Real Options in TelecommunicationNetwork Evolution Economics

John M. Charnes∗

The University of KansasSchool of Business—FEDS1300 Sunnyside Avenue

Lawrence, KS 66045jmc@ku.edu

Barry R. CobbThe University of KansasSchool of Business—FEDS1300 Sunnyside Avenue

Lawrence, KS 66045brcobb@ku.edu

January 19, 2003

1 Introduction

This document describes ongoing work to be performed on a research projectduring the period 16 September 2002 through 15 September 2003. In sub-sequent sections we provide background information for the project takenfrom the research proposal and present some ideas that were sent recentlyin a progress report to the providers of the research funds.

The goals of this research project are: (1) to provide Sprint and NortelNetworks with a usable valuation model for making decisions related to theevolution of the telecommunication network, and (2) to expand the existingbase of academic research related to valuation of real options. By usingreal data and opportunities to accomplish (1), we can determine generaltechniques that can be published to help accomplish (2).

This document contains preliminary results and is intended to accom-pany a presentation scheduled for January 24, 2003 in the Finance Seminarat The University of Kansas School of Business. Do not quote, cite, or dis-tribute without permission of the authors.

∗The authors gratefully acknowledge financial support from Sprint and Nortel Networksthrough The University of Kansas Center for Research, Inc., FEIN #48-0680117.

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2 Financial options and real options

An option is the right, but not the obligation, to buy (or sell) an asset at somepoint within a predetermined period of time for a predetermined price. RealOptions Analysis (ROA) has been used recently as an alternate methodol-ogy for evaluating capital investment decisions involving a high degree ofmanagerial flexibility, such as research and development projects or newproduct decisions. Unlike the simple net present value (NPV) method usedin traditional finance theory, ROA treats an investment opportunity as eithera single option or a compound option (a sequence of options). The tradi-tional NPV method cannot value managerial flexibility correctly because itrelies on the false assumption that the investment is either irreversible orthat it cannot be delayed.

With a financial option the initial investment in an options contract buysthe potential opportunity to enjoy positive cash flow when future pricechanges of the underlying financial asset favor doing so, but does not carrythe obligation to realize negative cash flow if unfavorable conditions pre-vail. This flexibility adds value to a financial option contract. With a realoption—an option on a real asset—the initial investment related to the as-set (e.g., an expansion of some portion of a telecommunications network)buys the potential opportunity to continue, expand, or abandon the use ofthe asset when it is favorable to do so, but does not carry the obligation torealize some losses when unfavorable conditions prevail. Because projectssuch as network expansion can be viewed as options, financial models sim-ilar to those used for determining financial option values can be used todetermine the value of the real options embedded in the opportunity fornetwork expansion.

The research proposal describes some of the methods available for valu-ing real options, and discusses how they can be developed to suit the needsof Sprint and Nortel Networks as they plan the evolution of telecommuni-cations networks over the next two to seven years.

3 Factors affecting option value

The Black-Scholes formula for a European call option on a stock that paysdividends at the continuous rate δ is

C(S,K,σ , T , δ, r) = Se−δTN(d1)−Ke−rTN(d2), (1)

where

d1 = ln(S/K)+ (r − δ+ 12σ

2)Tσ√T

(2)

d2 = d1 − σ√T (3)

2

andN(x) is the cumulative normal distribution function, which is the proba-bility that a number drawn randomly from the standard normal distribution(i.e., a normal distribution with mean 0 and variance 1) will be less than x.

The Black-Scholes formula for a European put option is

P(S,K,σ , T , δ, r) = Ke−rTN(−d2)− Se−δTN(−d1), (4)

where N(x) is the cumulative normal distribution function, and d1 and d2

are given by equations (2) and (3).According to the Black-Scholes option-pricing models (1) and (4), op-

tions derive their value from six main factors. These factors are most eas-ily expressed in terms of financial options, but the analogy to real optionsprovides insights into the factors associated with strategic investment de-cisions in network evolution. The factors are:

Stock price, S. The value of the underlying stock on which an option ispurchased. This is the stock market’s estimate of the present value ofall future cash flows arising from ownership of the stock. Its analogin a real options analysis is the present value of cash flows expectedfrom the network investment opportunity under consideration. Thesecash flows can be affected by the voice and data services providedthrough the network, the behavior of competitors in the marketplace,regulatory decisions, equipment reliability, or other determinants.

