1. Academy of Economic Studies, Bucharest Doctoral School of Finance and Banking Dissertation Thesis: July 2001 Supervisor: Professor Moisa Altar Real Options- An Investment Valuation Method Student: Oana Dămian

2. Introduction 1. Investment Projects Viewed as Real Options. Real Option Analogy with Financial Options 2. Financial Options Models & Numerical Analysis 3. Case Study. Dynamic Network Technologies Conclusions Real Options- An Investment Valuation Method Back to title

3. Introduction Back to contents Most firms do not explicitly use the real option concept when valuing investments. Nevertheless, firms do take into account management flexibility (wait for further information, adapt the project to new relevant information or even abandon the project). Management has a number of options to exercise and avoid future unfavorable developments or take advantage of the favorable ones. Real options are options to buy, sell or exchange real assets on possibly favorable terms.

4. Def: ” Similar to options on financial securities real options involve discretionary decisions or rights, with no obligations to acquire or exchange a asset for a specified alternative price” - Trigeorgis [1996] Back to contents 1. Investment Projects Viewed as Real Options. Real Option Analogy with Financial Options Investment Projects Viewed as Real Options

5. Back to contents Triantis [1999] mentions three real option categories depending on the project’s nature : a) Options to grow b) Contraction options c) Flexibility Options 1. Investment Projects Viewed as Real Options. Real Option Analogy with Financial Options Trigeorgis [1996] ranks real options depending on exclusiveness of ownership into : a) proprietary options b) shared options Trigeorgis [1996] basic types of real options: a) options to defer, b) options to contract /expand c) option to abandon for salvage value, d) option to switch use. Classifications:

6. Back to contents 1. Investment Projects Viewed as Real Options. Real Option Analogy with Financial Options Option to defer an investment The option to defer is a call option on the project gross present value. The exercise price that has to be paid is the project cost. exercise price (X) - investment costs underlying (S) - project gross present value risk- free interest rate (r) time to expiry (T-t) - period during which the investment opportunity is valid underlying volatility(σ) - standard deviation of the growth rate (percentage) of the project gross present value dividends(d) - value lost to competitors, cash outflows or necessary risk neutral adjustments “Call elements” The project entire value should be equal to the value of the call option together with the passive NPV: Expanded NPV= option premium + NPV

7. Back to contents 1. Investment Projects Viewed as Real Options. Real Option Analogy with Financial Options Options to defer and possible valuation methods

8. Back to contents 1. Investment Projects Viewed as Real Options. Real Option Analogy with Financial Options Real Option Analogy to Financial Options Financial option valuation techniques can be used in valuing real options.Yet, financial options models assumptions have to be met. A set of assumptions under which realoptions can be “financial option based” valued, Lander[1998]: 1) there is only one real option modeled and valued at a time 2) there is only one source of uncertainty 3) there is an approximation for the process governing the value of the underlying 4) “markets are complete, the firm is risk-neutral or risk is fully diversifiable” and adjustments can be made in order to get to work into a risk- neutral world 5) cash outflows/inflows (ex. dividends) are known and constant, can be determined from market prices or are a proportion of the value of the underlying 6) costs are known & there are no foregone earnings

9. 1) Assumptions regarding the project’s value geometric Brownian motion: dS=  Sdt +  dz jump model Wilner [1995]: dS=  Sdt +(  -  )SdN dN=1 w.p. dt or 0 w.p. 1- dt a mix of jump and geometric Brownian motion: Trigeorgis [1996] dS=(  -d)Sdt +(k-1)dN+  dz 1. Investment Projects Viewed as Real Options. Real Options Analogy with Financial Options Back to contents

10. 2) Assumptions regarding asset tradability and risk- neutral valuation 1. Investment Projects Viewed as Real Options. Real Options Analogy with Financial Options Back to contents Any derivative on an asset that could be ”something as far removed from financial markets as the temperature from the center of New Orleans “ can be valued in a risk neutral world - Hull [2000] When converting into a risk neutral world a dividend like adjustment has to be made. The dividend equals the difference between the return of a similar traded asset and the nontraded asset return.

11. 3) Assumptions regarding interactions among multiple real options embedded in a project 1. Investment Projects Viewed as Real Options. Real Options Analogy with Financial Options Back to contents Cox, Ingersoll & Ross [1985].

