Apresentação: Ângela Brandão, Bárbara Paes Leme, Liana Sfair Coordenação: Paulo R. Margotto
Distributions Introduction to @Risk Prof. Luiz Brandão [email protected] 2009.
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Transcript of Distributions Introduction to @Risk Prof. Luiz Brandão [email protected] 2009.
IAG PUC – Rio Brandão
2
Uniform RiskUniform (Min, Max)
Uniform(1, 4)X <= 3.8500
95.0%X <= 1.1500
5.0%
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.5 1 1.5 2 2.5 3 3.5 4 4.5
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
Uniform(1, 4)X <= 1.1500
5.0%X <= 3.8500
95.0%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.5 1 1.5 2 2.5 3 3.5 4 4.5
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
IAG PUC – Rio Brandão
3
Triangular
Triang(1, 2, 6)X <= 1.5000
5.0%X <= 5.0000
95.0%
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 1 2 3 4 5 6 7
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
RiskTriang (Min, Probable, Max)
Triang(1, 2, 6)X <= 1.5000
5.0%X <= 5.0000
95.0%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
IAG PUC – Rio Brandão
4
Histogram RiskHistogrm (Min, Max, {p})
Histogrm(0, 5, {p})X <= 0.55000
5.0%X <= 4.4500
95.0%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-1 0 1 2 3 4 5 6
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
Histogrm(0, 5, {p})X <= 0.55000
5.0%X <= 4.4500
95.0%
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-1 0 1 2 3 4 5 6
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
IAG PUC – Rio Brandão
5
Discrete RiskDiscrete ({x}, {p}), where {x} are the values the
variable can assume and {p} are the respective probabilities.
Discrete({x}, {p})X <= 4.0000
5.0%X <= 9.0000
95.0%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
3 4 5 6 7 8 9 10
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
Discrete({x}, {p})X <= 4.0000
5.0%X <= 9.0000
95.0%
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
3 4 5 6 7 8 9 10
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
IAG PUC – Rio Brandão
6
Normal Distribution RiskNormal (Mean, Standard Deviation)
Normal(3, 1)X <= 1.3552
5.0%X <= 4.6448
95.0%
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0 1 2 3 4 5 6
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
Normal(3, 1)X <= 1.3552
5.0%X <= 4.6448
95.0%
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
@RISK Student VersionFor Academic Use Only
PetroRio
Electric Bike, Inc.
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 0 Year 1 a 10
Investment (150.000)
Revenue 375.000Variable Costs (300.000)
Fixed Costs (30.000)Depreciation (15.000)
E.B.T. 30.000Tax (15.000)
Net income 15.000 + Depreciation 15.000
Cash Flow (150.000) 30.000
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 project’s NPV of possible fluctuations of these variables.
What is the risk of investing in this project
IAG PUC – Rio Brandão
15
Electric Bike Distributions
Price Distribution (Discrete)
Market = Triangular: 900 1,000 1,100
Market Share = Triangular: 0.04 0.10 0.16
Variable Costs = Normal: 3,000 300
Fixed Costs = Uniform: 20,000 40,000
Price Prob
3500 0.1
3750 0.4
3800 0.5
