Options Article

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by Scott Mathews, he Boeing ompany, inayDatar,Seattle niversity, nd Blake ohnson, tanford niversity

he field of rea l options has been slow o developbecause f the complexity of the techniquesand the difficulty of fitting thenr to the reali-ties of corporate trategic ecision-rnaking. uch

complexity, and the resulting challenge of gettitg seniormanagement buy-in," has been a major barrier o widercorporate adoption of real option techniques.

To overcome his barrier, The Boeing Comp any hasinvested heavily to develop state-of-the-art methods andtools. The goal s to create a real options approach hat usesthe language and f,rameworks f standard DCF analysis-aframework he company's inancial analysts nd managers realready amiliar with and feel comfortable using. The resulthas been a method of valuation (referred o at Boeing as he"f)M" Methodl) that, while algebraically quival ent o th eBlack,schole s ormula for valuing financial options,2 usesinformation that arises aturally n a standard )CF projectfinancial aluation. '

The main advantage f the DM Method is ts sirnplicityand transparency, hich allow for more nsightful strategicplanning and evaluation, and help decision-makers esignstrategies with high-benefit outcomes hat also minimizerisks.By contrast, he raditional NPV method eaves ecisionmakers without essential nformation about the impact ofmarket dynamics and sources f uncertainty.

The DM Method has the look and feel of an extendedNPV analysis. Because t is easily modeled n a spreadsheetusing off-the-shelf irnulation software o incorporate uncer-tainty and the timing of decisions, nalysts apidly earn hemethod and are able o benefit rom the associated isk analy-ses. Furthermore, executives ui.kly begin o appreciate heeffectiveness f the DM method in identiSring nvestments

that maximize the likelihood of success, hereby imitingdownside osses. inally, he rnethod can be used o givestruc-ture to early scenario-based trategic iscussions nd so provide

^wryof subjecting problenls o quantitative analysis.s

An trnvestrnent ecisisrlr he NpVCaseTo illustrate how the DM Method works, we first examinea simple nvestment ecision using standard NPV analysis.Boeing currently builds a small experimental unmannedaerial vehicle (UAV), or pilotless drone aircraft, that has anumber of possible pplicatiotrs,ncluding he monitoring ofelectrical ransmission n d pipe ine safery, orest health, and

border security. These kinds of nronitoring are currently doneby trained pilots fying small planes over remote stretchesof back countr y-a fironotonous, hazardous, nd expensiveundertaking. \We can envision a new market for a UAV thatpromises educed ost and higher efficiencies. ut the devel-opnrent of that market depends on advances n the currenttechnologies n aviation control systems, emote sensirg, andglobal positioning.

Of course, he actual rusiness ase or the UAV is complex,involving many factors, ncluding critical FAA. certification.But we can llustrate he concepts f this paper using a muchsirnplified business ase. able 1 sets orward sample projec-tions of revenues nd costs ollowirg the standard practicefor NPV-type business ase stimation using he most-likelyscenario. here s an mmediate $ 15 million outlay or R& Dengineering fforts n aviation ontrol systems, emote ensing,and global position echnology hat are expected o take upto two years.After that point, contingent on the success fthe R6cD efforts and

"for..ast of

"pro-ising market recep-

rion, Boeing hen expecrs o spend $325 million ro launchthe product, a one-time outlay for UAV design, esting, andfactory tooling. The estimated operating profit frorn UAVsales epends on assumptions bout product strategy an dmarket reception hat are surnmarized n Table 1.

Based n a corporate urdle rate of 15 /o,rhe project {PV

is estimated o be a negative 19 million, which suggests ha tthe project s not worth undertaking. But the rnanager mayoverride he NPV results ecause he believes he can exiblymanage he market esearch nd he technologyR&D efforts,

1. The method has been patented by The Boeing Company U.S. Patent 6862579\as he Datar-Mathews ethod or Quantitative eal Option Valuation, @ 2001, The Boe-ing Company, ll Rights Reserved.

2.Yinay Datar and Scott Mathews, European eal Optiofls: n Intuitive lgorithm orthe Bfack-Scholes ormula," ournal of Applied Finance, Vol 4 (1), 2A04.

