A Real Options and Game-TheoreticApproach to Corporate InvestmentStrategy Under Competition

Han T.J. Smit and LA. Ankum

Han Smit is an Assistant Professor of Finance at the Erasmus University of Rotterdam. The Netherlands.L.A. Ankum is a Professor of Finatice at the University of Amsterdam, The Netherlands.

U An investment strategy encompasses a sequence of tac-tical investment projects, of which several may yield a lowrelum when considered in i.solation. Often the value ofsuch an investment consists ofthe option to invest in thefuture growth of the finn. Eor example, the value of a pilotproject or an R&D investment does not derive so muchfrom the expecied cash inflows., but rather from the optionto invest in future commercial exploitation. Standard fore-casting of the expected cash inllows implicitly assumesinvesting in the follow-up project. Therefore, the tradi-tional discounted cash flow (DCE) method has seriousshortcomings in analyzing projects when infonnation con-cernini; future investment decisions is not yet known. The

We are indebted to Lenos Trigeorgis, Winfried Hallerbach, Tony Bouw-man. I ienk Berkman. Miehiel Zwijnenbuig and two anonymous refereesfor helpful comments. Any remaining errors are the responsibiliiy of theauthors. Financial supptirt from ihc Nelheriiinds Organization for Scien-tific Research (NWOJ is griitefully acknowledged.

application of option theory can be used as an analyticaltool to evaluate such projects and to support the overalloperating and investment strategy. Brennan and Schwartz111 examine the operational policy of a copper mine. Myers19], Trigeorgis [12], McDonald und Siegel [8|. Majd andPindyck [101, and Myers and Majd [10] provide otherexamples of flexible investmenl strategies.

We consider the option to defer investment in pro-duction facilities analogous to a call option on adividend-pay ing stock. In this investment strategy, deci-sions involving the creation of capacity may be ptistponedso that management can decide not to invest if marketdemand turns out to be unfavorable. On the other hand-deferral also has disadvantages since during the postpone-ment period the firm misses tiie net operating cash inflows.The analogy with a call option, of course, is not exact. Onedifference between financial caii options and future invest-ment possibilities is the exclusiveness ofthe latter. Kester[5] andTrigeorgis[12| have shown that competition in the

241

242 FINANCIAL MANAGEMENT / AUTUMN 1993

market may force the company to invest early, whicb mayerode the flexibility value of a deferred investmentstrategy.

Tbis paper casts the real options approach for projectliming in a microeconomic framework. We use microeco-nomic tools to analyze aspects of competition in the invest-ment strategy in forecasting tbe cash infiows. In this con-nection, we focus particularly on the concept of economicrents, i.e.. the excess profit above the opportunity cost ofcapital. Economic rents attract new entrants to the marketso that if the investment opportunity is not exclusive newentrants will diminish retums until expected and requiredretums are equal. Under rivalry, economic rents only existif the firm has a specific competitive advantage in therealization of the project. The finn, therefore, needs toidentify those markets in which it has a temporary orpermanent competitive advantage and concentrate invest-ment in these areas. If tbe competitive advantage is tem-porary, expected economic rents will decline over titne andpostponement will erode the value of tbe project. Based onthe finn's strength in relation to its competitors and thevalue of the project in relation to market uncertainty, wedevelop various investment tactics.

The paper is organized as follows. Section I discussesthe options approach to investment timing. Section IIstudies the concept of economic rents for strategic plan-ning purposes, as well as the influence of competition onthe expected economic rents over time. In Section III, weuse an options approach for titning investment strategy indifferent microeconotnic market contexts. Einally, SectionIV provides some concluding remarks and directions forfurther research.

I. The Option to Defer InvestmentSome investment projects can actually be seen as the

first links in a chain of subsequent investment decisions.Witb projects of this type, tbe firm essentially acquires anoption to invest in a potential follow-up project. For exam-ple, an R&D project, the development of a new technology,or entry into a new geographical market may create futureinvestment opportunities. In strategy, these projects areoften compared witb options for future company growtb(e.g.. see Myers [9J). We consider the option to defer aproject (see Kester \5] for a qualitative approacb. andTrigeorgis [12] or Kemna and Vorst [4J for a quantitativetreatment). The deferment of a capacity expansion pro-gram caused by uncertain market demand i.s seen to createflexibility for management. The titning of investment in a

Exhibit 1. Analogy of a Deferred Project With a CallOption

production facility is analogous to the timing of exercisingof a call option on a dividend-paying stock.