12. Back to contents Financial options models Black, Scholes & Merton (1973) - analytical valuation of European options Roll, Geske & Whaley(1977-79-81) – analytical valuation for American call option on a dividend paying underlying Margrabe(1978) – analytical valuation for an option to exchange one asset for another Wilner [1995], Trigeorgis [1996]- analytical valuation for models with jumps 2. Financial option models & numerical analysis

13. Numerical analysis 2. Financial option models & numerical analysis Back to contents 1.Monte Carlo simulation 2.Finite difference methods (implicit, explicit) 3.Lattice approach: binomial trees, trinomial trees, log-transformed binomial trees for valuing complex multi-option investments Trigeorgis [1991] Kulatilaka [1988], Trigeorgis [1996] general method for valuing options with multiple “options” (operating modes)

14. Back to contents 3. Case study. DNT- Dynamic Network Technologies DNT is one of the top 3 Internet Service Providers in Romania. Recently DNT has merged with Astral TV, a cable TV company. At the end of March 2001 Astral TV registered approximately 700 000 subscribers. Situation: starting from 2003, DNT is interested in introducing a new residential telephony service that uses voice over IP. Problem: What is the value of the project today ?

15. Back to contents 3. Case study. DNT- Dynamic Network Technologies Input data: - the product : software package & data transmission services ( cost of acquiring a new subscriber 200 USD, monthly fee/subscriber 12 USD, variable monthly costs/subscriber 7 USD, negligible fixed costs). - if the project were taken up today Year subscribers July 2001 65 000(by July 2002) - product development scenario: cost 200 mil USD Year subscribers (at year end) subscribers (growth rate) July 2001 65 000(by July 2002) 2003100 000- 2004200 000100.00% 2005350 000 75.00% 2006600 000 71.00% 2007 650 000 8.33% - WACC:(1-tax)r borrow =(1-25%)*12% -interest rate, time to expiry, proprietary option

16. Back to contents 3. Case study. DNT- Dynamic Network Technologies Assumptions: 1 risk neutrality adjustments for the nontraded asset are not needed 2 until 2003 the number of subscribers at the beginning is assumed to follow a geometric Brownian motion 3 The embedded option is a proprietary one 4 once a subscriber has bought the product it is assumed that he dose not give it up. A constant sum of discounted cash flows can be calculated per subscriber 5 the month to month growth rates of the number of subscribers remain the same (but are not equal to each other) under all possible states of nature, once the project has been undertaken

17. Back to contents 3. Case study. DNT- Dynamic Network Technologies

18. Back to contents 3. Case study. DNT- Dynamic Network Technologies Steps followed : 1. model the option underlying, the discounted present value of future cash-flows 2. find the parameters of the stochastic process the underlying follows 3. calculate expanded NPV and comment on it.

19. Back to contents 3. Case study. DNT- Dynamic Network Technologies 1. model the option underlying, the discounted present value of future cash-flows

20. Back to contents 3. Case study. DNT- Dynamic Network Technologies

21. Back to contents 3. Case study. DNT- Dynamic Network Technologies 2. find the parameters of the stochastic process the underlying follows The underlying growth rate has an approximated 28% mean and 25% volatility normal distribution on a 1.5 years basis. On 1 year basis the mean is 18.666% and approximately 20 %volatility.

22. 3. calculate expanded NPV and comment on it. Back to contents 3. Case study. DNT- Dynamic Network Technologies

23. Back to contents 3. Case study. DNT- Dynamic Network Technologies Expanded NPV = -200 000 + 193 435.1426+25 275.50036 = 18 710.64296 thousands USD The Greeks - delta, -vega, - theta, -rho.

24. Further research to be made in order to better account for the following: 1. other embedded real options should be considered 2. the growth path chosen, 3.in real life the cash flows per subscriber do change in time and should be closer to a market value rather than the number of subscribers is, 4 competition. Back to contents 3. Case study. DNT- Dynamic Network Technologies

25. Back to contents Conclusions One of the two objectives of the paper has been to shortly present the real options concept, the analogies with financial options and how real options can actually be priced. The conclusion is that once a real option has been found, a model has to be chosen and then make the required adjustments so as the model assumptions are fulfilled. The most permissive way (as far as the assumptions are concerned) to value a real option seems to be, up to now, the method of Kulatilaka [1988] and Trigeorgis [1991&1996]. The second objective of the paper has been attempting to value an Internet telephony project using the real options concept. The project has been valued as an option to defer. The expanded net present value has been calculated yet, results have been obtained under a number of powerful assumptions. Conclusions