Discounted cash flow modeling
See also: Insurance and finance risk analysis modeling introduction, Time series modeling in finance, Aggregate distributions introduction, Modeling with objects
First have a look at the following diagram:
A typical discounted cashflow model for a potential investment makes forecasts of costs and revenues over the life of the project and discounts those revenues back to a present value. Most analysts start with a 'base case' model and add uncertainty to the important elements of the model. Happily, the mathematics involved in adding risk to these types of models is quite simple. In this topic we assume that you can build a base case cashflow model that will look something like the example model shown below. We will then focus on the input modelling elements and some financial outputs.
Example model NPV of a capital investment (tab Static model)  a typical, if somewhat reduced, cash flow model.
There are a number of relevant topics that are covered in other parts of this help file. Please make sure you have a good understanding of these first:
In capital investment models we rely a great deal on expert judgement to estimate variables like costs, time to market, sales volumes, discount levels
We don't usually have a great deal of historic data to work with in capital investment projects because the investment is new. I have worked with a very successful retail company that investigates levels of pedestrian traffic at different locations in a town where it is considering locating a new outlet. It has excellent regional data on how that traffic converts to till receipts. That is quite typical of the type of data one might have for a cashflow analysis and we will go through such a model later in this topic. Hydrocarbon and mineral exploration will generally have improving levels of data about the reserves, but have specialised methods for statistically analyzing (e.g. Krieging) their data, so I won't consider them further here.
Simple forms of correlation modelling  recognizing that two or more variables are likely to be linked in some way  are very important in cashflow models.
The time series topics deal with many different technical time series models. GBM, seasonal and autoregressive models are useful for modelling inflation, exchange and interest rates over time in a cashflow model. Lead indicators can help predict market size a short time into the future. In this topic consider variables like demand for products and sales volumes which are generally built on a more intuitive basis.
Common errors in risk modeling
Risk analysis cashflow models are not generally that technically complicated, but our reviews show that the types of errors described under Common errors in risk modeling appear very frequently, so we encourage you to read that section carefully. The rest of this topic offers some ideas on model building that are very applicable to cashflow models.
Useful time series models of sales and market size
Effect of an intervention at some uncertain point in time
Time series variables are often affected by single identifiable 'shocks', like elections, changes to a law, introduction of a competitor, start or finish of a war, a scandal, etc. The modelling of the occurrence of a shock and its effects may need to take into account several elements:

When the shock may occur (this could be random);

Whether this changes the probability or impact of other possible shocks;

The effect of the shock: magnitude and duration
Consider the following problem: People are purchasing your product at a current rate of 88/month, and the rate appears to be increasing by 1.3 sales/month with each month. However, we are 80% sure that a competitor is going to enter the market and will do so between 20 and 50 months from now. If the competitor enters the market they will take about 30% of your sales. Forecast the number of sales there will be for the next 100 months.
Possible pathways generated by the model depending on whether the competitor enters the market
The model for this problem is shown in the figure above . The Bernoulli variable returns a 1 with 80% probability, otherwise a 0. It is used as a 'flag', the 1 representing a competitor entry, the 0 representing no competitor. Other cells use conditional logic to adapt to the scenario.
The StepUniform generates integer values between 20 and 50, and cell E4 returns the month 1000 if the competitor does not enter the market i.e. a time beyond the modelled period. It is a good idea if you use this type of technique to make such a number very far from the range of the modelled period in case someone decided to extend the period analyzed. A Poisson distribution is used to model the number of sales reflecting that the sales are independent of each other and randomly distributed in time. The nice thing about a Poisson distribution is that it takes just one parameter  its mean, so you don't have to think about variation about that mean separately (e.g. determine a standard deviation).
Example model Poisson_sales_with_competitor  Poisson sales affected by the possible entry of a competitor
Distributing market share
When competitors enter an established market they have to establish the reputation of their product and fight for market share with others that are already established. This takes time, so it is more realistic to model a gradual loss of market share to competitors.
Consider the following problem: Market volume for your product is expected to grow each year by (10%, 20%, 40%) beginning next year at (2500, 3000, 5000) up to a maximum of 20,000 units. You expect one competitor to emerge as soon as the market volume reaches 3,500 units in the previous year. A second would appear at 8,500 units. Your competitors' shares of the market would grow linearly until you all have equal market share after three years. Model the sales you will make.