Exhibit 1 illustrates this analogy. The utiderlying valueis the present value of tbe net operating casb inflows, Vf.Tbe (present value of tbe) investment outlay in the plant,/. is equivalent to the exercise price. If. in time, marketdemand develops favorably, the firm would invest imd thenet value of tbe project would equal its A'PV^ V,-/. If theproject does not prove to be lucrative and the net presentvalue tums out to be negative, management tnay decidenot to invest and the value is zero. Besides this advantageto wait and see, deferment also has disadvantages. Forexample, if we consider a project witb an infinite life,management misses the net operating casb inflows whenthe plant is not operative. The rnissed net operating cashinflow during the defennent period is equivalent to adividend.

Based on this analogy, we can use option valuationtechniques to value a deferred project atid support theinvestment strategy. The binomial option valuationmetbod of Cox, Ross, and Rubinstein [2] is a useful toolin this regard. We subsequently express the missed cashinflow during the postponement pericxl as a constant pro-portion of the state project value. The dynamics of marketdemand for the product result in a series of possible projectvalues, V,.(, in eacb state (s) over time (/). The investmenttiming problem is solved recursively, starting witb futurevalues and working backward. The investment opportunityvalue is equal to the maximum of Vf_, - / wben manage-

SMIT & ANKUM / A REAL OPTIONS AND GAME-THEORETIC APPROACH 243

ment invests, zero when management decides not to invest,and the option value when management defers the project.The essence of the investmeni timing strategy is to find forevery decision moment a critical project value V*. At thiscritical value, the missed net operating cash inflow equalsthe llexibility value from postponing one more period. Aslong as the value of the project is below this critical value,the project will be deferred. Should the project valueexceed the critical value, management would invest.

In asset valuation, we create shareholders' value byinvesting in projects for which the financial market value(of the cash inflows) exceeds the investment outlays.Therefore, we try to determine what the project would beworth if it were traded in a fmancial market. Optionvaluation models are often based on arbitrage argumentswith an option equivalent. An equivalent portfolio strategy,consisting of a position in the underiying asset partlyfinanced with a risk-free loan, is constructed so that it hasin every state the same payoff as the option, and shouldtherefore have the same value. In the real options case, thefinancial markei valuation of the postponed project isdetermined by a project equivalent in the financial market.We could justify the portfolio equivalent approach if afinancial instrument is traded with exactly the same riskcharacteristics as the project. If the underiying state vari-able is taken to be the price of a commodity, for example,an equivalent portfolio could be constructed with futuresin the commodity (e.g.. see Brennan and Schwartz [ I ] forthe valuation of a copper mine). In the case of postponinga plant for consumer products, however, the underlyingasset is an aggregate variable. If an identical plant is notexplicitly traded, application of the option valuationmethod seems questionable. However, if the financial mar-kets are complete, in that the securities traded are sufficientfor dynamic spanning ofthe underlying asset, the optionvaluation method can still be applied (see Mason andMerton [7]). In complete financial markets, there wouldexist portfolios of securities that replicate the dynamics ofthe present value ofthe project caused by the rate of changeof prices and market demand.

As noted, the analogy between a call option and adeferred project is not exact. A major difference is thedegree of exclusiveness uf the latter, so the cail optionanalogy must be seen in the context of market structure(e.g.. see Kester [5] and Trigeorgis [12]). A project in amonopoly situation is more analogous to a call option,since it involves an exclusive right to invest. A projectunder perfect competition, on the other hand, is like a"public good" of the whole industry. In this case, there is

a loss in value from postponement caused by the entry ofcompetitors. Emerging competition or rivalry may thuscreate an incentive to invest early, as postponement oftheproject may result in project value erosion. This is par-ticularly so if early investment would preempt competitiveentry (e.g., Kester |5], Trigeorgis 113]).

