Delay in the Expansion from 2.5G to 3G Wireless Networks: A Real Options Approach

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1 Delay in the Expansion from.5g to 3G Wireless Networks: A Real Options Approach ABSTRACT Prof. Fotios C. Harmantzis, PhD, Venkata Praveen Tanguturi Stevens Institute of Technology Wesley J. Howe School of Technology Management Department of Telecommunications Management Castle Point on Hudson Hoboken, NJ 07030, USA {fharmant, vtangutu}@stevens.edu The idea of Third Generation (3G) networks is to provide mobile users with seamless roaming, access to the Internet, and high quality services. Rapid changes in technology, demand new hardware to be purchased and installed to support these services. Our paper values the option that a network operator has to expand via rolling out a 3G network, in circumstances where the spectrum license fee has been paid or has not been acquired yet. Comparisons with traditional discount cash flow approaches are given. The effect of certain parameters, e.g., expansion/growth factor, volatility, and investment cost in the decision making process is studied. Our analysis suggests that the path to 3G depends not only on purchasing the spectrum, but on other factors that affect the value of the option. I. INTRODUCTION As mobile technology is evolving from voice-based services to multimedia services, the demand for spectrum is increased significantly. Even though wireless service providers have adopted advanced techniques to use their own spectrum more efficiently, it will certainly not be enough to accommodate new services in next generation wireless systems [4]. As we can see from the spectrum auctions, price paid for next generation wireless spectrum were exorbitant [4]. Some wireless providers attempt to own as much spectrum as they can, no matter how much it would cost them. Perhaps their notion of owning a spectrum is that whoever owns more spectrum will be able to generate more revenue than others, once the network architecture is in place. After a recent 3G spectrum auction in Europe, some wireless providers have realized that this is not always the case [4]. The requirement of network architecture that supports new bandwidth-intensive services is demanding and costly to implement. Even the new handsets for next generation wireless network are not likely to be ready soon because of its complexity to support new services. Corresponding author: Prof. Fotios C. Harmantzis, Assistant Professor, Stevens Institute of Technology, School of Technology Management, Department of Telecommunications, Hoboken NJ 07030, USA. Tel: + (0) 6-879, Fax: + (0) , fharmant@stevens.edu. PhD Student and Research Assistant, Stevens Institute of Technology, School of Technology Management, Department of Telecommunications, Hoboken NJ 07030, USA. vtangutu@stevens.edu.

2 The cellular market is going through dramatic changes. The need to transfer information has increased tremendously with growth of cellular network. New technological developments and emergence of new companies have increased the level of competition. This has forced the market participants to change their ways of doing business. Uncertainties related to the impact and timing of technologies has forced the market participants to reconsider their strategies. The fact is that the future is uncertain. Real options can be used to valuate investment decisions, help in decision making process, and identify which factors affect decisions the most. Real options methodology takes into account uncertainties in future benefits and costs. They are known as means to provide some assurance in today s unpredictable markets. They provide a framework to identify the key issues in investments and involved risks. The paper falls into the area of applications of real options theory in telecommunications, and more specifically in wireless networks. The objective is to highlight the strengths of applying this valuation approach as a decision making tool in expanding or delay expansion of a.5g network to the next generation of networks, the 3G. Two different scenarios are considered. The structure of the paper is as follows. In Section II, we first provide background information on spectrum auctions in the United States and Europe; then we review basic options theory and describe the transition from financial options to real options (the advanced reader should skip that part); finally, we review the literature of real options in telecommunications. In Section III, we present the problem, formulate it as a real option, solve it for a hypothetical company, considering two cases, and provide numerical results via pricing the option. Section IV is where we present our analysis, studying the effect of crucial problem parameters to the option price and ultimately to the decision of expanding the network or not expanding it. In Section V, we draw conclusions and summarize the paper. II. BACKGROUND A. Spectrum Auctions in the United States and Europe There are differences between United States and Europe in spectrum auctions. The history of spectrum auction in the U.S. has lasted for almost 0 years, starting in 993. The first spectrum auction in the U.S. was held after Congress granted the authority to the Federal Communications Commission (FCC), in the Omnibus Reconciliation Act of 993, to conduct spectrum auctions. Since then, the FCC has conducted over 37 auctions with total net high bids summing to over $40 billion []. The approach followed in designing the auctions by FCC was particularly effective. With the cooperation of the academic community, FCC has achieved a high level of success in their auction program. The auction format used by FCC, is a Simultaneous Ascending Auction (SAA). SAA is not the straight analogue of auction house style English auction, but a discrete approach [7]. Basically, bidding consists of several sequential rounds. In each round, bidders send in sealed bids. When the round is closed, the results are published including high bidders and the bids to top them. Bidders are given time to analyze the results and send in bids in the next round. This auction approach has been working very well. However, over the course of FCC auctions, there have been a few failures, with some of them being quite serious. One of the serious failures in the history of FCC spectrum auctions was the IVDS and C-block spectrum auction [], which resulted in bankruptcies of small businesses and reducing the amount that these businesses owed the FCC up to 84% of the winning price. The cause of failure in that particular spectrum auction was the generous installment payment on winning bids granted by FCC, which gave the misleading signal to the bidders. Another example of

