copyright © 2009 pearson education, inc. publishing as prentice hall 1 chapter 17: real options...

Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall

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Chapter 17: Chapter 17: Real Real

OptionsOptions

ObjectiveReal Options

Deferral OptionBlack-Scholes Formula

Real Options


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Chapter 17 ContentsChapter 17 Contents

• 17.1 Investing in Real Options17.1 Investing in Real Options

• 17.2 Deferral Options: The Case of 17.2 Deferral Options: The Case of Uncertainty and Irreversibility Uncertainty and Irreversibility

• 17.3 Applying the Black-Scholes 17.3 Applying the Black-Scholes Formula to Value Real Options Formula to Value Real Options


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IntroductionIntroduction• We show how to apply financial We show how to apply financial

economic theory to strategic economic theory to strategic decision making.decision making.

• We show how option theory may be We show how option theory may be applied to evaluate management’s applied to evaluate management’s ability to time the start of an ability to time the start of an investment project, to expand it, or investment project, to expand it, or to abandon it, after it has begunto abandon it, after it has begun


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17.1 Investing in Real 17.1 Investing in Real OptionsOptions• To date we have ignored To date we have ignored

management’s ability to management’s ability to – delay the start of a projectdelay the start of a project

– expand a projectexpand a project

– abandon the projectabandon the project

• Failure to take these options into Failure to take these options into account will result in an understated account will result in an understated NPVNPV


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The Movie Industry The Movie Industry (Example)(Example)• We will examine a decision in the We will examine a decision in the

movie industry in order to movie industry in order to understand the importance of understand the importance of options in evaluating projectsoptions in evaluating projects

• We add some hypothetical We add some hypothetical numbers, and to keep the central numbers, and to keep the central ideas clearly in focus, the example ideas clearly in focus, the example will the simplest possiblewill the simplest possible


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Derwyn Productions: Derwyn Productions: Time A, Rights Purchase Time A, Rights Purchase DecisionDecision

– Derwyn Productions, is considering Derwyn Productions, is considering purchasing the exclusive movie rights purchasing the exclusive movie rights to “Unfinished Business.” (An to “Unfinished Business.” (An unpublished book, authored by Lou unpublished book, authored by Lou Grymshew who has several movie Grymshew who has several movie ‘hits’, and a couple of ‘bombs’)‘hits’, and a couple of ‘bombs’)

– Cost $1 Million if purchasedCost $1 Million if purchased

– Cost $0 Million if not purchasedCost $0 Million if not purchased


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Derwyn Productions: Time Derwyn Productions: Time B, Book’s Debut (Event)B, Book’s Debut (Event)

– Critics and the public provide Critics and the public provide information valuable in determining the information valuable in determining the ultimate success of the movieultimate success of the movie

– Management has no influence over this Management has no influence over this nodenode


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Derwyn Productions: Derwyn Productions: Time C, Production Time C, Production DecisionDecision

– Contingency: Successful book (Prob=0.5)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)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


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Derwyn Productions: Derwyn Productions: Decision Tree (Decision Tree (yesyes, , nono))

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 aSuccess?


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Decision to Acquire RightsDecision to Acquire Rights

– If the decision to undertake the project is If the decision to undertake the project is made under the assumption of a single made under the assumption of a single up-front decisionup-front decision

– then the project must always be rejectedthen the project must always be rejected

– But…But…• If Derwyn makes the logical managerial If Derwyn makes the logical managerial

decision at each stage, then (as long as the decision at each stage, then (as long as the cost of capital for the project is less than cost of capital for the project is less than 100%) the project 100%) the project shouldshould be undertaken be undertaken


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Volatility and Project Volatility and Project EvaluationEvaluation

– There is a common notion that risk in There is a common notion that risk in investment decisions is something that investment decisions is something that needs to be penalized: Risky cash flows needs to be penalized: Risky cash flows are often discounted at a higher rateare often discounted at a higher rate

– But … we have just seen an investment But … we have just seen an investment decision containing an option-like feature, decision containing an option-like feature, and we know that options always become and we know that options always become more valuable with higher volatilitymore valuable with higher volatility


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““Unfinished Business” Unfinished Business”

– The publisher also has another book, The publisher also has another book, “Risky Business,” and Derwyn believes “Risky Business,” and Derwyn believes that it’s identical to “Unfinished Business” that it’s identical to “Unfinished Business” in all economic respects other than the in all economic respects other than the payoff, which is (-$8 million, 8 million)payoff, which is (-$8 million, 8 million)

– Running the numbers shows:Running the numbers shows:• the more volatile project increases the more volatile project increases

shareholders’ wealth more than the less shareholders’ wealth more than the less volatile onevolatile one


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SummarySummary

– Some projects are naturally rich in valuable Some projects are naturally rich in valuable managerial options (R&D), while other managerial options (R&D), while other projects have options that are relatively projects have options that are relatively hard to find, and then discovered, are not hard to find, and then discovered, are not particularly valuable (fast-food franchisee)particularly valuable (fast-food franchisee)

