1. 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

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

3. 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.

4. 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

5. 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. 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)

7. 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

8. 6.2.2 Normal Distribution

9. 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

10. 6.2.3 Log-Normal Distribution

11. 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

12. 6.2.4 Uniform Distribution

13. 6.2.5 Binomial Distribution
Two possible outcomes with fixed probabilities that sum to 1
Range: 0 to N

14. 6.2.5 Binomial Distribution

15. 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.

16. 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

17. 6.4 Application to a Pro Forma CF and NPV
See class example.

18. 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)