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1998 Defense and Civil Space ProgramsConference and Exhibit

Oct. 28-30, 1998 / Huntsville, AL

AIAA 98-5179Economic Uncertainty of Weight and MarketParameters for Advanced Space LaunchVehicles

J. A. WhitfieldJ. R. OldsSpace Systems Design LabGeorgia Institute of TechnologyAtlanta, GA

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Economic Uncertainty of Weight and Market Parameters forAdvanced Space Launch Vehicles

Jeff Whitfield*

Dr. John R. Olds†

Space Systems Design LaboratorySchool of Aerospace Engineering

Georgia Institute of Technology, Atlanta, GA 30332-0150

ABSTRACT

Market sensitivity and weight-based costestimating relationships are key drivers in determiningthe financial viability of advanced space launch vehicledesigns. Due to decreasing space transportationbudgets and increasing foreign competition, it hasbecome essential for financial assessments ofprospective launch vehicles to be performed during theconceptual design phase. As part of this financialassessment, it is imperative to understand therelationship between market volatility, the uncertaintyof weight estimates, and the economic viability of anadvanced space launch vehicle program.

This paper reports the results of a study thatevaluated the economic risk inherent in marketvariability and the uncertainty of developing weightestimates for an advanced space launch vehicleprogram. The purpose of this study was to determinethe sensitivity of a business case for advanced spaceflight design with respect to the changing nature ofmarket conditions and the complexity of determiningaccurate weight estimations during the conceptualdesign phase. The expected uncertainty associated withthese two factors drives the economic risk of theoverall program.

The study incorporates Monte Carlo simulationtechniques to determine the probability of attainingspecific levels of economic performance when the

market and weight parameters are allowed to vary.This structured approach toward uncertainties allowsfor the assessment of risks associated with a launchvehicle program's economic performance. This resultsin the determination of the value of the additional riskplaced on the project by these two factors.

NOMENCLATURE

CABAM Cost and Business Analysis ModuleCER cost estimating relationshipCSTS Commercial Space Transportation StudyDDT&E design, development, test, & evaluationEBIT earnings before interest and taxesESJ ejector scramjetHTHL horizontal take-off, horizontal landingIOC initial operating capabilityIRR internal rate of returnKSC NASA Kennedy Space CenterLCC life cycle costLEO low earth orbitLH2 liquid hydrogenLOX liquid oxygenMSFC Marshall Space Flight CenterNASA National Aeronautics and Space Admin.NASCOM NASA Cost ModelNPV net present valueRBCC rocket-based combined cycleRLV reusable launch vehicleROI return on investmentSSDL Space Systems Design LaboratorySSTO single-stage to orbitTFU theoretical first unitTRL technology readiness levelVTHL vertical take-off, horizontal landing

* - Graduate Research Assistant, School of Aerospace

Engineering.† - Assistant Professor, School of Aerospace Engineering,

Senior member AIAA.

Copyright © 1998 by Jeff Whitfield and John R. Olds.Published by the American Institute of Aeronautics andAstronautics, Inc. with permission.

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INTRODUCTION

With the advent of commercial space launchvehicles and the drive towards a balanced federalbudget, government financial participation in the spacelaunch industry has significantly declined. In order tofinance new programs and facilitate the advancement oftechnologies necessary to travel in space, privatecapital investment is needed. The growth in marketdemand for launch services has attracted the interest ofprivate investors. However, commercial investorsrequire a high rate of return on their investments inorder to take on the risk associated with these types ofprograms. In order to attain the necessary capitalinvestment required to initiate new programs, it isessential that designers incorporate financialassessments into the conceptual design phase. Theseassessments not only need to include the economicoutlook of the project, but also to include the riskassociated with the assumptions made in theprojection.

One methodology used in calculating the financialcosts of advanced space launch vehicle designsemploys parametric cost estimates. It has beendetermined that parametric cost estimates allow forgreater speed, accuracy, and flexibility in performingthese assessments than derived from using otherestimating techniques. 1 Parametric cost estimates usecost estimating relationships (CER) and relevantmathematical algorithms to determine cost estimates.

A cost estimate is not expected to precisely predictthe actual cost of a launch vehicle program, however itshould provide a realistic basis for evaluating theproject. The cost analyst should work towards thegoal of "cost realism," which is a term used to describethe items that make up the foundation of the estimate.These include the logic used in developing the model,the assumptions made about the future, and thereasonableness of the historical data used indetermining the estimate. By analyzing the effects ofuncertainty inherent in the predicted value, the analystis able to determine a more realistic view of theappropriateness of the results.