3 the serious failure in FCC spectrum auctions is the case of WCS and LMDS [], where the actual revenue from the auctions were a lot less than estimated. This is due to the auction being held too soon. There were also minor problems that occurred in the auctions due to withdrawals option and collusive activities [5]. Overall, however spectrum auctions in the United States has been quite successful, since there were few problems in the auction design so far. In Europe, there were enormous differences in the revenues gained from 3G spectrum auctions ranging from 0 Euros per capita in Switzerland, to 650 Euros per capita in the UK [4]. European 3G spectrum auction was first held in the UK. The auction format used was SAA. It was crucial for UK to be the first in the world to auction the 3G spectrum since UK auction attracted a large number of bidders to participate. The result was a record breaking revenue, since bidders overpaid their spectrum. Some other countries such as Netherlands, Italy and Switzerland tried to copy the UK auction design with additional rules. However, they were not as successful as the UK, because bidders learned their lessons from UK, especially incumbents, who sent collusive signals which kept out the new entrants from participating in the auctions. Therefore, there were few bidders (mostly incumbents) participating in 3G spectrum auction in those countries which resulted in high degree of collusion in the auctions. Regarding auction design, some particular countries, such as Switzerland, has set very low reservation price in order to attract new entrants [3]. However, since collusion activities kept out most of new entrants, low reservation price would even make the matter worse. Overall, European 3G spectrum auctions, besides UK, suffered from auction design flaws, collusion, and sequencing of auctions, which resulted in a high fluctuation of revenue gained. B. From Financial Options Theory to Real Options A real option is a methodological approach with which an investment can be analyzed while factoring for flexibility and uncertainty. Johnathan Mun, in his book, provides the following definition [3]: Real options is a systematic approach and integrated solution using financial theory, econometric analysis, management science, decision science, statistics, and econometric modeling in applying options theory in valuing real physical assets, as opposed to financial assets, in a dynamic and uncertain business environment where business decisions are flexible in the context of strategic capital investment decision-making, valuing investment opportunities, and project capital expenditures. Real Options Theory is derived from Derivatives Theory: an option is a contract giving the buyer the right, but not the obligation, to buy an underlying asset, at a specific price, on a certain future date. There are basically two types of options, call options and put options [,, 3]. Introduction to Financial Options A call option gives the holder the right, not the obligation, to buy the underlying asset at a certain date for a certain price. A put option gives the holder the right to sell the underlying asset at a certain date for a certain price. The price in the contract is known as the exercise price or strike price, the date is known as the expiration date or maturity. American options can be exercised at any time up to the expiration date. European options can be exercised only on the expiration date itself.

4 In order to price an option, we use five parameters: the current stock price S 0, the exercise price K, the time to expirationt, the risk free-rate of return r f, and the standard deviation of returns on the stock or volatilityσ. People who buy options are called call holders and those who sell options are called writers. Buyers are said to have long positions and sellers are said to have short positions. The writer of an option receives the cash up front but has potential liabilities later. Therefore, there are two sides to every option contract. On one side is the investor who has taken the long position. On the other side is the investor who has taken a short position. There are four types of options positions []:. A long position in a call option.. A long position in a put option. 3. A short position in a call option. 4. A short position in a put option. It is useful to characterize European option positions in terms of the terminal value or payoff to the investor at maturity. If K is the strike price and S T is the final price of the underlying asset, the payoff from a long position in a European call option is max( S T K,0) () The option will be exercised if S T > K and will not be exercised if S T K. The payoff to the holder of a long position in a European put option is max( K,0) () ST For call options, the option is said to be in the money if the share price is above the strike price. A put option is said to be in the money when the share price is below the strike price (see Figure ). Short Call K ST K ST Long Call Short Put K ST K ST Long Put Figure : Payoff from Options Traditionally, there are two methods for pricing options involving namely Binomial Trees and the Black-Scholes formula [].

5 Binomial Tree Approach for Pricing Binomial Tree represents different possible paths that the stock price might follow over the life of the option; S 0 is the current stock price, and f the current price of an option written to the underlying stock. The option lasts for a period of timet, i.e., the life of the option. We divide this period into n sub-intervals. At each time step dt = T / n, the stock price can either move up by a factor u with a probability of upward movement p, or it can move down by a factor d with probability p, where u > and d <. Let us consider a two-step binomial tree, i.e., n = (see Figure ). If the stock option moves up to S 0 u in the first step, we denote the payoff of the option as f u ; if the stock price moves down to d S 0, the payoff from the option is f d ; similarly, let f uu be the payoff from the option with two up movements, f dd the payoff in case of two down movements, and f ud the payoff from one up and down movement. Then, using no-arbitrage arguments (riskneutral valuation) the value of the option is given by: f rdt = e pf + ( p) f ] (3) [ u d where rdt e is the continuous discounting factor. S0u fuu p S0u fu p -p So f -p p S0ud fud 0 S0d fd -p dt dt Step Step S0d fd T Figure : Two Step Binomial Tree The parameters p, u and d are given by []: a d p = (4) u d u σ dt = e (5) d e σ dt = (6) rdt a = e (7) European Style Option: Example For example, consider a European call option with current stock price S 0 = $50, exercise price K = $50, risk-free interest rate r f = 0% or 0. per annum, volatilityσ = 40% or 0.4 per