3. The Boeing Leadership Center has begun exposing he company's inancial an dengineering anagers n the proper use of the DM Method. The aim of the course Criti-cal Thinking" s o help managers earn o identify, nalyze, nd manage isk n ways ha t

Journal f Applied orporate inance Volume 9 Number

are consistent with growing he business. n addition, he Global ntegrated SystemsEngineering GISE) rogram, graduate evel nterdisciplinary rogram ffered ointly bythe University f Washington's ollege f Engineering nd the Business chool n col-laboration ith The Boeing Company, rovides nstruction n the DM Method as a meansto solve difficultengineering nd inancial radeoffs. he GISE program emphasizes ys-tems engineering, project rnanagement, and finance to produce a new generation ofcomplex ysterns hinkers who can excel n a global business nvironment.

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Table NPV fiusiness;ase or UAVProject

Scenario Strategy

Most Likely Product ales rowth s approximatel y n ine with the ma*et at about 15% per year. nitial ales arget willbe moderate.

Discount Rate Assumptions

ProjectRiskRate L5 %

NPV Calculat ions Year

PVnOperating rofitsPVu aunch os tR&DExpensesTotalProject PV Value

$242($246)($ 5)($19)

Most Likely p ProfitsLaunch ostR&DExpenses ($15)

$0 $0 $52 $6 2$0 ($325)

$74 $tt $89 $104 $122

and because he market for UAVs might have a plausible, flower-probability, pside. Some managers might be temptedto declare he UAV project "strategic" and invest anywayin order to preserve he opportunity to explore he marketpoterltial. But this would mean sacrificing he authority anddiscipline hat comes rom managers' eing required o usequantitative methods, and thus defeat he purpose of havingany kind of rigorous analysis.

Given the uncertainty of the market and thus of th eproject outcorrle, here are good reasons or rnanagers olre skeptical about he recommendation ased n the NP Vanalysis. For starters, while there s likely to be a range ofpossible operating profit outcomes projected or the UAVproject, he mathematics f the NPV method require use ofa single alue or each ime period. This limiting approach sfurther reinforced by spreadsheet ormatting that constrainseach cell o a single alue.)As a consequence, ow-probabilityourconles re eliminated rom the analysis, nd only the most-likely survives he process.

Further, n this case, nd n most NPv-based approaches,all cash ows are discounted at a single project hurdle rate,regardless f possible diffbrences n risk. In sum, the NPVanalysis an bias decision-making gainst rojects ike UAVwith major uncertaint ies hat are expected o be resolved-inthis case, within two years. NPV analysis ends o reflectits conservative rigins in the banking industry by favor-irg annuity-like investments. Real options, by contrast, swell suited o evaluating nvestments with fexibility, criticaldecision oints, and major discontinuities.

The Dntar-fulsthew$ealOptionMethodMany srrategy iscussions egin with scenario lanning exer-cises esigned o embrace ew echnologies nd products. Thescenarios re he outcome of the forecasts nd insights gener-ated by gatherings f technologists nd engineers, Progranland marketing managers, inance pecialists, nd senior exec-

utives. The typical output from such meetings, more oftenthan nor, s a series f scattered otes and drawings, enerallyprovidirg little coherent basis or meaningful quantita-tive analysis. Much of the difficulty refects he challenge fsrructuring rusiness ropositions hat incorporate ebulous,disparate-seerning actors uch as uncertaittay, ontingent deci-sions, probability of success, iming, and risk versus eturn.The DM Method, and what we call "real options hinking,"has he potential to extract significant value rom scenarioplanning by providing a structure hat lends tself o quanti-tative analysis.

In conrrast o the NPV approach hat aims to reduce al lto a single most-likelyscenario, he more strategic pproach s

to stimulate iscussions routrd he various cenarios efect-i.g differenr market conditions that could be encounteredat the time of product launch. Such discussions lso ocuson other relevant actors such as he current technology orproduct readiness, he funding and time required o launchthe product, and project contingency plans n the event heengineers re unable o develop he necessary echnology orthe market outlook urns unfavorable. he underlying ealityis that as events unfold prior to the launch date and oneor another scenario begins o play out, decision managershave he ability to increase roject value by identifying andresponding o technology or market opportunities. Unlikethe NPV approach, eal options analysis s able o capturethe value of such exibility.

