1. Real Options Introduction to Real Options Prof. Luiz Brandão brandao@iag.puc-rio.br 2009

2. IAG PUC – Rio Brandão 2 Managerial Flexibility  Managerial flexibility is present in many projects Mining firms may choose to increase rate of extraction when prices rise, and reduce production when they fall. Auto firms can adjust production levels to market demand Hollywood movie studios have the flexibility to release a sequel to a blockbuster movie (Zorro I, II, Spiderman I, II, III, etc, Star Wars, Back to the Future, etc.) Drug firms can abandon new drug development if the trial tests show that the drug will not work as expected.  These flexibilities are options that the firm has to change the original development strategy of the product.  These options add value to the firm, but this value cannot be captured by traditional DCF analysis.

3. IAG PUC – Rio Brandão 3 An Investment Decision  Suppose a firm is analyzing the following investment project: Investment = $3.000 Project value in one year:  $5.500 with 50% probability  $2.200 with 50% probability Cost of capital is 10% per year.  What is the value of this project? High 5.500 Low 2.200 Invest -3.000 Value Do not Invest Decision

4. IAG PUC – Rio Brandão 4 Project with Flexibility  Note we implicitly are adopting the assumption that the project will be implemented now or never.  But what if the project can be delayed for one year?  In this case, we can wait for the uncertainty over the cash flows be resolved before committing to the project. Invest -3.000 + 5.500/1.1 No High Invest -3.000 + 2.200/1.1 No Low

5. IAG PUC – Rio Brandão 5 Evolution of Evaluation Methods DCF Sensitivity Analysis Decision Trees Simulation Models Financial Options Real Options NPV IRR Value of the Information Strategic Considerations Impact of Variables Risk Management Risk Analysis CAPM 1930-19501950196019701980

6. IAG PUC – Rio Brandão 6 DCF Method  Steps Project the expected future cash flow of the project Determine the appropriate discount rate that takes into consideration the risk of the project and the time value of money Determine the Present Value of the Project Deduct the implementation cost of the project to determine the NPV If the NPV > 0 invest on the project.  Assumptions The project will be executed now or never Once initiated, the project is not affected by future managerial decision. The expected future cash flows will happen with certainty The project’s risk does not change throughout its life

7. IAG PUC – Rio Brandão 7 DCF Method  Problems Ignores the value of the option to invest Ignores the project’s uncertainties Ignores the value of managerial flexibility Generally underestimates the value of projects that possess real options Can lead to sub optimal investment decisions

8. IAG PUC – Rio Brandão 8 The Investment Decision  Traditional Methods of Investment Evaluation involve the use of discounted cash flows (DCF) (NPV and IRR)  DCF was originally developed to value financial investments like stocks and company’s obligations.  These financial securities are passive in nature, since the investor has no influence over the return.  Real securities present important differences in relation to financial assets.  The statistical and mathematical modeling of real assets is more complex than the one for financial assets.  Many of the assumptions used for financial assets do no apply to real assets.

9. IAG PUC – Rio Brandão 9 Financial Securities and Real Securities

10. IAG PUC – Rio Brandão 10 Investment Decision  Characteristics of Investment Decision The Investment is generally Irreversible.  Independent of the result of the project, the capital invested, or the major part of it, cannot be recuperated The Future Cash Flows are Uncertain.  The uncertainties can be originated from many distinct sources. The uncertainties are a source of risk for the project. Many times there is a degree of Managerial Flexibility in the project  The cash flows of the project can be affected by managerial decisions taken after the project is initiated and the uncertainties are resolved.

11. IAG PUC – Rio Brandão 11 What is the Real Options Method?  It is project evaluation technique that uses option pricing methods to value projects with managerial flexibility.  Real Options value the existing managerial flexibilities on the projects that are not captured by traditional methods such as DCF.  Real Options complements, but does not substitute for the DCF method.  The degree of managerial flexibility and the level of uncertainty increases the value of a real options project.  Offers a valuation more consistent with the true value of the project.  Offers more specific and detailed decision rule for investment.

12. IAG PUC – Rio Brandão 12 Identifying Real Options  Traditional DCF treats the project as shown in Fig A  For some types of projects this can be an inadequate representation  This decision tree assumes that the manager won’t interfere in the operation of the project throughout its useful life Invest Don’t Invest Good News Bad News Good News Bad News A) This is not an option + $$$ 0 0 - $$$

13. IAG PUC – Rio Brandão 13 Identifying Real Options  Many times managers have the option to postpone an investment decision while they wait for better information.  The possibility to make decisions after receiving new information about the project can avoid negative results.  Intuitively, which of the two project (A or B) has a greater value? Invest Don’t Invest Good News Bad News Don’t Invest Invest B) This is an option 0 0 + $$$ - $$$ X

14. IAG PUC – Rio Brandão 14 Identifying Options Hollywood The value of a film may include the value of the option to make sequels.  Microsoft Windows is a basic platform that gives Microsoft the option to commercialize other compatible products.  Natural Resources Mining: Exploration decreases uncertainty and orients the investment decision. Oil: A lease concession is an option of exploration.  Energy Biofuels: Producers have option to choose inputs and even outputs.