Parametric models have been developed forassessing the financial viability of advanced spacevehicle launch programs. To create this type of

model, certain simplifications must be made. Thesesimplifications result in modeling uncertainties thattranslate into risk when trying to produce a realisticestimate of the financial feasibility of a project. Thisstudy analyzes and quantifies the risk associated withtwo of the assumptions made in performing this typeof assessment for two representative conceptual launchvehicles. This includes the market variability ofpredicting future demand inherent in any commercialmarket and the uncertainty in determining accurateweight estimates.

TOOLS

The tools used in this research include CABAM(Cost and Business Analysis Module) and Crystal Ball.CABAM is a tool that utilizes parametric economicanalysis to determine the financial feasibility ofadvanced space launch vehicles. Crystal Ball utilizesMonte Carlo simulation techniques to determine thepossible outcomes when variability is introduced intothe problem. By combining these two tools, ananalysis of the effects of variability in weight andmarket parameters was completed.

Background on CABAM

CABAM was developed at Georgia Tech inresponse to the need to have a tool that provides afinancial assessment of a conceptual launch vehicledesign. This tool incorporates not only the life cyclecost attributes associated with a project, but alsoidentifies the potential revenue streams and projectsseveral different evaluation metrics including netpresent value (NPV), internal rate of return (IRR), andreturn on investment (ROI).

CABAM is a Microsoft Excel® workbook basedsimulation tool developed for the analysis ofconceptual space launch vehicles. It requires the userto input basic launch vehicle system definitionsthrough component weights and economic parameterssuch as inflation rate, interest rate, and tax rate. Sinceit only requires these basic inputs, CABAM may beused for an economic assessment at the conceptualdesign stage.

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Annual market size and market capture percentagefor a launch vehicle simulation are determined fromkey market price variables supplied by the user.CABAM is a fiscal based analysis tool that utilizesfixed rates for all of its economic parameters for theentire life of the project. Yearly life cycle costs andrevenue are generated to provide annual cash flows forthe project being evaluated.

A schematic of the structure of CABAM is shownin Figure 1. CABAM has a modular structure that isdivided into the major components of life cycle costand revenue generation. The revenue side of CABAMis divided between the government market and thecommercial market, which is then further subdividedbetween cargo and passenger markets. The life cyclecost side of the program is divided into three sections,non-recurring costs, recurring costs, and financingcosts.

•cash flows•business and cost indicators•pro-forma financialstatements

LCC

Non-Recurring Costs

•DDT&E•reusable hardware costs•facilities costs

Recurring Costs

•operations andmaintenance costs•expendable hardware

Financing Costs

Program Definition

•assumptions•fleet size•flight rate

Program Summary

•commercial market elasticity•government market elasticity

Revenue

Market Assessment

Income•mission revenue•salvage value

Figure 1: Structure of CABAM

CABAM utilizes elastic market models that weredeveloped during the Commercial Space TransportationStudy (CSTS) performed by NASA in 1994.2 Whenthe user sets the launch prices for each of the fourmarkets, CABAM estimates the market size and sharecaptured and determines the flight rate and required fleetsize to accommodate that particular level of marketpenetration. From this information, yearly revenuestreams are calculated.

To determine the total non-recurring cost,CABAM first calculates the design, development,testing, and evaluation (DDT&E) and theoretical firstunit (TFU) costs for reusable system components.Weight-based CERs are used to estimate the costs forthe vehicle, which are broken down by majorsubsystems. The CERs are in the form of equation 1.3

Cost ($) = A * WB * Cf (1)

In the equation, W is the weight of each majorcomponent, A and B are constants and Cf is thecomplexity factor. The A and B values are systemcomponent-specific constants obtained from theunrestricted-release version of the NASCOM databasefor similar component groups.4 The complexity factoris determined based upon the mechanical and materialtechnology readiness of the components. Overallprogram wrap factors are also modeled afterNASCOM.

Enhancements to CABAM

During the past year, the Space Systems DesignLab (SSDL) at Georgia Tech has continued to upgradeCABAM. The most significant change made was theway in which the model calculates NPV and IRR. The fundamental change was to discount the “free cashflow” of the program, calculated in real dollars, by thereal discount rate. This alleviates the problem ofhaving to adjust all future cash flows by the expectedinflation rate. The free cash flow is calculated byadding depreciation to earnings before interest and taxes(EBIT) and then subtracting capital investments. Byusing this method, interest is correctly accounted for inthe discount rate and the effect of taxes is removed. This was done to simplify the process of usingCABAM in performing a business analysis of anadvanced space launch vehicle during the conceptualdesign phase.

