6. Risk Analysis for the New Venture Using Monte Carlo Simulation 6.1 Introduction 6.2 Probability Distributions 6.2.1 Properties of Common Distributions 6.2.2 Normal 6.2.3 Log-Normal 6.2.4 Uniform 6.2.5 Binomial 6.2.6 Others

6. Risk Analysis for the New Venture Using Monte Carlo Simulation 6.3 Monte Carlo Simulation Software: @RISK 6.4 Application to a Pro Forma CF and NPV 6.5 Analysis: Tornado Diagram & Cumulative Distribution Function

6.1 Introduction Traditionally, analyses combine single point estimates of a model’s variables to predict a single result (as we’ve seen in BP proformas). MC uses simulation to combine most of the uncertainties in risk variables to predict outcomes (CF’s and valuation). Essentially you are performing many “what if” scenarios and assigning using formal methods, and recording the probability of each outcome Combine the range of outcomes to get a sense of the extreme possibilities and the chance that the outcome will be within a that range.

6.1 Introduction Develop a Model define how your results occur Identify Key Uncertainties choose the key risk drivers and specify possible values and probability distributions Analyze the Model with Simulation determine the range of probabilities of possible outcomes for your model Make a Decision MC is a decision tool for deciding on a course of action based on potential outcomes and chance of occurrences

6.2 Probability Distributions Function that assigns chance of occurrence to values of a random variable. Used in MC risk analysis to assign chances to differing possible outcomes, e.g., future CF’s and valuations for a NV.

6.2.1 Properties of Distributions Usually no more than 4 parameters describe the distribution: mean (location) variance (dispersion) skewness (symmetry) kurtosis (thickness of tails)

6.2.2 Normal Distribution Mean is the center Variance describes the shape (dispersion) Symmetric; and has no skewness (= 0) Has no kurtosis or thick tails (= 0) Range is negative to positive infinity

6.2.2 Normal Distribution

6.2.3 Log-Normal Distribution Is asymmetric Origin is at 0 Describes data that cannot be negative: revenues sales (e.g. electric usage) interest rates Range is 0 to + infinity

6.2.3 Log-Normal Distribution

6.2.4 Uniform Distribution Every value has an equal chance of occurring Has finite end-points Has no skewness (symmetric) Range: any two values A and B

6.2.4 Uniform Distribution

6.2.5 Binomial Distribution Two possible outcomes with fixed probabilities that sum to 1 Range: 0 to N

6.2.5 Binomial Distribution

6.2.6 Other Distributions There are hundreds of probability distributions. Some analysts are not concerned about probability distribution choice; too much risk in analysis makes such a choice moot If you can reasonably choose the distribution, then do so, otherwise choose the normal.

6.3 @RISK MC SOFTWARE @RISK (copyright) is Monte Carlo software from Palisades Corporation Not endorsed by Rutgers but is commonly used here at the SBC EXCEL spreadsheet environment: useful for building and simulating financial statements Supports 37 distributions Most widely used in practice

6.4 Application to a Pro Forma CF and NPV See class example.

6.5 Analysis: Tornado Diagram & Cumulative Distribution Function Tornado Diagram: Shows sensitivity of objective to the risk variables Cumulative Distribution Function: shows the probability distribution of objective (values and chances of occurrence)