The advantage of the real options approach, hen, isits ability to take the wide range of "strategic ntelligence"produced by the scenario discussions nd translate t intoa business lan with flexibility and critical decision points.For example, he UAV strategy discussions esult n threescenarios imilar to those shown n Table 2. Provided withthe scenarios, Boeing's marketing department then helpsquantify each of them lry providing revenue orecasts, hilethe engineering epart ment provides stimates f one-time

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Table 2 RealSpti*nsBusine$s ase or UAVFrcject

Scenario Probabil i ty Strategy

Optimistic 7O"/" Superior roduct utsellshe market ith sales rowth p o 40o/on he irstyears, hen averaging 5"/"peryear; hereafter lowing.probability nitial ales arget s high ue o early market padework.

Most Likely Product ales rowth s n inewith he market t about 15% per year. ni t ia l ales arget wil lbe moderate.

Pessimistic l0% Intense ompetitionimits ales rowtho 5% per ear, itha potential arket ownturn wingo a weak conomy.nitial ales re owprobability ecause anufacturingosts rehigherhan xpected.

($ M) Year 0123

Optimist ic

MostLikely

Pessimist ic

Launch os t

$0 $0 $80 $i16 $153

$0 $0 $52 $62 $74

$0 $0 $20 $23 $2+

$o ($325)

$r77 $223 $268 $314

$77 $8e $104 $122

$18 $20 $20 $22

launch and recurring manufacturing costs.As can be seen n Figures 1 and 2, the thre e scenarios

result n three operating profit estimates or each year, withthe optimistic and pessimistic cenario cash lows eachassigned l0o/o robability. he three estimates an be viewedas epresenting he corners f a triangular distribution shownin Figu e 2) that refects a range of forecasts nd thus theuncertainty about annual operating profits.4LJrirrgMonteCarlo software, we created uch a triangular distribution fo reach year of the operating profit forecast.5

The Monte Carlo simulation provides a way of translat-itg the market forecast uncertainties origin ally envisionedin the scenario iscussions nto the variability of the projectcash ows. The Monte Carlo application works by takitgsuccessive andom "drawsr"o, "trials," rom all the operatingprofit cash-fow distributions, with the most frequent drawsnearest he most-likely alues. ach rial is a plausible cenarioand is calculated hrough in Excel, resulting n a cornpleteprofit/loss analysis or that one scenario nstance. typicalcomprehensive imulation analysis onsists f hundreds oreven housands f trials.6

The output of the simulated operating profits depicted n

Figures and 4 underscores he meaning of market uncertainty.The bar graph n Figure 3 shows he Optimal-Most Likely-Pessinristic anges or each year with the thicker middle sectionrunning from the 20th to the B0th percentiles f the distribu-tion). The ExcelNPV Function discounts o the present heoperating profit for each rial, and the Monte Carlo simulationsoftware reates histogram distribution (seeFigure 4) for thehundreds of trials.This distribution of discounted ash ows,which is called a Present Value Distribution, represents herange of present alues f future operating profits.

Each rial fbrecasts plausible UAV business ase cenario.But before calculating he net present alue, w€ must deter-mine the appropriate discount rate for the various cashfows within a single rial. Most NPv-based business asesuse, ncorrectly, a single discount rate (such as I5o/o) or al lcash ows regardless f their different risk levels. Vith realoptions, we can use different discount ates hat reflect he riskof the different cash lows.The operating profits are subjectto market risk and so the appropriate iscount ate br thesecash ows is the project's equired ate of return, I5o/o.

In c6ntrast, he aunch cost cash ow (or "strike price")has elatively ow risk because management ontrols he funds

4. Distributions ther han riangular an be used. Most isk distributions re skewed,including he riangular istributions sed n the case. A skewed i stribution aptures heriskyproject oncept f a low ikelihood ut high consequence henomenon. lognormaldistribution, sed n formal options heory, s a type of skewed istribution, ut ts defin-ing parameters, uch as mean and standard eviation, re more difficult o determine nthe context of standard engineering nd business ractices. he easily cornprehensibleparameters Max-Most Likely-Min hat define a skewed riangular istribution an moreor less approximate he formal ognormal istribution without material mpact on ana-lytical esults . Also note hat though here exists he NPV echnique f multiple scenarioanalyses, ome of its shortcomings re hat 1) there s no understanding f the probabil-i ty of any one of the scenarios, nd 2) there s no way to determine which of the severalvaluation esults ught o apply o the project nvestment ecision t hand.