II. Corporate Strategy and EconomicRents

In an efficient fmancial market, the prices of all tradedsecurities adjust rapidly to reflect all currently availableinformation. If information about a firni's profits or newprojects arrives in the financial market, investors bid up theprices until the retum equals that on investments withcomparable risk. Real markets are often less than perfectlycompetitive, so it is possible for a fimi to consistently eamexcess returns that exceed the opportunity cost of capital(see Shapiro 1111). We estimate the expected net operatingcash inflow as the opportunity cost of capital plus theexpected economic rent:

/ = 1,2.3. (1}

CF, = the expected net operating cash inflow./ = Ihe investmeni cash outflow./ = the opportutiily cost of capilal.

ER, = the expected economic rent.

In Equation (1), {f)i reflects the yearly opportunity cost ofcapital invested in a project with an infinite life.

Various microeconomic models can help in forecastingthe excess economic rents or expected profit. In a competi-tive market characterized by costless entry and exit andhomogeneous products, an eariy investment can produceonly temporary economic rents. The expected economicrents can have several sources; for example, they can resultfrom a new product introduction. Eventually, however,potential competitors will catch up and enter the industry.When the industry settles into long-run competitive equi-librium, all projects are expected to just eam their oppor-tunity cost of capital and their expected net present valuewill just be zero. Economic rents are not always temporary.If, for example, the fimi has a proprietary technologyprotected by enforceable patents, the economic rents couldbe persistent. As long as barriers to entry remain, the fumhas an exclusive or proprietary investment opportunity.Appendix A describes the modelling of economic rentsunder perfect competition, monopoly and oligopoly.

Under rivalry, economic rents would exist if the firmhas a competitive advantage in realizing the project. Bar-

244 FINANCIAL MANAGEMENT / AUTUMN 1993

riers to entry or a distinct competitive advantage overexisting competitors (e.g.. economies of scale and scope,absolute cost advantages or product differentiation) are thereal source of economic rents. Tlie finn therefore needs toidentify those markets in which it has a temporary orpermanent competitive advantage, and concentrate invest-ment in these areas. Understanding potential barriers toentry helps identify these markets and potential value-creating investment opportunities. One strategy, for exam-ple, will be directed towards increasing volume because ofeconomies of scale or broadening when economies ofscope are important in the market (see Hall [3]).

The present value of a project with an infinite life andconstant expected^ cash inflows, when the cost ofcapital is /. equals V,=_CF, / / . At the^nd of the period, thepresent value equals V'/"' ^ (1 + i){CF, / / ) . The differencebetween these present values reflects the net operatingcash inflow during the deferment period. CF,,. We sub-sequently express this cash inflow as a proportion of ihestate project value in the binomial option model, b,^Mf'so the present value. V, j , of the project equals(1 -^t.s)^u- Since there is no decline in expected eco-nomic rent and expected cash inflow under monopoly, apostponed project in monopoly is analogous to a calloption on a stock with a constant dividend payoutratio, 6,,,̂ .:

Exhibit 2. Simultaneous Investment Subgame

( 1 + 0 ' r=1.2, 3. (2)

Under perfect competition, the expected net operationalcash inflows will change over time until the project earnsjust the opportunity cost of capital.' The deferred projectunder perfect competition is thus analogous to a call optionon stock with a changing dividend payout ratio:

, f -1 .2 .3 .

(3)

In Equation (3), (/)/ reflects the yearly opportunity costof capital, while j l - ( | / { | + / ) ) e - ^ | jvf«<-(i+/)/[ re-flects Ihe economic rent in each state of nature. Note thatwhen the industry settles into competitive long-run equi-librium, the net present value of the project becomes zero

Assuming lhat an individual competitor does nol lake the value ofwaiting inio account.

FlrmBInveia Defer

Firm A

Defer

1

Vi — 1 V< — i

III

11

V I E — 1 Ci

IV

-I- /) = I), and 5,̂ v equals //(] + /) as with constantexpected cash inflows. If the projects have a positive netpresent value, competitors will enter and 5/ ^ > i/{\ + /}. Ifinstead projects have negative net present values, com-petitors will exit and 6,_̂ . < //(1 + ().

