Introduction to the New Methods
for Project Valuation:
The Real Options Approach
© Paulo Pereira, 2010
“For most investments, the usefulness of NPV
rule is severely limited…, [modern finance]
is now obliged to treat all major investment
decisions as option pricing problems”
(Stephen A. Ross, MIT)
© Paulo Pereira, 2010
1
“Discounted cash flow is going to look at an
average scenario. (…) But if you talk to any
manager, that's not how they think. They
think about contingencies — what's going to
happen, how would we react. And even if
they don't think that way, once it's
presented to them that way, they say, 'Yeah,
that's the way we should be thinking.'"
CFO Magazine, “Will Real Options take roots?”, July 2003
© Paulo Pereira, 2010
Limitations of Traditional Methods
• Rigid methods;
– The cash flows follow a rigid pattern and can be forecasted for
long periods of time.
• They assume “now or never” projects, ignoring the
chance for postponing the investment decision;
– Benefits from postponing: obtain more information about the
project, the market, competitive environment,… In a word:
reveal new relevant information…
– However, the uncertainty will never be totally eliminated.
© Paulo Pereira, 2010
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Limitations of Traditional Methods
• Assume a passive attitude of the manager;
– … as if no decisions would be necessary after implementing the
project;
– … as if the manager would only be needed for taking the
investment decision!!
© Paulo Pereira, 2010
Limitations of Traditional Methods
• The traditional methods ignore the capacity for
modifying the projects as time passes and new
information is revealed;
– ...i.e., ignore the capacity to adapt the project to the new reality,
if that is needed.
• Accordingly, they don’t capture the flexibility of the
project.
• As we will see, this flexibility corresponds to a set of
option embedded in the project.
© Paulo Pereira, 2010
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Limitations of Traditional Methods
• Assume no connection between current projects and
future investment opportunities;
• ... or, at least, do not treat those links in a adequate
manner;
• Basically, because those future investment
opportunities are options, and the NPV is not an
adequate method for evaluating them.
© Paulo Pereira, 2010
Limitations of Traditional Methods
• Those methods were initially developed for valuing
quasi-certain assets (and later adapted for project
valuation);
• They seem to work properly when the environment is
stable and the future is predictable.
• Do we live in this stable and predictable environment?
© Paulo Pereira, 2010
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Limitations of Traditional Methods
• For the traditional methods, more uncertainty mean
more risk premium and a higher discount rate, ...
decreasing the value of a project.
• The new approach should consider that investment
projects are, essentially, “options” or sets of “options”,
where the risk not always is a “value-destroyer”.
• … the owner of an option only cares about the up-side
of the possible payoffs.
© Paulo Pereira, 2010
Financial Options?
• A financial option gives the owner the right to buy or to
sell a given financial asset, the underlying asset (e.g., a
share), for a pre-determined price, the exercise price.
• To have this right, the investor must pay a premium
(the value of the option);
• The option to buy is a call. The option to sell is a put.
• Options can be European (the right can only be
exercised at the maturity date) or American (the right
can also be exercised anytime, prior maturity).
© Paulo Pereira, 2010
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Financial Options?
• At maturity date, the payoff of a call option is:
max[ST − X, 0]
• Notice that, at maturity:
– is always positive, or zero (never negative);
– the value of the options corresponds only to the intrinsic value;
– i.e., in that date, the time value of the option is zero.
• Before the maturity date, the value of the option
corresponds to the sum of the Intrinsic Value (I.V.) and Time
Value (T.V.),
Options Value = I.V. + T.V.
© Paulo Pereira, 2010
What about the Investment
Projects?
• According to the NPV, one should invest if the Present Value
of Cash Flows (PVCF) > Investment Cost (I).
• So, the payoff is:
max[PVCF − I, 0]
• Notice that this is similar to the payoff of a call option:
–
–
–
–
Zero is the lower-bound for the payoffs;
The value is given by the intrinsic value (i.e., the NPV);
At maturity the time-value of the option is zero;
However, before that moment, the time value of the option ca be
positive.
• But,
• ... what’s the maturity of a project?
• ... and, what’s the time-value of the project?
© Paulo Pereira, 2010
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Maturity if a Project?
• The maturity of a project corresponds to the moment when
the investment opportunity disappears..., after which it’s
impossible to undertake the project.
• Reasons for that?
– Contractual reasons (licences, concessions, patents, ...);
– Competitive reasons (the entrance of a competitor into the market
may completely destroy the chance to invest for the other firms);
– There are some situations where the companies have some special
rights over the projects, traducing in perpetual options: control over a
technology, businesses with significant entry barriers,…
• Example: the owner of a vacant land has the right to develop there a real
estate project.
© Paulo Pereira, 2010
Time Value?