Example model New_competitors  sales where the total market is divided with new entry competitors
The figure above shows the model. It is mostly selfexplanatory. The interesting component lies in Cells F10:L10 which divides the forecast market for your product among the average of the number of competitors over the last three years and yourself (the '1' in the equation). Averaging over three years is a neat way of allocating an emerging competitor 1/3 of your market strength in the first year, 2/3 in the second and equal strength from the third year on  meaning that they will then sell as many units as you. What is so helpful about this little trick is that it automatically takes into account each new competitor and when they entered the market, which is rather difficult to do otherwise. Note that we need three zeros in cells C8:E8 to initialise the model.
Reduced sales over time to a finite market
Some products are essentially a once in a lifetime purchase, e.g. a life insurance, big flat screen TV, a new guttering system and a pet identification chip. If we are initially quite successful in selling the product into the potential market, the remaining market size decreases although this can be compensated to some degree by new potential consumers. Consider the following problem: There are currently PERT(50000,55000,60000) possible purchasers of your product. Each year there will be about a 10% turnover (meaning 10% more possible purchasers will appear). The probability that you will sell to any particular purchaser in a year is PERT(10%,20%,35%). Forecast sales for the next 10 years.
Example model Finite_market  forecasting sales over time to a finite market
The figure above shows the model for this problem. Note that C8:C16 is subtracting sales already made from the previous year's market size but also adding in a regenerated market element. The Binomial distribution then converts the current market size to sales. In the particular scenario shown in the figure the probability of selling is high (26%) so sales start off high and drop off quickly since the regeneration rate is so much lower (10%). Note that some Monte Carlo software cannot handle large numbers of trials in their Binomial distribution in which case you will need to use a Poisson or Normal approximation.
Growth of sales over time up to a maximum as a function of marketing effort
Sometimes we might find it easier to estimate what our annual sales will be when stabilized, but be unsure of how quickly we will be able to achieve that stability. In this sort of situation it can be easier to model a theoretical maximum sales and match it to some ramping function. A typical form of such a ramping function r(t) is:
which will produce a curve that starts at 0 for t = 0 and asymptotically reaches 1 at an infinite value of t, but reaches 0.5 at . Consider the following problem: you expect a final sales rate of PERT(1800,2300,3600) and expect to achieve half that in the next PERT(3.5,4,5) years. Produce a sales forecast for the next 10 years.
The example model below provides a solution:
Example model Sales_with_maximum  forecasting ramping sales to an uncertain theoretical maximum
Summing random variables
Perhaps the most common errors in cashflow modelling occur when one wishes to sum a number of random costs, sales or revenues. For example, imagine that you expect to have Lognormal(100 000, 25 000) customers enter your store per year and they will spend $Lognormal(55, 12) each  how would you estimate the total revenue? People generally write something like:
= ROUND(Lognormal(100 000, 25 000),0) * $Lognormal(55, 12) (equation 1)
using the ROUND function in Excel to recognise that the number of people must be discrete. But let's think what happens when the software starts simulating. It will pick a random value from each distribution and multiply them together. Picking a reasonably high till receipt, the probability that a random customer will spend more than $70, for example, is:
=1VoseLognormalProb(70,55,12,1) = 0.11%
The probability that two people will do the same is 11% * 11% = 1.2%, and the probability that thousands of people will spend that much is infinitesimally small. However, Equation 1 will assign a 11% probability that all customers will spend over $70 no matter how many there are. The equation is wrong because it should have summed ROUND(Lognormal(100 000, 25 000),0) separate Lognormal(55, 12) distributions. That's a big, slow model so we use a variety of techniques to shortcut to the answer, which is the topic of aggregate modeling.
Summing variable margins on variable revenues
A common situation is that we have a large random number of revenue items that follow the same probability distribution but which are independent of each other, and we have independent profit margins that follow another distribution that must be applied to each revenue item. This type of model quickly becomes extremely cumbersome to model because for each revenue item we need two distributions: one for revenue and another for the profit margin and we may have many types of large numbers of revenue items. It is such a common problem that we designed a function in ModelRisk to handle this, allowing you to keep the model to a manageable size, speeding up simulation time, and making the model far simpler to review. Perhaps most importantly, it allows you to avoid a lot of conditional logic that is easy to get wrong. Consider the following problem: a capital venture company is considering investing in a company that makes TV shows. They expect to make PERT(28,32,39) pilots next year which will generate revenues of $PERT(120,150,250)k each independently and from which the profit margin is PERT(1%,5%,12%). There is a 30% chance that each pilot is made into a TV series run in that country running for Discrete({1,2,3,4,5},{0.4,0.25,0.2,0.1,0.05}) series, where each season of each series generates $PERT(120,150,250)k with margins of PERT(15%,25%,45%). There is a 20% chance that these local series would be sold to the US generating $PERT(240,255,1350) per season sold of which the profit margin is PERT(65%,70%,85%). What is the total profit generated from next year's pilots?
