Option to Default on
Debt (Limited Liability)
So far we have dealt with various operating or real
E+ = max(V+ - 1, 0)= max(180 - 64.8, 0) = 115.2,
options, implicitly assuming an all-equity firm. If we allow
for debt financing, then the value of the project to
equityholders can potentially improve by the additional
i.e., continue;
amount of financial flexibility (or the option to default on
debt payments deriving from limited liability) beyond
E = max(V - II, 0) = max(60 - 64.8, 0) = 0, (14)
what is already reflected in the promised interest rate. We
can illustrate how to incorporate the value of financial
i.e., default. The value of the investment opportunity (with flexibility by reevaluating the original investment opporthe option to default on future outlays) is given by:
tunity with project financing (where the firm consists
entirely of this oil project). Consider, for example, venture
capital financing of a single-project start-up oil company.
pE0 +(1 (1
-p)E
+r)
Suppose initially that venture capitalists (or "junk" bond
444 =-1.33 (15)
1.08
0.4 x 115.2 + 0.6 x 0
purchasers) would be content to provide funds in exchange
for contractually promised fixed-debt payments, and re-
quire an equilibrium return on comparably risky bonds
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TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 217
(that already reflects a premium for equity's option to
+ pE + (1 - p)E 0.4 x 264.08 + 0.6 x 48.08
El =
124.52,
(1 08
+ r) =
1.08
default) of 16.7%.10, 11
Specifically, suppose that I? = $44 out of the required
-+
immediate $104 outlay is borrowed
against the invest-
pE2 + (1l-p)E2 0.4 x 48.08 + 0.6
ment's expected future cash flows
to be
repaid
interest
E=
(118
= with
17.81.
(1 + r) 1.08
in two years at the promised equilibrium interest rate of
16.7% per year. The balance of IE = $60 is supplied by the
Finally, moving another step ba
firm's equityholders (i.e., the entrepreneurs). Equityvalue of the oil investment oppo
holders, of course, have an option to acquire the firm
financing) is:
(project) value V - which in the meantime is "owned" by
the debtholders (here, the venture capitalists) - by paying
back the debt (with imputed interest)
exercise
(I as
+ r)
1.08 price two
E0PE+ (1 - p)EIE = 0.4 x 124.52 +0.6 x 17.8160-4. (17)
years later. Thus, in year 2, equityholders will pay back
(expanded
or adjust
what they owe the debtholders This
(D2 = 44
x 1.1672 = 59.92)
the NPV
the all-equity
only if the investment value exceeds
the of
promised
pay-
tion
(2), liability
confirming
ment, else they will exercise their
limited
rights tothat d
librium
interest
rate (tha
default (i.e., surrender the project's assets to debtholders
equityholders'
option
and receive nothing), or E2 the
= max(V2
- D2, 0). Thus,
action.
Since,
inyears
this
depending on whether oil prices
move up
in both
case
(++), up in one year and down in the other (+ -) or down
12The 16.7%
return
in both years (- -), the equityholders'
claimsequilibrium
in year 2 will
option
be:
to
default
promised
face
E?+ = max(324 - 59.92, 0) = 264.08,
E2+
E2+-=
=E+
= max(108 - 59.92, 0) = 48.08,
debt
value
current
value
amount
that
payoff
of
to
the
equals
debtholders'
above
debt
or
the
example,
D+
ing on whether the oil market was up or down, would then
be, according to CCA:
=
the
at
d
rep
debt
(D
the
debthold
current
d
terminal
value
of
terminal
min(B,
d
in
(rD)
be
the
valuation
the
to
satisfies
where
the
rate
debt
the
of
The value of equityholders' claims back in year 1, depend-
account
interest
the
the
terminal
E2 = max(36 - 59.92, 0) = 0.
of
into
324)
p
the
peri
=
B,
D =D+ =min(B, 108)= B,
D2 = min(B, 36) = 36.