15. IAG PUC – Rio Brandão 15 Example: Option to Abandon  Biodata S.A. hopes to introduce a new product to the market, which will have a life of two years.  The investment is $100 millions and the cash flow of the project are highly uncertain.  Biodata competitors are also actively working to develop a similar product.  The project’s cash flow will be affected by the uncertainty of the market as well as by whether competitors will enter the market. 88.0 66.0 0.50 150 70 0.50 -30 -60 0.50 -100 t = 1t = 2t = 0

16. IAG PUC – Rio Brandão 16 Biodata: Cash Flow 88.0 66.0 0.50 150 70 0.50 -30 -60 0.50 -100 t = 1t = 2t = 0

17. IAG PUC – Rio Brandão 17 Example: Abandonment Option  What is the NPV of this project?  The negative NPV indicates that the company shouldn’t invest in this project.  Does the flexibility of being able to abandon the project at any moment have any impact on the decision?  How can we determine this?

18. IAG PUC – Rio Brandão 18 88.0 66.0 0.50 150 70 0.50 -30 --60 0.50 -100 t = 1t = 2t = 0 Example: Abandonment Option

19. IAG PUC – Rio Brandão 19 Exemplo: Opção de Abandono  What is the NPV with the option to abandon?  What is the value of the abandonment option? It is approximately the difference between the value of the project with and without the option.  What effect does this option have on the risk of the project? The existence of the option reduces the risk of the project

20. IAG PUC – Rio Brandão 20 Level of Uncertainty Level of Flexibility Capacity to react to new information ModerateHigh LowModerate Option Value Effect of flexibility and uncertainty

21. IAG PUC – Rio Brandão 21  StereoGram is analyzing an opportunity to invest in a government concession.  The investment cost is $115M, and the cash flows of the project will be $160 if the project does well or $80 otherwise.  The project’s risk is 20%, the probability of success is 50% and the risk free discount rate is 8%. How real options affect risk  For $20M, the company has the option to buy an insurance that would pay $120M if the project fails.

22. IAG PUC – Rio Brandão 22  StereoGram The expected value of the project without the insurance is: Given that the investment cost is $115, the project is not appealing to the company because its NPV will be negative. Ex: StereoGram Ltd.

23. IAG PUC – Rio Brandão 23  StereoGram With the insurance, the company has the option to receive $120M if the project fails, and the cash flow of the project will therefore be: In this case, the value of the project will be The NPV increases to Ex: StereoGram Ltd.

24. IAG PUC – Rio Brandão 24  StereoGram However, the previous analysis is incorrect, since purchasing the insurance gives the company the option to recoup the investments made on the project and guarantees its cash flow independent of the project. This way, the buying of the insurance actually eliminates any risk in this project, which makes the 20% rate of risk used previously no longer appropriate. The appropriate rate in this case is the risk free rate, and the real value of the project and its NPV are, respectively: Even buying the insurance for $20M, the company still increases its value by 51.67 – 20 = $31.67 Ex: StereoGram Ltd.

25. IAG PUC – Rio Brandão 25 Graham & Harvey (2001)  Survey done with 392 US and Canada CFOs indicates that 26.6% use real options “always or almost always” Journal of Financial Economics, vol.60, 2001, pp.187-243

26. IAG PUC – Rio Brandão 26 ROV Practice in Brazil  Mining (Vale) Value of investing in a coal mine in Australia Decision to shut down aluminum smelter  Oil and Gas (Petrobrás) Value of the exploration concession period Biodiesel option analysis.  Public Utilities (Endesa) Value of the flexibility of a small Hydroelectric Power Plant  Treasury Department (Federal Government) Value of government guarantees for infra-structure projects  Renewable Fuels: Value of flex fuel automobiles Value of flexibility in sugar cane conversion, Biodiesel plants

27. IAG PUC – Rio Brandão 27 The Challenge of Real Options  Since the work of Black, Scholes and Merton in 1973, the use of Financial Options grew rapidly in the following years.  The same growth was not observed with Real Options even two decades later.  The principal reason is the fact that Real Options are much more complex than Financial Options.  Some recent advancements allows us now to resolve some of these limitations and obtain practical results.  The Monte Carlo simulation and the decision trees are some of the tools that allows us to make stochastic simulations and model the flexibilities of a project.  These tools require the extensive use of computers to resolve automatically the mathematical models.