Exercise price, K. The predetermined price at which the option can be exer-cised. Its real options analog is the present value of all the fixed costsexpected over the lifetime of the network investment opportunity.

Volatility, σ . A measure of the unpredictability of stock price movements,usually expressed as the standard deviation of the growth rate of thevalue of future cash flows associated with the stock. Its real optionsanalog is a measure of uncertainty of the cash flows associated withthe network investment opportunity.

Time to expiration, T . The period during which the option can be exer-cised. Its real options analog is the period for which the networkinvestment opportunity is valid. This period depends on the usefullifetimes of network components, Sprint’s and Nortel Network’s com-petitive advantages, and contracts entered into by Sprint or NortelNetworks.

Dividends. Sums paid regularly to stockholders at a constant continuousrate, δ. These reduce a financial option payoff when the option is ex-ercised after a dividend payout, which reduces the stock value. Theirreal options analogs are the expenses that drain away potential projectvalue over the duration of the option. The cost of waiting could be highif competitors enter the market. Thus, the cost of waiting to invest

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might be reduced by locking-in key customers, or lobbying for regu-latory constraints that discourage competitors from exercising theiroptions to enter the market.

Interest rate, r . The yield on financial securities with the same maturity asthe duration of the option. The risk-free rate of interest is used inthe Black-Scholes model, but a different rate might be appropriate forsome of the alternate option valuation methods described below.

According to the Black-Scholes model, increases in stock price, uncer-tainty, time to expiration, and interest rates increase financial option val-ues, while increases in exercise prices and dividends reduce financial optionvalues. These qualitative relationships are generally true for real options aswell, but real options have additional features that distinguish them fromthe type of financial options for which the Black-Scholes model was derived.The Black-Scholes model is an exact solution to a pricing problem that wassimplified to make it solvable. The main simplification is called the Euro-pean feature of the option, which means that the option is assumed to beexercisable at only a single time point in the future. Most financial and realoptions are said to have American features, which means that those optionscan be exercised at any point in time between their purchase and expiration.The valuation of American-style options is more difficult than the valuationof European options. In practice, this difficulty can be overcome partiallyby assuming a Bermudan feature, which means that an option can exercisedat one of several discrete points between purchase and expiration (ratherthan continuously as with an American option). The Bermudan assumptionis consistent with reality if the decisions to make network investments willbe implemented only at discrete times (e.g., quarterly).

4 Real option valuation methods

Several models are available for determining the value of real options. Thissection briefly describes some of the valuation methods associated withthese models along with their advantages and disadvantages. Each of thesemethods will be considered for their ability to help Sprint and Nortel Net-works.

4.1 Black-Scholes model

This method calls for making simplifying assumptions about an investmentopportunity, then using the Black-Scholes formula for estimating the optionvalue. While this is useful to gain qualitative insights into the network in-vestment opportunity, the requisite assumptions are generally too restric-tive to give the estimates credibility with decision makers. For example, theEuropean exercise feature described above is usually not accurate, as in-vestment decisions may be made at more than point in time. This method

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also requires the user to assume a model for only one source of uncertainty.While it is possible to lump all sources of uncertainty into a single factorand estimate the parameters, many people are more comfortable with mod-els that allow for explicit modeling of each major source of uncertainty.Further, use of the Black-Scholes model dictates that asset prices be mod-eled as geometric Brownian motion, which was required for solution of thepartial differential equations that Black and Scholes used to frame the orig-inal problem. Geometric Brownian motion has proven to be adequate formodeling some financial asset prices, but its use is often questionable formodeling the price evolution of real assets.

