Real Options Analysis in Investments Finance Essay

Real options analysis is an innovative approach towards the evaluation of investment and financial decisions, investment appraisal, asset valuation and performance measurement. Furthermore Real option analysis facilitates us to incorporate our judgments on investments, operations and disinvestment. It is based on the perceptive that at least one of the value-determining variables is evolving unpredictability and following a random walk; however as that uncertainty unfolds our response would be flexible towards it. Additionally Real option analysis is an improvement from the approach by which financial markets value an option on a stock or investment. It assists us in decision making regarding how much capital we should spend to achieve an economic opportunity and when we should commit ourselves to one of the accessible decisions. Nowadays Real option analysis is progressively more being used by companies to value their intangible assets. Research and Development (R&D) is a recognized example of a real option, by virtue of what a company undertaking R&D has the option to make a decision in regards whether developing or launching a new product, otherwise instead carrying out further R&D in order to develop a conceivably secondary product. Since the main objective of my study is to focus on predictability of introducing or launching 3G technology or Universal Mobile Telecommunication System (UMTS), the literature review mainly spotlights on those models that are relevant and noteworthy to Research and Developments (R&D).

One might think that in today's time when it has already been almost a decade since the launch of 3G (UMTS) service, competitive investment real option models may be appropriate for valuation of introduction or adoption of 3G; however the choice of the model depends on the different circumstances. For instance in the case of Pakistan it is still required to consider R&D model for valuation of introducing 3G, the reason being that competition among different mobile operator seems to be a secondary issue whereas the primary issue is whether mobile operators are willing to take the risk by purchasing the licence for 3G spectrum. When taking Pakistan into account 3G seems to be a risky investment because historical data shows that mobile operators could not gain enough revenues from data service (mobile internet) provided. In Pakistan most of the revenue is generated from voice calls. . Furthermore although the Pakistani government is seeking high-cash injections to deal with the country's economic challenges, but at the same time the market is a very different proposition to India where mobile operators have currently invested multi billion dollars.

The reason being that Pakistan does not seem to be a profitable mobile market at the present is due to many of the barriers to entry for 3G services (UMTS) such as lower levels of literacy, low GDP per capita, high fluctuations in currency, severe price pressure with respect to a dominant prepaid market, high taxes with regards to import of handsets and a frequently disorganized distribution network. Mobile operators in Pakistan have been arguing for a few years that Pakistan is not yet ready to make investment with respect to adoption or introduction of 3G services. Furthermore we can also refer to revenues raised from EDGE which can be thought of a downgraded version of 3G which is although slower but at the same time also up to 60% cheaper. Analysis show that investments made with respect to adoption of EDGE was not a profitable strategy because in developing countries like Pakistan mobile internet is considered to be a luxury rather than a necessity. Therefore introducing 3G at this moment of crisis in Pakistan would be considered as a strategy of niche marketing which refers to serving to high end users. Although keeping in mind that 3G is a multibillion dollar investment, the mobile operators in Pakistan should definitely spend a few million dollars on R&D to judge the profitability of the investment.

Real R&D options are anticipated processes in R&D that assist researchers to attain flexibility in terms of timing, dedication, investment and research processes, which can be valued in terms of options. Real R&D options have been practical in the field of biotechnology, energy, and the primary focus of my study telecommunication research. In the upcoming, real R&D options may perhaps turn out to be incorporated with capital market prices, therefore as a result internal and external market valuation using option theory will possibly turn out to be more consistent and occasionally functional in making R&D capital allocation and other fundamental corporate finance decisions. Real R&D options in general are opportunities that refer to attaining, developing or disposing of real assets associated to R&D contained by an investment and operation cost determined in terms of present value that delivers benefits in the future. On the other hand, in contrast to financial options, real R&D options are not until now frequently traded, and are often tricky to recognize, with lack of information, and thus may engage complicated valuation methods. By far, real R&D option theory has been established to a broad range of elemental aspect of projects, that incorporates investment timings in monopoly and competitive environments, alternatives in R&D budgets, sequential option activities, consequential investment opportunities, and flexibility in R&D project development.