The number of firms active in an industry characterizesthe intensity of competition. In monopoly, only one t'lnnoperates in the market, whereas in perfect competition, thenumber of firms is very large. Oligopoly is between thesetwo extremes. In the case of duopoly, two linns aiv oper-ating so that the behavior of each individual competitordirectly influences the value of the project. The investmenttiming strategy of an incumbent firm in duopoly is coupledto the timing tactics of the rival. In the case of an earlyinvestment, it is sometimes possible to avoid a decrease invalue by preempting the competitor. The threat of preemp-tion is primarily determined by the strength of the linn andthe intensity of competition in the industry (e.g., see Tirole[14]).

Applying basic principles from game theory, we candevelop different investment tactics under each marketstructure. In duopoly, the timing of a project will beinfluenced by the development of market demand and thebebavior of the competitor. Instead of the maximum of{Vf,,( - /, 0) and the deferment value in the binomial optionmodel, the state value would now be equal lo the (Nashequilibrium) outcome of a simultaneous investment sub-game. Exhibit 2 presents an example of thi.s subgame inthe normal form (see Exhibit 6 for the option pricing modelin extensive form). There are four jrossible situalions: [i)both finn A and firm B decide to invest; (//) A decides toinvest but B waits; (///) A waits but B invests; and {iv) both

SMIT & ANKUM / A REAL OPTIONS AND GAME-THEORETIC APPROACH 245

A and B wait. The first number in each cell indicates theinvestment opptirtunity value for firm A. while the secondnumber is the value of a competing project of firm B. Theinvestment opportunity net value is estimated as the netpresent value, V/,v - L for a direct investment, or the optionvalue, C, (, for a postponed investment. Note that eachvalue depends on the tactic of the other firm (wait orinvest), particularly if an early investment preempts acompetitor or leads to a cost advantage;

III. Investment Timing Strategy andEconomic Rents

A crucial strategic choice for competing in emergingindustries is the timing of investment in capacity. We nextutilize a simple numerical example to illustrate the timingstrategy, first under perfect competition, and then undermonopoly. The firm in this example has invested in a pilotproject to get an early foothold in ihc market. If the marketopens up and creates expansion opportunities, the firm willincrease capacity significantly by investing in a follow-upproject. This pioneering strategy involves high risk, butalso involves low competition in the early stage of themarket leading to substantial expected economic rents.Here we assume:

(/) An industry portfolio is traded in the financialmarket with exactly tbe same risk characteristicsas the project, yielding an expected retum of 16%.The dynamics in the present value of the follow-upproject imply a 25% increase {ti = 1.25) or a 20%decline {d = 0.8) per year. This represents a stan-dard deviation in project present value of 22.315%per year. The real rate of interest is five percent peryear{/-= 1.05).

(/() The expected economic rent of the follow-up proj-ect in the first year is 10. Due to anticipated entry,the cash inflows will decline exponentially at a30% annual rate until the project earns the oppor-tunity cost of capital of 16%.

(//•/) The production facility has an infinite physical life.The required investment outlay is 500.

Given the declining expected economic rents and theopportunity cost of capital of 16%. the present value of theexpected operating cash intlows from the production facil-ities is estimated to be 524.- The net present value (NPV)therefore is 524 - 500 = 24. Based on the net present valuerule, management should invest immediately.

However, when we consider the option to defer capacityexpansion and wait to see how the market develops further,management should postpone. The dynamics of marketdemand for the product result in a series of possible projectvalues over time. Based on the binomial option pricingmodel, the value of the deferred project may increase by afactor of M( 1 - 6,,̂ ) per period if market demand tums outto be favorable, or it may decrease by a factor of(/(! -S/j) per period if market demand tums out to beunfavorable, i.e..

524 - - ^defer (28) -~^

548 ,--^^^^.^^^ invest (48) -

^ - ^ 397 --——defer (7) ---..,_

567^,,-* invest (67)

409~~ * defer(7)

447^ defer (10)

^~-~--* 332defer (5)

The net value (inside the parentheses) at each state is equalto the maximum of;

V,,v-/ invest

Cr 1 = ^ —— ' ~ defer

where p = -: is the risk-neutral probability.^

The value of the option to invest in the follow-up projectis 28. which is greater than the net present value of 24. Theoptimal strategy, therefore, is to defer the follow-up projectuntil the market develops favorably.