6 annum, expiration periodt = 0.5 years or 6 months and suppose we divide the life of option into two intervals of length three months (= 0.5 years) for the purpose of binomial tree. With dt = 0. 5 years and from (4)-(6): up factor u =.4, down factor d = 0.887, probability of up move p = 0.530, and probability of down movement p = Figure 3a shows the binomial tree for the European call option. At each node there are two numbers. The top one shows the stock prices at the node; the lower one shows the value of the option at the node. The option prices at the final nodes are calculated using equation () and then the intermediate nodes, through a process of backward induction. For example, the option price at node D is = The option prices at the penultimate nodes are calculated from the option prices at final nodes. For example, at node B, the option price is calculated using equation (3) (0.530 * * 0) * e 0.*0.5 =.30 whereas at the root A, the value is calculated as (0.530 * * 0) * e 0.*0.5 = 6.56 Working back through the tree, the value of the option at the initial node is $6.56. Now suppose that our option is a European put one. Figure 3b shows the binomial tree for the pricing of this put option. Observe that in European put option, the values of each parameter and price of underlying remain the same as in case of European call option. The option prices at the final nodes are calculated using equation () and then the intermediate nodes, through a process of backward induction. For example, the option price at node F is = The option prices at the penultimate nodes are calculated from the option prices at final nodes. For example, at node C, the option price is calculated using equation (3) (0.530 * * 6.484) * e 0.*0.5 = 7.88 whereas at node A it is calculated as (0.530 * * 7.484) * e 0.*0.5 = 3.78 The value of the option at the initial node is $ A 0 p = p = dt = 3 months B C dt = 3 months D E 50 T = 6 months (a) Call Option F A 0 p = p =0.487 dt = 3 months B C (b) Put Option dt = 3 months D E F T = 6 months Figure 3: Two Step Binomial tree for European call and put option

7 An important relationship between p and c is derived by the put-call parity. It shows that the value of a European call with a certain exercise price and exercise date can be deduced form the value of European put with the same exercise price and exercise date, and vice versa [] c + Ke rt = p + S 0 (8) Consider our previous example of European call and put options: the put-call parity result can be proved using equation (8) as: American Style Option: Example * e 0.*0.5 = = Consider now an American call option. Figure 4a shows the binomial tree for American call option. The procedure is to work back through the tree from the end to the beginning, testing at each node to see whether early exercise is optimal. The stock prices at each node and their probabilities are unchanged. The option prices at the final nodes are calculated using equation () and then the intermediate nodes, through a process of backward induction. For example, the option price at node D is = At node B, the option price calculated using equation (3) gives (0.530 * * 0) * e 0.*0.5 =.30 whereas the payoff from the early exercise is =.07. Clearly, the early exercise is not optimal, and the value of the option at node B is.30. At node C, equation (3) gives the value of the option as zero, and the payoff from early exercise is also zero. Therefore, at node A, the value given by equation (3) is (0.530 * * 0) * e 0.*0.5 = 6.56 and the payoff from early exercise is zero. In this case, early exercise is not optimal, and the value of the option is therefore $6.56. Consider now the American put option analogue. The stock prices at each node and the probabilities are unchanged. Figure 4b shows the binomial tree for an American put option. The procedure remains the same as in case of American call option. For example, the option price at nodes D and E are zero. At node F, the value of the option is = At node B, the option price, calculated using equation (3), is zero, whereas the payoff from early exercise is also zero. At node C, equation (3) gives the value of the option as (0.530 * * 6.484) * e 0.*0.5 = 7.87 whereas the payoff from early exercise is Clearly early exercise is optimal and the value of the option at the node C is At the final node A, equation (3) gives the value of the option as (0.530 * * 9.065) * e 0.*0.5 = 4.305

8 whereas the payoff from early exercise is also zero. Clearly early exercise is not optimal at node A, and the value of the option at this node A is A 0 p = p = dt = 3 months B C dt = 3 months (a) Call Option E D 50 T = 6 months F A 0 p = p =0.487 dt = 3 months B C (a) Put Option dt = 3 months D E F T = 6 months Figure 4: Two Step Binomial tree for American call and put option The Black-Scholes Formula The Black-Scholes (B-S) formula was developed in 973 by Fisher Black and Myron Scholes to price at time zero a European call and put option on a non-dividend-paying stock. The partial differential equation by B-S is relevant under some specific assumptions: () the underlying asset is a stock, () the short selling of securities with full use of proceeds is permitted, (3) there are no transactions costs or taxes. All securities are perfectly divisible, (4) there are no dividends during the life of the derivative, (5) there are no riskless arbitrage opportunities, (6) security trading is continuous, (7) the risk-free rate of interest, r f, is constant and the same for all maturities. The formulae for calculating the price of a European call c and put option p are given by []: rt c = S N d ) Ke N( ) (9) 0 ( d p = Ke rt N( d ) S0 N( d) (0) d ln( S0 / K) + ( r + σ / ) T = () σ T d = d σ T () where N (d) is the cumulative Normal density function. For example, consider a European call option with current stock price S 0 = $50, exercise price K = $50, risk-free interest rate r f = 0% or 0. per annum, volatilityσ = 40% or 0.4 per annum, expiration periodt = 0.5 years. Using equations () and () we get