3.1 TYPES OF REAL R&D OPTIONS:

First of all, Margrabe exchange option is an example of simple real option that assumes that all new investments regarding product development are at the date when the option expires, that is assumed to be product launch date. Furthermore there are a number of alternative models for 'compound' type real options; where initially there is R&D expenditure, followed by new product development expenditure. Lint and Pennings (2001) explained that R&D expenditure is analogous to a premium that is paid for a forward start option with timing determined by new product development management along with deterministic investment costs and future cash flows that are eventually uncertain, continuing in perpetuity. Additionally a compound options model has been offered by telecommunication practitioners, where there is a three stage life cycle, comprising of research, development and deployment. Moreover the compound option formula has been modified by Jensen and Warren (2001) by making use of bivariate normal distribution. Apart from that, Martzoukas (2002) has illustrated that real option models should acknowledge the fact that management can and will add value through endogenous actions, which bear a resemblance to jump processes with upward although stochastic values. As well Bellah (2002) presented a model for explicit information cost of an R&D project and on options relative to it since it was not understandable, if there was comprehensive information on cost of biotechnology R&D. Finally Quigg (1993) provided an application or a real option model to assess and value speculative developments, in the circumstance where both investment cost and consequent product value are stochastic.

3.2 SIMPLE EXCHANGE OPTION (MARGRABE):

It is extensively acknowledged that the traditional Net Present Value (NPV) method is inadequate to value real investment opportunities in an uncertain environment. Despite the fact that the exercise price is fixed and known in advance at the instant the option is purchased in a typical ("vanilla") call option, such case is exceptional in a real options situation. As a consequence of following, the real option to invest in the future corresponds to an exchange option and not to a typical call option, due to its uncertain exercise price. An American exchange option gives its owner the right to exchange one asset for another at any time till the expiration/maturity of the option. Margrabe (1978) values a European exchange option which provides its owner with such an exchange right only at expiration/maturity of the option. Margrabe (1978) was the first who initially extended the standard Black and Scholes (1973) formula in order to value European options in scenarios where stock price and exercise price are stochastic and follows a log-normal diffusion process (GBM).

The Margrabe (exchange) Real Option formula makes the same assumptions as American perpetual options for European calls, which are listed below. First of all it assumes that an asset price follows Geometric Brownian Motion (GBM) with constant AA´ and AÆ’. Furthermore it assumes that short selling is allowed with full use of the proceeds. Likewise there are no transaction costs or taxes. Apart from that, all assets are perfectly divisible. Moreover there are no riskless arbitrage opportunities. Additionally asset trading is continuous and finally the risk free rate of interest and expected volatility are constant. However unlike assumptions made by American perpetual options for European calls, The Margrabe (exchange) Real Option assumes that there is an instantaneous constant correlation between the two stochastic processes. Furthermore this formula is independent of the risk-free rate, in a risk neutral world, and the exchange volatility is the volatility of the spread. Margrabe developed an exchange option pricing model which is predominantly functional in pricing options for which exercise price is uncertain. Therefore this model is practical for those financial assets that allow the exchange of two assets (option to switch) where prices are stochastic at one pre-specified point in time.

Margrabe's model regarding the Exchange Options is not completely adequate because its European exchange option can only be exercised at maturity/Expiration. This characteristic of Margrabe's European Exchange Option is impractical because a company that owns an option to invest can principally exercise that option at any time until maturity. In other words, the investment opportunities are generally American options. Additionally the Margrabe model can value American options only in the specific situation where the underlying asset does not offer dividends. Due to this facts and limitations of Margrabe exchange model, it is restrictedly used to price real R&D options in E-commerce and in pharmaceutical industry for those R&D processes where the product launch is restricted to one point in time. However with reference to the main objective of my study that is to focus on predictability of introducing or launching 3G technology or Universal Mobile Telecommunication System (UMTS), where the product information can occur at any time rather than one pre-specified point in time, in such scenario the application of Margrabe exchange option seems to be less appropriate.