5. Spreadsheet Monte Carlo software such as Crystal Ball or @Risk) can be used o

Journal f Applied orporate inance Volume 9 Number

build he triangular is tributions nd add other simulation pecific unctionality. MonteCarlo oftrruare enerally ncludes correlation unction h at enables ny one distributi on obe "co-related" ith other distributions. or example, f there s one year of higVlow oper-ating profits, hen we can orecast, with some degree f predictability, hat next year's op-erating profitsmay also be high/low. n the UAV project, we estimat e he correlation o beabclut 0% based n historical valuation f similar projects, nd have used his value nthe correlation unction elating ll the years' distributions. f there s little or no correlationin year-over-year perating rofits, hen he simulation esults ollapse o a simple averagescenario, egating cenario ariability, nd effectively ullifying any strategic ptionality.

6. We recommend about 500 trials or preliminary esults and about 2,000 trials orfinal results. The more complex and uncertain he analysis, he more rials are required.Some analyses equiring ubstantial recision, uch as hat illustrated n Appendix l, needupwards of 10,000 trials, Another Monte Carlo unction determines ow draws are made;we recommend atin Hypercube o obtain good sampling of all the variable data.

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Figure Reai SpticnsSperating rofitSusiness ase ce narios

"r-'"s:*-il-@

Real Options Scenarios

0ptimistic

Most ikely

Pessimisticn+t0l

o-u0E

+t(g

(uo.o

Figure Mod*lingScenarios singRange orecast istributions or Operating rofits

T Optimistic

- Most urkelyMW PesSimistic

Range Forecastnnual Forecasts

Optimisticost Likelyv1Coo:=

)l.

5

and s expected o incur the aunch cost only if there are goodprospects or a successful utcome. Consequently, he aunchcost discount ate of 5o/o, ermed he nvestment are, s set at

Boeing's corporate bond rate. ' By thus applying an observ-able discount ate, he real options business ase s groundedin the realities of the capital markets, putting the resulting

profit and loss calculations on par with how shareholdersmight perceive he value of the same business pportunity, acompelling argument or senior management.s

The net profitsand osses or all UAV scenarios ollectivelydetermine ire real option value or the project. The optionvalue can be best understood s he appropriately iscounted

7. Within Boeing, he corporate ond erm rate s used n option valuation, Applyinga bond rate instead of the more standard isk-free ate has little material mpact on thevaluation and inal decision-making rocess, while significantly mproving managementunderstanding. ere he low rate, our least expensive ource of capital , can be under-stood as he resulting benefit of a diversified ortfolioeffect of a general obligation orpo-rate bond. One view of real options is that it contrasts he value of prospective iskyproject operating profits against paying off corporate bondholders. For llustration pur-poses, he risk-free ate can be used o derive a "market-based" aluation of the option.

8. The degree of risk aversion eflected n the option value s a function of the differ-ential discount ates. A risk neutral option valuation ccurs when the wo discount atesare equal, say 5%. Alternatively, etting he Project Risk Rate o 20% while maintainingthe Investment ate at 5%, will increase he risk aversion, ecreasing he option value.DM Method uses risk-averse ash low values, he same values as directly used an dprovided by marketing nd engineering. here s no need o convert o risk-neutral aluesand probabilities s required by some other real option methods, a barrier o transpar-ency and intuitiveness. n passing, we note hat we could apply, correctly, he differentialdiscount ates o the NPV business ase, but the resulting expected oss would be evenlarger, $69 million nstead f -$19 million,

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Figure UAV FrojectCashtlows ith Uncertainties

,* l l l l l$400

$200

$0 M

t$?001

{$4S0}

Year

I Operating rofits

t Launch Costs

ffi R&DExpenses

Figue 4 Present alueSistribution f the Sperating rofits

(J

o3cr(t'l

IL

average et profit, assumitg the project is terminated if aloss s forecast. We can see his visually n Figures 5 and 6.The dark shaded section on the right of the present valuedistribution in Figu e 5 corresponds o successful utcomesin which the discounted operating profits exceed he aunchcost of $295 million. The area o the left of the launch cost

consists f trialsn

which thecost s anticipated o exceed he

operating profits. n these ases,management s expected orationally avoid he oss by terminating the project.

