Real Options

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

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. Value Decision High 5.500 Invest -3.000 Low 2.200 Do not Invest 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?

4. Invest -3.000 + 5.500/1.1 High No Invest -3.000 + 2.200/1.1 Low No 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.

5. Evolution of Evaluation Methods Decision Trees Simulation Models Sensitivity Analysis Financial Options DCF Real Options

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. 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. 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. Financial Securities and Real Securities

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. 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. 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 A) This is not an option Good News + $$$ Invest Bad News - $$$ Good News 0 Don’t Invest Bad News 0

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? This is an option B) Invest + $$$ Good News Don’t Invest 0 Invest X - $$$ Bad News Don’t Invest 0

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. t = 0 t = 1 t = 2 0.50 150 0.50 88.0 0.50 70 -100 0.50 -30 0.50 66.0 0.50 -60 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.

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

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. Example: Abandonment Option t = 0 t = 1 t = 2 0.50 150 0.50 88.0 0.50 70 -100 0.50 -30 0.50 66.0 0.50 --60

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. Effect of flexibility and uncertainty Option Value Level of Flexibility Capacity to react to new information Level of Uncertainty

21. How real options affect risk • 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%. • For $20M, the company has the option to buy an insurance that would pay $120M if the project fails.

22. Ex: StereoGram Ltd. • 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.

23. Ex: StereoGram Ltd. • 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

24. Ex: StereoGram Ltd. • 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

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. 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. 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. Real Option Valuation Timeline 1973 Black-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 1979 Cox, 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. 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. 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. 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. S > X Region of Exercise The return of a Call is asymmetrical • The value of the option will never be negative S < X Region of no Exercise Call Value at Expiration Distribution of S at time T 0 X Value of Basic Security S

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

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

36. Call: Value before Expirations • 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. S < X S > X Inside the Money Outside the Money Call Value at Expiration 0 S X

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

38. Put Option: Value before Expiration S < X S > X Outside the Money Inside the Money Call Value at Expiration 0 S X • 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.

39. Factors that affect the value of the Option

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. 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. 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. Analogy between Financial Optiona dand Real Options Financial Options Option to buy (Call) Value of the option Exercise Price Time till Expiration Risk free discount rate Volatility of the Stock Dividends 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