SEQUENTIAL DEVELOPMENT AND SEQUENTIAL INVESTMENT MODELS:

Black and Scholes (1973) and Merton (1973) should be mentioned as originator of real option theory due to the fact that not all of their imaginary applications were with regards to traded assets. Brennan and Schwartz (1985) and McDonald and Siegel (1986) were the early developers of the theory that is consequently applied to R&D along with exploration and development regarding natural resources. The model of sequential development stages makes the assumption that R&D is single-sided, where R&D is a requirement in advance before completion of the project. In addition, it also assumes that the project volatility is a deterministic function of R&D expenditure that is reduced by the amount spent. The opportunity to make investments in stages or phases is a general attribute with respect to the numerous categories of investments. A few conventional examples of such investments refers to the launch of new products, R&D in the field of pharmaceuticals, exploitation of natural resources for instance petroleum, and finally the enlargement of an industrial plant and real estate developments.

The significant attribute of the sequential investment refers to the possibility of suspending or aborting the investment in the circumstance where the expected value of the complete project diminishes or otherwise if the cost to complete the investment amplifies. Additionally these investments take place in a continuing way in a timely manner only if the development of the product and market tests comes out to be favourable. Childs and Triantis (1999) observed R&D investment decisions and project values, where two investments can be developed in a sequence. They build up closed-form solutions with the objective of valuating the investment program and they analyzed the optimal decision and features that tend to influence the alternative between a few sequential and parallel investments. Carr (1988) identifies a sequential or a compound option as an option where the asset received is considered to be an another option where in contrast to a simple option the holder of the option obtains cash flows or shares from an investment project upon the exercise of the option.

Conversely, Geske (1979) has a different opinion on the definition of sequential options. He stipulates that a compound option exists on every occasion when the subsequently opportunities are available only in the circumstance where the previously opportunities are undertaken. Many researches emphasize that the real world investments are time and again sequential in nature which refers to the fact that investments take place in phases and that firm's management has the opportunity to react to changing state of affairs and the arrival of latest information. Furthermore Lint and Pennings (2001) lay emphasis on the fact that sequential investment is not at all standardised and as a result there is not one single model capable of fitting all kinds of staged investment opportunities. Although the standard assumption of sequential investment model is that volatilities tend to be constant throughout entire investment stages. However in contrast a bigger strand of models make assumption that the uncertainty bounded within the investment opportunities is diminished with the frame of time which is motivated by the development of those models that takes into account different volatilities for several phase of investment. Geske (1979) was the first to suggest the valuation a compound option where the call option on a stock was valued in a similar way as call option on firm's asset.

As for real options, the sequential option bear a resemblance to a variation of compound option known as instalment option where the price of option is paid sequentially over time in instalments. Furthermore, on one hand where the Geske (1979) model requires the total discounted present value of future cash flow to be stochastic, on the contrary Bar-Ilan and Strange (1998) takes a somewhat different approach as their model is expressed in terms of annual project revenues or in terms of output prices net of variable cost which are assumed to follow a GBM. However the main limitation of the model is that it only allows for two phases of sequential investment. Majd and Pindyck (1987) tend to overcome this limitation in their model. Their analysis is concerned with a contingent plan for making irreversible and sequential expenditures therefore the management can decide upon the completion of each stage whether or not to incur cost for the subsequent stage or whether deferral is optimal in the present.

According to their model, the firm makes investment continuously until the completion of the project. Also their analysis can be extended by taking into account the information cost that would be incurred regarding the study of decision whether suspending or starting the investment in the above models. Roberts and Weitzman (1981) emphasizes the role of gathering information in sequential investment. They were traditionally the first to develop a model in which uncertainty decreases with investment expenditures. In this kind of investments, early phases propose information about net payoff and costs to be incurred in later stages. Summing up, although the dynamic sequential investment models are on average based on more practical hypothesis, it is frequently complicated in practice to predict how precisely uncertainty decreases with expenditure all the way through different phases of investment. On the contrary, static sequential investment models are characteristically more appropriate in consideration to dynamic models.