A second major enhancement to CABAM was theaddition of detailed pro-forma financial statements.This includes an income statement, a balance sheet,and a cash flow statement broken down by year for theentire life of the program. Along with these upgrades,the user was given greater flexibility in choosingoptions related to the financing of the program.Included in the newest version of CABAM (version

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6.0) is the option to use either level-payment bonds orzero coupon bonds. Also, the user now has the abilityto include multiple equity investments made in theproject.

Crystal Ball

Crystal Ball® is a user-friendly, graphicallyoriented forecasting and risk analysis program thatprovides the probability of certain outcomes.5 Itutilizes Monte Carlo simulation techniques to forecastthe entire range of results possible for a givensituation. Crystal Ball also provides the confidencelevels so that the user will know the likelihood of anyspecific event taking place.

A Monte Carlo simulation is a system that usesrandom inputs for key inputs to measure the effects ofuncertainty in a model. This is achieved by firstspecifying the probability distributions for all of theuncertain quantitative assumptions. Next, a randomnumber is generated from the distribution for eachparameter to arrive at a set of specific values forcomputing the output of the simulation run. Thisprocess is then repeated numerous times to produce alarge number of output values. An approximation ofthe probability distribution of the output values maybe obtained by breaking the range of values into equalincrements and counting the frequency with which thetrials fall into each increment. As the number of trialsincreases, the frequencies will converge toward theactual probability.6

ANALYSIS

By utilizing the Monte Carlo simulationtechnique, an analysis of the effects of allowing certainvariables to vary within a predetermined range waspossible. This study investigated the effects ofallowing two variables, the market characteristics andweight estimates to vary within specified ranges todetermine the effect on the economic viability of theproject.

Calculating Weight Variability

The first step in setting up the analysis was todetermine an appropriate methodology for fluctuating

weight parameters during the simulation runs. Theoriginal vehicle weight statements included a 15%aggregate dry weight margin to allow for weightgrowth that normally occurs as the vehicle goesthrough the different stages of design. Since thedistribution of the dry weight margin is not known,CABAM uses only the base “best guess” (most likely)component weights to calculate DDT&E and TFUcosts, but then applies a 20% cost margin to the finalnon-recurring cost calculations.

The most-likely weights of the differentcomponent groups listed in Table 1 were allowed tovary by the percentages shown in the table. Avionicswas allowed to fluctuate equally on either side of themost-likely estimate because of the continualevolution in the development of smaller electroniccomponents compared to the normal weight growththat occurs with all components. The mainpropulsion was given the greatest allowance on themaximum side because of the complexity ofdeveloping new engines for advanced space flightlaunch vehicles.

Table 1: Variances by Component Group

Component Groups Minimum Max imumWing Group - 5 % 20%Tail Group - 5 % 20%Body Group - 5 % 20%TPS Group - 5 % 20%Landing Gear - 5 % 20%Main Propulsion - 5 % 25%RCS Propulsion - 5 % 10%OMS Propulsion - 5 % 10%Primary Power - 5 % 10%Electrical Conversion and Distribution - 5 % 10%Surface Control Actuation - 5 % 10%Avionics - 1 0 % 10%Environmental Control - 5 % 10%

CABAM was reconfigured to allow foradjustments to be made in the size of the payloadcapacity depending on the total combined weight of thecomponents in comparison to the original dry weightof the vehicle. Therefore, if the new dry weight of thevehicle calculated after the components weights wererandomly changed per Table 1 exceeded the originalbaseline weight (including its 15% dry weightmargin), the difference was then subtracted from thepayload capacity, thus reducing revenue for eachlaunch. The opposite also held true: if the new weightwas less than the original weight, then the payloadcapacity was increased resulting in additional revenue.

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For passenger missions, incremental changes inthe number of passengers carried per flight were onlypermitted for increments of 1800 lbs. It was assumedthat each passenger would generate that amount ofweight growth in the different systems required totransport a human into space.

As shown in Figure 2, a triangular distributionwas placed on each of the component groups for theMonte Carlo simulation. The minimum andmaximum weights allowed were calculated based uponthe percentages listed in Table 1.

