Post on 07-Apr-2018
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Do Real Options really have any value?
DO REAL OPTIONS REALLY HAVE ANY
VALUE?
A DEMO OF OPTION TO DELAY FOR A POWER
GENERATION PROJECT
Mohiuddin Asad
MBA(UK), ACCA, CMA, CIA, CFE, FFA, CCSA,
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Introduction
In this article, author has designed a real-life example to demonstrate
evaluation of real options. He has selected a Power Generators
Company which is reviewing an Option to delay for a special solar
power generators project. Author has collected current data from
market and has made realistic assumptions about future cash flows,
volatility and time horizon. Based on this information, he has first
calculated the value of project using discounted cash flow techniques
and then calculated the value of the project by real option valuation
techniques, using Black-Scholes model. He has used excel
spreadsheets for above computations and has varied critical inputs to
demonstrate their impact on net present value (NPV) and real option
value which is supported by graphical illustrations also.
In the final section, Author has discussed the difference between NPV
and real option value, explaining why or why not one should always be
greater than the other and which variables affect the difference
between these two valuations. Finally, he has assessed the reliability of
the conclusions obtained using NPV versus real options approach.
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Overview of the Project
ABC Company is a medium sized limited liability company which was
incorporated in 1990 in a Middle eastern country. It produces and sells
specialized Power generators, ranging from 10kva to 600kva. ABC is
now considering a project to produce and sell solar energy power
generators which shall mainly be used in remote parts of the country.
Accordingly, a Three year project named Project solar is under
review. The project will cost $80 million and is expected to generate
cash flows of $34.12 million per year for three years. ABCs weighted
average cost of capital (WACC) is 8% which is same as its required rate
of return but considering risk of the project, it has added a risk
premium of 2% so the adjusted required rate of return is 10%. Current
risk-free rate for three years is 1.06% which is derived from latest US
treasury bills rate. Marketing department of ABC has carried out a
detailed market research, based on which they have forecasted that
that there is a 28% chance of high demand in which case, future cash
flows shall be $50 million per year. There is a 43% chance of average
demand, with future cash flows of $36 million per year and a 29%
chance of low demand with future cash flows of $16 million per year
only. The management of ABC is very concerned about future
prospects of the project. Though the project looks feasible and is
expected to generate positive NPV, yet if the demand does not pick up
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as expected, ABC will have to sustain heavy losses. This uncertainty is
further enhanced by the rumours that government is considering a
plan to supply electricity to the remote areas of the country.
ABC has advantage in this project because of its existing resources and
set up; otherwise barrier to entry is quite high. Due to the special
characteristics, Project solar has an investment timing option and can
be delayed for one year. ABC is interested to evaluate whether such
option would be valuable. In line with special features of the project
and for the sake of simplicity, it is assumed that the cost will still be
$80 million at the end of the year, and the cash flows for the
mentioned scenarios will still last three years; hence, there is no cost
to delay. Since the barrier to entry is very high, there is no possibility
for competitors to snatch business during deferral period. The deferral
can help ABC to understand and analyse the level of demand in a
better way so that it will implement the project only if it adds value to
the company. Value of any real option increases if the underlying
project is very risky and if there is a long time before option must be
exercised. Since Project solar is risky and has one year before ABC
must decide, so the option to delay seems valuable.
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Valuation
Based on the above information, we can first calculate the Net present
value of the project using the classical discounted cash flow method,
without considering any option. Below table shows NPV of the project
using Present value annuity table for 3 years at 10% i.e.
$34.12mx2.487= $84.85m - $80m = $4.85m.
