1. Managing Strategic Investment in an Uncertain World: A Real Options Approach Roger A. Morin, PhD Georgia State University FI 8360 January 2003

2. 3 Valuation Frameworks Discounted Cash Flow (DCF) Comparables Option Value

3. Agenda F The value of flexibility F Real options as a way to capture flexibility F Real options and financial options F So what? The importance of real options F Implementing real option valuation F Next steps

4. Capital Investments as Options All kinds of business decisions are options!

5. Virtually every corporate finance decision involving the issuance of securities or the commitment of capital to a project involves options in one way or another.

6. Real Options Defined F Nobel Prize-winning work of Black-Merton-Scholes F Applications for real (nonfinancial) assets F Extensions for how real assets are managed F What is the value of a contract that gives you the right, but not the obligation to purchase a share of IBM at $100 six months from now? F What is the value of starting a project that gives you the right, but not the obligation, to launch a sales program at a cost of $7M six months from now? F We operate in a fast changing and uncertain market. How can we better make strategic decisions, manage our investments, and communicate our strategy to Wall St?

7. Why An Options Perspective? F Some shortcomings in the use of ordinary NPV analysis can be overcome F Common ground for uniting capital budgeting and strategic planning can be established F Risk-adjusted discounted rates problem

8. Investment Decisions 1. Irreversibility 2. Uncertainty 3. Flexibility –Timing –Scale –Operations

9. Investment Decisions 1 & 2 3 is valuable 1 & 2 & 3 Option (flexibility) valuation

10. Option Value ( a.k.a. flexibility) F Can be large F Sensitive to uncertainty F Explains why firms appear to underinvest

11. Flexibility: Investments have uncertainty and decision-points Fund First Develop Test Product Sales Brand Retire Research Results More Market Launch Extension Product Your decision New Information

12. What types of investments does this describe? F R&D related businesses - biotech, pharmaceuticals, entertainment. F Natural resource businesses - extractive industries. F Consumer product companies F High-tech companies

13. Invest/ Grow Scope Up Switch Up Scale Up Defer/ Learn Study/Start Disinvest/ Shrink Scope Down Switch Down Scale Down Real Option Category Real Option Type

14. Current Applications: Some Frequently Encountered Real Options F Timing -- now or later F Exit -- limiting possible future losses by exiting now F Flexibility -- today’s value of the future opportunity to switch F Operating -- the value of temporary shutdown F Learning -- value of reducing uncertainty to make better decision F Growth -- today’s value of possible future payoffs

15. Future Growth Options F Valuable new investment opportunities (“follow- on projects”) can be viewed as call options on assets F Examples: –Exploration –Capacity expansion projects –New product introductions –Acquisitions –Advertising outlays –R&D outlays –Commercial development

16. Investment Project Options: Examples F Growth Option (“Follow-On Projects”) –Nortel commits to production of digital switching equipment specially designed for the European market. The project has a negative NPV, but is justified by the need for a strong market position in this rapidly growing, and potentially very profitable, market. F Switching Option –Atlanta Airways buys a jumbo jet with special equipment that allows the plane to be switched quickly from freight to passenger use or vice versa.

17. Investment Project Options: Examples F Timing Option –Dow Chemical postpones a major plant expansion. The expansion has positive NPV, but top management wants to get a better fix on product demand before proceeding. F Flexible Production Facilities –Lucent Technologies vetoes a fully-integrated, automated production line for the new digital switches. It relies on standard, less-expensive equipment. The automated production line is more efficient overall, according to a NPV calculation.