4.2 Lattice models

These methods are based on a simple representation of the evolution of thevalue of the underlying asset. The simplest and most widely used of thesemethods is the binomial lattice, which calls for breaking up the life of theoption into many time periods and assuming that in each time period thevalue of the underlying asset can take on only one of two possible values.This method is essentially a discrete approximation to the Geometric Brow-nian model used by Black-Scholes, and is popular because it doesn’t requirestochastic calculus to obtain a solution. The approximation gets better asthe number time periods is increased, but the number of calculations ex-plodes geometrically with the number of time periods, which makes evalu-ation more difficult. It is possible to model multiple sources of uncertaintywith this method, but the geometric explosion of the number of calculationsis exacerbated by the addition of more sources of uncertainty. This addedcomputational burden is sometimes called the curse of dimensionality.

4.3 Decision Tree models

A decision tree is a systematic way of organizing and representing the vari-ous decisions and uncertainties that a decision-maker faces. This is a long-standing method for attempting to capture the value of flexibility. Themethod uses a diagram composed of decision nodes and event nodes thatentail the use of a discrete set of possible outcomes for each event, suchas asset prices. The output of a decision tree is often computed as the netpresent value (NPV) of a project involving flexibility.

The decision tree method is often criticized on the grounds that the cor-rect discount rate used to compute the NPV is difficult to ascertain. Unlikethe Black-Scholes method, the risk-free rate is not appropriate unless cer-tainty equivalents are used in place of actual cash flows, and the weightedaverage cost of capital is not considered the correct rate to use either be-cause the outcomes are weighted by their probabilities of occurrence. An-other criticism of the decision tree method is that it gives no indication ofthe riskiness of investment opportunities without further sensitivity analy-

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sis. Although it too suffers from the curse of dimensionality, an advantageof the decision tree method is its clear depiction of the decision alternativesand uncertainties associated with the real option.

4.4 Monte Carlo Simulation

Monte Carlo simulation uses a sophisticated “what-if” analysis based onrandom sampling from probability distributions selected to represent therandom outcomes associated with the real options. On each simulation trial,a random number is drawn from each probability distribution specified inthe model. The probability distribution parameters can be estimated sub-jectively be managers or based on empirical data for similar projects. Theset of random numbers and the associated value of the output constitute ascenario that could possibly be realized in the future. By using Monte Carlosimulation to calculate many such scenarios and constructing a frequencydistribution of the outputs, a decision maker can assess the riskiness andother characteristics of the situation being modeled.

Monte Carlo simulation allows for construction of straightforward, easy-to-interpret models that can accommodate many decisions and sources ofuncertainty. Of course, simulation models become more complex as moredecisions and sources of uncertainty are added to the model, but the compu-tational complexity grows at a slower rate than it does with other numericalmethods. Because it suffers less from the curse of dimensionality, and usesstraightforward, easy-to-interpret models, Monte Carlo simulation is an ex-cellent tool for valuing the relatively complex real options embedded in thesituations being considered by Sprint and Nortel Networks in the evolutionof telecommunication networks.

4.4.1 Example

To illustrate the use of Monte Carlo simulation for valuing real options,consider a simple example in which a firm can invest in a project having a3-year life and a terminal value at the end of the third year that depends onthe cash flow in the final quarter of the third year. In this simple example,there are only two sources of uncertainty:

1. Average quarterly revenue growth, which is assumed to be normallydistributed with mean 5% and standard deviation 5%; and

2. Variable Cost (as a percentage of revenue), which is assumed to benormally distributed with mean 50% and standard deviation 5%.

The discount rate is 12.5%. First-quarter revenue is assumed to be $100.00and Fixed Costs associated with the project are assumed to be $60.00. Theinitial investment in the project is $300.00.

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No Flexibility. The spreadsheet segment in Exhibit 1 shows the calculationof the net present value (NPV) of this project in cell B18 when the revenuegrowth rate and the variable cost percentage are both set to their meanlevels. For this model, it is assumed that there is no flexibility, i.e., once theproject is begun, it is run to the end of its three-year life with no expansionif it is successful and no abandonment if it is unsuccessful during its life.