Now we can use decision tree analysis to calculate NPV of the project
with the investment timing option. First, we will calculate NPV
assuming that ABC implements the project now. Scenario A in following
Table shows NPV, Variance, Standard deviation and coefficient of
variation calculated assuming that the project is started now :
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Scenario B shows NPV, Variance, Standard deviation and coefficient of
variation calculated assuming that the project is implemented after
one year, only if optimal:
It should be noted that in Scenario B, cost of the project is discounted
at the risk-free rate, since the cost is known. However, operating cash
flows are discounted at adjusted required rate of return (RRR). The
option to defer the project resembles a financial call option. Inputs
needed to apply option pricing theory to valuing the option to delay
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are the same as those needed for any option. We will need value of the
underlying asset, the variance in the value of underlying asset, the
time to expiration on the option, the strike price, the risk less rate and
the equivalent of the dividend yield i.e. cost of delay which is not
applicable in ABCs case as assumed earlier.
According to our base case, ABC has until Year 1 to decide whether or
not to implement the project, so the time to expiry of the option is one
year. If ABC exercises the option, it must pay a strike price equal to
the cost of implementing the project. If it executes the project, it gains
the value of the project. Like when a call option is exercised, a stock is
received that is worth equal to whatever its price is. Similarly If ABC
implements the Project; it will gain a project whose value is equal to
the present value of its cash flows. Thus, the present value of a
project's future cash flows can be used in place of current value of a
stock. The rate of return on the project is equal to its cost of capital.
To find the value of a call option, we also need variance of its rate of
return; hence, to apply call option formula, we will need standard
deviation of the projects expected rate of return, square of which is
equal to Variance.
Firstly, we need to find the value of the project's future cash flows, as
of the time the option must be exercised. We will also need the
standard deviation of the project's value as of the date it must be
exercised. This calculation is shown in Table below:
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The above figure of $84.85m is the future cash flows which should be
converted into present value of the project's future cash flows as
calculated below:
As discussed earlier, to find the value of real option, we need variance
of the projects expected rate of return. This can be done using direct
approach to estimate the variance of the project's rate of return as
shown in table below and:
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the indirect approach which starts by estimating the coefficient of
variation (CV) of the project's value at the time the option expires. We
have already calculated that (CV=0.38) above. Putting figures into
below formula, we get Variance of the projects rate of return that is
13.5%.
We now have all information ready to use the black Schole model to
calculate value of ABC option to delay as follows:
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t
]1CVln[2
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Therefore, for Project solar ABC has an option to delay worth
$10.41m. Considering NPV of $4.85m, total value of the project without
any option is $4.85m whereas total value of the project including
option to delay is $4.85 + $10.41= $15.26m.
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Variation in inputs and their impact
We will now vary some critical inputs in our base case and see how
these impact our NPV of $4.85m and real options value (ROV) of
$10.41m. Firstly, let us assume that the initial investment required was
$79m instead of $80m with other things remained same. This will
increase NPV from $4.85m to $5.85m. The increase in NPV is obvious
because now less cost is required to get the same benefits. This
change will also result in an increase in ROV from $10.41m to $10.81m
because the strike price has been reduced now. For the same reasons,
if we increase the initial investment from $80m to $81m, keeping
everything else constant, the NPV and ROV will reduce to $3.85m and
$10.02m respectively. Now let us suppose that required rate of return
or cost of capital is increased from 10% to 11% in our base case. This
will reduce NPV from $4.85m to $3.38m and ROV from $10.41m to
$9.34m. This is because that a higher discount rate will reduce the
present value of the cash inflows and consequently the NPV will be
reduced. Similarly for ROV, a decrease in underlying assets value will
lead to a reduction in the option value. For the same reason if required
rate of return or cost of capital is decreased from 10% to 9%, NPV will
increase from $4.85m to $6.37m and ROV will increase from $10.41m
to $11.59m. Now let us increase uncertainty or volatility and see its
impact on NPV and ROV. When the uncertainty is higher, the project is
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more risky and consequently NPV is lesser. However, this has opposite
impact on ROV, the higher the uncertainty or variance, the greater is
the value of option. In our base case, when we raise standard deviation
of returns from 32.17 to 35.54, NPV goes down from 4.85m to 4.3m.
However, this results in an increase in variance; hence ROV goes up
from $10.41m to $11.22m.
