The value of management flexibility—a real option approach toinvestment evaluation

K.T. Yeo*, Fasheng Qiu

Division of Systems and Engineering Management, School of Mechanical and Production Engineering,

Nanyang Technological University, Nanyang Avenue, 639798 Singapore

Received 24 January 2002; accepted 9 April 2002

Abstract

Traditional project evaluation based on discounted cash flow analysis ignores the upside potentials to an investment from man-agerial flexibility and innovations. A real option approach that borrows ideas from financial options offers a fresh perspective. It

views investment strategy as being crafted as a series of options that are continually being exercised to achieve both short and longterm returns on investment. Management’s flexibility to adapt to changes in technology and market introduces a skewness in the dis-tribution of investment payoffs with improved upside potentials. This paper critically reviews the fundamental differences in assump-tions between the traditionally passive approach and the active real options model. The roles of various real options in expanding

bandwidth of opportunity, technology investment and business acquisition decision as real options are discussed and illustrated.# 2003 Elsevier Science Ltd and IPMA. All rights reserved.

Keywords: Real options; Financial options; Project evaluation; Flexibility; Uncertainty

1. Introduction

Corporate managers plan vigorously for success in thefuture, and constantly look out for opportunities forinvestment be it high-tech research and development,entrance to new product market, implementation of amajor enterprise information system, business acquisi-tion or a direct foreign investment of an offshore man-ufacturing facility. Companies, operating in a changingand turbulent marketplace, must be flexible, and cansucceed by making brilliant short-term investments thatlead to long-term results. The belief is that these com-panies are agile; and by making the right moves today,they open up windows of opportunity for learning andprofitability. They learn from mistakes, learn faster thancompetitors, and make quick adjustments to seize oppor-tunities by exercising the options presented to them.In competitive markets, it is unlikely that corporate

executives would succeed by formulating and followinga detailed long-term plan and operating strategy rigidly.Many of these executives now realize that the tradi-tional project investment methods, particularly the dis-

counted cash flow (DCF) based measures are no longeradequate. The DCF method assumes that companieswill follow a predetermined plan (with streams of rev-enues and expenditure, interest rates), regardless of howfuture events unfold.Luehrman [1] suggested that a better valuation

approach would incorporate both the uncertainty (var-iations) inherent in business and the active decisionmaking required for a strategy to succeed. Actions andshort-term initiatives are proactively taken and craftedto control potential variations or to improve payoffs.Proactive options can be exercised to deliver extrainsights and bring long-term benefits. With the under-standing of the option pricing method it is now feasibleand desirable to analyze business and investment stra-tegies as a series of real options to be exercised, someimmediately, while others are deliberately deferred. Thedeferment of decisions allows time for learning and anupturn market condition to unfold.

2. Traditional investment evaluation

2.1. Discounted cash flow approaches

Traditionally, organizations use various types ofquantitative analysis methods to estimate costs and

0263-7863/03/$30.00 # 2003 Elsevier Science Ltd and IPMA. All rights reserved.

doi:10.1016/S0263-7863(02)00025-X

International Journal of Project Management 21 (2003) 243–250

www.elsevier.com/locate/ijproman

* Corresponding author. Tel.: +65-6790-5502; fax: +65-6791-

1859.

E-mail address: mktyeo@ntu.edu.sg (K.T. Yeo).

values associated with a proposed project. The typicalapproaches to project evaluation are based on Dis-counted cash flows (DCF) analysis which providesmeasures like net present value (NPV), internal rate ofreturn (IRR), payback and maximum cash exposure.Net present value (NPV) is defined as the difference

between the present value of the estimated net cashinflows and the present value of the estimated net cashoutflows. It is used when the discount rate (the cost ofcapital, required rate of return, hurdle rate) is known orspecified. According to the NPV approach, the projectshould be accepted if its NPV is positive.From an investment evaluation viewpoint, share-

holder value is created when the present value of aproject’s expected cash inflows exceeds that of theoutflows, resulting in a positive NPV. Cash flows arediscounted to their present value by the firm’s cost ofcapital or a minimum attractive rate that appro-priately reflects perceived project risk. Selecting theappropriate discount rate is a difficult task, especiallyfor projects that are characterized by substantialuncertainty. A conventional approach to deal withinvestment uncertainties, is for the business to developa project-specific, risk-adjusted discount rate based onthe capital asset pricing model (CAPM). The CAPMsays that the cost of equity is the risk-free rate, asrepresented by a government-backed security, plus arisk premium.DCF based approaches assume implicitly that a pro-