71,494.00 76,197.50 80,901.00 85,604.50 90,308.00

Body Group

Assumption: Body Group

Triangular distribution with parameters:Minimum 71,494.00Likeliest 75,257.00Maximum 90,308.00

Selected range is from 71,494.00 to 90,308.00Mean value in simulation was 79,032.87

Figure 2: Representative Triangular WeightDistribution

Calculating Market Volatility

To evaluate the sensitivity of the model tochanging market conditions, an approximation of thevolatility of demand was assumed. The authorsestimated that greater volatility exists in the lowerprice segments compared to that occurring in thehigher price market. The reason for this estimationwas based upon the fact that market demand is alreadyknown for higher price segments based upon currentmarket conditions, thus lower risk exists for

competing in this price range. As shown in Table 2,it was assumed that at the lower price segment, a 30%fluctuation in the size of the commercial market and a15% fluctuation in the size of the government marketmay exist from current estimations. At the higherprice segment, a 5% fluctuation was included for bothmarkets.

Figure 3 shows the market estimations forcommercial cargo, which was one of four markets usedin this study. The solid line represents the baselinecase and the long dash lines represent the variabilitypossible in market demand. This graph depicts thetapering of market variability as the price increases.

0

2000

4000

6000

8000

10000

12000

14000

16000

$100 $1,000 $10,000

Price ($/ lb)

Pa

ylo

ad

(k

lb)

Baseline Payload (klb) Minimum Payload (klb) Maximum Payload (klb)

1197698

Figure 3: Commercial Cargo Market

Two equations were derived to determine the sizeof the market captured under the predefinedassumptions. By using these equations, the marketvolatility was quantified for a specified price. For thecommercial cargo market, the market demandfluctuated between 1,197,000 lb. and 698,000 lb. at aprice of $820/lb. as shown in Figure 3 by thehorizontal dotted lines. The first equation gives the

Table 2: Prices and Market Fluctuation for Each Market Segment

Market Segment Un i ts Opt imal High Low High LowCommercial Cargo $ / l b 820 5,000 100 30% 5 %Commercial Passengers M$/passenger 0.52 5.0 0.2 30% 5 %Government Cargo $ / l b 1 ,650 5,000 100 15% 5 %Government Passengers M$/passenger 7.12 15.0 0.2 15% 5 %

P r i c e Market Fluctuation

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total demand in pounds for the market.

F * S * B + B = M (2)

In equation 2, F is the factor that is allowed tovary between 1 and –1 during the Monte Carlosimulation creating the effect of either being greaterthan or less than the expected value. As shown inFigure 4, a triangular distribution was placed on F forthe simulation run. B is the base value of the marketdemand determined by the price. S is the scale factorthat fluctuates linearly between 5% and 30% for thecommercial market and between 5% and 15% for thegovernment market depending on the price. The resultof this equation, M, is the net market size captured bythe particular project under evaluation.

S = S2 - (P2 - P)S2 - S1

P2 - P1(3)

Equation 3 was used to calculate S for equation 2.P is the price to launch either a pound of payload orone person into low earth orbit (LEO). For each ofthe four market segments, the price was set at apreviously determined optimal level to achieve themaximum rate of return for the program (Table 2). Agrid search optimization strategy was used to determinethe optimal pricing strategy for this class of vehicles.7

- 1 . 0 0 - 0 . 5 0 0.00 0.50 1.00

Commercial Cargo

Assumption: Commercial Cargo

Triangular distribution with parameters:Minimum - 1 . 0 0Likeliest 0 .00Maximum 1.00

Selected range is from -1.00 to 1.00Mean value in simulation was 0.00

Figure 4: Representative Triangular MarketDistribution

The prices used in the analysis are shown in Table2. P1 is the price at the lower bound and P2 is theprice at the upper bound. These bounds are representedby the high and low figures also shown in Table 2. S1

is the maximum fluctuation allowed in the market andS2 is the minimum fluctuation allowed. Thesepercentages are also shown in Table 2.

Sample Vehicles

To provide analysis data for this research, twocandidate single-stage-to-orbit (SSTO) reusable launchvehicle (RLV) designs were chosen to serve asreference vehicles. For both vehicles, the initialoperating capability (IOC) was projected to be 2008and steady state operation was assumed for the periodfrom the year 2010 to 2025. The baseline case for thetwo vehicles had a cargo capacity of 44,000 pounds ortwenty-four passengers.

The first concept selected, which takes advantageof more off-the-shelf technologies, was an all-rocketSSTO vehicle with vertical take-off and horizontallanding (VTHL). This concept, which utilizes fiveLOX/LH2 rocket engines, is shown in Figure 5. Eachvehicle was configured to allow for cargo andpassenger service to low earth orbit (LEO, due eastfrom KSC).