SEQUENTIAL EXCHANGE OPTION MODEL:

The sequential exchange option model is a more practical classification of R&D options in comparison to standard American or European exchange option model in the circumstance where R&D projects take the form of phases of research or sequential investment opportunities. Roberts and Weitzman (1981) represented the benefits of terminal R&D being a geometric Brownian motion process where the primary concern was an optimal stopping limitation. Furthermore Weitzman et al. (1981) also made same assumptions except for the fact that costs were assumed to be stochastic along with reducing process volatility over time. Carr (1988) model integrates and build up collectively on the essentials of both Geske (1979) compound option and the Margrabe exchange option for the purpose of valuation of European sequential exchange options. As a result the model obtained is a combination of an exchange option that refers to operating option and a time-to-build option that corresponds to growth option. Additionally Carr (1988) also illustrates estimation for an American sequential exchange option. The valuation of sequential exchange option provided by Carr (1988) has been indirectly applied in Childs et al. (1998), Taudes (1997) and by Bar-Ilan and strange (1998) towards the formulation of real R&D options. Moreover Lee and Paxon (2000b) based their foundation on the model which was proposed by Carr (1988) in order to present another model for the valuation of a sequential pseudo-American exchange option and are also able to demonstrate that their analytic approximation generates more precise results than Carr (1988). The analytic approximation proposed by Lee and Paxon (2000b) takes into consideration a two-phased investment process.

Despite the fact that the initial expenditure only takes place after a specified span of time, the firm can consequently take decision regarding the product launch and pay the cost of implementation at any point in time until the expiration of exchange option. As a consequence, Lee and Paxon (2000b) tends to present a more practical structure for several investment related opportunities in comparison to Carr (1998) method for the valuation of European sequential exchange option. Lee and Paxson (2000b) method seems to be more suitable and well-organized as compared to Carr (1998) due to the fact that it can be learned from the past that almost all the mobile operators have initially postponed their first announcement regarding the launch of UMTS and in such a scenario Lee and Paxson (2000b) approach plays an important role by providing flexibility to the firm with regards to launch of the project within a certain period of time. There are a number of ordinary solutions for American sequential exchange options where the underlying asset refers to perpetuity, which can observed in Dixit and Pindyck (1994), furthermore in replacement investments in Mauer and Ott (1995), and finally when concerning sequential investments in Childs, Ott, and Triantis (1998).

Additionally by means of related assumptions, Bar-Ilan and Strange (1998) demonstrated closed-form solutions in order to attain optimal sequential investments in both the circumstances referring to, with and without suspension of operations and investments, and additionally with regards to costly suspension. Despite the fact that there are no closed-form solutions for those American exchange options when dividends are taken into account, however several substitute analytic approximations have been anticipated. By utilizing the two-point Richardson extrapolation, Carr (1988) proposed an analytic approximation for an American exchange option, which is imitated by a portfolio consisting of two European Margrabe exchange options along with one European compound exchange option. Moreover Bjerksund and Stensland (1993) suggested a closed-form solution for an American exchange option through transformation of their vanilla American call option approximation. Finally, Lee and Paxson (2001, 2003) estimated American option models that are extended in context to a sequential exchange, given for exercise of option at optimal times after the completion of required interim expenditure. Schwartz and Moon (2000a) proposed a numerical solution for multiple sequential exchange options that refers to exchange model which comprises of more than two stages. In the same way to Majd and Pindyck (1987) they allowed for highest rate of expenditure along with the authority to take decision after completion of each phase whether it would be optimal to incur subsequent phase's expenditure or otherwise it would be better to wait. However in contrast to Majd and Pindyck (1987), the model proposed by Schwartz and Moon (2000a) not only provide for stochastic present values for project's future cash flows but also for stochastic total investment cost.

PREEMPTION MODELS:

Most of the earlier Real option models give an idea about the importance of deferring "sunk cost" expenditures which considers the fact that what is gained by waiting to invest. On the contrary, Kulatilaka and Perotti (1992, 1998) consider the fact that what is lost by waiting to invest. When taking a competitive market into account, early investments may give benefit of a greater market share which refers to pre-emption along with incentives of early cash flows. Dixit and Pindyck (1994) suggest a pre-emption model that lays its foundation on the model that developed earlier on by Fudenberg and Tirole (1985) and Smets (1993) which takes into account an oligopolistic industry. Furthermore Williams (1995) explains several characteristics of real options which differentiate them from financial options and some of these properties are also incorporated by pre-emption models. The first property of real options in contrast to financial options is concerned with downward sloping demand curve which refers to the fact when real options are exercised, they tend to increase the aggregate supply of developed assets and in this manner the equilibrium price of each unit of output is reduced.