Note that the project has a negative NPV of −$72.66 under this scenario.However, when 10,000 simulation trials (scenarios) are run, the resultingdistribution of NPVs under each scenario has a mean of $17.91, as shown inthe forecast chart in Exhibit 2. This chart shows that the project may be agood investment, on average. However, the Forecast Chart also shows thatthere is a significant probability (43.12%) that the project will have a NPVless than $0.00. In the extreme cases, the project could realize NPV as lowas −$1,000.00 or as high as $1,500.00.

Abandonment Option. Now consider the same project with the option toabandon when unfavorable circumstances occur. The decision rule usedin the spreadsheet segment shown in Exhibit 3 is to begin checking in thesecond quarter of the second year, and to abandon the project if there arethree consecutive quarters of negative cash flow.

Although the scenario appearing in Exhibit 3 looks identical to the sce-nario shown in Exhibit 1, the abandonment option adds value to this project.The value of the abandonment option can be estimated by comparing theresults in Exhibit 4 to those in Exhibit 2.

The probability of realizing a negative NPV is virtually unaffected by theabandonment option, but the model in Exhibit 3 is more realistic than themodel in Exhibit 1 in that it accounts for the fact that a project managermight well cut the losses in unfavorable scenarios according to the decisionrule stated above.

Abandonment and Expansion Options. Now consider the same projectwith the option to abandon when unfavorable circumstances occur, and theoption to expand when favorable circumstances occur. The spreadsheetsegment in Exhibit 5 uses the same abandonment decision rule as that usedin Exhibit 3, but also contains a rule to expand the project when favorablecircumstances occur. The expansion decision rule used in the spreadsheetsegment shown in Exhibit 5 is to begin checking in the second quarter ofthe second year, and to expand the project if there are three consecutivequarters of cash flow greater than $15.00. The model in Exhibit 5 assumesthat the investment in expansion will be $200.00, and that expansion willdouble the quarterly revenue from the project.

Again, the scenario appearing in Exhibit 5 looks identical to the scenariosshown in Exhibits 1 and 3. However, the expansion option adds even morevalue to this project. The value added can be estimated by comparing theresults in Exhibit 6 to those in Exhibits 2 and 4.

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By subtracting the mean NPV of the model with the abandonment op-tion, $49.09, from the mean NPV of the model with both the abandonmentand expansion options, $281.82, we can estimate the value of the expan-sion option as $232.73. Further, the forecast chart in Exhibit 6 shows thatthe expansion option greatly increases the potential gains, with the extremevalues on the high side being near $2,500.00. The probability of realizinga negative NPV is slightly affected by the expansion option because undersome scenarios revenues decline after expansion and the investment in ex-pansion contributes to negative NPV. However, the model in Exhibit 5 ismore realistic than either of the models in Exhibits 1 or 3 in that it accountsfor the fact that a project manager might well cut the losses in unfavor-able scenarios or expand the gains in favorable scenarios according to thedecision rules stated above.

The simple example above is meant only to demonstrate how MonteCarlo simulation can be used to place a value on real options. Although theoptions embedded in the possible evolution of the network under considera-tion by Sprint and Nortel Networks are undoubtedly more complicated thanthe those described in this example, the same technique can be used to valuethem. As stated above, simulation suffers less from the curse of dimension-ality than the other methods, and it is often easier to understand the logicof the model and convey the results to decision makers than it is with theother methods. Further, simulation does not depend on the assumption ofgeometric Brownian motion for the revenue processes. However, all of thereal option valuation methods described above will be considered for useduring the research project. If another method is found to be easier to useor otherwise yields better results than simulation, it will be used instead.

5 Future Research

If you have read this far, thank you for not exercising your abandonment op-tion. Work on this project continues, and much, much more will be revealedat the presentation. Stay tuned!

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Exhibit 1. Spreadsheet segment for project with no managerial flexibility included in the model.

Exhibit 2. Forecast chart showing distribution of possible values of NPV for project with no

managerial flexibility included in the model.

Exhibit 3. Spreadsheet segment for project with an abandonment option included in the model.