– Sometimes, management’s ability to Sometimes, management’s ability to recognize the options in a business situation recognize the options in a business situation is the key that distinguishes a winning is the key that distinguishes a winning business from its less successful siblingsbusiness from its less successful siblings


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17.2 Deferral Option: The 17.2 Deferral Option: The Case of Uncertainty and Case of Uncertainty and IrreversibilityIrreversibility

• Investments in projects can be Investments in projects can be undertaken now or postponedundertaken now or postponed

• Postponing or deferring a project Postponing or deferring a project allows managers to obtain allows managers to obtain information about future payoffsinformation about future payoffs


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The Decision to InvestThe Decision to Invest

• Decision: Build a factory today, one Decision: Build a factory today, one year later, or not at allyear later, or not at all

• Cost to build, I, zero salvage value, zero Cost to build, I, zero salvage value, zero operating costs (zero marginal costs)operating costs (zero marginal costs)

• One unit of output produced per year, One unit of output produced per year, current price of output Po. Price next current price of output Po. Price next year and every year thereafter: year and every year thereafter: PP11=P=P22=P=P33=. ..=P=. ..=P∞∞


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Decision to Invest Decision to Invest (continued)(continued)

• Future price uncertain: it can go up by Future price uncertain: it can go up by u with a probability of q; it can go u with a probability of q; it can go down by d with a probability of 1-q.down by d with a probability of 1-q.

• Value of project (assume perpetual Value of project (assume perpetual cash flows), NPVo (I, Pcash flows), NPVo (I, Poo,q,u,d,r) where r ,q,u,d,r) where r is the discount rateis the discount rate

• NPVNPVo o =-I + P=-I + Po o + P+ Po o [q(1+u)/r + (1-q)(1-[q(1+u)/r + (1-q)(1-d)/r]d)/r]


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Decision to Invest Decision to Invest (Continued)(Continued)

• I = $1,600, PI = $1,600, Poo=$200, u=$100, d = =$200, u=$100, d = $100 q=.5, 1-q = .5.$100 q=.5, 1-q = .5.

• Expected value of perpetual cash flows Expected value of perpetual cash flows when price is $300: .5($300)/.10 = when price is $300: .5($300)/.10 = $1500$1500

• Expected value of perpetual cash flows Expected value of perpetual cash flows when price is $100: .5($100)/.10 = $500when price is $100: .5($100)/.10 = $500

• Expected NPVExpected NPVoo = = −−$1600+$1600+$200+$1500+$500=$600$200+$1500+$500=$600


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• At t=1 we know what the price will At t=1 we know what the price will be, either $100 or $300.be, either $100 or $300.

• If PIf P11=$100, NPV=$100, NPV11 = = −−$1600+$1600+$100+$100/.10 = -$500 and we $100+$100/.10 = -$500 and we reject the project.reject the project.

• If If P P11=$300, NPV=$300, NPV11 = = −−$1600+$1600+$300+$300/.10 = $1700 and we $300+$300/.10 = $1700 and we accept the project.accept the project.


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• The expected NPV of the project at t The expected NPV of the project at t =o is: [.5(1700) +.5(0)]/.10 = $772.73=o is: [.5(1700) +.5(0)]/.10 = $772.73

• Note at time 1 if PNote at time 1 if P1 1 =$100 we do not =$100 we do not undertake the project and NPVundertake the project and NPV11 = 0 = 0

• Conclusion: Option to defer Conclusion: Option to defer investment is valuable, NPV at t =o investment is valuable, NPV at t =o increases by $172.73= $772.73-increases by $172.73= $772.73-$600.00$600.00


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NPVNPV Profiles for Current and Profiles for Current and Deferred DecisionsDeferred Decisions


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NPVNPV Sensitivities to Initial Sensitivities to Initial Price Parameter (PPrice Parameter (P00))


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NPVNPV Sensitivities to Initial Sensitivities to Initial Investment Cost (I)Investment Cost (I)


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Value of the Deferral Option Value of the Deferral Option Using the Binominal Option Using the Binominal Option Pricing ModelPricing Model• Consider the deferral option as a call Consider the deferral option as a call

option on a stream of factory output option on a stream of factory output one period from now and that the one period from now and that the exercise price of the option is the exercise price of the option is the investment cost of the factory, so E investment cost of the factory, so E = I.= I.