ject will be undertaken now and operated on con-tinuously at a set time scale, until the end of its expecteduseful life, even though the future is uncertain. There-fore the DCF ignores the upside potential of addedvalue that could be brought to the project through theflexibility and innovations of management to alter thecourse of investment. Such managerial interventions oroperating decisions during the life of the projectaccording to changes in market conditions over timeprovide companies with a better chance to reap higherreturns or minimize loss in a volatile marketplace.The weakness of DCF is its failure to account for how

uncertainty, rather than implying a higher risk-adjusteddiscount rate, can increase the value of a project invest-ment. Therefore, by assuming management’s passivecommitment to a certain ‘‘operating strategy’’, DCFbased methods usually underestimate the upside valueof investment [2].In essence, the NPV approach makes implicit

assumptions concerning a certain ‘‘expected scenario’’of cash flows. Treating projects as independent invest-ment opportunities, and decision is then made to accepta project for which the computed NPV is positive. TheDCF approach thus, in effect, implies an inflexiblemanagement who makes at the outset an irrevocablecommitment to a certain operating strategy, and abidesby it, until the end of its pre-specified project life. This is

of course an unrealistic assumption and not a reflectionof reality.

2.2. Value of managerial flexibility

An anticipative management may postpone or defer aproject until market conditions are more favorable toachieve a higher return. Similarly, the decision to aban-don a project during the life of the project may benecessary to cut loss. This flexibility of decision impliesthat management has the ability and influence to limitthe downside risk of loss, but retain relatively unlimitedupside potential for profit. Sustainable successes can beachieved by management’s continuous learning in themarketplace and their ability to react correctly to chan-ging dynamics. Performance is driven by a flexible andadaptive strategy that can be implemented rapidly.In the real world of uncertainty and competitive interac-

tions, the realization of cash flows will probably differ fromwhat management originally expected. As new informationbecomes available and uncertainty about future cash flowsis gradually resolved, management may find that variousprojects allow it varying degrees of flexibility to departfrom and revise the operating strategy it originally antici-pated. Management may proactively choose to defer,expand, contract, abandon, or in various other ways alter aproject at various stages during its useful life.Management’s flexibility to adapt its future actions

introduces an asymmetry or skewness in the probabilitydistribution of NPV or payoff that expands the invest-ment opportunity’s true value by improving its upsidepotential while limiting downside losses relative tomanagement’s initial expectations under passive man-agement (see Fig. 1).In the absence of such managerial flexibility, the

probability distribution of NPV would be reasonablysymmetric, in which case the static (or passive) expectedNPV (mean value of the symmetric distribution) wouldcoincide with its mode or most likely estimate [seeFig. 1(a)]. With managerial flexibility, such as exercisingof options and other innovations, it introducesenhanced upside potential so that the resulting actualdistribution is skewed to the right [see Fig. 1(b)]. Thetrue expected value of such an asymmetric distributionexceeds its mode by an option premium, reflecting thevalue of managerial flexibility, with the expected NPV1being enhanced to NPV2. Hence, NPV2 (active)=NPV1(passive)+c, where c=value of managerial flex-ibility afforded by embedded real options.NPV1 is the passive NPV of an investment. Since the

value of managerial flexibility is not a tangible cashflow, it does not enter NPV1’s computation. NPV2 isthe active NPV, which recognizes that real optionsenable management to flexibly change traits of theinvestment in order to add value. The option pricingmethods compute this value separately and then add it

244 K.T. Yeo, F. Qiu / International Journal of Project Management 21 (2003) 243–250

to NPV1. The option value can quite possibly turn anegative NPV1 into a positive NPV2. An originallyrejected project is now viable based on NPV2.DCF based approaches provide an easy and instruc-

tive way to analyze the decision whether to commitresources to a new investment in a stable environment.Nevertheless, they are likely to fail in cases when mar-kets move unpredictably and managers have the possi-bility to adapt their decisions in real-time. Recentresearch in economics, finance and MIS has consistentlyhighlighted the fact that traditional financial measures,such as net present value, do not correctly value invest-ment opportunities that contain real options [3–7]. Theneed for a better method to replace the outdated DCFbased approaches is the motivation for the real optionsanalysis, which is a method for valuing flexibility [3].