28. IAG PUC – Rio Brandão 28 Real Option Valuation Timeline 1973Black-Scholes-Merton equations for European Options  Exercised only at expiration  Basic security doesn’t pay dividends  Constant volatility  Simple Options  Only one source of uncertainty 1979Cox, Ross and Rubinstein Binomial Model 1980 -Electronic forms for use in the PC 1990 -Efficient programs for tha analysis of Monte Carlo, Decision Trees 2001 -Copeland and Antikarov proposes discrete models 2004 - Practical modeling for real problems with: (BDH)  American Options  Basic security with dividends  Variable volatility  Composed options  Multiple sources of uncertainty

29. Options

30. IAG PUC – Rio Brandão 30 What is an option?  An opportunity or a contract that gives you a right but not an obligation... Asymmetry of returns Exercise only if advantageous Cost to acquire  … of doing something… Usually buying or selling some security  … now or in the future… Usually there is a time limit after which the option will expire  … for a pre-determined price. The price of the security is distinct from the price of the option

31. IAG PUC – Rio Brandão 31 The value of a project depends on:  Value of its assets Current production capacity Expected cash flows Generally evaluated by the DCF method  Value of the Option Option to postpone Option to abandon Option of growth and expansion: investment opportunities Option to suspend, resume or substitute input or outputs of production Cannot be evaluated with the DCF method, it is necessary to use option evaluation methods

32. IAG PUC – Rio Brandão 32 Options: Basic Concepts  Basic Security(S) The security that will be received or given if the option is exercised.  Financial Option Its an option where the basic security is a title negociated in the financial market or a comodity.  Real Option It s an option where the basic security is a real security.  Option to Buy - Call The right to buy the basic security.  Option to Sell - Put The right to sell the basic security.  Exercise Price (X) The pre-determined price for which the holder of the option can buy or sell the security.  Expiration Date (T) The date the rights guaranteed by the option cease.  Premium Is the price paid to acquire an option. Equals the value of the option.  Volatility Represents the degree of uncertainty on the future price of a basic security  Types of Options European and American

33. IAG PUC – Rio Brandão 33 The return of a Call is asymmetrical Value of Basic Security S X Call Value at Expiration S < X Region of no Exercise S > X Region of Exercise 0 Distribution of S at time T  The value of the option will never be negative

34. IAG PUC – Rio Brandão 34 The return of a Call is asymmetrical Value of Basic Security S X Call Value at Expiration S < X Region of no Exercise S > X Region of Exercise 0  The value of the option will never be negative Distribution of S at time T

35. IAG PUC – Rio Brandão 35 Expected Return increases with uncertainty X S < X S > X 0  Probability of S > X increases with the volatility of S Value of Basic Security S Call Value at Expiration Region of no Exercise Region of Exercise Distribution of S at time T

36. IAG PUC – Rio Brandão 36 Call: Value before Expirations S X S < X S > X Outside the Money Inside the Money 0  Before the expiration the option can have value even if S < X. This occurs due to the uncertainty in the value of S at expiration. Call Value at Expiration

37. IAG PUC – Rio Brandão 37 X S < X S > X 0  Value at Expiration is F = max (0, X - S) Put Option: Value at Expiration Value of Basic Security S Call Value at Expiration Region of Exercise Region of no Exercise

38. IAG PUC – Rio Brandão 38 S X S < X S > X Outside the Money Inside the Money 0  Before the expiration the option can have a value even if S>X.  This occurs due to the uncertainty in the value of S at expiration. Call Value at Expiration Put Option: Value before Expiration

39. IAG PUC – Rio Brandão 39 Factors that affect the value of the Option

40. IAG PUC – Rio Brandão 40 Black and Scholes Formula where and N(.) is the cumulative normal distribution function  Assumptions: The value of the basic security grows exponentially and its distribution is lognormal The basic security does not pay dividends Applicable only to European options

41. IAG PUC – Rio Brandão 41 Example  Ex: A European option to buy stock has exercise price of $120 and expires in a year. The actual value of the stock is $100, the volatility is 35% and the risk free discount rate is 10%. What is the value of the option today?  Using the B&S formula: (Hull) S = $100 X = $120 σ = 35% r = 10% T = 1 C = 10.59

42. IAG PUC – Rio Brandão 42 Example  Use the Derivagem Software to determine the value of the following option: S = $50 X = $50 σ = 20% r = 6% T = 4  Analytic European  Binomial European 4 steps  Binomial European 20 steps

43. IAG PUC – Rio Brandão 43 Financial Options Option to buy (Call) Value of the option Exercise Price Time till Expiration Risk free discount rate Volatility of the Stock Dividends Analogy between Financial Optiona dand Real Options Real Options Option to Invest PV of the project PV of the investment Expiration time Risk free discount rate Volatility of the Project Project Cash Flows

44. Real Options Introduction to Real Options Prof. Luiz Brandão brandao@iag.puc-rio.br 2009