• Value of call at maturity: Value of call at maturity: C C11(P(P1) 1) = P= P11+ P+ P11/r –I if P/r –I if P11+ P+ P11/r > I /r > I 0 otherwise 0 otherwise


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Deferral Option Using Deferral Option Using Binomial Option Pricing Binomial Option Pricing Model Con’tModel Con’t

• Value of contingent claims: Value of contingent claims: CC11(100) = 0, C(100) = 0, C11(300) = $1700(300) = $1700

• Value of hedge ratio h: Value of hedge ratio h: h = [C h = [C11(300) - C(300) - C11(100)]/($300-(100)]/($300-$100) =8.5 $100) =8.5


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• Cash flows associated with hedged Cash flows associated with hedged portfolio: CFportfolio: CFoo = = CFCFo o – 8.5($200), – 8.5($200), CFCF1 1 = = 8.5P8.5P11 + (0.10)8.5(200) – C + (0.10)8.5(200) – C11(P(P11))

• If the price falls the payoff is: If the price falls the payoff is: 8.5($100) + $170 -0 = $10208.5($100) + $170 -0 = $1020

• If the price rises the payoff is: If the price rises the payoff is: 8.5($300) + $170 - $1700 = $10208.5($300) + $170 - $1700 = $1020


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• Now find CFo, the initial outlay needed to lock in Now find CFo, the initial outlay needed to lock in $1020 on period later: CFo = -Co + 8.5($200) $1020 on period later: CFo = -Co + 8.5($200) =$1,020/1.10 = $927.27=$1,020/1.10 = $927.27

• Solve for the current value of the deferral option: Solve for the current value of the deferral option: Co = 8.5($200) -$927.27 = $1700 - $927.27 = Co = 8.5($200) -$927.27 = $1700 - $927.27 = $772.73$772.73

• Conclusion: Do not exercise the option to invest Conclusion: Do not exercise the option to invest today, invest one year later when price today, invest one year later when price uncertainty is resolved.uncertainty is resolved.


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17.3 Applying the Black-17.3 Applying the Black-Scholes Formula to value Scholes Formula to value Real OptionsReal Options

• This section shows how to apply the This section shows how to apply the Black-Scholes option pricing formula Black-Scholes option pricing formula in capital budgeting by using two in capital budgeting by using two examplesexamples


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Raider’s Takeover of Target Raider’s Takeover of Target using an optionusing an option• Suppose that Raider Inc. is considering Suppose that Raider Inc. is considering

acquiring Target Inc. Assume:acquiring Target Inc. Assume:

– that both companies are 100% financed by that both companies are 100% financed by equity divided into 1-million shares equity divided into 1-million shares

– that Target is worth $100,000,000that Target is worth $100,000,000

– Target offers Raider the option to purchase Target offers Raider the option to purchase 100% of Target’s shares one year from now100% of Target’s shares one year from now

– RRff=6%, cost of option $6 million, =6%, cost of option $6 million, TargetTarget=0.20=0.20


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Raider’s Takeover of Raider’s Takeover of Target Using Options: Target Using Options: ComputationComputation• Observe that the Targets Future is equal Observe that the Targets Future is equal

to the option’s strike, so the simplified to the option’s strike, so the simplified BS equation may be usedBS equation may be used

• The NPV of the investment is therefore The NPV of the investment is therefore $(8-6) millions = $2 millions (do it)$(8-6) millions = $2 millions (do it)

– The premium distributed to the shareholdersThe premium distributed to the shareholders

million 98.7$21

*20.0*000,000,100$2

TSC


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Implicit Options: Implicit Options: ElectroUtilityElectroUtility

• ElectroUtility has the opportunity to ElectroUtility has the opportunity to invest in a project to build a power-invest in a project to build a power-generating plantgenerating plant

• Phase 1:Phase 1:– invest $6 million now for the buildinginvest $6 million now for the building

• Phase 2:Phase 2:– purchase equipment costing $106 million purchase equipment costing $106 million

in one yearin one year


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• Suppose that, viewed from today’s Suppose that, viewed from today’s perspective, perspective, – the value of the completed plant is the value of the completed plant is

$112 $112

– the standard deviation of the capital the standard deviation of the capital return from the project is 0.20return from the project is 0.20


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• The expected value of the cash flow The expected value of the cash flow from the plant a year from now is from the plant a year from now is $(122-106) million$(122-106) million– The initial project outlay is $6 million, The initial project outlay is $6 million,

so a conventional DCF would so a conventional DCF would rejectreject this this project (for any positive cost of capital)project (for any positive cost of capital)

– But:But:


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• But:But:– management management willwill abandonabandon the project (and the project (and

not invest the additional $106 million) if not invest the additional $106 million) if the value of the plant is less than $106 the value of the plant is less than $106 millionmillion

– The cash flows of ElectroUtility are The cash flows of ElectroUtility are identical to those of Raider, so taking the identical to those of Raider, so taking the option into account, the project has a NPV option into account, the project has a NPV of $2 millionof $2 million


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Implicit OptionsImplicit Options

– We conclude that accounting for We conclude that accounting for managerial flexibility explicitly always managerial flexibility explicitly always increases the value of a projectincreases the value of a project

– From option theory, we know that From option theory, we know that increasing volatility always increases an increasing volatility always increases an option’s value. Using simplified BS:option’s value. Using simplified BS:• a sigma of 0.40 gives the NPV of the project a sigma of 0.40 gives the NPV of the project

of $(16-6) million = $10 million: an increase of $(16-6) million = $10 million: an increase of $8 million over the sigma of 0.20 caseof $8 million over the sigma of 0.20 case

copyright © 2009 pearson education, inc. publishing as prentice hall 1 chapter 17: real options...

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