• The time value corresponds to the value of the option to
defer the project implementation;
• If the project is not at maturity, the option to defer can be
exercised;
• Two important questions arise:
– How to value the option to defer?
– What’s the optimal timing for implementing the project?
• Later on we’ll answer to this questions.
© Paulo Pereira, 2010
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Real Options
• The are similarities between financial options and real
options:
– Both give rights to the firm ( without obligation counterparts);
– … which correspond to the capacity to modify the project as time
passes.
• According to Copeland and Antikarov (2001), “a real option
is the right, but not the obligation, to take an action (e.g.,
deferring, expanding, contracting, or abandoning) at a
predetermined cost called the exercise price, for a
predetermined period of time - the life of the option.”
© Paulo Pereira, 2010
Types of Real Options
Uncertainty, Flexibility, and Real Options
163
Table 5.3
Common real options
Real option type
Description
Relevant industries
Deferral or waiting
option
Management can wait before
making the investment to see
how the market unfolds.
Resource extraction
industries, real-estate
development, capitalintensive industries.
Staging or
time-to-build
option
When a managerial decision
takes time or is done in stages,
management can default if
market prospects prove worse
than expected.
Technology-based firms
(R&D), longdevelopment capitalintensive industries
(e.g., electric utilities),
startup ventures.
Expand or extend
option
If the project turns out better
than expected, management can
spend more to expand the
project scale or it can extend
the project’s useful life.
Natural-resource
industries (e.g., mining),
real-estate development.
Contract or
abandon option
If the market prospects are
worse than expected, managers
can contract or abandon it for
salvage.
Capital-intensive
industries (e.g., airplane
manufacturers), new
product introductions.
Switching option
Management can select among
the best of several alternatives,
e.g., inputs, outputs or locations,
under the prevalent market
conditions.
Multinational firms with
production facilities in
different currencies,
platform strategy in the
automotive sector.
Compound option
If investment takes place in
stages, the first project can be
valued in view of the future
growth options it creates.
High-tech, R&D,
industries with multiple
product generations,
strategic acquisitions.
© Paulo Pereira, 2010
As summarized in table 5.3, management can benefit from different
types of real options. We here discuss common types of real options in
the context of an electric utility. The necessary tools to quantify the
values of such real options are discussed in the subsequent section.
Deferral or timing option Management is not always confronted with
a now-or-never investment decision. Often it might have the flexibility
to time its investment decision after observing how events unfold.
Suppose that French utility EDF has identified that in the Brittany
region reserve margins are falling to such low levels that they may jeopardize power supply security. EDF, being authorized to open up nuclear
power plants in France, resolves to operate such a plant in Brittany if it
is deemed worthwhile. Since the involved capital investment cost I is
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Real Options
• Analogy between Financial Options and Real Options:
Financial Options
Real Options
Price of the underlying asset
Gross project value (PVCF)
Exercise price
Investment cost
Time to maturity
Time until when the project can be
deferred
Volatility of the underlying asset
Volatility of the PVCF
Risk-free interest rate
Risk-free interest rate
Dividend-yield
Opportunity cost of deferring
© Paulo Pereira, 2010
Real Options
• Fundamental difference: financial options give the owner an
exclusive right; however, real options are, commonly,
rights shared with the competitors.
• This aspect turns the real options models different (and
normally, more complex) from those developed for valuing
financial options.
• In this course we only use some basic models: binomial at
B&S.
© Paulo Pereira, 2010
9
The roles of uncertainty,
irreversibility and flexibility
• The real options value comes from three important
characteristics, which are common to a major part of
the real world investment opportunities:
– Investment decisions are taken under uncertainty, and so the future
about the project cannot be fully predicted;
– Projects have some degree of flexibility which gives the firm, not only,
the possibility to delay the project implementation, but also to modify
the original plans, if and when necessary;
– The investment cost is, at least in part, irreversible, which means that
the investment cost cannot be totally recovered, if the project
performs worse than initially expected.
– If one of these characteristics is not there, the real options approach is
unnecessary, and the traditional NPV becomes an appropriate
method. Why?
© Paulo Pereira, 2010
The roles of uncertainty,
irreversibility and flexibility
• Why?
– If there is no uncertainty surrounding the project, no future
contingent decisions are necessary. In fact, without uncertainty, the
firm can predict the future and can plan all the decisions/actions
accordingly, being none of them contingent to some random event;
– If a project is totally non flexible the investment decision cannot be
deferred, or, once implemented, no decisions can be taken in order to
modify it. If this is the case in a given investment opportunity, it
means that the project has no options, and so no additional value
exists, compared to the traditional NPV;
– If a project can be abandoned giving the firm the possibility of a total
recovery of the capital that was spent, then there is no opportunity
cost for investing today (giving up the chance to postpone the
decision), since the firm can jump out without penalty..
