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1、Chapter 18Real Options and Cross-Border Investment,18.1Types of Options18.2The Theory and Practice of Investment18.3Puzzle#1:Market Entry and the Option to Invest18.4Uncertainty and the Value of the Option to Invest18.5Puzzle#2:Market Exit and the Abandonment Option18.6Puzzle#3:The Multinationals En
2、try into New Markets18.7Real Options as a Complement to NPV18.8Summary,Options on real assets,A real option is an option on a real assetReal options derive their value from managerial flexibilityOption to invest or abandonOption to expand or contractOption to speed up or defer,Options on real assets
3、,Simple options European-Exercisable at maturityAmerican-Exercisable prior to maturityCompound option An option on an optionSwitching option-An alternating sequence of calls and putsRainbow optionMultiple sources of uncertainty,Two types of options,Call optionAn option to buy an asset at a pre-deter
4、mined amount called the exercise pricePut optionAn option to sell an asset,The conventionaltheory of investment,Discount expected future cash flows at an appropriate risk-adjusted discount rateNPV=St ECFt/(1+i)tInclude only incremental cash flowsInclude all opportunity costs,Three investment puzzles
5、,MNCs use of inflated hurdle rates in uncertain investment environments MNCs failure to abandon unprofitable investments MNCs negative-NPV investments in new or emerging markets,Puzzle#1Firms use of inflated hurdle rates,Market entry and the option to investInvesting today means foregoing the opport
6、unity to invest at some future date,so that projects must be compared against similar future projectsBecause of the value of waiting for more information,corporate hurdle rates on investments in uncertain environments are often set above investors required return,An example of the option to invest,I
7、nvestment I0=PV(I1)=$20 millionThe present value of investment is assumed to be$20 million regardless of when investment is made.Price of oilP=$10 or$30 with equal probability EP=$20 Variable production cost V=$8 per barrelEproduction=Q=200,000 barrels/year Discount rate i=10%,Valuing investment tod
8、ayas a now-or-never alternative,The option to invest asa now-or-never decision,NPV(invest today)=($20-$8)(200,000)/.1-$20 million=$4 million$0 invest today(?),Invest todayor wait for more information,The option to wait one yearbefore deciding to invest,NPV=(EP-V)Q/i/(1+i)-I0In this example,waiting o
9、ne year reveals the future price of oil,The investment timing option,NPV(wait 1 yearP=$30)=($30-$8)(200,000)/.1)/(1.1)-$20,000,000=$20,000,000$0 invest if P=$30 NPV(wait 1 yearP=$10)=($10-$8)(200,000)/.1)/(1.1)-$20,000,000=-$16,363,636$0 do not invest if P=$10 NPV(wait 1 yearP=$10)=$0,The investment
10、 timing option,NPV(wait 1 year)=Probability(P=$10)(NPV$10)+Probability(P=$30)(NPV$30)=($0)+($20,000,000)=$10,000,000$0 wait one year before deciding to invest,Option value=intrinsic+time values,Intrinsic value=value if exercised immediately Time value=additional value if left unexercised,The opportu
11、nity cost of investing today,Option Value=Intrinsic Value+Time Value NPV(wait 1 year)=Value if exercised+Additional valueimmediatelyfrom waiting$10,000,000=$4,000,000+$6,000,000,A resolution of Puzzle#1Use of inflated hurdle rates,Managers facing this type of uncertainty have four choicesIgnore the
12、timing option(?!)Estimate the value of the timing option using option pricing methodsAdjust the cash flows with a decision tree that captures as many future states of the world as possible Inflate the hurdle rate(apply a“fudge factor”)to compensate for high uncertainty,Option value=intrinsic+time va
13、lues,Intrinsic value,Option value,Call option value determinants,Relation tocall optionBPOption value determinant value example Value of the underlying asset P+$24 millionExercise price of the option K-$20 millionVolatility of the underlying asset sP+($3.6m or$40m)Time to expiration of the option T+
14、1 yearRiskfree rate of interest RF+10%Time value=f(P,K,T,sP,RF),Volatility and option value,Option value,Value of the underlying asset,Exercise price,Exogenous price uncertainty,Exogenous uncertainty is outside the influence or control of the firm Oil price exampleP1=$35 or$5 with equal probability
15、EP1=$20/bbl NPV(invest today)=($20-$8)(200,000)/.1)-$20 million=$4,000,000$0 invest today?,Exogenous price uncertainty,NPV(wait 1 yearP1=$35)=($35-$8)200,000/.1)/1.1-$20 million=$29,090,909$0 invest if P1=$35NPV(wait 1 yearP1=$5)=($5-$8)(200,000)/.1)/1.1-$20 million=-$25,454,545$0 do not invest if P
16、1=$5,Exogenous price uncertainty,NPV(wait one year)=()($0)+()($29,090,909)=$14,545,455$0 wait one year before deciding to invest,Time value&exogenous uncertainty,Option value=Intrinsic value+Time value$10$10,000,000=$4,000,000+$6,000,000$15$14,545,455=$4,000,000+$10,545,455 The time value of an inve
17、stmentoption increases with exogenous price uncertainty,Puzzle#2Failure to abandon losing ventures,Market exit&the option to abandonAbandoning today means foregoing the opportunity to abandon at some future date,so that abandonment today must be compared to future abandonmentBecause of the value of
18、waiting for additional information,corporate hurdle rates on abandonment decisions are often set above investors required return,An example of the option to abandon,Cost of disinvestment I0=PV(I1)=$2 millionPrice of oilP=$5 or$15 with equal probability EP=$10 Variable production cost V=$12 per barre
19、lEproduction=Q=200,000 barrels/year Discount rate i=10%,Abandon todayor wait for more information,The option to abandon asa now-or-never decision,NPV(abandon today)=-($10-$12)(200,000)/.1-$2 million=$2 million$0 abandon today(?),The abandonment timing option,NPV(wait 1 yearP=$5)=-($5-$12)(200,000)/.
