1. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 1 Chapter 17: Real Options Objective Real Options Deferral Option Black-Scholes Formula Real Options

2. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 2 Chapter 17 Contents 17.1 Investing in Real Options17.1 Investing in Real Options 17.2 Deferral Options: The Case of Uncertainty and Irreversibility17.2 Deferral Options: The Case of Uncertainty and Irreversibility 17.3 Applying the Black-Scholes Formula to Value Real Options17.3 Applying the Black-Scholes Formula to Value Real Options

3. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 3 Introduction We show how to apply financial economic theory to strategic decision making.We show how to apply financial economic theory to strategic decision making. We show how option theory may be applied to evaluate management’s ability to time the start of an investment project, to expand it, or to abandon it, after it has begunWe show how option theory may be applied to evaluate management’s ability to time the start of an investment project, to expand it, or to abandon it, after it has begun

4. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 4 17.1 Investing in Real Options To date we have ignored management’s ability toTo date we have ignored management’s ability to –delay the start of a project –expand a project –abandon the project Failure to take these options into account will result in an understated NPVFailure to take these options into account will result in an understated NPV

5. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 5 The Movie Industry (Example) We will examine a decision in the movie industry in order to understand the importance of options in evaluating projectsWe will examine a decision in the movie industry in order to understand the importance of options in evaluating projects We add some hypothetical numbers, and to keep the central ideas clearly in focus, the example will the simplest possibleWe add some hypothetical numbers, and to keep the central ideas clearly in focus, the example will the simplest possible

6. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 6 Derwyn Productions: Time A, Rights Purchase Decision –Derwyn Productions, is considering purchasing the exclusive movie rights to “Unfinished Business.” (An unpublished book, authored by Lou Grymshew who has several movie ‘hits’, and a couple of ‘bombs’) –Cost $1 Million if purchased –Cost $0 Million if not purchased

7. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 7 Derwyn Productions: Time B, Book’s Debut (Event) –Critics and the public provide information valuable in determining the ultimate success of the movie –Management has no influence over this node

8. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 8 Derwyn Productions: Time C, Production Decision –Contingency: Successful book (Prob=0.5) Make the movie, NPV of movie = $4 millionMake the movie, NPV of movie = $4 million Don’t make the movie, NPV movie = $0 millionDon’t make the movie, NPV movie = $0 million –Contingency: Unsuccessful book (Prob=0.5) Make the movie, NPV of movie = -$4 millionMake the movie, NPV of movie = -$4 million Don’t make the movie, NPV movie = $0 millionDon’t make the movie, NPV movie = $0 million

9. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 9 Derwyn Productions: Decision Tree (yes, no) Buy the movie rights to book? (Cost $1 Million) (Probability = 0.5) Make the Movie? (NPV -$4 Million) (Probability = 0.5) Make the movie? (NPV $4 Million) Book a Success?

10. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 10 Decision to Acquire Rights –If the decision to undertake the project is made under the assumption of a single up- front decision –then the project must always be rejected –But… If Derwyn makes the logical managerial decision at each stage, then (as long as the cost of capital for the project is less than 100%) the project should be undertakenIf Derwyn makes the logical managerial decision at each stage, then (as long as the cost of capital for the project is less than 100%) the project should be undertaken

11. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 11 Volatility and Project Evaluation –There is a common notion that risk in investment decisions is something that needs to be penalized: Risky cash flows are often discounted at a higher rate –But … we have just seen an investment decision containing an option-like feature, and we know that options always become more valuable with higher volatility

12. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 12 “Unfinished Business” –The publisher also has another book, “Risky Business,” and Derwyn believes that it’s identical to “Unfinished Business” in all economic respects other than the payoff, which is (-$8 million, 8 million) –Running the numbers shows: the more volatile project increases shareholders’ wealth more than the less volatile onethe more volatile project increases shareholders’ wealth more than the less volatile one

13. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 13 Summary –Some projects are naturally rich in valuable managerial options (R&D), while other projects have options that are relatively hard to find, and then discovered, are not particularly valuable (fast-food franchisee) –Sometimes, management’s ability to recognize the options in a business situation is the key that distinguishes a winning business from its less successful siblings

14. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 14 17.2 Deferral Option: The Case of Uncertainty and Irreversibility Investments in projects can be undertaken now or postponedInvestments in projects can be undertaken now or postponed Postponing or deferring a project allows managers to obtain information about future payoffsPostponing or deferring a project allows managers to obtain information about future payoffs

15. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 15 The Decision to Invest Decision: Build a factory today, one year later, or not at allDecision: Build a factory today, one year later, or not at all Cost to build, I, zero salvage value, zero operating costs (zero marginal costs)Cost to build, I, zero salvage value, zero operating costs (zero marginal costs) One unit of output produced per year, current price of output Po. Price next year and every year thereafter: P 1 =P 2 =P 3 =...=P∞One unit of output produced per year, current price of output Po. Price next year and every year thereafter: P 1 =P 2 =P 3 =...=P∞

16. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 16 Decision to Invest (continued) Future price uncertain: it can go up by u with a probability of q; it can go down by d with a probability of 1-q.Future price uncertain: it can go up by u with a probability of q; it can go down by d with a probability of 1-q. Value of project (assume perpetual cash flows), NPVo (I, P o,q,u,d,r) where r is the discount rateValue of project (assume perpetual cash flows), NPVo (I, P o,q,u,d,r) where r is the discount rate NPV o =-I + P o + P o [q(1+u)/r + (1-q)(1-d)/r]NPV o =-I + P o + P o [q(1+u)/r + (1-q)(1-d)/r]

17. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 17 Decision to Invest (Continued) I = $1,600, P o =$200, u=$100, d = $100 q=.5, 1-q =.5.I = $1,600, P o =$200, u=$100, d = $100 q=.5, 1-q =.5. Expected value of perpetual cash flows when price is $300:.5($300)/.10 = $1500Expected value of perpetual cash flows when price is $300:.5($300)/.10 = $1500 Expected value of perpetual cash flows when price is $100:.5($100)/.10 = $500Expected value of perpetual cash flows when price is $100:.5($100)/.10 = $500 Expected NPV o = −$1600+$200+$1500+$500=$600Expected NPV o = −$1600+$200+$1500+$500=$600

18. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 18 Decision to Invest (Continued) At t=1 we know what the price will be, either $100 or $300.At t=1 we know what the price will be, either $100 or $300. If P 1 =$100, NPV 1 = −$1600+$100+$100/.10 = -$500 and we reject the project.If P 1 =$100, NPV 1 = −$1600+$100+$100/.10 = -$500 and we reject the project. If P 1 =$300, NPV 1 = −$1600+$300+$300/.10 = $1700 and we accept the project.If P 1 =$300, NPV 1 = −$1600+$300+$300/.10 = $1700 and we accept the project.

19. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 19 Decision to Invest (Continued) The expected NPV of the project at t =o is: [.5(1700) +.5(0)]/.10 = $772.73The expected NPV of the project at t =o is: [.5(1700) +.5(0)]/.10 = $772.73 Note at time 1 if P 1 =$100 we do not undertake the project and NPV 1 = 0Note at time 1 if P 1 =$100 we do not undertake the project and NPV 1 = 0 Conclusion: Option to defer investment is valuable, NPV at t =o increases by $172.73= $772.73-$600.00Conclusion: Option to defer investment is valuable, NPV at t =o increases by $172.73= $772.73-$600.00

20. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 20 NPV Profiles for Current and Deferred Decisions

21. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 21 NPV Sensitivities to Initial Price Parameter (P 0 )

22. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 22 NPV Sensitivities to Initial Investment Cost (I)

23. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 23 Value of the Deferral Option Using the Binominal Option Pricing Model Consider the deferral option as a call option on a stream of factory output one period from now and that the exercise price of the option is the investment cost of the factory, so E = I.Consider the deferral option as a call option on a stream of factory output one period from now and that the exercise price of the option is the investment cost of the factory, so E = I. Value of call at maturity: C 1 (P 1) = P 1 + P 1 /r –I if P 1 + P 1 /r > I 0 otherwiseValue of call at maturity: C 1 (P 1) = P 1 + P 1 /r –I if P 1 + P 1 /r > I 0 otherwise

24. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 24 Deferral Option Using Binomial Option Pricing Model Con’t Value of contingent claims: C 1 (100) = 0, C 1 (300) = $1700Value of contingent claims: C 1 (100) = 0, C 1 (300) = $1700 Value of hedge ratio h: h = [C 1 (300) - C 1 (100)]/($300-$100) =8.5Value of hedge ratio h: h = [C 1 (300) - C 1 (100)]/($300-$100) =8.5

25. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 25 Deferral Option Using Binomial Option Pricing Model Con’t Cash flows associated with hedged portfolio: CF o = CF o – 8.5($200), CF 1 = 8.5P 1 + (0.10)8.5(200) – C 1 (P 1 )Cash flows associated with hedged portfolio: CF o = CF o – 8.5($200), CF 1 = 8.5P 1 + (0.10)8.5(200) – C 1 (P 1 ) If the price falls the payoff is: 8.5($100) + $170 -0 = $1020If the price falls the payoff is: 8.5($100) + $170 -0 = $1020 If the price rises the payoff is: 8.5($300) + $170 - $1700 = $1020If the price rises the payoff is: 8.5($300) + $170 - $1700 = $1020

26. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 26 Deferral Option Using Binomial Option Pricing Model Con’t Now find CFo, the initial outlay needed to lock in $1020 on period later: CFo = -Co + 8.5($200) =$1,020/1.10 = $927.27Now find CFo, the initial outlay needed to lock in $1020 on period later: CFo = -Co + 8.5($200) =$1,020/1.10 = $927.27 Solve for the current value of the deferral option: Co = 8.5($200) -$927.27 = $1700 - $927.27 = $772.73Solve for the current value of the deferral option: Co = 8.5($200) -$927.27 = $1700 - $927.27 = $772.73 Conclusion: Do not exercise the option to invest today, invest one year later when price uncertainty is resolved.Conclusion: Do not exercise the option to invest today, invest one year later when price uncertainty is resolved.

27. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 27 17.3 Applying the Black- Scholes Formula to value Real Options This section shows how to apply the Black-Scholes option pricing formula in capital budgeting by using two examplesThis section shows how to apply the Black-Scholes option pricing formula in capital budgeting by using two examples

28. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 28 Raider’s Takeover of Target using an option Suppose that Raider Inc. is considering acquiring Target Inc. Assume:Suppose that Raider Inc. is considering acquiring Target Inc. Assume: –that both companies are 100% financed by equity divided into 1-million shares –that Target is worth $100,000,000 –Target offers Raider the option to purchase 100% of Target’s shares one year from now –R f =6%, cost of option $6 million,  Target =0.20

29. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 29 Raider’s Takeover of Target Using Options: Computation Observe that the Targets Future is equal to the option’s strike, so the simplified BS equation may be usedObserve that the Targets Future is equal to the option’s strike, so the simplified BS equation may be used The NPV of the investment is therefore $(8-6) millions = $2 millions (do it)The NPV of the investment is therefore $(8-6) millions = $2 millions (do it) –The premium distributed to the shareholders

30. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 30 Implicit Options: ElectroUtility ElectroUtility has the opportunity to invest in a project to build a power- generating plantElectroUtility has the opportunity to invest in a project to build a power- generating plant Phase 1:Phase 1: –invest $6 million now for the building Phase 2:Phase 2: –purchase equipment costing $106 million in one year

31. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 31 Implicit Options: ElectroUtility Suppose that, viewed from today’s perspective,Suppose that, viewed from today’s perspective, –the value of the completed plant is $112 –the standard deviation of the capital return from the project is 0.20

32. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 32 Implicit Options: ElectroUtility The expected value of the cash flow from the plant a year from now is $(122-106) millionThe expected value of the cash flow from the plant a year from now is $(122-106) million –The initial project outlay is $6 million, so a conventional DCF would reject this project (for any positive cost of capital) –But:

33. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 33 Implicit Options: ElectroUtility But:But: –management will abandon the project (and not invest the additional $106 million) if the value of the plant is less than $106 million –The cash flows of ElectroUtility are identical to those of Raider, so taking the option into account, the project has a NPV of $2 million

34. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall 34 Implicit Options –We conclude that accounting for managerial flexibility explicitly always increases the value of a project –From option theory, we know that increasing volatility always increases an option’s value. Using simplified BS: a sigma of 0.40 gives the NPV of the project of $(16-6) million = $10 million: an increase of $8 million over the sigma of 0.20 casea sigma of 0.40 gives the NPV of the project of $(16-6) million = $10 million: an increase of $8 million over the sigma of 0.20 case