The second property is concerned with the aggregate constraint in term of rate of exercise which refers to the fact that when the developers deal with either increasing costs or limited capacity, the development costs ultimately depends on the demand for development. Furthermore the third property relates to limited supply of real options which according to which the supply of underdeveloped assets can be possibly constrained with the supply of developed assets which seems to essential specifically when taking real options into account. Additionally the fourth property relates to monopolistic or oligopolistic exercise according to which investments made by competitors tend to decrease the value of company's own investment opportunities. Finally we consider the property of real options regarding portfolio effects where with respect to monopolistic or oligopolistic situations, the exercise of individual real option is able to have pessimistic influence on the value of other options enclosed in company's portfolio. As already mentioned above the previous models with proprietary assumptions that were taken into account were not well suited to incorporate the following properties of real options, however the pre-emption models incorporate at least a few of these characteristics.

Apart from that the study aims to focus on the impact of competitive behaviour with respect to value of an investment opportunity. The primary initiative is that once a competitor has already entered the market, the option to enter the market becomes less valuable for other competitors. The following piece of evidence makes pre-emption which refers to prior entrance into market compare to other competitors, more attractive. According to Paxson (2003), although entering first in the market has several incentives but at the same time a competitor can also play an opposite strategy by waiting and learning from leader's mistakes before entering the market. Lambrecht and Perraudin (1997) further extended the standard models that incorporate irreversible investment by means of including strategic entry by competing firms. Additionally Lambrecht (2000) also modelled competitive R&D phases, where in the first phase there is a trade-off between the cost of being pre-empted and the value that arise as a consequence of waiting to invest. In the second phase "sleeping patents" inventions are taken into consideration which may not be instantaneously put into use.

FIRST MOVER ADVANTAGES:

In this section the main focus of the study is to spotlight the significance of strategic consideration. The particular focus is on the advantage of being first to enter the market prior to other competitors along with quantifying the outcome of such an advantage on valuation of investment and exercise policies. I will specifically refer to the model that has been explained in Paxson and Pinto (2003) in relation to magnitude of first mover's advantages or the degree of pre-emption to completely parameterized, which enables to measure their effects on decision to enter along with game equilibria. Paxson and Pinto (2003) takes into account two competing firms in the scenario of uncertain profitability which have option to enter the market where the option to enter the market is a kind of American call option that incorporates an exercise price equivalent to the investment cost along with underlying security that is considered as the net profitability formulated from operating in the market. Conversely, exercising the option by one firm in order to enter the market has consequences on the option value of both the competing firms. Under the scenario of this model, leader who is supposed to be the first to enter the market has to sink the investment cost earlier but at the same time leader also has an incentive by means of securing a greater market share in comparison to the competitor.

An attractive element of this model's framework is that it acknowledges the opportunity that the first-mover advantages can either be temporary or permanent. Furthermore according to Paxson and Pinto (2003) model, the other competitor (follower) can take the decision when it would be optimal to sink the investment cost in order to claim lower market share than that of the leader. When the follower makes the decision to enter the market the underlying game comes to an end which results in a duopoly market structure where sharing the market by leader and follower seems to be a precise function of the magnitude of pre-emption factor. After the value functions and market share of leader and follower are determined then the consequence of the magnitude of first-mover's advantage can be assessed. The most important implication is that first mover's advantage guarantees a higher market share for the leader along with optimal rival entry according to which leader has the incentive of monopoly in the market till the entrance of follower. The model illustrated by Paxson and Pinto (2003) is based on the work provided by Smets (1993) in relation to foreign direct investment and the following implementation of Smets (1993) model by Grenadier (1996) in the context of real estate market.

Paxson and Pinto (2003) model acknowledges the likelihood of both simultaneous and sequential exercise equilibria likewise Smets (1993) and Grenadier (1996) depending on preliminary circumstances and degree of first mover's advantages. Additionally Paxson and Pinto (2003) model is enhanced and can acknowledge their consequence on value function much better in comparison to other two models discussed above. Above all unlike Smets (1993) and Grenadier (1996) the model ensures that first mover's advantage is permanent as leader will retain a higher proportion of market share ever after the entry of follower. As discusses above Grenadier (1996) formulates a pre-emption duopoly model which is based on work of Smets (1993). Nonetheless his model assumes that firms are already competing in an existing market where the new investment opportunity boosts the profitability of the firm. However according to this model the first mover's advantage is temporary since both the firms will equally share the market after the follower has entered and completed its investment. Followed by Grenadier (1996), Pawlina and Kort (2002) demonstrated a similar model making the assumption that two firms already competing in an existing market where the new investment opportunity boosts the profitability of the firm, while diminishing the profitability of competitor.