1oFor
a
good
ments,
ment
see
of
1I
a
adjust
n
addition
high
sation
in
to
required
in
the
the
form
context),
rather
through
better
form
of
capital
financing,
(1 + r) 1.08 1.08'
to
financial
ano
fina
flexibility
(1 + r) 1.08
fixed
prefer
equity
or
their
for
debt
(or
preferred
a
ownership
to
r)
place(1 +their
since
they
investment
power.
tax-free
of
the
pDT capitalists
+ (l - p)DY
venture
a
stock)
pa
equity
funds
can
through
in
the
generally
the
0.4B + 0.6(0.4B + 21.6)
of
(especially
debt's
fo
exe
cove
The
44 =
debt principal may al
1.082
recovery of capital for youn
not
be resulting
feasible
with
the com
in B = 59.94. From
D(1l + rD)2 = Bstock
with DO = 44, thisuntil
implies
consider
the
simpler
case
of all-d
that here
rD = 16.7%. The fact
that the project
NPV remains unchanged
with
financing in Equation (17) confirms
that this is thedebt-equity
equilibrium rate
but laterdebtconsider
mixed
fi
we
capitalists.
financi
present
+ (1(recapitalization).
-p)D2 0.4B+0.6x36
overpD
time
Some
voting
may
Initially
[72]
pD
+-(1 - p)D2 0.4B
+ 0.6B B
between
corporate
refer
percentage
may
over
public.
venture
a
common
that
Triantis
venture Finally,
capitalists
may
want
ofyear
thei
moving
another
steppart
back to
0
of
stock's
and
they
level
warrants).
mechanism
firms
debt
rate),
control
the
where
contractually
however,
than
effective
held
firm's
Mauer
interactions
decisions,
the
The value of debtholders'
claims back in year
1 then is:
discussion
of venture
capital
[88].
dynamic
investment
to
qualitative
Sahlman
that fairly prices the default option ex ante.
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218
FINANCIAL
rate
does
The
on
debt
not
is
an
change
firm
default
MANAGEMENT
/
AUTUMN
1993
equilibrium return, the p
I p(E-)' + (1 -p)(E-)' 0.4 x 59.72 + 0.6 x 0
with the introduction of deb
Eo = (1+r) 1.08 = 22.12.(18)
compensates
the
lenders
ex
ante
th
premium embedded in the pr
Thus, the incremental value of the operating default opti
librium rate in exchange for financial flexibili
in the presence of financial flexibility is 22.12 - (- 4)
Of course, if lenders were to accept a lower
26.12 or about one-fourth of gross investment value, f
interest rate of, say, 12% that did not incorp
exceeding the three percent value of the equivalent ope
fair premium for the option to default, E0
ating option to default under all-equity financing in Equ
instead be - 1.40, resulting in an additional va
tion (16) above. This confirms that the incremental val
cial flexibility to equityholders (resulting from
of an option in the presence of other options may diff
to default on debt) of -1.40 - (- 4) = 2.60, or
significantly from its individual value in isolation, and th
percent of the investment's gross value. In
financial and operating flexibility options may interact
potential interactive effects between operatin
These option interactions may be more pronounced if
cial flexibility may further magnify the amou
lenders accept a lower interest than the fair equilibriu
valuation caused by traditional DCF techniqu
return of 16.7%. For example, had the promised intere
consider the presence of both financial flexibil
rate been only 12%, Eo' would instead be 23.74 and th
from equityholders' limited liability rights to
the
B.
option
operating
combined value of the operating option to default
default option analyzed earlier.
planned cost installments (determined separately to b
Potential
and Financial Default Flexibilities
about three percent in Equation (16)) with the extra finan
Interaction
O
cial flexibility to defaultBetween
on debt (separately estimated
about three percent in the preceding section) would b
about 28%. This combined value far exceeds the sum of
Suppose now that ID = $44 were borrowed as before
from venture capital sources (or by issuing junk bonds)separate
to
option values, indicating the presence of substan-
be used immediately as an investment start-up cost for
tial positive interaction (i.e., 28% > (3 + 3)%). Such posiinfrastructure, while the $60 equity contribution is totive
be interaction effects are typical in compound option
situations such as these. 14
potentially expended (with earned interest) as a secondstage investment "installment" for building the processing
plant in year 1 (as I, = 64.8).13 Thus, equityholders now
have extra operating flexibility to abandon the project C.