If we consider a project with the same economic rent,FR\, in a monopoly, the expected net operating cash in-flows are constant. The present value of the productionfacilities is now 563. and the NPV equals 563 - 500 = 63.When we consider the option to defer capacity expansion,management should invest immediately;

^524 =10 + 0.16(500) ^ 7.4 + 0.16(500) ^ 5.5+0.16(.'S0())

1.16 (1.16)^ (1.16)^0 + 0.16(500)

(1.16)"

V is the probability tliat would prevail if investors were risk-neutral. Thisvalualion principle is based on arbitrage arguments with a replicatingportfolio.

246 FINANCIAL MANAGEMENT/AUTUMN 1993

Exhibit 3. Investment Timing Strategy Under Perfect Competition and Monopoly

perfect competition monopoly

present value ofthe follow-upproject (V)

present value ofthe follow-upproject

V.

time

V*

time

563invest (63)

606invest (106)

388defer (3)

653invest (153)

418defer(5)

268defer (0)

Exhibit 3 illustrates how the dynamics in present valtie,V,, and the critical value above which it becomes optimalto invest, V^, relate to each other. In the case in which thefirm shares the investment opportunity with competitors,atiticipated entry causes a decline in ihe expected presentvalue of the project. V,, and a low critical value, V^. Theabsence of a structural competitive advantage may resultin a tendency to invest early to preclude erosion in the valueofthe project. The figure on the righthand side of Exhibit3 shows how the dynamics in present value and the criticalvalue relate to each other in the case of an exclusiveinvestment opportunity. Under monopoly, postponementof the project does not necessarily imply a decrease inexpected value. Assuming the project has an infinite life,the critical value would be constanl over titne. In cotnpari-.son to perfect competition, there is a stronger tendency topostpone projects under monopoly with relatively low netpresent values. However, if the project has a relatively highNPV due to pennanent economic rents, there would be anincentive to invest early.

Now consider the timing of the follow-up project in aduopoly market. The expected net operating cash inflowsare constant until a competitor invests in a competingproject. However, in the case of an early investment, it issometimes possible to avoid a decrease in value by pre-etnpt ing the markel. Instead ofthe maximumof(VVv-/. 0)or the deferment value in the binomial option model, thestate value would now equal the (subgame perfect equilib-rium) outcome of a simultaneous investment subgame.

Consider an example with two identical fimis pursuingsimilar tactics for investment in the follow-up project."*Exhibit 4 illustrates the net values of a two-period game inextensive form. The actions to invest {/) or defer (D) arereflected by the branches. When both firms A and B invest,the game ends; when both firms defer, nature (iV) movesand the game is repeated: and when one firm invests first.nature moves and the follower may then decide to investlater. The strategy of each fimi consists of mapping Iheinformation set about the competitor's actions and thedevelopment of market demand {N moves) to an action bythe firm. The subgame perfect equilibrium set of strategiescan be found by backward induction, starting from thefuture project values for both firms and working backalong the tree. The bold branches along the tree reflect theoptimal actions along the equilibrium path. In this exam-

'̂ In Ihe symmetrical duopoly example, we use u = 1.5. ci = 0.66. r= 1,1.p = 0.52. e = 0.55. V = 0.5, K(, = 100. and / = 50. The values in Exhibit 4are rounded and ba.sed tm more periods.

SMIT & ANKUM / A REAL OPTIONS AND GAME-THEORETIC APPROACH 247

Exhibit 4. Project Value Outcomes of a Gatne in Extensive Form When Two Competitors Have Symmetrical MarketPower

pie. both firms have an identical strategy, i.e.. deferring (D)the follow-up project and investing (/) if. in the early stage,market demand turns out to be favorable (i.e., /V moves up);or deferring the project further if market demand turns outto be unfavorable (i.e.. A' moves down) and continuingdeferment in the later stage ofthe market (N moves down,up or down, down),

Consider next the subgame following initial deferral(D) by both firms and favorable demand {N moves up) inwhich both firms follow a strategy to defer (D) and marketdemand turns out to be favorable (A' moves up). In thiscase a decision to invest has a higher net value for thefollow-up project, compared to deferral, regardless ofwhether the competitor decides to invest or not (34 > 25and 42 > 30). Both firms have a strictly dominant strategyto invest, resulting in net present values of (34,34) for bothfollow-up projects. If the niitrket develops unfavorably inthe last stage {N moves down), the dominant strategy forboth tlrms is to defer, leading to (3, 3) values. Calculatingthe state values recursively along the nodes results in(17, 17) option values of the investment opportunitieswhen both defer {D) in the earlier stage of the market.-̂ Tlie