9 d = , d = If the option is European call, its value, c, is given by c = 50N(0.38) 50e 0.*0.5 N(0.0354) If the option is a European put, its value, p, is given by p = 50N( ) 50N( 0.38) Using the polynomial approximation for the Normal random variable, we have N(0.38) = 0.648, N(0.0354) = 0.54, N( ) = , N( 0.38) = so that c = 6.78, p = 4.4 Comparing the binomial model and the Black-Scholes model for valuing options, for the same input, the binomial model yields a call price of c = 6.56 using two time steps, while the Black-Scholes model yields a call price c = 6.78, representing an absolute error of If the time steps are increased to 500, the binomial method yields a call price of c = 6.78 with an absolute error of 0.0. Mapping between Investment Opportunities and Financial Options: Investment options can generally be mapped into financial options, e.g., stock options. Table gives the mapping between the two: Table : Mapping between investment opportunity and financial options [] Investment Opportunity Variable Financial Options Expenditure required to acquire the assets K Exercise price Present value of the assets S 0 Stock price Length of time to expiration T Time to expiration Riskiness of underlying assets σ Variance of returns Time value of money R Risk free rate The above table helps managers to identify the parameters in financial options and map them to real options and model the investment problem. For example, projects involve investment to be done in order to build or buy a product. This is like exercising an option in which the amount invested is equivalent to the exercise price K and the present value of the asset is the current stock price S 0. The length of time the firm can wait is the time of expirationt, and the riskiness of the project is reflected in the standard deviation of the assetσ. Time value of money is given by risk-free rate f r. Real Options have been used in many fields such as Pharmaceuticals and Biotechnology (where are a lot of patents), Energy, Oil, Mining, Information Technology, etc. [3]. In telecommunication, they have been used in valuation of products, technologies and companies, forecasting in demand and capacity [3]. We here use Real Options Theory in valuing the option to expand from.5g to 3G, for operators who own the licenses and for other who have not paid for the licenses yet.

10 The Option to Expand An option to expand provides the management, the ability and right to expand into different markets, products and diversify its operations. This is an option that allows management to make further investment into existing products, increase its output, and market share. It is the best example of strategic option wherein the management has the right to choose whether or not to take some action now or at some future time. Expansion option enables the firm to capitalize on future growth opportunities with a higher cost to position it, for future. Management has the flexibility to alter the course of action at different times during the life cycle. The project can be modeled as an American call option because the option to expand its operations can be exercised at any time until the expiration date, i.e., life of the license. The procedure to develop the binomial tree for underlying asset remains the same as explained earlier in the paper for an American call stock option. At the end nodes, the option value is greater between two values: expansion (exercise) or continue operations (do not exercise). At earlier nodes, the value of the option is greater between the value given by equation (3) and expand. We will discuss the option to expand in more detail in Section III. C. Real Options in Telecommunications Real Options Theory is applicable when the business process includes an option, investment is irreversible and there is uncertainty about the value of investment and possibility of losses. The real options theory is applicable in markets characterized by high volatility such as the telecommunication market. James Alleman has shown how Real Options Theory is relevant to telecommunication industry in terms of strategic evaluation, estimation and cost modeling [0]. Nicholas Economides studied the economic principles on which cost calculations should be based [9]. The Telecommunications ACT of 996 imposes mandatory interconnection, unbundling, and number portability. In calculating the cost of the UNEs, it is important to define correctly the cost of capital. In calculating the cost, demand and supply uncertainty, as well as the asymmetric position of incumbents and entrants, should be taken into account. Close examination of the issue of uncertainty in the local telecommunications networks reveals that an incumbent does not face higher cost by investing. There are no real options results under conditions of oligopoly where the investing firm may have strategic advantage over a reseller. Second, large customers prefer to buy from an owner rather than a reseller. Third, according to real options theory, the cost of capital for UNE may be higher only if two requirements are met: the network element has a zero resale value, and there is significant uncertainty about the network elements of zero resale value. Applications of real options theory to the conditions of the telecommunications market may imply a lower cost for the affected unbundled network elements than if real options theory were not applied. Peter Forsyth et. al studied the underlying risk factor in the bandwidth market [4]. They introduce a concept where bandwidth market players could settle a contract within seconds similar to buying or selling currency. They draw an analogue between the bandwidth market and the financial market. Since the price at expiry is known, the model tries to find prices before expiration. The model assumes its owner receives continuous payments at the maximum transmission rate. They assume price is a decreasing function of time. Upgrade when usage reached 50% of the maximum transmission rate. Due to uncertainty in demand, it may be optimal to wait until the maximum capacity for a line is reached. Real Options help determine optimal timing investment into new capacity.