(by Venture
choosing not to expend the "equity cost
Capitalists' (Lender's) Option to
Abandon
Via
Staged Debt Financing
installment," Il,
if it turns out to exceed the project's value) in year 1.
So far we have focused on the financial option to default
on debt payments held by the equityholders (entrepreAgain, starting from the end and moving backward, the
neurs).
The venture capitalists, however, may also wish to
value of equity's claims in year 2 (with debt repayment)
generate an option to abandon the venture themselves by
remains unchanged, but in year 1 now becomes the maxion providing staged or sequential capital financmum of its value in the previous case (in the absenceinsisting
of
ing. For example, they could insist on actually providing
any outlay for continuing) minus the "equity cost" I, now
only half the requested $44 amount up front, I0 = $22 (to
due, or zero (if the project performs poorly and equity-
holders default), i.e., (El)' = max(E1 - If, 0):
(E)' = max(124.52 - 64.8, 0) = 59.72 (continue);
(El)' = max(17.81 - 64.8, 0) = 0 (abandon).
be repaid at the 16.7% required rate as $29.96 in two
years), with the remaining portion (allowed to grow at the
eight percent riskless interest rate, Ii = $22 x 1.08 = 23.76)
to be provided next year, contingent on successful interim
progress. Following a successful first stage, the second
stage would be less risky so that a lower 12% rate would
The value of the investment (with both operating and
be agreeable (with the $23.76 to return $26.61 a year later).
financial default flexibility) is:
The equityholders would thus also need to contribute (IJ
= 22) toward the $44 upfront cost for infrastructure
13Notice that this case is identical to the operating default case in Section
II.B.4. above, with the only difference being that the initial outlay now
comes from borrowed money.
(I0 = I0 + I = 22 + 22), as well as (If = 41.04) toward the
14See also Trigeorgis [106] for the nature of real option interactions.
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TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 219
the value
of equity's
default opt
potential second-stage $64.8 Thus,
processing
plant
cost one
capitalists'
option toat
abandon b
year later (II = I, + IE = 23.76 venture
+ 41.04),
if the venture
that time appears worth pursuing
vide
further.
second-stage financing, is 10.0
14% of gross
project
value.
Suppose that the venture capitalists
would
choose
to
provide second-stage financingThis
(at the
lower
value
is less12%
thanrate)
the 26% equit
value(i.e.,
found
in Subsection
B above, w
only if the first stage is successful
following
a "+" oil
price state in period 1), but would
otherwise
chooseoption.
to
capitalists'
abandonment
The
abandon the venture in midstream.
In this
case, equityshould thus
be willing
to pay a prem
holders' value in the intermediate
states
in year their
2 may
(million)
to preserve
option to
differ, contingent on first year
apparent
success.
That
is, value
debt
financing.
Still, the
above
that in
Section
III.A.,case,
where
the full $4
E2- would differ from E ~+, since,
in
the first
the
venture capitalists would be repaid
$26.61 for the
secondwas unequivocally
committed
upfront.
stage financing they would provide
following
a successful
venture
capitalists are
better off via the
first stage, in addition to thethe
$29.96
repayment
for
the
venture
by refusing
to contribute
s
upfront debt financing. Thus,
ing in case of interim failure. This, in
equityholders to obtain better financ
saving
debt interest costs.