Gross Weight 2,381,000 lb.Dry Weight 235,200 lb.Payload 44,000 lb.Mass Ratio 7.471

9.9 m24 m

49.7 m

LH2 TankLOX Tank

Payload Bay (9.1 m dia. x 3.66 m)

Main LOX/LH2Engines (5)

He Pressurant Spheres (4)Aft OMS/RCSTanks (LOX/LH2/He)

Forward RCS Tanks(LOX/LH2/He)

OMS Engines (2)

jro/1.97

Figure 5: SSTO All Rocket Vehicle

The second concept, an advanced launch vehiclenamed Hyperion, is currently being investigated bystudents in the SSDL at Georgia Tech. This concept,shown in Figure 6, represents a RLV with horizontaltake-off and horizontal landing (HTHL). The

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propulsion system of this vehicle consists of fiveLOX/LH2 ejector scramjet (ESJ) rocket-basedcombined–cycle (RBCC) engines.8

The technology readiness level (TRL) for theHyperion vehicle was much lower than the all rocketvehicle mainly because of the use of RBCC engines.This resulted in higher complexity factors forHyperion compared to those used for the other vehicle.Since Hyperion utilizes a horizontal take-off, largerlanding gear, wings, and tail were required. Thesefactors resulted in an overall heavier dry weight forHyperion.

RESULTS

Using Crystal Ball, a Monte Carlo simulation of5000 trails was run for each vehicle with the pre-defined assumptions. The results show that the modelwas more sensitive to changes in the marketparameters than to changes in the weights. As Figure7 and Figure 8 show, the highest correlation existedbetween the economic indicators, in this case NPV,and the commercial cargo market.

These charts show that market volatility exertedgreater influence over the financial outcome of the

project compared to fluctuations in weight parameters.Specifically, changes in the demand for the commercialcargo market had the greatest impact upon theeconomic viability of an advanced space launch vehicleprogram under the parameters set forth in this analysis.This was a common result for both vehicles, howeverthe results for weight parameters differ betweenHyperion and the all-rocket vehicle.

For the weight parameters, the resultscorresponded with the weight breakdowns for thevehicles in terms of significance. For Hyperion, thebody, wings, landing gear, and main propulsion

Nose Gear

Film Cooled Nozzle

70.1 m

Axisymmetric Forebody

13.4 m

Ducted Fans (2 LH2)

Ejector Scramjet RBCC Engines (5 LOX/LH2) ( 240,200 N Thrust ea.)

33.5 m

Sunroof-style Payload Bay Door(Payload bay - 9.6 m x 4.9 m x 4.9 m)

RMS Bay

OMS Engines

SHARP Leading Edgeand Nosecap TPS

Vehicle Characteristics:

Gross Weight 1,729,800 lb.Dry Weight 272,900 lb.Payload 44,000 lb.Mass Ratio: 4.95

Figure 6: Hyperion Vehicle

Target Forecast: NPV

Commercial Cargo 71.4%

Body Group 11.2%

Government Cargo 5.3%

Wing Group 3.9%

Main Propulsion(less cowl) 3.4%

Landing Gear 3.2%

Commercial Passengers 0.5%

Tail Group 0.5%

Government Passengers 0.1%

TPS Group 0.1%

Surface Control Actuation 0.1%

OMS Propulsion 0.1%

Environmental Control 0.0%

RCS Propulsion 0.0%

Electrical Conversion & Dist. 0.0%

Primary Power 0.0%

Avionics 0.0%

0% 25% 50% 75% 100%

Measured by Contribution to Variance

Sensitivity Chart

Figure 7: Sensitivity Chart for Hyper ion

Target Forecast: NPV

Commercial Cargo 66.7%

Body Group 20.0%

Main Propulsion 5.9%

Government Cargo 5.2%

OMS Propulsion 0.6%

TPS Group 0.4%

Government Passengers 0.3%

Wing Group 0.3%

Commercial Passengers 0.2%

Tail Group 0.1%

Landing Gear 0.1%

RCS Propulsion 0.1%

Electrical Conversion & Dist. 0.1%

Avionics 0.0%

Surface Control Actuation 0.0%

Primary Power 0.0%

Environmental Control 0.0%

0 % 2 5 % 5 0 % 7 5 % 1 0 0 %Measured by Contribution to Variance

Sensitivity Chart

Figure 8: Sensitivity Chart for RocketVehicle

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system were the most significant in terms of weightrequirement. From this information, the economicvalidity of utilizing horizontal take-offs might bequestioned due to the need for heavier components thatresult from this feature.