3. The real option approach

Since the early 1980s, advances in the real options lit-erature have fundamentally changed the way peoplethink about investment opportunities. Dixit and Pin-dyck [3] made an excellent introduction to real optionstheory. According to them, firms should not invest inprojects, which are expected to earn only the opportu-nity cost of capital. Managers can make choices aboutthe project’s characteristics and this flexibility createsembedded options. These options add value to the pro-ject and invalidate the traditional DCF based rules.Typical options include the option to decide the timingof investment, the option to hold or abandon an activeproject, the option to expand or to reduce the produc-tion capacity, or the option to choose the productiontechnology, products and markets.

3.1. Financial options

An option gives the holder a right but not an obliga-tion to buy or sell a share of stock at a specified price[8]. Financial options are options on financial assets. A‘‘call’’ option gives the holder the right to buy a stock,and a ‘‘put’’ option gives the holder the right to sell astock. If the option can be exercised before maturity, itis called an American option and if only at maturity, aEuropean option. The call option is particularly rele-vant to project investment evaluation.Now let us give an example of the financial option.

One might acquire an option to buy 1000 shares ofNetscape stock at $100.00 per share on 1/12/2002 bypaying a sum of money (say, $20.00 per share) today.This transaction is an example of buying a Europeanfinancial call option. The $20 per share paid to acquirethe option is called the option premium and the price of$100 per share of Netscape is called the strike price. Theoption holder could buy 1000 shares of Netscape stockat $100 per share (this is referred to as exercising theoption) if the transaction is likely to yield a profit (forexample, if the selling price for Netscape shares were$150 on 1/12/2002). On the other hand, the optionholder is not required to exercise the option if condi-tions were unfavorable (for example, if Netscape shareswere priced at $75.00) on 1/12/2002.

3.2. Options pricing model

In the early 1970s, Black and Scholes published thefirst successful model for pricing financial options whichis applicable to simple put and call options on equities[9]. They valued financial options by calculating theexpectation as a function of a Brownian Motion and

Fig. 1. Value of management flexibility.

K.T. Yeo, F. Qiu / International Journal of Project Management 21 (2003) 243–250 245

derived a differential equation that must be satisfied bythe price of any derivative dependent on a non-divi-dend-paying stock. Black and Scholes in their path-breaking paper [9], derived that, in a risk neutral world,the price of a European call option at maturity in a riskneutral world has a closed form solution:

c ¼ SN d1ð Þ � Xe�rðT�tÞN d2ð Þ ð1Þ

where:c: the price of the European call option. S: the stock

price. r: risk free rate of return. X: strike price of theoption. T: expiry date of the option. N xð Þ: the cumula-tive probability distribution function for standard nor-mal distribution. And d1and d2 are given by:

d1 ¼ln S=Xð Þ þ rþ �2=2

� �T� tð Þ

�ffiffiffiffiffiffiffiffiffiffiffiT� t

p

d2 ¼ d1 � �ffiffiffiffiffiffiffiffiffiffiffiT� t

p

Since Black and Scholes [9], the financial option the-ory has become a flourishing branch of probability andmathematical analysis and a large majority of mathe-matical finance research has been carried out in thisfield. The methodologies, which they introduced, havebeen expanded for use in pricing a wide variety of deri-vative instruments and contingent claims. Financialoption pricing methods are now also considered suitablefor the evaluation of technology investments embeddingreal options.

3.3. Real options

The insight in option pricing can be extended todevise a more general contingent claims valuationmodel even when the uncertainty arises from sourcesother than traded security prices [8]. Through the 1980s,financial option evaluation methods had been applied toevaluate flexibility associated with physical investments.This extension has been labeled real option. Realoptions are options on real assets, which can be definedsimply as opportunities to respond to changing circum-stances of a project by management. These opportu-nities to change are rights but not obligations to takesome action in the future [4].A company that wishes to invest in a project possesses

the option to wait for better conditions to implementthis investment. Luehrman [1] made a simple analogybetween a project investment and a financial call option,as shown in Fig. 2. Many projects involve spendingmoney to buy or build a productive asset. Spendingmoney to exploit such a business opportunity is analo-