E2 = max(324 - (29.96 + 26.61),
0) on
= 267.43
Indeed, as discussed further below, s
E2 = max(108 - 56.57, 0) = 51.43
nancing deal in contingent stages to m
the inherent resolution of uncertainty o
(while following a "-" state in period 1 only the upfront
different stages can make both parties
debt repayment need be made:
ample, providing equity financing in st
upfront, would not only benefit the ve
E2+ = max(108 - 29.96, 0) = 78.04
their option to abandon, but may also
E2 = max(36 - 29.96, 0) = 6.04.)
neurs to raise equity capital later at a
favorable valuation resulting in less eq
following
a bad 1,
interim
state, of
entrepren
If there were no outlays required
in period
the value
ably have more information and may
equityholders' claims would be:
project is worthwhile to pursue) can pr
of the venture by the lenders by renego
+ 0.4 x1.08
267.43 + 0.6 x 51.43= 127.62
priate second-stage financing terms g
El - 1.08127.62
0.4 x 78.04 + 0.6 x 6.04
(with E- = 1.08 = 32.26).
higher risks, thus generating mutual g
underlying agency or underinvestme
case. More generally, the flexibility to a
Since equityholders would actually need to contribute terms of a financing deal to better ma
I4 = 41.04 in period 1 for the venture to proceed, the correct operating project risks, whether incre
(revised) value is the maximum of the above value in the as the project moves into its various s
absence of any outlays minus the "equity cost" If, or zero compared to a passive alternative whe
(if the venture performs poorly and is abandoned in mid- terms are irrevocably committed to fro
stream), i.e., (El)' = max(E1 - I, 0):
less complete information. The value c
solving this information problem via f
(E-)' = max(127.62 - 41.04, 0)= 86.58,
financing arrangements can be of mut
parties.
but when (EL)' = 0, after a disappointing first stage, the
venture would be abandoned. Finally, the time-0 value of
equityholders' claims becomes:
p(EI)' + (1 -p)(E)' E 0.4 x 86.58 + 0.6 x 0
E (1r) -10- 1.08 -22= 10.07. (19)
D. Mixed (Debt-Equity) Venture Capital
Financing
Consider now the case where the venture capitalists
finance the full $44 start-up cost, half in the form of debt
(to be repaid at a 16.7% rate as $29.96 in two years) and
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220
FINANCIAL
MANAGEMENT
/
AUTUMN
1993
the other half in exchange
for
an upfront
22%
debt-equity
financing
results in a gross
inv
ownership share.15 Thus,
the
total
equity
(after both
adding the
104 costs)
of $136.4.
Of th
return and the risk are
divided
proportionately
22%
or $30 would
go to the venture capital
among the entrepreneurs
and
capital
for their
$22the
initial venture
equity investment).
Vent
group
of
equityholders
would
still
make
an of
upfron
are also better
off
in the case
staged de
(compared
to an upfront
capital commitme
(using
the cash
provided
by v
capitalists in exchange for
the
share),
m
would
have equity
better control
of (partand
of) thei
bution
of
I0
=
22
cially in the event of disappointing interim r
a discretionary follow-up equity cost outlay of 1
the project proceeds well.
In this
case,
If venture
capital
equity financing is also
E2
=
max(324
-
stages, the reduced operating uncertainties
29.96,
0)= into
294.04,
proceeds
its later stages) and the highe
+- = E =max(108 -29.96,0) = 78.04,
E2 = max(36 08- 29.96, 0) 78 = 6.04.
venture capitalists following a successful fi
result in less equity dilution for the entrep
example, suppose that the venture capitalists
the first $22 upfront in the form of debt, bu
In the absence of a period-I outlay, the value of equity- decision to contribute the rest ($23.76 in a
holders' claims in year 1 would be:
change for an equity share to be determined
successful interim progress next year. The
+ 0.4 x 294.04
+ 0.6 x152.2,
78.04 152.26,
1.08
- 0.4 x 78.04 + 0.6 x 6.04
values would remain the same as above, an
would change only to the extent that now I
El = 1.08 32.26.
provided by venture capitalists in exchange
1.08
Adjusting for the I = 64.8 discretionary outlay in case the
23.76 of the 64.8 discretionary year-1 outla
the first stage is successful). Thus,
project is continued,
(E )"= max(152.26 - 41.04, 0) = 111.22 (co
(E4)' = max(152.26 - 64.8, 0) = 87.46
i.e., continue;
(El)" = 0 (abandon).