Example model TV_series_profits  forecasting profits from a TV series
The problem is not technically difficult but the scale of the modelling explodes very quickly. We worked on the model for a real investment of this type and it had many more layers: pilots in several countries, merchandising of various types, repeats, etc. and it took a lot of effort to manage. The figure shows how using objects for modeling allows us a surprisingly succinct model: rows 2 to 12 are the input data, rows 14 to 16 are the actual calculations.
There are a few things to point out. In Cell F2, ½ is subtracted and added to the minimum and maximum estimates respectively of the number of pilots to give a more realistic chance of their occurrence after rounding. Distributions are input as ModelRisk objects in cells F3, F4, F6, F7, F8, F10 and F11 because we want to use these distributions many times. Cell C16 and elsewhere uses the VoseSumProduct function to add together revenue * margin for each pilot where the revenue and margin distributions are defined by the distribution Objects in Cells F3 and F4 respectively. Cell F14 simulates the number of pilots that made it to become series, from which the model determines how many of those become series also sold into the US in Cell E14, the difference being the number of pilots that only became local series in Cell D14. Setting up the logic this ways ensures that we have a consistent model: the local only and US & local series always add up to the total series produced. Cells D15 and E15 use the VoseAggregateMC(x, y) function to simulate the sum of x random variables all taking the same distribution y defined as an Object.
Financial measures in risk analysis
The two main measures of profitability in DCF models are net present value (NPV) and internal rate of return (IRR). The two main measures of financial exposure are VAR and expected shortfall. Their pros and cons are discussed below.
Net Present Value
Net Present Value (NPV) attempts to determine the present value of a series of cashflows from a project that stretches out into the future. This present value is a measure of how much the company is gaining at today's money by undertaking the project: in other words, how much more the company itself will be worth by accepting the project.
An NPV calculation discounts future cashflows at a specified discount rate r that takes account of:

the time value of money (e.g. if inflation is running at 4%, £1.04 in a year's time is only worth £1.00 today);

the interest that could have been earned over inflation by investing instead in a guaranteed investment;

the extra return that is required over (1) and (2) to compensate for the degree of risk that is being accepted in this project;
Parts (1) and (2) are combined to produce the risk free interest rate, r_{f}. This is typically determined as the interest paid by guaranteed fixed payment investments like government bonds with a term roughly equivalent to the duration of the project.
The extra interest r^{*} over r_{f} needed for (3) is determined by looking at the uncertainty of the project. In risk analysis models, this uncertainty is represented by the spread of the distributions of cashflow for each period. The sum of r^{*} and r_{f} is called the riskadjusted discount rate r.
The most commonly used calculation for the NPV of a cashflow series over n periods is as follows:
where are the expected (i.e. average) values of the cashflows in each period and r is the riskadjusted discount rate.
NPV calculations performed in a risk analysis spreadsheet model are usually presented as a distribution of NPVs because the cashflow values selected in the NPV calculations are their distributions rather than their expected values. Theoretically, this is incorrect. Since an NPV is the net present value, it can have no uncertainty. It is the amount of money that the company values the project at today. The problem is that we have double counted our risk by first discounting at the riskadjusted discounted rate r and then showing the NPV as a distribution (i.e. it is uncertain).
Two theoretically correct methods for calculating an NPV in risk analysis are discussed below, along with a more practical, but strictly speaking incorrect, alternative:
Theoretical approach 1: Discount the cashflow distributions at the risk free rate.
This produces a distribution of NPVs at r_{f} and ensures that the risk is not doublecounted. However, such a distribution is not at all easy to interpret since decision makers will almost certainly never have dealt with risk free rate NPVs and therefore have nothing to compare the model output against.
Theoretical approach 2: Discount the expected value of each cashflow at the riskadjusted discount rate.