gous to exercising an option on a share of stock. Theamount of money expended corresponds to the option’sexercise price (X), in terms of the notation used in Eq.(1).The present value of the asset built or acquired cor-

responds to the stock price (S) at the time of exercisingthe option. The length of time the company can deferthe investment decision without losing the opportunitycorresponds to the option’s time to expiration (T�t).The uncertainty about the future value of the project’scash flows corresponds to the standard deviation ofreturns on the stock (�). Finally, the time value ofmoney is given in both cases by the risk-free rate ofreturn (r).Real option evaluation accounts for the value of flex-

ibility embedded within projects as illustrated in Fig. 1.Real options thinking compels managers to go beyond asingle point estimate of the likely future but to recognizea broader domain of possible opportunities. Whereastraditional investment evaluation models limit the con-sideration of opportunities for investment, real optionsprovide powerful mechanisms for funding the pursuit ofa broader bandwidth of opportunities. Many invest-ment scenarios can be considered as sets of options.

3.4. Real options versus financial options

Real options in option thinking are based on the sameprinciples as financial options. To have a real optionmeans to have the possibility for a certain period toeither choose for or against something, without bindingoneself up-front. Real options are valuable because theyincorporate flexibility and potentials. However, the factthat real options are like financial options does notmean that they are the same.The major difference between financial options (e.g.

stock options) and real options is that real options areapplicable to real assets [10]. A real asset is usuallysomething tangible, such as a factory, machinery, etc.,while a financial asset typically consists of stocks,bonds, currency, etc.Some financial options solutions may be useful in the

real investment context with some relevant adaptations

Fig. 2. Mapping an investment opportunity onto a call option.

246 K.T. Yeo, F. Qiu / International Journal of Project Management 21 (2003) 243–250

using financial analogies. The return from an invest-ment, like the return from a stock, comprises the capitalgain and the dividends. Over time, the expected rate ofreturn from a real investment is equal to the sum of theexpected growth rate plus the convenience yield of theunderlying commodity. However, we cannot simplyapply the theory of financial options to the field of realoptions, because of some important differences in theorientation of the two fields.First, financial options are typically short-lived (less

than 1 year to expiry), while real options are long-lived,and some have no expiry date.Second, financial options are written on underlying

assets that are traded in various markets. The tradedassets cannot have a negative price. In real options, theunderlying asset can be a notional asset that is not tra-ded, so there is nothing preventing its price from beingnegative. Usually there is no observable market pricefor the underlying asset of real options because realoptions do not refer to traded assets.Third, financial options are generally quite simple in

the sense that they involve a simple option with a singleexercise price. However, the exercise price of realoptions may vary over time and, may be random. Fre-quently there may be several real options with the sameunderlying asset. For example, performing research anddevelopment (R&D) creates an option to adopt a tech-nology with unknown benefits. If the R&D is successful,there is a subsequent option to expand the product line.While the product becomes obsolete, there is the optionto abandon. So the R&D option will include the valueof the subsequent expansion and abandonment ofoptions.Fourth, option value and optimal time to exercise are

influenced by the market position of the companyholding the option. If competition is imperfect it may beoptimal to exercise options as quickly as possible to pre-empt competitive response and to take full advantage offuture growth opportunities. When the strategic advan-tage is strong, increased uncertainty encourages invest-ment in growth options [11]. In practice, strategicconsiderations may call for an early investment at thesame time that waiting would decrease total project risk:the optimal choice then has to balance the two [12].

4. The role of real options

4.1. Expanding bandwidth in the new economy

The typology of real options based on Amram andKulatilaka [13] and Benaroch [14], may be summarizedinto seven main types of real options that are relevantfor expanding the bandwidth of opportunity in businessmanagement development. The role and examples ofthese options are as follow:

(1) Growth options: infrastructure-based projects inindustries: (1) with multiple product generations, (2)exploring new generation products or processes or newmarkets, or (3) where strategic core capabilities areneeded. Another example of growth options is an entryinto initially loss-making business operations that maymake way for potentially valuable follow-on invest-ments. Internet ventures like ICQ, Hotmail and Geo-cities striving to establish a critical mass of subscribers,are examples.(2) Staging options: when benefits are uncertain,

commit investments in stages thus, retaining the optionto abandon at different stages while retaining the abilityto grow. The multi-stage investments by Lotus to createNotes; and Sun’s alliance with AOL regarding Netscapeare examples of exercising staged options. Multi-stageddevelopment oil and gas exploration and productionhas been commonly used as a risk management strategy.In R&D intensive industries such as pharmaceuticals,long development capital-intensive projects use stageddevelopment. Staged development also has a learningand uncertainty reduction effect.(3) Deferment options: a project that can be post-

poned allows learning more about a potential project orproduct and market outcomes. Stochastic nature ofprices and demands as well as production costs makedeferment options before making a commitment desir-able. For instance, the flexibility associated with projectinitiation timing can be valuable for the offshore oillease operator, who can choose when to develop theoilfield during the lease period.(4) Exit (abandonment or divestment) options: exit

when opportunities do not present themselves. Theproject can be abandoned if market conditions worsenseverely to cut loss, so that project resources could bedivested or put to another use. Exit options can bevaluable when used to minimize losses by de-couplingfrom the mainstream operations; or to explore alliancesand partnerships.(5) Sourcing options: develop multiple input sources

for content, channels and platforms. OEM outsourcingarrangements are examples in manufacturing industry.Project development packages can be sub-contractedout to third parties. Outsourcing and subcontractingcan transfer risk of in-house failure or avoid committinginternal resources.(6) Business scope options: a business operational

capacity and scale can be either expanded or contracted,depending on market conditions in prices and demand.Scope options allow management flexibility, which isimportant when choosing among alternative productiontechnologies, for instance, when conducting life cyclecost analysis. Initial over-capacity creates flexibility toproduce more when demand picks up. Developing theplatform to change project or product scope or to allowbusiness model changes are also business scope options.

K.T. Yeo, F. Qiu / International Journal of Project Management 21 (2003) 243–250 247

Netscape shifting from being a browser company tobecoming an Internet portal; Amazon.com distributingnot only books but also music and video; and Yahoo!offering auctions are real cases.(7) Learning options: investing in operating options

can be used to create a window for education and learn-ing, and lead to enhanced organizational capabilities andconsequential reduction of risk. R&D investment toexplore and learn about different technologies is anexample. Start with a pilot or prototype project to learnabout customer acceptance and production costs isanother example. Sub-options may be created due tolearning and for becoming more knowledgeable.When a company is able to systematically consider

these options, it will be able to expand the bandwidth ofopportunity and be better positioned to leverage theopportunities than those firms that prematurely closecertain options because of constraints of operatingresources or cash flows. These options collectively allowa company to significantly enhance the bandwidth byenhancing the upside potentials, without excessivelyincreasing the downside risks. Nonetheless, at the sametime, sound economic justifications cannot be aban-doned. Even when investments are viewed as options,rigorous business justifications are still required.

4.2. Technology investments as real options

Many technology investments have the options char-acteristics. Real options embedded in a technologyinvestment are valuable, because they allow manage-ment to take rational, value-adding actions that couldfavorably affect operational traits of the investment interms of timing, scale, and scope. For options to havevalue, they must be carefully planned and designed to fiteach investment differently to evolving circumstances.For instance, an investment in data warehouses cre-

ates value over time through the ability to quicklydevelop new applications. Similarly, an open archi-tecture creates sourcing options. One place to startusing the real options approach is to define the types ofoptions frequently encountered in technology invest-ments, allowing decision makers to quickly grasp thesize and relative importance of the various options. Theimplementation team can then determine the degree ofdetailed analysis required to fully detail the proposedalternatives.Examples from IT and high-tech related options are

illustrative. Firms usually invest in two types of tech-nology options: growth (strategic) options and operat-ing flexibility (operating) options:Growth options: the strategy is to adjust the scale of

technology investment over time corresponding to busi-ness growth. Consider a firm whose business strategyrequires an aggressive market expansion into variousparts of Asia. From the IT investment point of view, a

successful expansion will significantly increase the flowof transactions through the supply chain managementsystem. There is, however, uncertainty about the timingand size of market success. In this case, a real optionsanalysis would help decision-makers think through thetiming of the IT capacity expansion. This is achieved bylinking the value of IT investments to the range of pos-sible business outcomes, and by identifying the triggerpoints of key business variables that signal when thenext stage of expansion is warranted. These growthoptions are usually spawned by investments that aim atdeveloping core technologies and/or building experiencewith promising technologies that could become the dri-vers of future organizational capabilities.Flexibility options: operational flexibility options are

