do real options really have any value

8/3/2019 Do Real Options Really Have Any Value

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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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http://en.wikipedia.org/wiki/Discounted_cash_flowhttp://en.wikipedia.org/wiki/Discounted_cash_flow


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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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do real options really have any value

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