The net profit-equal to the difference between heoperating profit and launch cost n a successful utcome andzero when the pro ect s terminated-also has a distribudon.

Figure 6 shows his payofffrequency histogrxrrr,with the termi-nated cases 600/o) aving azero outcome, while the remainingsuccessful ases ield a range of expected net profits.e Theaverage alue of this PayoffDistribution is the real opdon value,approxirnately 23 million in this example. This value s ourbest estimate oday of the discounted uture expected et profit,contingent on rational decision making at the time of launch.

Table 3 summarizes he calculations nd shows hat thetotal project value s $ B million-the difference etween he$23 million oprion value and t he $ 15 million RS.D cosr.Therefore the project is worth undertakirg. The formalcalculation of the real option value s done using he Boeing

9. The erm "non-linear" s often applied o real options. This simply means hat theproject payoff has two different outcomes: zeto or the terminated cases and a positivenet profit or the successful ases, eflecting he contingent decision-making. real op-tion valuation s always positive denoting a rational decision o invest he significantlaunch costs only f today we forecast a positive isk-adjusted NPV at launch ime. A realoption valuation oes not preclude hat conditions t launch ime may change ecessitat-

Journal fApplied orporate inance Volume 9 Number

ing a re-valuation f the prospective roject NPV profitability, or that the launch nvest-ment decision tself will be financially risk-free. Conversely, n the capital markets hetactical isk of owing he underlying sset s requently liminated y exercising n n-the-money inancial ption call and simultaneously elling he equivalent hares of stock ora cash settlement.

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Figure Risk-adjusted perating rofitOutcomes ased n Rational ecision'making t TimeO

(JE(u5crq,

lt

$352

Figure 6 UAV Froject Payoff, or Net Frofit, Distrlbution

(JC(u=CT(uL|r.

$150M23 M

Datar-Mathews Method, which has he following spreadsheetformula:

Real option value =

Average[MAX operating rofits launch cost, 0)] .

The formula captures he intuition descrilred abo't .10The operatirg profits are the range of possible discountedvalues n Figu c 4. For each rial, Excel calculates he MA Xfunction, which involves etermining whether he discountedoperating profit exceeds he launch cost. The function thushas a rninimum threshold of zero,which corresponds o theshaded egion o the eft in Figu e 5. Calculating he MAXvalue for several hundred simulated trials creates he payoffdistribution in Figu e 6, with the option value equal o the

average f all the net profit outcomes.\Wecan also provide an additional ntuitive understanding

of realoptions, which is useful during those trategy iscussions,by using an estimator f the realopdon value hat s expressed sa function of successful utcomes n the following formula:

Real option value =Risk Adjusted Success robability x (Benefits Costs).

For example, s eported n Figure 5, the risl


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Table 3 R**i*ptians Business ase or UAVFrcj*ct

DiscountRate Assumptions

icalbut as yet not well articulated art of our decision-makingprocess, pplying real options thinking provides a welcomestructure o scenario iscussions. Moreover, he ability of theDM method to simpli$r the real option value calculations

to farniliar NPV techniques and create ransparency n theprocess ccelerates anagers' doption of real option think-irg. Finally, he DM Method gracefully ollapses o an NPVcalculation when the uncertainties re nconsequential thecash low distributions converge o a most-likely point value)and there are no timed investment decision events.

Real options methods work for strategic ecisions ecauseof their ability to simplify and manage complex nvestmentproblems. t's generally ot possible o know all of the poten-tial factors hat might affect he outcome of such nvestrnent.But it is suf{icient n an uncertain environment o boundthe problem, yet still be confident in the decision-makitgprocess. By acquirirg the initial resources nd information

necessary for informed decisions, eal options allows us to"prune" possible ad outcolnes nd concetltrate ur resourceson those ruly promising opportunities. The DM Methodsimplifies he calculatiou ehind his thinking.