common in technology investments that yield directmeasurable payoffs. However, these operational optionsmust be planned and designed to fit each investmentdifferently. The flexibility (operating) strategy allows afirm to more easily and quickly switch product featuresor service offerings to meet changing market conditions.Investment in flexible manufacturing systems which is aclassic example of one that creates product and pro-duction flexibility options in terms of changing productmix and production throughput at later dates.In the utility sector, an electricity generating firm

investing in a new power plant makes a choice betweenplant designs that burn oil only or both oil and coal.The dual-fuel plant option offers the flexibility to switchbetween fuels whenever beneficial fluctuations in fuelprices occur.In the IT world, new software development tools

allow the mass customization of the information andservices of the e-commerce experience. Investment inthese software packages is the acquisition of an optionto allow a future opportunity to quickly and effectivelydevelop new businesses, enabled by this new softwareplatform. Operational options are not inherent in tech-nology investments itself, but must be planned anddesigned to fit each investment differently.

5. Investments embedded with options: case examples

Successful business development can be either tech-nology or market opportunity driven. The value ofmanagerial flexibility by adopting a real options mind-set when entering an emerging market with upsidepotentials can be illustrative.

5.1. Example 1: a case of entering the China markets:adopting a real option mindset

The real option perspective is particularly relevantand valuable when considering entry into the hugeChina market. Foreign companies, either wholly foreign

248 K.T. Yeo, F. Qiu / International Journal of Project Management 21 (2003) 243–250

owned or equity joint ventures, can and are actuallymaking money from their investments in China, as theylearn to appreciate the value of management flexibilityand learn their lessons quickly. Innovative competitorscan even exercise influence in shaping the rules of thegame and creating fresh opportunities in the emergingmarket. The following are some of the lessons learnedthat are in agreement with the real options mindset: (1)recognizing the importance of managerial flexibility bylearning and adapting fast to the changing market andconsumer needs; and (2) learning to capitalize on thechanging market conditions and implement shrewdstrategies by making a series of small but smart movesto drive profitability [15].The case of Volkswagen: Volkswagen after setting up

its assembly plants in Shanghai, China, was quick toadjust its assumptions and operating paradigms andachieved success in an emerging offshore market.Volkswagen adopted a scalable growth strategy. It wasset out initially to serve the commercial market first,and build an aggressive distributor network and salesforce. This created a growth platform to push volumethrough its distributors and achieved critical mass. Itlater exercised an operational option to meet the risingdemand for taxi services by exploiting the potential taxifleet market by selling its locally assembled cars to taxicompanies in Shanghai. The company gained scaleseconomies and drove down prices; while Peugeot,though an early entrant to the emerging China market,was not flexible enough in its market strategy, and itsuffered loss. Sustainable long-term positions are neces-sarily built on a series of successful short-term moves byexercising a series of options, especially in a turbulentand changing market. A virtual cycle for success can beset in motion from a series of small successes throughthese real options.

5.2. Example 2: a numerical example

A company, ABC, in the automobile industry decides toenter the China market. As the first step, they consideredacquiring an established local automobile manufacturer Z,which is willing to transfer its ownership to the foreignbuyer. The market valuation put the company at $460 mil-lion (I�). Assuming that with no follow-up investmentmade after acquisition, Z can still generate revenues for 3years, and the expected cash flow of Z is as shown inTable 1.After 3 years, ABC has the option to make an addi-

tional investment at $1000 million (I1), to expand itsproduction line, which might generate more cash flowand profit and lead to a sustainable business with amarket value of $1200 million (V1).When calculating NPV, a 25% annual discount rate is

used, which is the weighted average cost of capital forABC firm.