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Difference between NPV and Real option value
Net present value (NPV) is the main tool in discounted cash flow (DCF)
analysis and is a standard method for using the time value of money to
appraise long-term projects in Capital budgeting decisions. It measures
the excess or shortage of cash flows, in present value terms, once
financing or required charges are met. In other words, NPV of an
investment or project is equal to the difference between the present
value of all future cash inflows and present value of all, initial as well
as future cash outflows, using the required rate of return. According to
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this method, a project with positive NPV is acceptable while a project
with negative NPV should be rejected. Although NPV measurement is
widely used for making investment decisions, a limitation of NPV is that
it does not account for flexibility or uncertainty after the project
decision.
The NPV approach assumes that management will be "passive" as
regards their Capital Investment once committed. It uses information
that is known at the time of the appraisal and choice is all-or-nothing.
As compared to this, real options value (ROV) approach is not about
simply calculating a single NPV before the project begins and then
making a decision to reject or accept the project and sitting back
passively until the projects term runs out. Instead, real options provide
a framework for strategic decision making as the project goes along.
The choice is an initial choice, followed by more choices as information
becomes available. Real option can be described as the right but not
the obligation to acquire the gross Present value of future cash flows
by making an irreversible investment on or before the date the
opportunity expires.
We can explain real option concept by a basic example. Suppose we
want to buy a house and have chosen one for $1m but our loan
application is pending for approval with the bank and expected to be
decided within one week. If we leave the deal open, other buyers will
purchase that house. To cope with this situation, we may agree with
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the seller to hold the house for one week by paying an amount of say
$2000. By this payment, we are in fact buying an option to wait
whereby if our loan is approved, we can proceed with the deal and if
rejected; we can let the option expire at a cost of $2000 only.
Since NPV only offers decision makers the choice of investing or not
investing, a defining distinction between real options and NPV is based
on the choices that each method offers. NPV rule does not take into
account how the ability to delay irreversible investment expenditure
can profoundly affect the decision to invest (Dixit and Pindyck, 1994).
Thus the basic assumptions of real options and net present value,
specifically regarding investment deferral and reversibility, are
important for comparison. Dixit and Pindyck (1994) state that being
able to delay an irreversible investmentundermines the simple net
present value rule, and hence the theoretical foundation of standard
neoclassical investment models. NPV does not recognize the
managerial alternative of waiting, delaying the start of, or phasing the
investment of a project whereas real options theory recognizes that an
investment decision can be delayed, expanded, contracted or
abandoned.
Thus to sum up, one of the most important differences between NPV
and ROV approaches is the Flexibility. NPV implicitly assumes that
management will be "passive" as regards to their Investment once
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committed, whereas ROV assumes that they will be "active" and can
modify (i.e. defer, abandon, expand, or contract) the investment as
necessary. Another important difference arises from the element of
Uncertainty. In NPV method, higher uncertainty means higher
discount rate and thus lower NPV. To contrast, in real options theory,
higher uncertainty leads to higher option values.
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Should one always be greater than the other, why or why
not?
In the absence of uncertainty over time, both the real option value and
the net present value are equal to the present value of the project
assets less the expenditure required to obtain those assets. However,
when there is uncertainty, the real options value of a project is always
higher than the NPV. According to Bodie and Merton (2000), the net
result of uncertainty is, by not accounting for managerial flexibility,
the NPV of the project will be underestimated relative to the real
options approach (Bodie and Merton 2000). Glantz (2000) states that
net present value essentially disregards any opportunities in
investment analysis to change the game plan. Because flexibility is the
epitome of real options theory, NPV consequently underestimates
projects that are clearly elastic (Glantz, 2000). Hence to sum up,
flexibility has value because it can help in increasing profit or reducing
losses of an investment in uncertain situations. Since NPV does not
account for this flexibility in its valuation whereas real option does, the
value of a projects ROV is always higher than the projects NPV in
uncertain situations.
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Which variables affect the difference between the two?
To explain which variables affect the difference between Real options
value (ROV) and net present value (NPV), we shall first see what basic
variables are used in each valuation method. We shall try to map these
variables and then identify the ones that cause the difference.