- 1 7 .

dilemma of this subgame (A, B defer, A' moves up) isknown as the prisoner's dilemma. Firm A's dominant strat-egy is to invest whether the competitor decides to invest ornot. The dominant strategy for firm B is also to investimmediately (15 > 13 and 21 > 17). Thus, both firms willchoose to invest. The paradox is that the outcome {15, 15)is worse for both, compared with the situation when bothdefer (17,17). If both firms coordinated their investtnentstrategies, they would be better off in the latter situation.If market demand develops favorably (N moves up), bothfirms would invest and the NPV of the projects are (15,15), whereas, if the market develops unfavorably {N movesdown), both firms would defer and the option values of theinvestment opportunities are (1, 1). Using these outcomesin the backward valuation process results in (8, 8) optionvalues for the investment opportunities when both firmsdefer in the first slage.

In the previous example, we assumed identical tacticsand equal market power for the two competitors. Ofcourse, the strengths of each firm in an industry are notalways identical. Subsequently, we focus on the influenceof asymmetrical market power on a finn's investmenttactics. A dominant position in the industry may give acompetitive advantage to the finn in the realization ofproject value. Consider, for example, the case where back-

248 FINANCIAL MANAGEMENT / AUTUMN 1993

Exhibit 5. Project Value Outcotnes of a Game in Extensive Form When Two Competitors Have Asymmetrical MarketPower

ward induction leads to the asymmetrical game between adominant and a weak firm shown in Exhibit 5.^

When both firm.s deter in the early stage (D) and markeldemand develops favorably (A' moves up), the compeliliveadvantage of firm A resuUs in a higher net present valuefrom immediately investing in the project and a lowervaiue of waiting. Thus, for firm A. the dominant strategyis to invest early, irrespective ofthe strategy of competitorB (15 > 13 and 21 > 18). Because u comparable projectwill have a lower value for the weaker competitor, thecompetitor will not invest first. Knowing that firm A willinvest, the dominant strategy for firm B is to defer (7 > 2).In this example, the two firms pursue different strategies.Dominant firm A itivests and preempts the market (receiv-ing 21) if, in the early stage, market demand tums out tobe favorable, or further defers if market demand tums outto be unfavorable. The preferred strategy for the weak firmis in each case to defer the project, waiting until the marketdevelops sufficiently before entering with its project.

In general, market power can influence the threat ofpreemption. Typically, projects with low prcsetit valuefrom immediate investment would be postponed. The lowproject value of weaker competitors gives them little abil-ity to preempt a stronger competitor with high project

'In the asymmetrical duopoly exampie, we use the same input variablesas in Ihe symmetricai game, except Ibr the present value ofthe investtnentopportunity of the weak firm B. For firm B's project, we use V,, = 80 and/ = 50 instead.

value. The market power of a firm may also influence thevalue erosion associated with preemption of a competitor.By investing early, a weak competitor may only gain asmall share ofthe total market, but the potential loss in thevalue of the project would be minimal. The loss in value,if the finn becomes a followei, will be larger as the tnarketpower of the leader grows, because then an early invest-ment can take significant market share away.

Based on the rnarket strength ofa firm in relation to itscompetitors and the value of the project in relation tomarket uncertainty, we can distiriguish the following in-vestment tactics:

(/) Projects with relatively small net present valuesfrom immediate investment in uncertain marketshave relatively larger decision flexibility valuefavoring postponement. If the fimi has a dominantposition in the industry, there is little threat ofcomplete preemption by competitors. The firm cansafely postpone the project, and invest only if themarket develops favorably or if the weaker com-petitor invests first. It is even possible that a dom-inant firm can delay investing even when a weakercompetitor invests. This could be the case if thecompetitor can test the market without taking awaya significant market share.