This is the application of the above formula. It results in a single figure for the NPV of the project. A risk analysis is run to determine the expected value and spread of the cashflows in each period. The discount rate is usually determined by comparing the riskiness associated with the project's cashflows against the riskiness of other projects in the company's portfolio. The company can then assign a discount rate above or below its usual discount rate depending on whether the project being analyzedexhibits more or less risk than the average. Some companies determine a range of discount rates (three or so) to be used against projects of different riskiness.
The major problems of this method are that it assumes the cashflow distributions are symmetric and that no correlation exists between cashflows. Distributions of costs and returns almost always exhibit some form of asymmetry and in a typical investment project there is also always some form of correlation between cashflow periods: for example, sales in one period will be affected by previous sales, a capital injection in one period often means that it doesn't occur in the next one (e.g. expansion of a factory) or the model may include a time series forecast of prices, production rates or sales volume that are autocorrelated. If there is a strong positive correlation between cashflows, this method will overestimate the NPV. Conversely, a strong negative correlation between cashflows will result in the NPV being underestimated. The correlation between cashflows may take any number of, often complex, forms. Financial theory does not offer a practical method for adjusting the NPV to take account of these correlations.
In practice, it is easier to apply the riskadjusted discount rate r to the cashflow distributions to produce a distribution of NPVs. This method incorporates correlation between distributions automatically and enables the decision maker to compare directly with past NPV analyses.
As I have already explained, the problem associated with this technique is that it will double count the risk: firstly in the discount rate and then by representing the NPV as a distribution. However, if one is aware of this shortfall, the result is very useful in determining the probability of achieving the required discount rate (i.e. the probability of a positive NPV). The actual NPV to quote in a report would be the expected value of the NPV distribution.
Internal Rate of Return
The Internal Rate of Return (IRR) of a project is the discount rate applied to its future cashflows such that it produces a zero NPV. In other words, it is the discount rate that exactly balances the value of all costs and revenues of the project. If the cashflows are uncertain, the IRR will also be uncertain and therefore have a distribution associated with it.
A distribution of the possible IRRs is useful to determine the probability of achieving any specific discount rate and this can be compared with the probability other projects offer of achieving the target discount rate. It is not recommended that the distribution and associated statistics of possible IRRs be used for comparing projects because of the following properties of IRRs:
· Unlike the NPV calculation, there is no exact formula for calculating the IRR of a cashflow series. Instead, a first guess is usually required, from which the computer will make progressively more accurate estimates until it finds a value that produces an NPV as near to zero as required.
· If the cumulative cashflow position of the project passes through zero more than once, there is more than one valid solution to the IRR inequality. This is not normally a problem with deterministic models because the cumulative cashflow position can easily be monitored and the smallest of any IRR solutions selected. However, a risk analysis model is dynamic, making it difficult to appreciate its exact behaviour. Thus, the cumulative cashflow position may pass through zero and back in some of the risk analysis iterations and not be spotted. This can produce quite inaccurate distributions of possible IRRs. In order to avoid this problem, it may be worth including a couple of lines in your model that calculate the cumulative cashflow position and the number of times it passes through zero. If this is selected as a model output, you will be able to determine whether this is a statistically significant problem and alter the first guess to compensate for it.
· IRRs cannot be calculated for only positive or only negative cashflows. IRRs are therefore not useful for comparing between two purely negative or positive cashflow options, e.g. between hiring or buying a piece of equipment.
· It is difficult to compare distributions of IRR between two options unless the difference is very large. This is because a percentage increase in an IRR at low returns (e.g. from 3% to 4%) is of much greater real value than a percentage increase at high returns (e.g. from 30% to 31%). It is therefore very difficult to compare the value of two projects in terms of the IRR distributions they offer. One project may offer a long righthand tail that can easily increase the expected IRR but in real value terms this could easily be outweighed by a comparatively small diminishing of the lefthand tail of the other option.
An example of the nonlinear relationship between IRR and real (or present) value.