In NPV, main variables are cash inflows, cash outflows and time value
of money.
A corporate investment opportunity resembles a call option because
the company has the right but not the obligation to invest. Thats why
financial option pricing models are widely used to value real options.
The main variables in an option pricing model are: Risk free rate (Rf),
Cost to implement the project or Strike price (X), Current value of the
project (P), Time until the option expires (t) and Variance of the
project's rate of return (V). As we know that NPV is the difference
between how much the assets are worth i.e. their present value and
how much they cost, cash outflows or initial investment in NPV is
similar to the strike price or cost to implement the project in ROV
whereas present value of cash inflows in NPV resembles the current
value of the project in ROV. Time value of money is given by risk free
rate in both methods. Hence, the variables which cause the main
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difference are time until the option expires and Variance of the
project's rate of return. Uncertainty & flexibility to deal with it are the
main factors that cause the difference as these are what give birth to
options. In a 100% sure world, options will not have any value.
In a deferral option situation, the possibility of deferral gives rise to
two sources of value. The first source of value is the interest that can
be earned on the required capital expenditure by investing it later
rather than sooner. The second source of value is that while we wait,
asset value may change and affect our investment decision
favourably (Timothy, 1998). NPV misses these extra values because it
assumes that decision cannot be put off. On the contrary, option
pricing presumes the ability to defer and provides a way to quantify
the value of deferring.
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How reliable are our conclusions using NPV versus real
options approach?
Both NPV and real option approaches draw their inputs from future
estimations, hence reliability of both results largely depend on the
quality and accuracy of the forecasts.
For instance, NPV calculation is very sensitive to the discount rate,
future cash flows, Cash flow timings and projects expected life. A
small change in these estimations can bring a big change in NPV.
Similarly it is also true that the initial step in most real option analyses
is the present value of an underlying asset, for which a NPV has to be
computed. Hence, reliability of the input is the first thing which
contributes to reliability of the out put from both methods. Further, it
should be noted that Real option valuation (ROV) method is not a
replacement of net present valuation method i.e. these are not
mutually exclusive but rather ROV is an extension of or supplement to
NPV method, so both have their importance and their results can be
relied upon based on their objectives. NPV works fine for safe cash
flows. It also works fine for assets or businesses whose value depends
primarily on forecasted cash flows and not on real options (Page 187,
SFM, Module book,2008). However, the extended benefits offered by
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real option valuation are that unlike NPV, real options enable firms to
cope with high levels of uncertainty about the upside potential or
downside risk of an investment and allow for high levels of flexibility.
Real options hold additional importance because they recognize that
managers can obtain valuable information after the acceptance of a
project. Though real options are not a cure all for capital budgeting
projects, yet Informed actions can make a significant difference to
the overall value of a project. As Baldwin (1987) noted, given the
increase in variability in both product and financial markets worldwide,
companies that recognize option values and build a degree of flexibility
into their investments are likely to be at a significant advantage in the
future, relative to companies that fail to take account of options in the
design and evaluation of capital projects. (Baldwin, 1987) In view of
the current fast changing economic and financial world, Baldwins
vision more strongly support utilizing real options approach. Thus we
may conclude that NPV has its own utility and importance, however, in
today s highly uncertain and challenging business environment, real
option valuation provides a more informed, flexible and reliable basis
for capital budgeting decisions.
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References:
Dixit, A. and R.S. Pindyck, (1994) Investment under Uncertainty,
Princeton University Press, Princeton, New Jersey.
Bodie, Z. and R.C. Merton, (2000) Finance, Prentice Hall, Upper Saddle
River, New Jersey.
Glantz, Morton (2000), Scientific Financial Management, American
Management Association, New York.
Timothy A. Luehrman (1998), Investment Opportunities as Real
Options: Getting started on the Numbers, Harvard business review,
July-August 1998.
Baldwin, C. Y. (1987), the Capital Factor: Competing for Capital in a
Global Environment,
Midland Corporate Finance Journal 5 (No. 1), pp. 43-64.
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