The simple UAV example n this ar ticle presents heunderlying intuition and basic methodology of the DMMethod. But the method can be extended n a number ofways hat enable r oader pplications. onre xamples re heinclusion of a dynarnic market demand curve and productionvariability,and the extension o multi- stage compound) andAmerican options. Perhaps most promising s the method'sability o show how the option value can nc rease hile simul-taneously educing cost and market uncertainty. Althoughthis might appear o contradict the academic doctrine onoptions, n reality conrpanies xert considerable ffor t toreduce osts and market uncertainty, while also counting onobtainirg the highest alue or its products. The richness fpotential applications of the DM rnethod, combined withits intuitive appeal, suggests t can be a powerful strategicplanning and decision-makirg ool.

scorr H. tr,rATnE\xrss an Assaciate echnical ellow t The BoeingCornpany nd s technical ead or the Cornputat ional inance nd$tachastic dodelingeam or he Madeling nd Sinrulationection ithinthe Bo*ing esearch nd development ivision.vrNAy D,rtAR s Professor f Finance t Seattle University. is areas finterest nclude irrance, nternational usiness rrd oreign xchange isk.BLAKE OHNSOw s Consulting ssistant rofessor n Stanford niver-sity'sDepartment f Management cience nd ngineering, here hi swork ocuses n quantification ncjmanagement f riskand lexibilityorind strial ornpanies.

$pecial hanks o Shen Liuat Eoeing or helping o prepare he [xcelrnodels.

ProjectRiskRate

Investment at e

r5%

5Y"D-M Method Calculations ($M)

PVoOperating rofits

PVo aunch osts

ProjectPayoffMAX(OP-lC,0)

Project ption Value

R&DExpenses

TotalProject alue

9242($2e5)

$0$2 3($15)

$8

Real option value 4Ao/o ($lSZ - $295) * $23M.

In sum, real options help address ontingent srategicinvestment challenges, hose hat require preparatory esourceallocation n advance of an anticipated use. n this case, uranalysis ells us hat the UAV project has a contingent presentvalue of $23 million rwo years rior to launch. And since ourengineers ave nformed us hat they need $ 5 million in R&Dfunds today to advance he necessary echnology o a state ofreadiness t the time of launch, the UAV project option canbe purchased or $8 million less han ts estimated alue.Thisis a good deal or shareholders; he real option value exceedsthe initial RS{D expense equest, nd we should approve andfund the R&D portion of the project.

Another way of interpreting our findings s that the abiliryof Boeing'"s ngineers o solve aviation challenges ith a highdegree of efficiency s a competitive advantage-one thatallows us to "b,ry" the UAV option at below market value.This contrasts with the NPV analysis, which shows a loss of$ 19 million and he resulting onclusion o abort his businessopportunity with no RBcD investment. While the outcomeof the initial RScD investment will not be known for sometime, our expectation s that the R&D will inrproveour insightinto the true value of the project, hereby educing uncertaintyand putting us n a better position o make a correct decisionabout whether o fund the much arger aunch costs. nd if theproject s terminated prior to launch because f poor forecastprojections nd no further nvestments re committed, our lossis imited to the upfront R&D expense.

Csncl#ding ThcughtsThe f)atar-Mathews Real Option Method is gaining accep-tance among managers t Boeing as a framework or anilyzingstrategic pportunities with both high payoff outconres ndhigh risk. Ve made he point earlier hat much of the value ofreal options resides ot in the actual calculation f the optionvalue, but rather n "realoptions hinking." Because t is a crit-

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Table 4 eurnBaring he SM and Slack-$chsles ptian Methads n Excel

Operating rofitsInvestment

o. .g

$372($s25)

Operating rofitsat Time2

Time t)

Risk FreeRate Rf)

Discount ate Rr )

Black Scholes Method

Asset S)

Exercise X)

SigmaOptionValue

25.O%

15.0%

$275.58$2e4.07)

79.6%$22.97

Operating rofitsMeanStdDev

372105

-0.100.460.35

$ 15 0 $372 $600= EXP(-Rr*t)*(Mean)= EXP(- f t)*| nvestment= SQRT(LN( + (StdDev/Mean) 2))/SQRT(I)= Nd_L S-(Nd_z*(-X))

= (LN S/(-nvestment)) (Rf+ 0, 5*(S gma 2 )*t)/(Sgma*SQRT(t))= NORMSDIST(d_l)= NORMS lST(d_1 (Sigma*SQRT(t)))

d1N(d )N(d2)

Datar Mathews Method

Asset A)

Exercise X)

Payoff

$215.58 = EXP(-Rr*t)*OpProfits($294 A7)= EXP(-Rf*t)*lnvestment

$0.00 =MAX(A+X,0)r F((A>-X),A+X,0)$22.97 =Average(Payotf)ptionValue

AppendEs: ffixtensicnss the SM Meth*dOne of the simplest xtensions s the conversion f the DMMethod formula to an Excel ogic function:

Real option value =Average if f(ffi-launchcost)) 0n(@-launchcost ) ,011 .