11 Peter Forsyth et. al applies modern financial option valuation methods to the issue of management of wireless network capacity [5]. The study determines when it is optimal to increase capacity for each base station contained in a cluster (group of base stations), and calculate the optimal time to upgrade in terms of observed usage to existing capacity. They impress the importance of financial criteria in terms of maximizing net revenues whereas in practice, upgrade decisions are often based purely on quality of service. Patrick Herbst and Uwe Walz adopt Real Options approach to analyze the value of recently auctioned UMTS-license, focusing on Germany, the largest European market [0]. They developed a real options model with an abandonment and growth option. The paper shows that for a license, the growth option is often a decisive factor: in its absence, the total net value of the investment is negative and the telecom firms do not earn the money they have spent. The paper points out two important variables that affect the total value of the investment, particularly the initial customer base of a firm and the net cash flow generated per user. It turns out the cash flow generated by the each user is a vital variable besides the relative position of the individual licensees. The main message of the analysis is that investment will pay off for an incumbent player; it will be an uphill battle for Greenfield firms. In summary, the model is simple in nature but it does not incorporate the variability of the cash flow generated from each user which will make the model more realistic. Secondly, the model works well for well established incumbent players but not for Greenfield firms. J. Edelmann et.al has used Real Options approach to shed light on the complicated issues of strategic alternatives in the telecommunication sector [9]. The paper puts lot of stress on the importance of having strategic options, i.e., the right to choose whether or not to take some action now or at some future time. The authors have used the real options framework to assess the risk. They have used the real options tool to help analyze the choices between various projects, products, factors of production, partners and customers and how to gain competitive advantage with the chosen path. Nalin Kulatilaka explains the current situation in 3G deployment with the help of fundamental critical management question such as What, Why, When and How real options approach helps in the decision making process in a comparative manner [8]. The process explained by the author points in the direction where management should identify the current desired business capabilities based on the organization s strategy. Design a program, and invest in a manner that achieves the desired capabilities, estimate the cost and benefits related to the investment, and determine the market value of the investment through the cash flows. The important points the author mentions are the need for flexibility in the approach, the culture, identify the changes in the market place, and redirect resources in response to these changes. III. PROBLEM FORMULATION The wireless industry has undergone many changes. It has taken a span of 0-30 years to mature to its current glory. 3G on the other hand faces a time constraint for its launch. The promise of better data and voice services has long been delivered by 3G without actual implementation. Post auction issues raise questions such as what options a network operator has to layout the network. Real Options Theory provides tools for valuing investment projects, such as options to expand the network, to delay investment into developing a product, to switch to alternative technologies, to contract operations to third parties and compound options to develop new product and simultaneously test the product in the market. As mentioned earlier, spectrum auctions demand the network operator to build predetermined percentage coverage area. The next step is to expand the network, since time to market is very important. The proposed model in this paper is based on an option to

12 expand. It focuses on the options that a network operator has to consider in rolling out 3G network. We are considering two scenarios: In the first scenario the company has acquired the spectrum to upgrade from.5g to 3G and considers expanding the network using the real options toolkit. In the second scenario, the company has not acquired the spectrum to rollout 3G network yet. We have made certain assumptions in our paper to perform the analysis. Our hypothetical company covers a large metropolitan area e.g., New York City. We have considered the current value of the company to be $7,76m. This forms the underlying asset for our derivative. Currently, there is a total of 5 cell sites serving the subscribers. The cost of erecting a single cell site is approximately $5m. The life of the project is projected to be five years. As far as option parameters concerns, our calculations are as follows: the maturity of the option T is five years, which is typical in auctions rules to have percentage network developed and deployed in US [7]; the current price of the underlying S 0, i.e., the value of the company, is $7,76m; in order to obtain the volatility of the assets σ, we looked at historical price movements of stock price of company, and estimate it at 8% annually; we consider risk-free rate r f of 3.%, after we looked at the current US Treasury Bond rates 3 corresponding to the life of the our option e.g., five years. For the option to expand we use two more parameters: a) investment cost K : in the first scenario comprises of capital expenditure (CapEx) which is the cost of upgrading the entire network and is calculated in the following section. In the second case, K is the sum of CapEx and the license cost L, which is assumed to be $ m. b) expansion factor E : which is the post-expansion growth factor of the company, assumed fixed for the life time of the project. Since it is a key factor in our decision analysis toolkit we consider a range of different values. The scope of the analysis is to identify which of the parameters are more influential in the decision making process: the expansion factor, the volatility or the investment cost. The model is general enough so it can be further enhanced for an entire foot print of the operator. A. Cash Flow Break Down and Estimates Figure 5, shows the cash flow break down to capital expenditure (CapEx), operational expenditure (OpEx), and revenues, along with their corresponding attributes. Cash Flow CapEx OpEx Revenues Cell Site Construction Base Station Cost Switch Cost Antennas Radios Integration Cell Site Lease Power Telco Cell Site & Switch Software Mobile Mobile Roaming Data Figure 5: Cash Flow for the operator [5] 3 United States Department of the Treasury,