If, contingent on first-stage success, venture
(E1)'= max(32.26 - 64.8, 0) = 0,
since equityholders would abandon the venture. Finally,
the time-0 value of the combined equityholder group's
receive a 13.5% equity share in exchange fo
contribution, the entrepreneurs would then
of $111.22 or $96.2 in the good state
entrepreneurs' time-0 value would be:
claims (with default flexibility) is:
0.4 x 96.2 + 0.6 x 0
Eo" = - 22 = 13.63. (21)
1.08
0.4 x 87.46 + 0.6 x 0
Eo?= 32.4. (20)
1.08
This exceeds the $10.07 value of
The entrepreneurs would receive 78% of
this $32.4
net
under
all-debt
staged financing,
value, or $25.27 (million). This represents
an improvementsavings due to the
representing
over the $22.12 value of an all-debt capital
upfront
com-more flexible, conti
result
of the
mitment of Equation (18) (as well as staging
comparedequity
to the financing sequentia
$10.07 value in the previous case of all-debt
financthestaged
venture
capitalists better off
ing of Equation (19), that gives venture
capitalists anbut would also allo
to abandon),
option to abandon). Note further that this
case
of mixed
raise equity
capital later at a po
valuation. These results confirm
better off if the financing deal is f
'SNote that the $22 committed now amounts to 22% of the gross project
it better
value of $100, assuming a required 20% return on an equity position of
and valuation.
comparable risk.
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matches the evolution o
TRIGEORGIS / REAL OPTIONS, FINANCIAL FLEXIBILITY 221
passive alternative
where
IV. Summary, Conclusions
and
the financing terms are irrevo
cably committed to from the very beginning under less
Extensions
complete information. Building-in flexibility in a financ
Following a comprehensive thematic overview of the
ing deal may determine whether the venture will continue
evolution of real options, this paper has illustrated, through
and eventually succeed or fail when interim performanc
simple examples, how to quantify in principle the value of
does not meet initial expectations.
various types of operating options embedded in capital
Thus, contrary to what is often popularly assumed, th
investments, both for enhancing upside potential (e.g.,
value of an investment deal may not depend solely on th
through options to defer or expand), as well as for reducing
amount, timing, and operating risk of its measurable cas
downside risk (e.g., via options to abandon for salvage
flows. The future operating outcomes of a project can
value or switch use, and to default on staged planned
actually be impacted by future decisions (by eithe
outlays). We have also noted a number of fruitful future
equityholders or lenders) depending on the inherent or
research directions, including more applications and imbuilt-in operating and financial options and the way the
plementation problems, empirical and field studies, theo-
deal is financed (e.g., the staging of financing or th
retical extensions combining options theory with Bayesian
allocation of cash flows among debt and equity claimants
analysis to model learning, with game theory to model
In such cases, interactions between a firm's operating an
competitive and strategic interactions, with agency
thefinancial
decisions can be quite significant, as exemplifie
ory/asymmetric information to model/correct misuse
of typical venture capital case. These interactions ar
by the
managerial discretion, as well as interactions between
likely to be more pronounced for large, uncertain, long
operating and financial flexibility.
development and multistaged investments or growth op
Taking a first step in the latter direction, we extended
portunities, especially when substantial external (particu
the analysis in the presence of leverage within a venture
larly debt) multistaged financing is involved. Understand
capital context and examined the potential improvement
ing these interactions and designing a proper financin
in equityholders' value as a result of additional financial
deal that recognizes their true value, while being flexib
flexibility, starting from the equityholders' optionenough
to de- to better reflect the evolution of a project's oper
fault on debt payments deriving from limited liability.
The
ating
risks as it moves through different stages, can mean
beneficial impact of staging venture capital financing
in
the difference
between success or failure. Options-based
installments, thereby creating an option to abandon by
valuation
the
can thus be a particularly useful tool to corporat
managers and strategists by providing a consistent and
lender, and when using a mix of debt and equity venture
unified
capital was also examined. Staging capital financing
may approach toward incorporating the value of both
the real and financial options associated with the combined
be beneficial not only to venture capitalists (by preserving
and financial decision of the firm.
an option to abandon), but also to entrepreneurs asinvestment
well,
since it allows potentially better financing terms in later
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