For the rocket vehicle, the body and the mainpropulsion system were the most significant.Therefore, designers could infer from these findingsthat changes in the weight of the body group wouldhave a significant impact upon the financial outlook ofthe design. Conversely, improvements in the weightsof avionics, surface control actuation, primary power,and environmental control would have minimal impactupon the profitability of the overall program.

The results for the two vehicles broken down byeconomic indicators, NPV and IRR, are shown inFigure 9. The charts depict the frequency distributionsfor each vehicle, with the corresponding statisticslisted below each of the charts. The statisticshighlight the important findings from each of thesimulation runs.

The NPV showed a variability of +-50% of themean value for both vehicles. The rocket vehicle had aslightly higher average than Hyperion and a slightlylower standard deviation. Based upon these findings,the rocket vehicle would be a superior investmentbecause of the higher return coupled with the lowerrisk value. However, the difference in return betweenthese two vehicles was marginal. The simulation runsfor the forecast value IRR resulted in the exact samestandard deviation for both vehicles. As a percentage ofthe mean value, the standard deviation wasapproximately 6% for both simulations. Thesestatistics show that by varying the weight and marketparameters by the values defined previously results insignificant volatility in the financial outcome of theproject.

Reward-to-Variability Ratio

In performing a financial analysis of a project, itis imperative that the reward be taken in context withthe amount of risk assumed. The Sharpe ratio is aneconomic indicator that combines both factors into a

single metric. Introduced in 1966 by ProfessorWilliam Sharpe of Stanford University, the Sharperatio was intended to measure the performance ofmutual funds. It has gained considerable popularity inthe financial community as a metric for comparingdifferent investments. As shown in equation 4, toarrive at the Sharpe ratio, the risk-free rate, rrf, issubtracted from the average return of the project, whichis then divided by the standard deviation of the return,σ(x).9

SR(x)r x r

x

rf= ( ) −( )σ (4)

For illustration purposes, the Sharpe ratio of aportfolio held from 1954 to 1994 containing sharesfrom all stocks with a market capitalization over $150million was 43.10 From the analysis, the Sharpe ratiowas calculated for Hyperion as a somewhatdisappointing 7.2 and for the all rocket SSTO vehicleas 7.3 using a risk-free rate of 5.27% as shown inTable 3.11 The risk free rate was derived from thecurrent yield on 30 year government bonds. In termsof the Sharpe ratio, higher numbers indicate betterrisk-adjusted returns.

Table 3: Values Used in Sharpe Calculation

SR(x)Hyperion 5.27% 9.65% 0.61% 7.2

Rocket 5.27% 9.75% 0.61% 7.3

σr x( )rrf

The 30 year government bond yield was chosenbecause it contains no default risk and matches theterm in years of the launch vehicle program. It mightbe argued that a shorter term government securitywould eliminate interest rate risk, which should not beincluded in the calculation of the Sharpe ratio for thistype of analysis. However, short-term governmentsecurities do not reflect expected long run changes ininflation. Therefore, there is a trade-off in using eitherrate, but the overall implications to the value obtainedfrom the Sharpe ratio calculation are marginal.

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Frequency Chart

millions

.000

.006

.012

.018

.025

0

30.7

61.5

92.2

1 2 3

2,500.00 3,375.00 4,250.00 5,125.00 6,000.00

5,000 Trials 23 OutliersForecast: NPV

Hyperion Rocket

Statistics: ValueTrials 5 0 0 0Mean 4,231.28Median 4,220.15Mode - - -Standard Deviation 653.06Variance 426,488.36Skewness 0.05Kurtosis 2 .74Coeff. of Variability 0 .15Range Minimum 1,657.69Range Maximum 6,279.83Range Width 4,622.14Mean Std. Error 9 .24

Frequency Chart

Percent

.000

.006

.013

.019

.025

0

31.5

6 3

94.5

1 2 6

8.00 8.88 9.75 10.62 11.50

5,000 Trials 25 OutliersForecast: IRR

Statistics: ValueTrials 5 0 0 0Mean 9.65Median 9.67Mode - - -Standard Deviation 0 .61Variance 0.37Skewness - 0 . 1 7Kurtosis 2 .90Coeff. of Variability 0 .06Range Minimum 6.85Range Maximum 11.38Range Width 4 .53Mean Std. Error 0 .01