In contrast to previous model, this model does not assume that two firms are identical by providing one of the firms an incentive in terms of lower investment cost. However also according to this model the first mover's advantage remains temporary. Similarly dixit and Pindyck (1994) illustrated a simplified duopoly model by implementing Smets (1991) approach. Also according to this model the first mover's advantage remains temporary as the leader only receives the full market revenues until the entrance of follower. Furthermore Boyer and Clamens (2001) explain a duopoly model of pre-emption by means of multiple investments along with Bertrand competition. Mason and Weeds (2000) demonstrated the implementation of technology when there is first mover's advantage of being the first adopter. Other academic literature with reference to pre-emption model and first mover's advantage includes Williams (1993), Leahy (1993) and Fries et al. (1997) which take into account real investment decisions in perfectly competitive industry equilibrium. Apart from that Tsekrekos (2003) derived model based on Smets (1991) and Grenadier (1996) which has similar views to that of Paxson and Pinto (2003) according to which the first mover's advantage is permanent as leader will retain a higher proportion of market share ever after the entry of follower.

Additionally with respect to possible equilibria it is revealed that both simultaneous and sequential equilibria can result. Finally in their article "THIRD GENERATION MOBILE GAMES- An application of real competition games", Paxson and Pinto (2004) formulated analytical solutions with respect to the leader and follower options to invest in the market along with quantitative explanation for the optimal investment timing of the leader. The main objective of demonstrating the model was to determine the optimal timing for a mobile company to make investment with respect to a major technological change such as 3G. The reason why this real option model is appropriate for analyzing telecommunication mobile market is because first of all it is a competitive sector which implies that there is a natural application for game theory models and moreover it a considered to be a license race market. The models which has been demonstrated by Paxson and Pinto (2004) were actually developed in Paxson and Pinto (2003-a) where two firms are bearing in mind the option in order to enter a new market. The firm that would be the first to enter the market would be defined as the leader from now onwards and will get hold of a first mover advantages in terms of a higher share of the market as compare to a follower that would be second firm or in other words the competitor to enter the market.

The roles of the leader and the follower are characterized endogenously in the opinion obtained from Fudenberg and Tirole (1985) where the two firms are supposed to be symmetrical ex- ante however they tend to be asymmetrical ex-post. Above all the leader will always be having a competitive advantage over the follower in terms of first mover advantages, therefore with respect to the upshot each of the firm will want to acquire the position of the leader, which generates a pre-emption effect. These models formulated by Paxson and Pinto (2004) best suits the circumstance of a duopoly environment where the first firm to enter the market is considered as a leader and the second firm or the competitor is considered to be a follower and therefore are most suitable for the purpose of my research which refers to introduction of 3G (UMTS) technology in Pakistan's mobile telecommunication market.

GENERAL OPINIONS ON REAL R&D OPTION MODELS:

Traditionally capital investment appraisal technique such as "Net Present Value" (NPV) and "Discounted Cash Flow" (DCF) approach were used to evaluate investment opportunities however they were imprecise since it is not straightforward to estimate the risk adjusted discount rates appropriate for cash flows when they arise from expansion, abandonment, deferral and other options. Therefore the real option analysis is a better approach as it is able to account for the controllability of cash flows through the management of firms. Although the Black-Scholes model is widely accepted for the valuation of stock options, its applicability to R&D projects is questionable. Ross (1991) recommended using the Black-Scholes formula in order to analyse R&D projects, however this method created some problems. For instance, Newton and Pearson (1994) explained the complications with evaluating the volatility of an R&D investment project and in addition Trigeoris (1993) discussed the inconvenience of real option valuation using a risk-free rate of return. Margrabe developed an exchange option pricing model which is predominantly functional in pricing options for which exercise price is uncertain. Therefore this model is practical for those financial assets that allow the exchange of two assets (option to switch) where prices are stochastic at one pre-specified point in time.