Beginning with Q2 of Year 2, the project will be abandoned if negative cash flows were realized in all of the three previous quarters.

Exhibit 4. Forecast chart showing distribution of possible values of NPV for project with the option

to abandon the project under unfavorable scenarios.

Exhibit 5. Spreadsheet segment for project with abandonment and expansion options included in the

model. The decision rule for abandonment of the project is the same as that used in Exhibit 3. The decision rule for expansion is: Beginning with Q2 of Year 2, expand the project if cash flows exceed

$15.00 in all of the three previous quarters.

Exhibit 6. Forecast chart showing distribution of possible values of NPV for project with the option

to abandon the project under unfavorable scenarios, and expand the project under favorable scenarios.

Exhibit 7. Graphical depiction of links between Option Valuation Tool and existing NPV calculations in Sprint/Nortel Networks business cases

Sprint or

Nortel Networks

Business Case

NPV Calculations

Decision Variables kddd ,,, 21 K

Stochastic Assumptions naaa ,,, 21 K

Random Outputs, e.g., NPV

Option Valuation Tool

),,,;,,,( 2121 nk aaadddgNPV KK=

)],,,;,,,([,,,

maxfinds Tool ValuationOption

212121

nkk

aaadddgEddd

KKK

1

OptimizationOptimization

Using OptQuestUsing OptQuest

jmc@ku.edu • 24 January 2003 33

American Put OptionAmerican Put Option

•• Early exercise feature makes valuation Early exercise feature makes valuation difficultdifficult

•• In practice, find value of In practice, find value of BermudanBermudan put put option, which can be exercised only at a option, which can be exercised only at a finite number of opportunities, finite number of opportunities, kk, before , before expirationexpiration

T

r SKeP

≤

+− −=

τ

ττ

τ

times stopping allover

])([Emax

2

jmc@ku.edu • 24 January 2003 34

Valuing Bermudan Put OptionsValuing Bermudan Put Options

•• Analytical solution given by Analytical solution given by GeskeGeske and and Johnson, JF 1984, for small Johnson, JF 1984, for small kk

•• Simulation approach given by Simulation approach given by BroadieBroadie and and GlassermanGlasserman, JEDC 1997, for small , JEDC 1997, for small kk

•• Forward Monte Carlo method (Charnes Forward Monte Carlo method (Charnes and Shenoy 2000)and Shenoy 2000)

•• With OptQuest, package for stochastic With OptQuest, package for stochastic optimization using optimization using tabutabu searchsearch

jmc@ku.edu • 24 January 2003 35

FreeFree--Boundary ProblemBoundary Problem

•• For each exercise opportunity, must estimate For each exercise opportunity, must estimate optimal earlyoptimal early--exercise boundary, the prices exercise boundary, the prices below which put option should be exercised below which put option should be exercised and above which put option should be heldand above which put option should be held

•• See See BermuPut.xlsBermuPut.xls on on www.ku.edu/home/jcharneswww.ku.edu/home/jcharnes

•• Uses Uses TabuTabu search to select an optimal policy, search to select an optimal policy, then a final set of iterations to estimate value then a final set of iterations to estimate value under optimal policyunder optimal policy

3

jmc@ku.edu • 24 January 2003 36

Example: Example: Bermudan Put OptionBermudan Put Option

•• Current Stock Price = 80Current Stock Price = 80•• Strike Price = 100Strike Price = 100•• Volatility = 0.4Volatility = 0.4•• RiskRisk--free rate = 0.06free rate = 0.06•• Time until expiration, T = 0.5Time until expiration, T = 0.5•• May exercise at T/3, 2T/3, or TMay exercise at T/3, 2T/3, or T

jmc@ku.edu • 24 January 2003 37

CB ModelCB Model

4

jmc@ku.edu • 24 January 2003 38

jmc@ku.edu • 24 January 2003 39

Real Options Valuation ExampleReal Options Valuation Example

jmc@ku.edu • 24 January 2003 41

Optimal SolutionOptimal Solution