Frequency Chart

millions

.000

.007

.014

.021

.028

0

34.7

69.5

1 0 4

1 3 9

2,500.00 3,375.00 4,250.00 5,125.00 6,000.00

5,000 Trials 15 OutliersForecast: NPV

Statistics: ValueTrials 5 0 0 0Mean 4,282.63Median 4,271.14Mode - - -Standard Deviation 635.96Variance 404,440.04Skewness 0.06Kurtosis 2 .74Coeff. of Variability 0 .15Range Minimum 2,123.13Range Maximum 6,344.48Range Width 4,221.35Mean Std. Error 8 .99

Frequency Chart

Percent

.000

.007

.013

.020

.027

0

33.5

6 7

1 0 0

1 3 4

8.00 8.88 9.75 10.62 11.50

5,000 Trials 16 OutliersForecast: IRR

Statistics: ValueTrials 5 0 0 0Mean 9.75Median 9.76Mode - - -Standard Deviation 0 .61Variance 0.38Skewness - 0 . 1 7Kurtosis 2 .84Coeff. of Variability 0 .06Range Minimum 7.39Range Maximum 11.51Range Width 4 .12Mean Std. Error 0 .01

Figure 9: Comparison of Results for Both Vehicles

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In this analysis, the results of using the Sharperatio only quantify the risk associated with marketvolatility and variances in the weight parameters of thedifferent components. Many other factors create riskin this type of project that might adversely orpositively affect the financial viability for an advancedspace launch program. Therefore, the identification ofthe Sharpe ratio obtained by a stock portfolio in aprevious paragraph was not meant as a comparison tothe results obtained from the two vehicles, but ratherto provide an illustration of the numeric valuesexpected.

DISCUSSION

In the analysis section, the Sharpe ratio wasintroduced as a metric that might be used for thefinancial analysis of advanced space launch vehicleprograms during the conceptual design phase. Thisratio was originally developed for the sole purpose ofevaluating mutual funds based upon past performance.Experts in the field might question the validity ofusing this ratio for the purposes outlined in this paper.It has been suggested that derivatives of the equationmight be preferable for this type of evaluation.

A possible alternative for equation 4 would be toeliminate the use of the risk free rate, thereby dividingthe average return by the standard deviation. Thiswould result in values of approximately 16 for the twovehicles analyzed in this paper. It has also beensuggested that average return should be divided by thestandard deviation squared. This would raise the valueto approximately 26 for Hyperion and the rocketvehicle. These two derivative equations wouldsimplify the process for the conceptual designer aswell as eliminate the controversy associated withdetermining an appropriate value for the risk free rate.

If the relationship between the total economic riskof the project and the risk associated with the twofactors considered in this paper (i.e. component weightand market variability) was known, then a scale factorcould be applied to the ratio. This would provide aresult that could be used in a comparative environmentwith other launch programs as well as otherinvestment projects.

CONCLUSIONS

The goal of this research was to investigate theeffects of uncertainties associated with weight andmarket parameters in determining the economicviability of advanced space launch vehicles. Marketsensitivity and weight-based cost estimatingrelationships are key drivers in determining thefinancial viability of a project. The expecteduncertainty associated with these two factors drives theeconomic risk of the overall program. Monte Carlosimulation techniques were incorporated into theanalysis to determine the sensitivity of the model tochanges in market and weight parameters. From this,the risk generated by the variability of these twoparameters was quantified.

From the findings of the Monte Carlosimulations, it may be concluded that the volatility ofthe market will play an integral role in the viability ofcommercial advanced space flight vehicle programs.These findings emphasize the importance of the needfor accurate market demand forecasts. For weightparameters, the results suggest that certain componentgroups, depending on the vehicle type, dominate othersin terms of significance to the overall economicviability of a launch program. From this, it may beconcluded that improving the accuracy of the estimatesof weight for certain component groups will minimizethe risk associated with weight estimations.

In addition to these findings, a metric wasintroduced which would quantify the risk as it relatesto the return of the project. This provides designerswith a basis from which to work in identifying thevalue of different factors that may affect the financialoutcome of an advanced space flight program. In termsof weight estimations, by improving the confidencelevel of the predictions made about the weights ofspecific components, the Sharpe ratio may be increasedfor the whole program, thereby improving thefinancial viability of the design. Utilizing CABAMand Crystal Ball, further investigations may be madeinto other factors that create uncertainty in thefinancial outlook of space launch vehicles.