13 Capital Expenditure The capital expenditure (CapEx) is the necessary amount of money to acquire the physical assets to upgrade the infrastructure. It is usually comprised of cell site construction cost, base station cost, switch cost, antenna cost, radio cost, and integration cost paid for building a single cell site, etc. The amount of capital required to upgrade the network during the life of the project e.g., the next five years, is estimated based on the number of cell sites the company has in the metro area in the current year. We assume the cost of erecting a single cell site is $5.75m and is constant for the life of the project. The following table shows the projections for the life of project. New cell sites are added every other year as it can be seen from Table. The first year the company constructs 66 cell sites and in subsequent years the constructions of cell sites decreases. Then as we reach the end of the project, required cell sites go up again. The numbers shown are based on prior experience on similar projects and personal conversations with people in the industry. These growth numbers are typical for any network operator who operates in a large metropolitan area. Table : Capital Expenditure Projections for the expansion project (Source: Authors Estimates) Year Year Year Year 3 Year 4 Year 5 Initial Cell Sites New Cell Sites CapEx (in million) $67.76m $54.49m $67.4m $7.9m $87.44m Operational Expenditure and Revenues: Operational Expenditure (OpEx) is the expenses that are incurred to operate and manage infrastructure. It is usually comprised of cell site lease, power, Telco, cell site, switch software cost etc. Unlike CapEx, OpEx is an ever growing expenditure, mainly due to increasing rate of new subscribers and physical requirements such as power, telco, billing and software fees. Revenues comprise of revenues generated from voice and data subscribers, roaming, and mobile mobile. Revenues can be estimated from average revenue per user (ARPU), phone subsidy, and total number of subscribers. In our paper, we use capital expenditure as part of investment cost to perform analysis for the two scenarios mentioned earlier. In the current phase of our research we do not consider operational expenditures and revenue, as estimating cash flows for them is a challenging task. Scenario A: Investment cost excludes spectrum license cost In Scenario A, we calculate the investment cost K, comprised of the capital expenditure figures shown in Table. We intend to compare the value of the project obtained through the traditional approach of discount cash flows and the option to expand analysis, to show which approach values the project more.

14 No Growth Assumption and Traditional Valuation Table 3 shows the capital expenditure required for each year for the network operator over the life of project for deploying 3G network. Table 3: Present value calculation of investment cost Year Year Year Year 3 Year 4 Year 5 CapEx (in million) $67.76m $54.49m $67.4m $7.9m $87.44m Discount Factors The present value of the investment cost K i.e., above indicated capital expenditure, is given by where 5 = Fn ( P / F, i%, N) N = K (3) F n is the future capital expenditure at the end of th N period, and i is the discount rate per period (here we assume that it remains the same during the life of the project). In our study, we assume we discount the cash flows using the weighted average cost of capital (WACC) [] of the firm i.e., the return required by both equity holders and creditors of the firm, taking into account the corporate tax rate e.g. 35% in the US, and the leverage of the firm. For our company, we assume that the WACC equals 0% for the time of project, which is slightly higher from the industry wide telecommunication average WACC []. From (3) and Table 3 which shows the discount factors and cash flow F, we calculate the present value of investment cost K as n K = F P / F,0%, ) + F ( P/ F,0%,) + F ( P/ F,0%,3) + F ( P / F,0%,4) + F ( P /,0%,5) ( F = $ 67.76*(0.833) + $54.49*(0.6944) + $67.4*(0.5787) + $7.9*(0.483) + $87.44*(0.409) = $ 86.00m The Discount Cash Flow (DCF) method asserts how much the investment will cost assuming the future outcomes are fixed and discounted at the risk-adjusted cost of capital, e.g., WACC. By applying DCF, the management will get the outcomes assuming there will be no drastic changes in the market conditions. The Net Present Value (NPV) is the difference between the present value of the asset and the required investment cost K for scenario A. Therefore, NPV = PV (asset worth) PV (capital expenditure) (4) For Scenario A, NPV = S 0 K, i.e., NPV of project = $ 7,76 $86.00 = $7,475m.

15 Option to Expand Our company has already acquired the license, which gives them an option to roll out the 3G network in the metropolitan area any time within the next five years. It is an American call option with parameters: volatility 8%, risk-free rate 3.%, current value of the underlying asset $7,76m, and time to maturity 5 years. From equations (4), (5), and (6) we can calculate the parameters of the binomial tree as u =.97, d = and p = The evolution of the tree for the underlying asset, i.e., the firm value, is shown on the left of Figure 6 (A), considering that each time step of the tree equals one year (all figures shown in millions). A $7,76.00 $33,35.95 B $3,87.94 C $39, D $7,76.00 E $9,368.9 F $47, G $33,35.95 H $3,87,94 I $6,77.67 J $57,033. K $39, L $7,76.00 M $9, N $3,5.73 P Q R S T $68,8.04 $47, $33,35.95 $3,87.94 $6,77.67 A $7,8.54 $33, B $3,4.47 C $39,93.83 D $7, E $9, F $47, G $33,30.5 H $3,00.76 I $6,77.67 J $57,36.4 K $39,9.35 L $7, M $9,368.9 N $3,5.73 P Q S T $68, Expand $47,88.45 Expand R $33,8.3 Expand $3,87.94 Do not Expand $6,77.67 Do not Expand O O U $,86.78 U $,86.78 Do not Expand A. Expansion Option (Underlying Asset Tree) B. Expansion Option (Valuation Tree) Figure 6: Binomial Trees for underlying asset (A) and option to expand (B) For the option to expand we use two more parameters: the investment cost K, which equals $86m as calculated already, and the expansion factor E, which is assumed to be.0, e.g. % growth in the company value post-expansion, for this particular case. Starting at the end of the tree at terminal node P, the value of the option can be obtained as follows: it is the maximum between exercising the option i.e., company decides to expand its network or not exercising i.e., continues its current operations (no expansion). From the trees above Expand = (.0) * $68,8.04 $86.00 = $68, m vs. Continue = $68,8. 04 Clearly the operator will choose at node P to exercise the option i.e., expand the network to 3G. Therefore, the value of the option at this node is $68,677.85m. We similarly follow the same calculation for all terminal nodes. For example, at node U, the operator should not exercise the option because the value of continuing with current network operation is $,86.78m which is greater than value of expansion which is.0*($,86.78) $86.00 = $,3.64m. We can see that when the market conditions and macro-economic factors are favorable, it is worthwhile to expand the current network; in cases when the market conditions drive the value of the company to lower levels, such as at node U, it is optimal to continue with the current network.