An advantage of the logic formula is greater clarity of thereal option strategy, essentially he logic of business eci-sion-nraking. n addition, business nalysts an capturefairly complex what-if scenarios or "operating profits" and"launch cost" n spreadsheet odels. For example, perating

profit volatility is more accurately rodeled by integrating adynamic deman d curve and production uncertainty.The DM Method framework can also incorporate

additional options. For example, he launch cost, which isfixed or the sample ase, an also be a distribution a "variablestrike" option) one of the most common situations n realoptions. 7e can integrate his option together with an exitoption to either icense or sell the technology developed,say or $5 million, in the event of project ermination. Th evalue of the terminated, unsuccessful roject s therefbre $5million, nor $ 0. The spreadsheet ormula for the complex

102 Journal fApplied orporateinanceVolume 9Number

project option that combines hese wo features ecomes:

Real option value =

Average MAX ("peffi - tr"".h .*r, 5)]

A project type that frequently arises at Boeing is anopportunity to bid on a fixed price proposal, where theuncertainty s the cost ("strike price") of the systenr. n thiscase, he traditional option variables are reversed, with thebenefit, or proposal price, being the fixed value. The DMMethod is able o c alculate he option value of the proposalbid opportunity:

Real option bid value _

Average MAX ({ixedprice - system osts, 0)].

These are all call options hat will p^y off only if there san increase n value. A common put option, which will payoff if there s decrease n value, such as a service uarantee orcustomer ervice greements CSA), or, for expensive easedassets uch as cars and airplanes, a residual value guarantee(RVG). Put options are often used n contingent clauses ncontracts o tailor the value o the performance isks of thecontract. The DM Method values a put option as ollows:

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Figure Operating rofitOutcomes ased n Rational ecision-making t Year

C'g(u5(t(l,t-

l

$150M $325M $422M

Figure 8 Secision Tree at Year ?

RiskNeutral robabilities-

'-67o/"

33%

$97M$422 $325)

$o

Real put option value =

AverageIMAX (guarantee alue actual rilue, 0)]"

Appendlx l; Ccsnparinghe DM Method o Black-$chsl*sThe DM Method is mathematically equivalent o the BlaclcScholes ormula under certain assumptions. able 3 illustratesthis with a simple but typical DCF analysis. he DM Methoduses he distribution of forecasted ashflows o find the optionvalue, whereas Black-Scholes ses he volatility, o.r2 Further-more, the DM Method implicit ly adjust s he discount rate

to accourlt or the underlying isk. The option value s easilyunderstood as the expect d payoff resulting from r ationalexercise ecisions. The fexibilitv of the DM Method also

allows t to better deal with the real world deviations rom thestrict theoretical ssumptions f Black-Scholes. or example,the DM Method can easily deal with non-lognormal cash-flow distributions and random exercise rice.

Appendixll: HowRiskUndercuts lecision reesDecision rees rovidea graphic epresentation f the possiblepaths or the project outcome, but they do not correctly valuethe project. Whereas NPV analysis ypically undervaluesproject because t does not include the value of flexibiliry,adecision ree usually overvalues he pro ect because t doesnot appropriately djust he investment isk.l3

To see hy, we construct a decision tree for the UAVproject. Monte Carlo simulations applied to the informa-tion in Table 2 create he distribution for operatirg profits

12. The DM formula s: C 0 = E e pt 5-.- t t X ]* ,

an expectation here 5 is the random variable or operating rofits , and r are herisky-asset nd the risk-free iscount ates, espectively, nd + is the MAX unction.The simulation or the DM Method s typically un or 10 - 20,000 trials as it graduallyconverges n the Black-Scholes alue.The Black-Scholes ormula s:

C o = s 9N(d )- XetT trt{d2)

13. Remarks lso generally pply o a closely elated iscipline, ecision nalysis. eci-sion analysis practice ncludes he application f utility curves o assess project manag-er's risk aversion nd therefore assign an appropriate isk-adjusted iscount ate, whichcan differ rom, sometimes ubstantially, he corporate urdle ate. However, n my obser-vations he utility curve assessment s very infrequently onducted wing o its subjectivenature, which runs counter o the corporate eed or intuitive and transparent nalysis.