When evaluating the acquisition investment usingDCF based calculation and reasoning, we get the valueof the firm Z with second stage expansion option as:NPV(Z)=NPV1+NPV2+NPV3+(1200–1000)/(1+0.25)3=344.0+(614.4–512)=446.2The net value of this acquisition opportunity can be

given as: NPV0(Z)=NPV(Z)�I�=446.2�460=�13.8According to DCF evaluation criterion, the proposed

acquisition of company Z is economically not viablesince the NPV is negative.The second stage expansion option held by ABC with

the acquisition of Z is analogous to a call option on astock. Hence we can use Black and Scholes formula tovalue this option of follow-up investment. Table 2draws the parallel between the inputs needed in valuingcall option on stock and this expansion real option.Now we apply the option theory. With the net present

value of the follow up investment as the initial valueS=614.4 and the investment as the strike priceX=1000. The time to maturity T is 3 years. We estimatethe volatility of the automobile industry to 50%, i.e.�=0.5, and risk free interest rate is 5%. Input thesenumber into Black and Scholes formula, we get thevalue of this second stage investment option isc=140.23. The value of the option c feeds on �, thevolatility of the automobile-related stock value V(S),and on T, the option’s time to maturity. The asymme-trical distribution of V as illustrated earlier in Fig. 1,also implies that the upside potential is good with higheroption value, c, with increasing � (and risk) and T.So the value of the acquisition of firm Z should equal

the option value added to the NPV’s for the first threeyears, i.e.

NPVðZÞoption ¼ NPV1þNPV2þNPV3þ c ¼ 344:0

þ140:23 ¼ 484:23

Therefore the net value of this acquisition opportu-nity of firm Z to ABC is:

NPV0ðZÞoption ¼ NPVoptionðZÞ � I� ¼ 484:23�460

¼ 24:23

Table 1

Cash flow analysis (NPV is calculated with annual discounted rate of

25%) (value in $million)

NPV

Year

Revenue Cost Profit (r=0.25) I1 NPV(I1) V1 NPV(V1)

1

900.00 �870.00 30.00 24.00

2

950.00 �930.00 20.00 12.80

3

1100.00 �500.00 600.00 307.20 1 000 512 1200 614.4

344.00

K.T. Yeo, F. Qiu / International Journal of Project Management 21 (2003) 243–250 249

Now the NPV turns positive and should be accep-table. One may now ask how come the investmentrejected by DCF based evaluation looks attractive froma real option point of view, that is by taking into con-sideration the value of the option? Where did this addi-tional value come from? By assuming that ABCcommits to completing the second stage expansioninvestment, the DCF valuation ignored an importantvalue of flexibility that the firm really had.The real options analysis recognizes that these con-

tingent decisions would in fact reduce the risk exposureof ABC while retaining all the upside benefits, so thereal option based evaluation gives more realistic esti-mate for investment decision making by leveraging onthe benefits of managerial flexibility.A pertinent lesson learned from the above examples is

that when taking a real option perspective in investmentevaluation, a decision maker will take several steps. Hewill first identify and define the investment and its riskprofile; and then he must recognize any embeddedoptions and use them to craft his investment-structuringstrategy and option alternatives to maximize investmentvalue.

6. Conclusions

Traditional discounted cash flow based project eva-luation approaches are outdated, as they do not reflectthe dynamic and constantly changing reality of busi-nesses. The static approaches, using forecast scenariosand abided by a rigid operational strategy, and adoptedby a passive management, underestimate the upsidepotentials of investment and the value of being flexible.The real option approach in investment project evalua-tion appreciates the value of managerial flexibility and

the potential of achieving improved returns on invest-ment. In recent years, real options have found readyacceptance in the mining, petroleum, pharmaceuticaland life science related industries, where volatility anduncertainty is high and the need for flexibility is at apremium. Real options model has a place in the tool kitsof corporate decision-makers because of the highuncertainty and costs of irreversible investment. Execu-tives may informally exercise options whenever theystrive for flexible, extensive, and scalable investment.The challenge is now, how to go about institutionalizingthe process of recognizing, evaluating, and exercisingthe options embedded in future investment projects,especially in a market that is turbulent and uncertain,but holds great promises for both short and long termsresults.

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Table 2

Valuation of real option

Call option on a stock

Real option of expansion

S: Current stock price

NPV of benefits from

expansion investment

(i.e. NPV=614.4)

X: Strike price

Launch cost (I�=1000)

(T�t): Time to expiration

Time to launch (3 years)

r: Risk-free rate of interest

Risk-free rate of interest (5.0%)

�: Volatility of the

stock price

Volatility of the value of the

automobile industry (estimated from

the automobile related stock volatility)

250 K.T. Yeo, F. Qiu / International Journal of Project Management 21 (2003) 243–250