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 VoseCLTSum
 VoseAggregateMoments
 VoseRawMoments
 VoseSkewness
 VoseMoments
 VoseKurtosis
 VoseAggregatePanjer
 VoseAggregateFFT
 VoseCombined
 VoseCopulaBiGumbel
 VoseCopulaBiClayton
 VoseCopulaBiNormal
 VoseCopulaBiT
 VoseKendallsTau
 VoseRiskEvent
 VoseCopulaBiFrank
 VoseCorrMatrix
 VoseRank
 VoseValidCorrmat
 VoseSpearman
 VoseCopulaData
 VoseCorrMatrixU
 VoseTimeSeasonalGBM
 VoseMarkovSample
 VoseMarkovMatrix
 VoseThielU
 VoseTimeEGARCH
 VoseTimeAPARCH
 VoseTimeARMA
 VoseTimeDeath
 VoseTimeAR1
 VoseTimeAR2
 VoseTimeARCH
 VoseTimeMA2
 VoseTimeGARCH
 VoseTimeGBMJDMR
 VoseTimePriceInflation
 VoseTimeGBMMR
 VoseTimeWageInflation
 VoseTimeLongTermInterestRate
 VoseTimeMA1
 VoseTimeGBM
 VoseTimeGBMJD
 VoseTimeShareYields
 VoseTimeYule
 VoseTimeShortTermInterestRate
 VoseDominance
 VoseLargest
 VoseSmallest
 VoseShift
 VoseStopSum
 VoseEigenValues
 VosePrincipleEsscher
 VoseAggregateMultiFFT
 VosePrincipleEV
 VoseCopulaMultiNormal
 VoseRunoff
 VosePrincipleRA
 VoseSumProduct
 VosePrincipleStdev
 VosePoissonLambda
 VoseBinomialP
 VosePBounds
 VoseAIC
 VoseHQIC
 VoseSIC
 VoseOgive1
 VoseFrequency
 VoseOgive2
 VoseNBootStdev
 VoseNBoot
 VoseSimulate
 VoseNBootPaired
 VoseAggregateMC
 VoseMean
 VoseStDev
 VoseAggregateMultiMoments
 VoseDeduct
 VoseExpression
 VoseLargestSet
 VoseKthSmallest
 VoseSmallestSet
 VoseKthLargest
 VoseNBootCofV
 VoseNBootPercentile
 VoseExtremeRange
 VoseNBootKurt
 VoseCopulaMultiClayton
 VoseNBootMean
 VoseTangentPortfolio
 VoseNBootVariance
 VoseNBootSkewness
 VoseIntegrate
 VoseInterpolate
 VoseCopulaMultiGumbel
 VoseCopulaMultiT
 VoseAggregateMultiMC
 VoseCopulaMultiFrank
 VoseTimeMultiMA1
 VoseTimeMultiMA2
 VoseTimeMultiGBM
 VoseTimeMultBEKK
 VoseAggregateDePril
 VoseTimeMultiAR1
 VoseTimeWilkie
 VoseTimeDividends
 VoseTimeMultiAR2
 VoseRuinFlag
 VoseRuinTime
 VoseDepletionShortfall
 VoseDepletion
 VoseDepletionFlag
 VoseDepletionTime
 VosejProduct
 VoseCholesky
 VoseTimeSimulate
 VoseNBootSeries
 VosejkProduct
 VoseRuinSeverity
 VoseRuin
 VosejkSum
 VoseTimeDividendsA
 VoseRuinNPV
 VoseTruncData
 VoseSample
 VoseIdentity
 VoseCopulaSimulate
 VoseSortA
 VoseFrequencyCumulA
 VoseAggregateDeduct
 VoseMeanExcessP
 VoseProb10
 VoseSpearmanU
 VoseSortD
 VoseFrequencyCumulD
 VoseRuinMaxSeverity
 VoseMeanExcessX
 VoseRawMoment3
 VosejSum
 VoseRawMoment4
 VoseNBootMoments
 VoseVariance
 VoseTimeShortTermInterestRateA
 VoseTimeLongTermInterestRateA
 VoseProb
 VoseDescription
 VoseCofV
 VoseAggregateProduct
 VoseEigenVectors
 VoseTimeWageInflationA
 VoseRawMoment1
 VosejSumInf
 VoseRawMoment2
 VoseShuffle
 VoseRollingStats
 VoseSplice
 VoseTSEmpiricalFit
 VoseTimeShareYieldsA
 VoseParameters
 VoseAggregateTranche
 VoseCovToCorr
 VoseCorrToCov
 VoseLLH
 VoseTimeSMEThreePoint
 VoseDataObject
 VoseCopulaDataSeries
 VoseDataRow
 VoseDataMin
 VoseDataMax
 VoseTimeSME2Perc
 VoseTimeSMEUniform
 VoseTimeSMESaturation
 VoseOutput
 VoseInput
 VoseTimeSMEPoisson
 VoseTimeBMAObject
 VoseBMAObject
 VoseBMAProb10
 VoseBMAProb
 VoseCopulaBMA
 VoseCopulaBMAObject
 VoseTimeEmpiricalFit
 VoseTimeBMA
 VoseBMA
 VoseSimKurtosis
 VoseOptConstraintMin
 VoseSimProbability
 VoseCurrentSample
 VoseCurrentSim
 VoseLibAssumption
 VoseLibReference
 VoseSimMoments
 VoseOptConstraintMax
 VoseSimMean
 VoseOptDecisionContinuous
 VoseOptRequirementEquals
 VoseOptRequirementMax