Journal fApplied orporate inance Vof me 19 Number A Morgan tanley ublication Spring OO7 103


10/10

discounted o Year 2, the decision ate' As seen n Figurc7'

67a/o f the outcomes are a success, ith a mean operatitF

profit of $422 miltion and a net profit of $97 million'A

,i.rrpl. decision ree with rwo br"nches n Figure 8 illustrares

the decision ourcomes t Year 2. Discounting.the net p.rofitar 15o/o oTime 0 values he project at around $49 milliol'

$ze million higher han the option value.

The differJnt values are a consequence f how the two

methods handle isk. A decision ree applies isk neutral valua-

tion. A person who is risk neutral ould be willing to_p y$49

million-for the UAV project wo years n advance' However'

there s a fair chance hat th. project will be terminated a'd

the original investment orfeited. A risk averse nvestor ares

about his loss, a'd the real options merhod akes his inro

account. The estimated rojectvalue of $23 million effectively

lessens he invest'r's *por,rre to the amounr of capital at risk.

The smaller nvestm.ri poritions he 'vesror ot.1higher ate

of return should he UnV project be successfu['1'*The success ercenrages n Figures 5 and 7 dlffetbecause

the former is based o' the risk averse Percenmges t Time 0,

while the latter shows he risk neurral percenrages tYear2.

Time 0 risk aversion an be severe ecause substantial um of

money s nvested well before he aunch oPPorty"iry is viable'

This translates nto a perceived eduction in the chances of

success. he DM M.tfrod implicidyadjusts he probabilities

to accounr or risk aversiorr. h. intent of the initial invest-

menr s o resolvemany of the project uncerrainties.t5 yYear

2, some of the ulcertainty is n the past, andwe can examipe

the launch prospects n a less isky framework. At that time,

we call d...r*it. *hether the project meets our required ate

of return of 5o/ousing standard NPV analysis'

f)ecisior, r.., ,rrd"birromial attices have a more practical

limitation. They are not easy o implement.in-spreadsheets'

the ndusrry r"nd"rd for buri'.rs case nodels. Most business

cases nvorve ozens, nd occasionally undreds of variables,

with multiple sources of uncertainty that can quickly

overwhelm'" ,pr."dsheet decision ree. Instead, * p-toi".tly

srrucrured pr.odsheet-based usiness ase with embeddedMonte crrlo simulation adequarely ecreares he branchirg

of a decision ree.

14. An option's ate of return s given y:

In(cr-/c-o).,where o s he option alue t Time , or $23 million; Tl l impl ied =-

is he project atue ril, r,uiio^ui u.hion-makingt Year , or $97million'.Il,,"o'.0h.el

equafs 2%. Options re iskybut highry everagednvestments ndherefore re ac-

companied y a sufficientryrgh ot, trot. hat highly everagednvestments ithsig-

nificant ut risky ates f return orrespond ellw''th ur concept fhe nature f R&D

investments. ccaiionarfyimprieris ermed he "rate f earning" againor he nature f

reveraged eturns n R&b'tiitrr;orogynvestments. r s "implied" ecausehe rate of

104 Journal of Applied Corporate inance Volume 19 Number2

return f he option an onry e determined nce he option alue as beenalculated;

limoriecannot e determined priori'r 5, There s a croseryerated henomenon n isk version nd

probabiritiesobserve

when lecture o universitiesr business roups. will often ffermyaudience o pur-

chase,a ottery,nrt rvr out $100 on a correct all f a coin oss,therwise,$0. I

rarely etpurchai. ti.r, above 40 (or 40%) wingo he iskaversion fhe audience,

even hough he objective robabiritiesndicate he gambre hould eworth 50 50%)'

a riskneutral nvesiment. isk version hiftshe perceived robabilities'

A Morgan tanley ublication Spring OO 7

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