FIN 614: Financial Management Larry Schrenk, Instructor

1.What is Monte Carlo Simulation? 2.Monte Carlo Simulation Example 3.Issues in Monte Carlo Simulation

Computerized version of scenario analysis using continuous probability distributions. Values randomly selected for each variable based on probability distributions. Output is a probability distribution for NPV with probability of obtaining a positive NPV The simulation only works as well as the information that is entered

Pick a random variable for unit sales Substitute these values in the spreadsheet and calculate NPV Repeat the process many times, saving the input variable and the output (NPV)

Zvi Wiener

1. Construct a model of cash flows and NPV’s 2. Specify a probability distribution for the uncertain variable 3. Computer selects random draw form the distribution for each variable 4. Calculate NPV 5. Repeat 3) and 4) 10,000 or 100,000 times 6. Calculate expected NPV and standard deviation.

New Game Project Investment $1,000,000 Annual Fixed Cost $500,000 Variable Cost $10/unit Revenue$100/unit Time Horizon 3 years Initial Sales10,000 units Annual Sales Growth10% Discount Rate8% Monte Carlo Simulation Initial Sales Distribution Normal Distribution Mean = 10,000 Standard Deviation = 5,000

1,000 Random Numbers ~N(10,000, 5,000) Non-Negative Constraint Average NPV = $295,345

One Variable Easy in Excel Multiple Variables Must specify correlations or assume independence (questionable)

Reflects the probability distributions of each input Shows range of NPVs, the expected NPV, σ NPV Gives an intuitive graph of the risk situation

More realistic selection of variables Shows the results of many possiblities Indicates how likelihood any particular outcome Considers the interrelations between variables

Computationally expensive Difficult to specify probability distributions and correlations Simulation results are experiment-specific Only as good as probability estimate Models need to be continually updated

Sensitivity, scenario, and simulation analyses do not provide a decision rule. They do not indicate whether a project’s expected return is sufficient to compensate for its risk. Sensitivity, scenario, and simulation analyses all ignore diversification. Thus they measure only stand-alone risk, which may not be the most relevant risk in capital budgeting.

FIN 614: Financial Management Larry Schrenk, Instructor