• Notice that these arguments do not reduce the situations
where real option can be applied. In fact, an exception would
be a project without these characteristics.
© Paulo Pereira, 2010
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What influences the timing?
• A central aspect is: what’s the optimal moment for
implementing a project?
• Notice that the NPV ignores this question.
• The determination of the optimal moment comes from the
equilibrium between the aspects that contribute to the
deferment and those aspects that contribute to the
anticipation.
• Which aspects?
© Paulo Pereira, 2010
What influences the timing?
• Deferment “costs”:
– Lost cash flows (why?)
– Competitive damage (why?)
• Benefits from deferring:
– More information about market conditions: demand, price, costs,
competitors, technology, legal environment…
© Paulo Pereira, 2010
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Descrete-time model:
the binomial method
© Paulo Pereira, 2010
The Binomial Model
u = es
Dt
1
d=
u
( 1 + rf ) - d
p=
u-d
q = 1- p
p
u xV
V
q
d xV
Where:
- s represents the volatility;
- rf represents the risk free rate;
- Dt represents the time-step (if s and rf are annual, Dt=1);
- p e q represent the probabilities for an up and down movements;
- u e d represent the “dimension” of the up and down movements.
© Paulo Pereira, 2010
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The Binomial Model
© Paulo Pereira, 2010
The Option to Defer
© Paulo Pereira, 2010
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CASE 1
Assume a company facing the chance to invest real estate
project. The gross project value (present value of the future
cash flows) is e12.5 million and the investment cost is e10
million, which increases 10% if deferred for a year. The firm
estimates that the volatility of the gross project value is about
35% (per annum). The investment decision can be deferred for
one year, after which the investment opportunity disappears.
Additionally, the firm knows that the risk-free rate is 5% (per
annum continuously compounded).
Questions:
1) What’s the project value according to the NPV method? And
what it says about the timing of the investment?
2) What type of flexibility the firm has? Is that an option?
3) What’s the true value of this investment opportunity?
4) What’s the value of the option identified in 2)?
5) Where (and why) the NPV fails?
Solution:
The inputs:
u = es Dt = e 0,35 1 = 1,4191
1
d = = 0,7047
u
(1 + r f ) - d (1 + 0,05) - 0,7047
p=
=
= 48,34%
u-d
1,4191 - 0,7047
q = 1 - p = 51,66%
© Paulo Pereira, 2010
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Solution:
u = 1,4191; d = 0,7047; p = 48,34%; q = 51,66%
Next year the PVCF can increase
upto 17,7m€ (w/ prob. = 48,3%) or
decrease to 8,8m€ (w/ prob. = 51,6%)
Payoff of the decision
to invest
In this situation
17,7
6,7
the company
invests
(17,7 – 11 = 6,7)
0,0
In this situation
the company
do not invest
(8,8 < 11).
p
3,10
12,5
q
t=0
8,8
t=1
t=0
t=1
Value of the option to invest within 1 year:
(6,7 x 0,4834 + 0 x 0,5166)/1,05 = 3,1 m€
Solution:
NPV = 12,5 – 10 = 2,5m€
Value of the option to invest next year: 3,1m€
How to interpret the results?
It is more valuable to keep the option to invest alive,
instead of investing immediately; so the correct
decision is to defer the implementation of the project.
What is the value of the Option to Defer (OD)?
Corresponds to the time-value of the option:
3,1m€ - 2,5m€ = 0,6m€
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The binomial method for valuing the
option to abandon and the option to
expand
© Paulo Pereira, 2010
A company is going to invest in highly volatile market, which, in the
next two years, can perform good or badly. Assume that the present
value of the expected cash flows is €1M and investment cost is €0.9M.
The firm can, in next two years, either expand the business (by
increasing the global cash flows in about 30% at a cost of €0,42M) or
abandon the market (for a salvage value of €0.7M). Additionally, the
firm estimates the volatility as being 30%, and knows that the risk
free rate is 5%.
Questions:
1) What type of options the firm has?
2) What’s the value of the project according to the standard methods?
3) What’s the value of the options identified in 1)?
4) What’s the true value of the project?
5) Assume now the salvage value is €0,8M. What is, in these
circumstances, the value of the option to abandon the market?
© Paulo Pereira, 2010
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The value of the project?
NPV = 1000 – 900 = 100k€
But, what’s the value of the project knowing the company can:
a) Abandon if the “environmnt” becomes unfavorable;
b) Expand if the “environmnt” becomes favorable.
