1. Distributions Introduction to @Risk Prof. Luiz Brandão brandao@iag.puc-rio.br 2009

2. IAG PUC – Rio Brandão 2 Uniform RiskUniform (Min, Max)

3. IAG PUC – Rio Brandão 3 Triangular RiskTriang (Min, Probable, Max)

4. IAG PUC – Rio Brandão 4 Histogram RiskHistogrm (Min, Max, {p})

5. IAG PUC – Rio Brandão 5 Discrete RiskDiscrete ({x}, {p}), where {x} are the values the variable can assume and {p} are the respective probabilities.

6. IAG PUC – Rio Brandão 6 Normal Distribution RiskNormal (Mean, Standard Deviation)

7. PetroRio

8. IAG PUC – Rio Brandão 8 Modeling Layer Thickness

9. IAG PUC – Rio Brandão 9 Modeling Recovery Rate

10. IAG PUC – Rio Brandão 10 Modeling Area

11. IAG PUC – Rio Brandão 11 Results: Production

12. Electric Bike, Inc.

13. IAG PUC – Rio Brandão 13 Electric Bike Data: Market is one million units per year Market share is 10% Unit price is $3,750 Anual fixed costs are $30 million Unit variable costs are $3,000 Investment is 150 million Project life is 10 anos, tax rate is 50% WACC is 10% a.a. Electric Bike is considering manufacturing an electric motorcycle. Year 0Year 1 a 10 Investment(150.000) Revenue 375.000 Variable Costs(300.000) Fixed Costs(30.000) Depreciation(15.000) E.B.T.30.000 Tax(15.000) Net income15.000 + Depreciation15.000 Cash Flow(150.000)30.000

14. MSIS 383N University of Texas at Austin 14 Dealing with Uncertainty Even though the project has a positive NPV, the managers at Electric Bike are concerned about the uncertainty affecting some of the project variables. They are particularly concerned about possible variations in the expected market size, market share, price and also variable and fixed costs. They would like to know what would be the impact on the projects NPV of possible fluctuations of these variables. What is the risk of investing in this project

15. IAG PUC – Rio Brandão 15 Electric Bike Distributions Price Distribution (Discrete) Market =Triangular:9001,0001,100 Market Share =Triangular:0.040.100.16 Variable Costs =Normal:3,000300 Fixed Costs =Uniform:20,00040,000 PriceProb 35000.1 37500.4 38000.5

16. Distributions Introduction to @Risk Prof. Luiz Brandão brandao@iag.puc-rio.br 2009