16 Moving to intermediate nodes, at node K for example, the company has two choices: to exercise the option i.e., expand the network to 3G or continue with existing.5g network. From the trees in Figure 6 Expand = (.0) *($57,033.) $86.00 = $57,37. 45m Vs. KeepingOpt ionopen( Continue) = [0.547 *($68,677.85) * ($47,88.45)]* e = $ 57,36.4m 0.03* Clearly, the operator will choose at node K to continue with the current network i.e. not to expand the network. Similarly, we walk backwards in the tree continuously discounting, facing the same decision maximization problem between expansion and keeping the option open (continue or no expansion) in every node. As it can be seen from Figure 6 (B), the value the option to expand is $7,8.54m. By using the static valuation method in expansion, the value of project is.0* (7,76.00) $86.00 = $7,75.6, assuming an expansion factor of %. On the other hand, using the real options framework, the value of the project is $7,8.54m. Therefore, there is an extra premium of $ 7,8.54 $7,75.6 = $69.93m. The real option is worth an additional of 0.0%. Scenario B: Investment cost includes spectrum license cost. In Scenario B, we first calculate the investment cost K, which is the sum of the capital expenditure shown in Table, plus the license cost L, which is assumed to be $6,350m [5]. Similarly, we calculate and compare the value of the project, using both the traditional approach and the option to expand. No Growth Assumption and Traditional Approach The present value of the investment cost K is sum of the investment cost K and the license cost L, i.e., K = K + L (5) We calculate the present value equivalent of investment cost K using equation (5) as K = $ $6, = $6, m As we can see, K is 3 times higher than K, due to the high license cost. Assuming we expand with no growth, the NPV is the difference between the present value of the asset S 0 and the required investment cost K which is (4) NPV of project = $7,76.00m $ m = $,5.00m Option to Expand Our company is thinking of purchasing the spectrum which gives them an option to roll out 3G network in metropolitan area any time within next five years. The parameters of the options are same as in Scenario A. The only difference is the investment cost K equals

17 $6,636.00m, and the expansion factor E, which is assumed to be 0% here (we assumed a high expansion factor, so we get higher probability of exercising the option, since strike price is much higher than in scenario A). A $7,76.00 $33,35.95 B $3,87.94 C $39, D $7,76.00 E $9,368.9 F $47, G $33,35.95 H $3,87.94 I $6,77.67 J $57,033. K $39, L $7,76.00 M $9,368.9 N $3,5.73 O P Q R S T U $68,,8.04 $47, $33,35.95 $3,87.94 $6,77.67 $,86.78 A $7, $33,50.66 B $3,87.94 C $39,88.6 D $7,76.00 E $9,368.9 F $47,69. G $33,35.95 H $3,87.94 I $6,77.67 J $57,34.7 K $39, L $7,76.00 M $9,368.9 N $3,5.73 O P Q S T U $68,473.5 Expand $47, Do not Expand R $33,35.95 Do not Expand $3,87.94 Do not Expand $6,77.67 Do not Expand $,86.78 Do not Expand A. Expansion Option (Underlying Asset Tree) B. Expansion Option (Valuation Tree) Figure 7: Binomial Tree for underlying asset (A) and option to expand (B) The pricing procedure remains the same as explained earlier for scenario A: at each node, we maximize between exercising the option, i.e., expand, or not exercise i.e., continue the current operations (no expansion). As it can be seen from Figure 7(B), we value the option to expand at $7,768.74m which is lower than the one in Scenario A, since investment cost is higher (strike price of the option much higher), although growth factor is higher. By static valuation methods, the project is currently valued at.0*($7,76.00) $6, = $3,90.0m assuming expansion factor of 0%. On the other hand, using the real options framework, the value of the asset is $7,768.74m. Therefore, there is an extra premium of $ 7, $3,90.0 = $ m. The real option is worth an additional 6%, much higher premium than Scenario A. IV. ANALYSIS OF NUMERICAL RESULTS In this section we want to study the effect of various parameters in our decision making process. Effect of Expansion Factor on Option Value Figure 8 shows the expansion factor with respect to the value of the options for both scenarios. The expansion factor varies from.0 to.0. We keep the rest of the parameters unchanged i.e., S 0 = $7,76m, volatilityσ = 8%, risk-free rate r f = 3.%, maturity T = 5years, investment cost without license fee K = $86.00m, investment cost with license fee of K = $6,636.00m.