From the analysis, it was determined that the all-rocket SSTO vehicle was a slightly better investmentdue to the higher Sharpe ratio. In terms of IRR, both

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vehicles displayed the same risk value for weight andmarket parameters as a whole, however the rocketvehicle had a slightly higher return. Since the analysiswas performed at a conceptual design stage, thedifference in the financial viability was marginal andshould not be a determinant in choosing between thetwo vehicles at this stage of development. It shouldalso be noted that the analysis was performed basedupon subjective assessments of weight variability andmarket volatility (Tables 2 and 3). With thoseassumptions and the CSTS launch marketassumptions also used, neither vehicle results in aparticularly attractive economic scenario for potentialinvestors.

FUTURE WORK

Future work for this research may include theinvestigation of other factors that might affect theeconomic viability of a launch program. This wouldinclude not only items directly related to the design ofa vehicle, but also economic factors and governmentincentive programs that could have far reachingimplications for the advancement of space flight.

Other possible areas of interest for this type ofinvestigation might include the analysis of targetedmarketing efforts. Certain areas of the market mayprovide a higher level of stability for commerciallaunch service providers, but at what cost to return?For example, if a launch service concentrated solely onthe government passenger market, the risk would besignificantly reduced, however the return might beconsiderably lower, thus resulting in an overall lowerquality project in terms of financial viability.

An expansion upon the use of the Sharpe ratio indetermining the economic performance of advancedspace launch vehicle programs might be another areaof consideration for investigation. The intention herewould be to try to incorporate and quantify the totalrisk of the program, thereby providing a metric for usein the comparison of alternative launch programs.

CABAM will continue to be improved byexpanding upon the modules within the model and byadding new components to the overall structure.

ACKNOWLEDGEMENTS

The authors would like to thank the members ofthe Georgia Institute of Technology Space SystemsDesign Laboratory for their support. John Bradford,Laura Ledsinger, David McCormick, Jeff Scott, andJeff Whitfield generated design data and graphics for thevehicle Hyperion. David Way, John Bradford, LauraLedsinger, David McCormick, Jeff Scott, and JeffWhitfield generated design data and graphics for the all-rocket SSTO vehicle.

The authors would also like to thank Eric Shaw ofNASA’s Marshall Space Flight Center (MSFC) forhis support in providing insight into the economics ofRLVs and methodologies used for business simulationanalysis.

This work was sponsored by NASA - MarshallSpace Flight Center, Engineering Cost Office undercontract NAG8-1417.

REFERENCES

1. "Parametric Cost Estimating Handbook JointGovernment/Industry Initiative," Department ofDefense, Fall 1995.

2. “Commercial Space Transportation Study (CSTS)– Executive Summary,” NASA–Langley ResearchCenter, Hampton, VA, April 1994.

3. Lee, H., and Olds, J. R. “Integration of CostModeling and Business Simulation intoConceptual Launch Vehicle Design,” AIAA 97-3911, 1997 AIAA Defense and Space ProgramsConference & Exhibit, Huntsville, AL,September 23-25, 1997.

4. “The Marshall Space Flight Center’s NASA CostModel (NASCOM) Database Version 2.0:Volume 1, Executive Summary,” ARI/92-R-009,Applied Research, Inc., January 1993.

5. “Crystal Ball Version 4.0 User Manual,"Decisioneering, Inc., 1996.

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6. Boardman, A. E., Greenberg, D. H., Vining, A.R., Weimer, D. L., “Cost-Benefit Analysis:Concepts and Practice,” Prentice Hall, Inc., UpperSaddle River, NJ, 1996

7. Olds, J. R. and Steadman, K. B., “Cross-PlatformComputational Techniques for Analysis CodeIntegration and Optimization,” AIAA 98-4743,Symposium on Multidisciplinary Analysis andOptimization, St. Louis, MO, September 2-4,1998.

8. Olds, J. R. and Bradford, J., “SCCREAM(Simulated Combined-Cycle Rocket EngineAnalysis Module): A Conceptual RBCC EngineDesign Tool,” AIAA 97-2760, 33rd

AIAA/ASME/SAE/ASEE Joint PropulsionConference & Exhibit, Seattle, WA, July 6-9,1997.

9. Sharpe, W. F., “The Sharpe Ratio,” The Journalof Portfolio Management, Fall 1994.

10. O’Shaugnessy, J. P., “What Works on WallStreet, A Guide to the Best-PerformingInvestment Strategy of All Time,” McGraw-Hill,New York, NY, 1997.

11. “Investment Figures of the Week,” BusinessWeek, McGraw-Hill, September 21, 1998, 145.