 VoseOptRequirementMin
 VoseOptTargetMinimize
 VoseOptConstraintEquals
 VoseSimVariance
 VoseSimSkewness
 VoseSimTable
 VoseSimCofV
 VoseSimPercentile
 VoseSimStDev
 VoseOptTargetValue
 VoseOptTargetMaximize
 VoseOptDecisionDiscrete
 VoseSimMSE
 VoseMin
 VoseMin
 VoseOptDecisionList
 VoseOptDecisionBoolean
 VoseOptRequirementBetween
 VoseOptConstraintBetween
 VoseSimMax
 VoseSimSemiVariance
 VoseSimSemiStdev
 VoseSimMeanDeviation
 VoseSimMin
 VoseSimCVARp
 VoseSimCVARx
 VoseSimCorrelation
 VoseSimCorrelationMatrix
 VoseOptConstraintString
 VoseOptCVARx
 VoseOptCVARp
 VoseOptPercentile
 VoseSimValue
 VoseSimStop
 Precision Control Functions
 VoseAggregateDiscrete
 VoseTimeMultiGARCH
 VoseTimeGBMVR
 VoseTimeGBMAJ
 VoseTimeGBMAJVR
 VoseSID
 Generalized Pareto Distribution (GPD)
 Generalized Pareto Distribution (GPD) Equations
 ThreePoint Estimate Distribution
 ThreePoint Estimate Distribution Equations
 VoseCalibrate
 ModelRisk interfaces
 Integrate
 Data Viewer
 Stochastic Dominance
 Library
 Correlation Matrix
 Portfolio Optimization Model
 Common elements of ModelRisk interfaces
 Risk Event
 Extreme Values
 Select Distribution
 Combined Distribution
 Aggregate Panjer
 Interpolate
 View Function
 Find Function
 Deduct
 Ogive
 AtRISK model converter
 Aggregate Multi FFT
 Stop Sum
 Crystal Ball model converter
 Aggregate Monte Carlo
 Splicing Distributions
 Subject Matter Expert (SME) Time Series Forecasts
 Aggregate Multivariate Monte Carlo
 Ordinary Differential Equation tool
 Aggregate FFT
 More on Conversion
 Multivariate Copula
 Bivariate Copula
 Univariate Time Series
 Modeling expert opinion in ModelRisk
 Multivariate Time Series
 Sum Product
 Aggregate DePril
 Aggregate Discrete
 Expert
 ModelRisk introduction
 Building and running a simple example model
 Distributions in ModelRisk
 List of all ModelRisk functions
 Custom applications and macros
 ModelRisk functions explained
 Tamara  project risk analysis
 Introduction to Tamara project risk analysis software
 Launching Tamara
 Importing a schedule
 Assigning uncertainty to the amount of work in the project
 Assigning uncertainty to productivity levels in the project
 Adding risk events to the project schedule
 Adding cost uncertainty to the project schedule
 Saving the Tamara model
 Running a Monte Carlo simulation in Tamara
 Reviewing the simulation results in Tamara
 Using Tamara results for cost and financial risk analysis
 Creating, updating and distributing a Tamara report
 Tips for creating a schedule model suitable for Monte Carlo simulation
 Random number generator and sampling algorithms used in Tamara
 Probability distributions used in Tamara
 Correlation with project schedule risk analysis
 Pelican  enterprise risk management
 ModelRisk Cloud system
 ModelRisk Cloud introduction
 Getting your software ready
 Starting ModelRisk Cloud
 Uploading a risk analysis model
 Creating a new scenario for the risk analysis model
 Running a Monte Carlo simulation of the model
 Uploading a SID (Simulation Imported Data file)
 Building a risk analysis model that uses SIDs
 Viewing the Monte Carlo results from a simulation run
 Administrator's use of ModelRisk Cloud
 Preparing a risk analysis model for upload to ModelRisk Cloud
 ModelRisk Result Viewer
Enterprise Risk Management software (ERM)
Learn more about our enterprise risk analysis management software tool, Pelican