20、1)/(1.1)-$2 million=$10,727,273$0 abandon if P=$5NPV(wait 1 yearP=$15)=-($15-$12)(200,000)/.1)/(1.1)-$2 million=-$7,454,545$0 do not abandon if P=$15,The abandonment timing option,NPV(wait 1 year)=Probability(P=$5)(NPV$5)+Probability(P=$15)(NPV$15)=($10,727,273)+($0)=$5,363,636$0 wait one year befor
21、e deciding to abandon,Opportunity cost of abandoning today,Option Value=Intrinsic Value+Time Value NPV(wait 1 year)=NPV(abandon today)+Additional valuefrom waiting 1 year$5,363,636=$2,000,000+$3,363,636,Hysteresis,Cross-border investments often have different entry and exit thresholdsCross-border in
22、vestments may not be undertaken until the expected return is well above the required returnOnce invested,cross-border investments may be left in place well after they have turned unprofitable,Puzzle#3Negative-NPV entryinto emerging markets,Firms often make investments into emerging markets even thou
23、gh investment does not seem warranted according to the NPV decision ruleAn exploratory(perhaps negative-NPV)investment can reveal information about the value of subsequent investments,Growth options and project value,VAsset=VAsset-in-place+VGrowth options,Consider a negative-NPV investment,Initial i
24、nvestment I0=PV(I1)=$20 millionPrice of OilP=$10 or$30 with equal probability EP=$20 Variable production cost V=$12 per barrel Eproduction=Q=200,000 barrels/year Discount rate i=10%,The option to invest asa now-or-never decision,NPV(invest today)=($20-$12)(200,000)/.1-$20,000,000=-$4 million$0 do no
25、t invest today(?),Endogenous price uncertainty,Uncertainty is endogenous when the act of investing reveals information about the value of an investment Suppose this oil well is the first of ten identical wells that BP might drilland that the quality and hence price of oil from these wells cannot be
26、revealed without drilling a well,Invest today in order to reveal information about future investments,Investing today,reveals information,EP=$20/bbl,P=$30/bbl,P=$10/bbl,The investment timing option,NPV(wait 1 yearP=$30)=($30-$12)(200,000)/.1)/(1.1)-$20,000,000=$12,727,273$0 invest if P=$30 NPV(wait
27、1 yearP=$10)=($10-$12)(200,000)/.1)/(1.1)-$20,000,000=-$53,272,727$0 do not invest if P=$10,A compound option in the presence of endogenous uncertainty,NPV(invest in an exploratory well)=NPV(one now-or-never well today)+Prob($30)(NPV of 9 more wells$30)=-$4,000,000+(9)($12,727,273)=$53,272,727$0 inv
28、est in an exploratory oil welland reconsider further investmentin one year,A resolution of Puzzle#3 Entry into emerging markets,The value of growth optionsNegative-NPV investments into emerging markets are often out-of-the-money call options entitling the firm to make further investments should cond
29、itions improveIf conditions worsen,the firm can avoid making a large sunk investmentIf conditions improve,the firm can choose to expand its investment,Why DCF fails,-3s,-2s,-1s,0,+1s,+2s,+3s,Option value,Value of the underlying asset,Exercise price,Why DCF fails,NonnormalityReturns on options are no
30、t normally distributed even if returns to the underlying asset are normalOption volatilityOptions are inherently riskier than the underlying assetChanging option volatilityOption volatility changes with changes in the value of the underlying asset,The option pricing alternative,Option pricing method
31、s construct a replicating portfolio that mimics the payoffs on the optionCostless arbitrage then ensures that the value of the option equals the value of the replicating portfolio,Underlying asset values are observableFor example,the price of a share of stockLow transactions costs allow arbitrageMos
32、t financial assets are liquidA single source of uncertaintyContractual exercise prices&expiration dates result in a single source of uncertaintyExogenous uncertainMost financial options are side bets that dont directly involve the firm,so uncertainty is exogenous,Pricing financial options,Pricing re
33、al options,Underlying asset values are unobservableWhat is the value a manufacturing plant?High transactions costs impede arbitrageReal assets are illiquidMultiple sources of uncertaintye.g.exercise prices can vary over timee.g.exercise dates are seldom knownEndogenous uncertainInvesting reveals inf
34、ormation,Advanced:Pricing real options,Suppose the value of an oil well bifurcates by a continuously compounded 4 percent per year for 4 years4 successive bifurcations result in 24=16 price paths Value after 1 year is P1=P0e0.04($24m)e-0.04=$23.06m($24m)e+0.04=$24.98meach with 50 percent probability
35、,4 percent for 4 periods,24=16 possible price paths,n=12341114131261314112n=24816,End-of-period distribution for n=4,More frequent compounding,Rather than 4%per annum for 4 years,suppose we apply the binomial model with 1%per quarter for 16 quartersThis results in 2n=216=256 price paths and n-1=15 p
36、ossible end-of-period prices,1 percent for 16 periods,End-of-period distribution for n=16,The Binomial and B-S OPMs,As the binomial process generating up and down movements bifurcates over shorter and shorter intervalsthe binomial distribution approaches the normal distribution and continuous-time option pricing methods such as the Black-Scholes option pricing model can be used,