18. Investment Project Options: Examples F Fuel Switching –A power plant has the capacity of burning oil or gas. Mgrs can decide which fuel to burn in light of fuel prices prevailing in the future F Shut-Down Option –A power plant can be shut down temporarily. Mgt. can decide whether or not to operate the plant in light of the avoided cost of power prevailing in the future F Investment Timing –Mgt. can invest in new capacity now or defer when more information on demand growth and fuel prices is available

19. Which is a closer analogy to these types of projects? BondOption

20. Standard NPV analysis treats projects like bonds Average promised cash flow up-front investment

21. Learn Decide Do not invest Invest NPV ignores valuable flexibility

22. Shortcomings of NPV Analysis –Passive, assumes business as usual with no management intervention –Strategic factors ignored –NPV understates value u Operating flexibility ignored u Valuable follow-on investment projects ignored –Many investments have uncertain payoffs that are best valued with an Options approach –Risk-adjusted discounted rates problem

23. NPVROV Certainty is a narrow path!

24. Flexibility Active Management

25. NPV ’ = NPV passive + Option Value

26. Financial Options A Brief Review

27. What is an option? F An option provides the holder with the right to buy or sell a specified quantity of an underlying asset at a fixed price (exercise price) at or before the expiration date of the option. F Since it is a right and not an obligation, the holder can choose not to exercise the right and allow the option to expire. F Two types – call options (right to buy) and put options (right to sell).

28. Call Options F A call option gives the buyer of the option the right to buy the underlying asset at a fixed price (E) at any time prior to the expiration date. The buyer pays a price for this right (premium) F At expiration, –If the value of the underlying asset S > E u Buyer makes the difference: S – E –If the value of the underlying asset S < E u Buyer does not exercise F More generally, –Value of a call increases as the value of the underlying asset increases –Value of a call decreases as the value of the underlying asset decreases

29. Payoff on Call Option Price of underlying asset Net payoff on call option Exercise price If asset value < exercise price, you lose what you paid for call

30. Payoff on IBM Call Option IBM Stock price Net payoff E = $100 Maximum loss = $5 Breakeven = $105

31. Put Options F A put option gives the buyer of the option the right to sell the underlying asset at a fixed price (E) at any time prior to the expiration date. The buyer pays a price for this right (premium) F At expiration, –If the value of the underlying asset S < E u Buyer makes the difference: E – S –If the value of the underlying asset S > E u Buyer does not exercise F More generally, –Value of a put decreases as the value of the underlying asset increases –Value of a put increases as the value of the underlying asset decreases

32. Payoff on Put Option Price of underlying asset Net payoff on put Exercise price If asset value > exercise price, you lose what you paid for put

33. Determinants of Call Option Value F Stock Price - the higher the price of the underlying stock, the greater the option’s intrinsic value F Exercise Price - the higher the exercise price, the lower the intrinsic value F Interest Rates - the higher interest rates, the more valuable the call option F Volatility of the Stock Price - the more volatile the stock price, the more valuable the option F Time to Maturity - call options increase in value the more time there is remaining to maturity

34. Effect of Volatility on Option Values Asset Price Probability Time to expiration is one year. 30% Volatility 10% Volatility Call Option Payoff

35. Effect of Maturity on Option Value Asset Price Probability Volatility is 20%. 1 Yr Expiration Call Option Payoff 5 Yrs Expiration

36. Option Premium vs Intrinsic Value 0 X Call option price C C Stock Price X = Exercise Price CC = Call option premium as function of stock price Intrinsic value Time value

37. Determinants of option value F Variables Relating to Underlying Asset u Value of Underlying Asset u Variance in that value u Expected dividends on the asset F Variables Relating to Option u Exercise Price u Life of the Option F Level of Interest Rates

38. Summary of Determinants of Option Value FactorCallPut Increase in Stock Price Increase in Exercise Price Increase in risk Increase in maturity Increase in interest rates Increase in dividends paid

39. American vs European Options F American: exercise at any time F European: exercise at maturity F American options more valuable u Time premium makes early exercise sub-optimal F Exception: u Asset pays large dividends

40. Option Valuation F Binomial Option Pricing Model –Portfolio Replication Method –Risk Neutral Method F Black-Scholes Model –Dividend adjustment –Diffusion vs Jump process

41. Binomial Option Pricing Model F The Binomial Option Pricing Model assumes that there are two possible outcomes for the price of the underlying asset in each period. F Although this assumption is artificial, realism can be achieved by partitioning the time horizon into many short time intervals, so the number of possible outcomes is large F Useful first approximation