18 $34, $33, $3, Value of Option (Millions) $3, $30, $9, $8, Expansion is favored at E =.06; Value = $ Value of Option W/O License Cost (Scenario A) Value of Options W/ License Cost (Scenario B) $7, $6, $5, Expansion is Favored at E =.098, Value = $7, Expansion Factor Figure 8: Effect of Expansion Factor to Option Value (both scenarios). In scenario A, the expansion of the option is favored first time when E =.06. After that point, the option is always exercised. At this point, the value of the option equals $8,38.0m which is much higher than the NPV of the project using DCF, which is as calculated as $7,75.6m in scenario A. As we can see from Figure 8, the value of the option increases linearly with respect to the expansion factor. As the expansion factor grows, the value of option increases; as long as the underlying is above the strike price i.e., the investment cost K, the option is in the money and should be exercised. Therefore, the higher the expansion factor, the higher the price of the underlying asset, and higher the payoff of the option. For scenario B, the investment cost K, i.e., strike of the option, is higher than in scenario A. Therefore, as the expansion factor increases, the option value is not exercised (not being in the money), remaining constant up to the point E =. 09. At E =. 098, the expansion is favored, i.e., the company should expand the network to 3G, since the value of the option is $7,763.4m, which is clearly higher to the calculated NPV via DCF which equals $3,90.0m. As we can observe from the analysis above, the option value is high when the investment cost is low. In addition, for situations when the investment cost are high, it requires at least 0 fold increase in company s value to expand the network, when investment cost is low, it is other way round, even a small expansion factor can lead to exercising the option. Effect of Volatility on Option Value Figure 9 shows how the volatility affects the value of the option, when expansion factor is at E =. 0, i.e., kept constant for both scenarios. The volatility is varied from 5% to 80%. We keep the rest of the parameters unchanged.

19 $8, $7, Value of Option(Millions) $7, $7, $7, $7, Value of Option W/O License Cost (Scenario A) Value of Option W/ Lincese Cost (Scenario B) $7, $7, Volatility (%) Figure 9: Effect of Volatility to Option Value (both scenarios): Expansion Factor % In scenario A, the value of the option increases linearly with respect to volatility. As it is expected, the higher the volatility of the underlying asset, the greater the value of the option. In scenario B, high strike price case, expansion is favored for the first time when volatility hits 65%. For volatilities below that level, the option value remains constant as we can see from the plot. This is because the option is out of money and therefore is not exercised. At higher volatilities, the value of the option increases and expansion is favored. Even though the volatility is increasing, it does not give enough influence to the decision maker to expand the network because the cost of investment is too high in scenario B and expansion factor is low (only %). We are now interested in studying the affect of the volatility to the value of the option at a higher expansion factor level e.g. E =. 0. Figure 0 shows how the volatility affects the value of the option when expansion factor E =. 0 is kept constant for both scenarios. Volatility is varied from 5% to 80%. We keep the rest of the parameters unchanged. $33, Value of Option W/O License Cost (Scenario A) $3, Value of Options W/ License Cost (Scenario B) $33, $3, $33, $30, Value of Option (Millions) $33, $33, $33, Value of Option (Millions) $9, $8, $33, $33, $7, $33, $6, Volatility (%) Volatility (%) Figure 0: Effect of Volatility to Option Value (both scenarios): Expansion Factor 0%

20 Interestingly the results obtained when expansion factor is high are opposite to the results obtained at lower expansion factor shown before. In scenario A, the value of the option remains constant when volatility is from 5% to 55%. The value of the option for this range of volatilities remains constant at $33,068.5m which is much higher than the NPV of the asset, calculated at $7,475m. For volatilities above 55% the value of the option is slightly higher. In scenario B, the value of the option increases linearly with volatility. For all volatilities, the value of the option is much higher than the strike price i.e., the investment cost K. With low investment cost, i.e., scenario A situations, and high volatilities, it is a good decision to expand the network since the value of the option is high. With high investment cost, i.e., scenario B situations, and high volatilities, it is not favorable to expand the network since the value of the option is low. V. CONCLUSIONS AND FUTURE WORK The promise of better data and voice services has been long delivered by 3G without actual implementation. Experts believe with the deployment of 3G services, operators will increase their profitability substantially. Our analysis shows that the path to 3G depends not only on purchasing the spectrum but on other factors too such as expansion factor, volatility and investment cost. In this paper, aiming realism, we consider two cases: in the first, the company owns the spectrum license and considers if expansion is favorable; in the second case, the company considers the spectrum fee as an investment cost, since it has not acquired it yet. In both cases, the current price is much higher than the strike. The model can be easily applied to telecommunications companies of smaller value. When expansion factor is varied, our analysis suggests that the option value is high when the investment cost is low. In addition, for situations when the investment cost are high, it requires at least 0 fold increase in company s value to expand the network, when investment cost is low, it is other way round, even a small expansion factor can lead to exercising the option. With low investment cost, and high volatilities, it is a good decision to expand the network since the value of the option is high. With high investment cost, and low volatilities, it is not favorable to expand the network since the value of the option is low. Selection of input parameters and assumptions play an important role in real option analysis and they are key factors for its success. For example, the volatility factor used to measure change in the value of underlying asset is difficult to estimate in reality. Even when we use the historical stock price movements, people raise criticism. In regards to capital expenditure, we had assumed they will remain constant during the course of expansion. However, as the technology progresses, the cost of purchasing the infrastructure will come down. The capital expenditures are not as large as the spectrum license cost to deploy the network. The marketing and operational costs will be the largest part of the total investment cost due to increase in subscriber base and the cost incurred to keep the network functionally running at all times. But in our paper, we have only considered capital cost as investment cost. It can be extended to have operational expenditure as well. We believe that the capital expenditure for both the incumbents and green filed players will remain the same. The difference can be large in the case of operational expenditure and marketing costs for incumbents and green field players.