(//) Projects with relatively large net present values instable market environments have rchitively smallflexibility values. The opportunity cost of defer-ment in the form of missed cash inflows during the

SMIT & ANKUM / A REAL OPTIONS AND GAME-THEORETIC APPROACH 249

deferment period i.s high, and so the dominant firm{linn A in the previous example) will inve.st early.

(///) If the finn has a weak position in the market andthe project does not have a large net present value,it may be better to wait until the market developssufficiently in the future to start tlie project (finnB in the previous example).

(iv) If the firm has a weak market position but theproject appears to have a positive net present value,it would invest immediately if early investment canpreempt a competitor or create a cost advantage.Ht>wever, because of the weak position of thecompany, a stronger competitor may come in anderode its net present value (even turn it negative).

IV. ConclusionsThe net present value (NPV) method has serious short-

comings in analyzing projects when future decisions arecontingent on intermediate developments in an uncertainenvironment. Option theory provides a better analyticallool to evaluate such projects. One important differencebetween a real investment opportunity and a call option isthe exclusiveness ofthe latter. If we u.se the analogy witha call option to value an investment opportunity, we haveto take this difference into account.

Using simple numerical examples, we have illustratedthe intluence of competition on project value and invest-ment timing. Postponement under perfect competition im-plies a loss in the expected value of the project due toanticipated competitive entry. Absence of a structural com-petitive advantage may thus result in a tendency to investearly if the firm can preclude this erosion of value. Aninvestment opportunity in a monopoly is exclusive, soduring the postpotienient period there is no expected lossin value due to competition. In comparison with perfectcompetition, there i.s a stronger tendency under monopolyto postpone projects with relatively low net present values.On the other hand, an exclusive project with large presentvalue creates a tendency to invest early.

01 igopoly lies between these two extremes. Here, a fewilmis are operating in the industry with individual marketpower. In duopoly, il may be attractive for both firms todefer investment when there is low project value anduncertain market demand. If the firms can coordinate theirinvestment, both will postpone. However, as soon as oneofthe finns invests, the other firm will follow suit with asimilar project. If competitive rivalry is intense and thereis no coordination, both firms will invest immediately,which ma) be suboptitnal. In the case where t1mis in the

industry have asymmetric market power, we have distin-guished various investment tactics based on the firm'sstrength in relation to its competitors, and the net presentvalue from immediate investment in relation to marketuncertainty.

In general, a firm will postpone projects when netpresent value is low, market demand is uncertain, andinterest rates are high. In contrast to a financial option, thedegree of nonexclusiveness of the investment opportunityinfluences the investment strategy. When there are manycompetitors, each with a negligible market power, antici-pated entry can erode the value ofthe project. With a fewcompetitors having individual market power, there may bea threat of complete preemption. Future research can bedirected toward applying the option valuation approach inreal cases. Extension of the theory can be directed towardmodelling option pricing in combination with dynamicgame theory and incomplete infomiation. However, withhigher mathematical complexity, much ofthe intuition ofviewing projects as real options may be sacrificed.

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250 FINANCiAL MANAGEMENT / AUTUMN 1993

Appendix A. Forecasting Cash Inflowsin Different Market Structures

This appendix relates cash inflows to economic rents.We estimate the expected net operating cash inflow as theopportunity cost of capital plus the expected economicrent, according to Equation (1). We assume that (/) thefmancial market is efficient; and (/() the project has aninfinite physical life.

I. Perfect CompetitionIn perfect competition, economic rents are expected to

decline exponentially, as follows:

ER, = - < / ' t= 1.2.3, (A!)

II. MonopolyIn monopoly, the expected economic rents are constant.

lil. DuopolyIn oligopoly, the timing of a project will be influenced

by the behavior of a competitor. Instead of the maximumof (S^t.s " !' 0) 2nd the defeniient value in the originalversion of the binomial model, a state value equals theoutcome of a simultaneous subgame. The investment tim-ing problem is then solved by backward induction leadingto a subgame perfect equilibrium. The details are shown inExhibit 6.

- present value of operating cash inflows as ifthere is no competitioti.

9 =

V =

proportion of value left when the firmpreempts the market.proporlion of value left when both firmsitivest simultaneously.

6, - proportion of value expressing net operatingcash ititlow.

p = risk-neutral probability.

t= 1.2.3. {A2)

Exhibit 6. The Game in Extensive Form