42. Binomial Price Path S SuSu S u2 S ud S d2 SdSd

43. Binomial Price Path $100 $110 $90 $120 $100 $80 t = 0t = 1t = 2

44. Creating a replicating portfolio F Objective: use a combination of risk-free borrowing- lending and the underlying asset to create the same cash flows as the option being valued u Call = Borrowing + Buying Δ of Underlying Stock u Put = Selling short Δ on Underlying Asset + Lending u The number of shares bought or sold is called the option delta F The principles of arbitrage then apply, and the value of the option has to be equal to the value of the replicating portfolio

45. Creating a Replicating Portfolio Value of PositionValue of Call If S goes up to S u ΔS u - $B (1 + r) C u If S goes down to S d ΔS d - $B (1 + r) C d

46. Replicating Portfolio Δ S u - $B (1 + r) = C u Δ S d - $B (1 + r) = C d Δ = No. of units of underlying asset bought C u - C d Δ = S u - S d

47. Replicating Portfolio: Example 1 $55 Stock: $50 $45 1-yr Call, E = $50 R f = 5%  C = $3.57 all investors agree!

48. Replicating Portfolio: Example 1 Call - Stock Payoffs: (55, 5) (50, ?) (45, 0) We can duplicate the above payoffs with a position in common stock and borrowing, that is, by “portfolio replication”.

49. Replicating Portfolio Δ S u - $B (1 + r) = C u Δ S d - $B (1 + r) = C d C u - C d $5 - $0 Δ = = = 0.50 S u - S d $55 - $45 Δ = 50 shares ! B = $2,142 !

50. 50 shares of stock + 1-year loan of $2,142.86 Portfolio is now worth: 50 x $50 - $2,142.86 = $357.14 Portfolio payoffs: 50 x $55 - 2,250 = 500 (50, ?) 50 x $45 - 2,250 = 0 SAME AS CALL OPTION PAYOFFS! FAIR VALUE OF 100 CALLS = $357.14

51. No Free Lunch! Absence of Riskless Arbitrage Profits If C > $357.14, sell overpriced call buy duplicating portfolio KEY: can construct a levered position in underlying stock that gives the same payoffs as the call option.

52. Binomial Valuation: Example 2 $50 $70 $35 $100 $50 $25 t = 0t = 1t = 2 E = $50 R f = 11% $50 $0 Call

53. Binomial Valuation: Example 2 $50 $70 $35 $100 $50 $25 t = 0t = 1t = 2 E = $50 R f = 11% $50 $0 Call

54. Replicating Portfolio When S = $70 $70 $100 $50 t = 1t = 2 E = $50 R f = 11% $50 $0 Call Replicating Portfolio 100 Δ - 1.11B = 50 50 Δ - 1.11B = 0 Solving: Δ = 1 B = 45 Buy 1 share, borrow $45

55. Value of Call at t = 1 70 Δ - B = 70 - 45 = $25

56. Binomial Valuation: Example 2 $50 $70 $35 $100 $50 $25 t = 0t = 1t = 2 E = $50 R f = 11% $50 $0 Call

57. Replicating Portfolio When S = $35 $35 $50 $25 t = 1t = 2 E = $50 R f = 11% $0 Call Replicating Portfolio 50 Δ - 1.11B = 0 25 Δ - 1.11B = 0 Solving: Δ = 0 B = 0

58. Binomial Valuation: Example 2 $50 $70 $35 $100 $50 $25 t = 0t = 1t = 2 E = $50 R f = 11% $50 $0 Call

59. Replicating Portfolios for Call Value $50 $70 $35 t = 0t = 1 E = $50 R f = 11% $25 from Step 1 $0 from Step 1 Call Replicating Portfolio 70 Δ - 1.11B = 25 35 Δ - 1.11B = 0 Solving: Δ = 5/7 B = 22.5 Buy 5/7 share, borrow $22.5

60. Value of Call at t = 0 Cost of replicating portfolio = value of call 50 Δ - B = 50 x 5/7 - 22.5 = $13.20

61. Binomial Pricing Risk-Neutral Method $55 Stock: $50 $45 1-year Call, E = $50, R f = 5%

62. Binomial Pricing: Risk-Neutral Method Step 1 Solve for probability of rise 0.05 = 0.10 p + (-0.10) (1 - p) p = 0.75 Step 2 Solve for expected future value of option C 1 = 0.75 x $5 + 0.25 x $0 = $3.75 Step 3 Solve for current value of option C 0 = $3.75/1.05 = $3.57 Note: This is an extremely powerful and useful result from the perspective of devising numerical procedures for computing option values.