However with reference to the main objective of my study that is to focus on predictability of introducing or commercializing 3G technology or Universal Mobile Telecommunication System (UMTS), where the product information can occur at any time rather than one pre-specified point in time, in such scenario the application of Margrabe exchange option seems to be less appropriate. Carr (1988) identifies a sequential or a compound option as an option where the asset received is considered to be an another option where in contrast to a simple option the holder of the option obtains cash flows or shares from an investment project upon the exercise of the option. The significant attribute of the sequential investment refers to the possibility of suspending or aborting the investment in the circumstance where the expected value of the complete project diminishes or otherwise if the cost to complete the investment amplifies. Summing up, although the dynamic sequential investment models are on average based on more practical hypothesis, it is frequently complicated in practice to predict how precisely uncertainty decreases with expenditure all the way through different phases of investment.

On the contrary, static sequential investment models are characteristically more appropriate in consideration to dynamic models. The sequential exchange option model is a more practical classification of R&D options in comparison to standard American or European exchange option model in the circumstance where R&D projects take the form of phases of research or sequential investment opportunities. Therefore, Lee and Paxson (2000b) model which is a classification of sequential exchange model seems to be more suitable and well-organized with respect to my study where the main objective of the study is to focus on ROV for introducing or adopting 3G technology or Universal Mobile Telecommunication System (UMTS). The primary reason being that it can be learned from the past that almost all the mobile operators have initially postponed their first announcement regarding the launch of UMTS and in such a scenario Lee and Paxson (2000b) approach plays an important role by providing flexibility to the firm with regards to launch of the project within a certain period of time. In addition, when taking a developing country like Pakistan into account then a sequential option seems to be appropriate because mobile operators over there will prefer to make a tremendous multibillion dollar investments in phases that is involved in adoption of 3G services since it is a risky investment and keeping the demographics in mind, it is obvious that currently in Pakistan 3G gives a view of luxury rather than a necessity.

When taking a competitive market into account, early investments may give benefit of a greater market share which refers to pre-emption along with incentives of early cash flows. In pre-emption models the particular focus is on the advantage of being first to enter the market prior to other competitors along with quantifying the outcome of such an advantage on valuation of investment and exercise policies. Particularly Paxson and Pinto (2003) model which is among the classification of pre-emption models takes into account two competing firms in the scenario of uncertain profitability which have option to enter the market where the option to enter the market is a kind of American call option that incorporates an exercise price equivalent to the investment cost along with underlying security that is considered as the net profitability formulated from operating in the market. When relating to the main objective of the study which focuses on ROV for introducing or adopting 3G technology or Universal Mobile Telecommunication System (UMTS)

Paxson and Pinto (2003) seems to be a precise and suitable model for determining the optimal timing for entering the market of both the leader and the follower. Furthermore Paxson and Pinto (2004) formulated analytical solutions with respect to the leader and follower options to invest in the market along with quantitative explanation for the optimal investment timing of the leader. These models formulated by Paxson and Pinto (2004) best suits the circumstance of a duopoly environment where the first firm to enter the market is considered as a leader and the second firm or the competitor is considered to be a follower and therefore are most suitable for the purpose of my research which refers to commercialization of 3G (UMTS) technology in Pakistan's mobile telecommunication market. This model proposed by Paxson and Pinto (2004) belongs to the class of pre-emption models.

However, like sequential models they take the strategic consequences on the worth of an investment opportunity into consideration that tends to result from the competitor's behaviour. Summing up Paxson (2002a) emphasizes that there is no single best model which can completely capture all the requirements due to the fact that each investment decision is subject to different assumptions and constraint. However, different models have a mixture of advantages and limitations over other models and deciding which model would be optimal to use depends on Parameters embedded in the model along with the state of affairs and the circumstances to be captured by the model. Keeping in mind that different models can fit certain investment situations better or worse, in my opinion the two models illustrated by Paxson and Pinto (2004) seems to be most appropriate than the models demonstrated by other authors with respect to my study on commercialization of 3g technology and are perhaps more realistic than other models in relation to the proposition of permanent first mover advantages.

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