© Paulo Pereira, 2010
The Value of the Option to Abandon
© Paulo Pereira, 2010
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Solution:
The inputs:
u = es Dt = e 0,3 1 = 1,34986
1
d = = 0,74082
u
(1 + r f ) - d (1 + 0,05) - 0,74082
p=
=
= 50,77%
u-d
1,34986 - 0,74082
q = 1 - p = 49,23%
© Paulo Pereira, 2010
Solution:
u = 1,34986; d = 0,74082; p = 50,765%; q = 49,235%
1000,00
1349,86
max(1349,86; 700)
Do not Abandon
740,82
max(740,82; 700)
Do not Abandon
1822,12
max(1822,12; 700)
Do not Abandon
1000,00
max(1000; 700)
Do not Abandon
548,81
max(548,81; 700)
Abandon
© Paulo Pereira, 2010
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Solution:
u = 1,34986; d = 0,74082; p = 50,765%; q = 49,235%
1000,00
1349,86
max(1349,86; 700)
Do not Abandon
740,82
max(740,82; 700)
Do not Abandon
1822,12
max(1822,12; 700)
Do not Abandon
1000,00
max(1000; 700)
Do not Abandon
700,00
max(548,81; 700)
Abandoning CF
© Paulo Pereira, 2010
Solution:
u = 1,34986; d = 0,74082; p = 50,765%; q = 49,235%
1000,00
1349,86
max(1349,86; 700)
Do not Abandon
811,71
max(740,82; 700)
Do not Abandon
Value incorporating the option to abandon
(1000 x 0,50765 + 700 x 0,49235)/1,05
1822,12
max(1822,12; 700)
Do not Abandon
1000,00
max(1000; 700)
Do not Abandon
700,00
max(548,81; 700)
Abandoning CF
© Paulo Pereira, 2010
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Solution:
u = 1,34986; d = 0,74082; p = 50,765%; q = 49,235%
Value incorporating
the option to abandon
1033,24
1349,86
max(1349,86; 700)
Do not Abandon
811,71
max(740,82; 700)
Do not Abandon
1822,12
max(1822,12; 700)
Do not Abandon
1000,00
max(1000; 700)
Do not Abandon
700,00
max(548,81; 700)
Abandoning CF
© Paulo Pereira, 2010
Solution:
A different way for valuing the option to abandon:
Payoff of abandoning= 700 – 548,82
= 151,19
Value of the Option to Abandon:
-2
= 151,19 x 0,49235 x 0,49235 x 1,05
= 33,24 k€
© Paulo Pereira, 2010
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The value of the Option to Expand
© Paulo Pereira, 2010
Solution:
Expand!
1822,12
max(1822,12; 1,3 x 1822,12 - 420)
1349,86
max(1349,86; 1,3 x 1349,86 - 420)
1000
max(1349,86; 1334,82)
740,82
max(740,82; 1,3 x 740,82 - 420)
max(740,82; 543,07)
max(1822,12; 1948,76)
1000
max(1000; 1,3 x 1000 - 420)
max(1000; 880)
548,81
max(548,81; 1,3 x 548,81 - 420)
max(548,81; 293,45)
© Paulo Pereira, 2010
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Solution:
The value of the Option to Expand?
Expansion Payoff
= (1,3x1822,12 – 420) – 1882,12
= 126,64
Value of the option to expand
-2
= 126,64 x 0,50765 x 0,50765 x 1,05
= 29,60 k€
© Paulo Pereira, 2010
What’s the value of this project?
Project Value
= NPV + Value of the Options
= NPV + Value OA + Value OE
= 100k€ + 33,24k€ + 29,60k€
= 162,88k€
Conclusion?
The NPV undervalue the project by not
considering the flexibility (the options)
the project has.
© Paulo Pereira, 2010
22
Challenge:
Determine the value of the option to
abandon for a salvage value of 800k€.
© Paulo Pereira, 2010
Challenge
u = 1,34986; d = 0,74082; p = 50,765%; q = 49,235%
1349,86
max(1349,86; 800)
Do not abandon
1000
?
740,82
max(740,82; 800)
Abandon
1822,12
max(1822,12; 800)
Do not abandon
1000
max(1000; 800)
Do not abandon
548,81
max(548,81; 800)
Abandon © Paulo Pereira, 2010
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What is the optimal timing for
abandoning?
(...)
(...)
251,19 x 0,4923 x 1,05
740,82
max(740,82; 800)
Abandon
0
1
Payoff OA1 = 59,18
-1
548,81
max(548,81; 800)
Abandon
2
Payoff OA2 = 251,19
Value of the OA1: 59,18
Value (at moment 1) of the OA2: 117,78
What is the optimal timing for
abandoning?
Value of the OA1: 59,18
Value (at moment 1) of the OA2: 117,78
If we abandon in moment 1 we “kill” the option to abandon in
moment 2: we incur in an opportunity cost!
Question:
The payoff of OA1 more than compensate that opportunity cost?
No!
Then, the option to abandon should not be exercised in moment 1.
We should defer the decision and eventually abandon in moment 2.
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