63. The Limiting Distributions…….. F As the time interval is shortened, the limiting distribution, as t 0, can take one of two forms: –as t 0, price changes become smaller, the limiting distribution is the normal distribution and the price process is a continuous one. –as t 0, price changes remain large, the limiting distribution is the Poisson distribution, i.e. a distribution that allows for price jumps F The Black-Scholes model applies when the limiting distribution is the normal distribution, and assumes that the price process is continuous and that there are no jumps in asset prices

64. Black-Scholes Model F C = S N(d 1 ) - K e -iT N(d 2 ) F Where : –C = value of the call option –S = current stock price –N(d 1 ) = cumulative normal density function of d 1 –K = the exercise price of the option –i = the risk-free rate of interest –T = expiration date of the option (fraction of a year) –N(d 2 ) = cumulative density function of d 2 –s = standard deviation of the annual rate of return

65. F C = S N(d 1 ) - K e -iT N(d 2 ) Where : d 1 = [ln(S/K) + (i + 0.5s 2 )T] / sT 1/2 d 2 = d 1 - sT 1/2 F The replicating portfolio is embedded in the Black- Scholes model. To replicate this call, you need to: – Buy N(d 1 ) shares of stock; N(d 1 ) is the option delta – Borrow K e -iT N(d 2 ) Black-Scholes Model

66. Adjusting for Dividends F If the dividend yield (y) of the underlying asset is expected to remain unchanged during the life of the option, the Black-Scholes can be modified: F C = S e -yT N(d 1 ) - K e -iT N(d 2 ) Where : d 1 = [ln(S/K) + (i – y + 0.5s 2 )T] / sT 1/2 d 2 = d 1 - sT 1/2

67. Application Problems 1.Underlying asset may not be traded; difficult to estimate value and variance of underlying asset 2.Price of the asset may not follow a continuous process 3.Variance may not be known and may change over the life of the option 4.Exercise may not be instantaneous 5.Some real options are complex and their exercise creates other options (compound) or involve learning (learning options) 6.More than one source of variability (rainbow options)

68. Jumping from financial options to real options

69. Real Options: Link between Investments and Black-Scholes Inputs PV of project Free Cash Flow Outlay to acquire project assets Time the decision can be deferred Time value of money Risk of project assets Stock price Exercise price Time to expiration Risk-free rate Variance of returns S X s2s2 i T

70. NPV “X” Investment S avg “S” Value of Developed Project “S - X” Conditional NPV of project NPV

71. “X” Investment S avg “S” Value of Developed Project “S - X” Intrinsic Value of Option Live Option Value Dead Option Value Option Value: dead and live

72. “S” “S - X” When options really matter In the Money At the Money Out of the Money

73. “S” “S - X” When options really matter In the Money At the Money Out of the Money

74. Characteristics of Projects Where Optionality is Important F “Long-shot” projects (out of the $) F Substantial flexibility ignored in project F Examples: Valuing investments in oil fields –Where you are valuing the rights to an “expensive” field –Where you are valuing the rights to produce in a very cheap field

75. “ I’m sold, but what do I do?”

76. Technique F First step is framing the question F Next, there are a variety of techniques –Force-fit problem into stylized model, like Black- Scholes. –Create customized model to recognize the complicated set of managerial choices F Finally, you have to work through some important nuances.

77. Framing the question is critical F Identifying the optionality –What is the flexibility? –Is it like a call? A put? A more complicated structure? F Scope out the importance F Is this flexibility that is likely to be important to you? Is the project “marginal” under NPV, but there is phased investment and learning?