Stochastic Model for
Estimating the Budget of a
Project using @RISK.
May, 2012.
Who Are We
EPM is the second largest business group in Colombia, consisting of 42 enterprises (18 in Colombia,
and 24 overseas) that acts in the sectors of Electric Energy, Natural Gas, Waters and
Telecommunications, with investments in most of Colombia, Panama, Guatemala and El Salvador.
Maxseguros is EPM’s captive reinsurer, founded in Bermuda in 2008, , with the purpose of reinsuring
the risks of its parent company and its subsidiaries.
Under Bermuda Insurance Act, Maxseguros is a Class 2 captive reinsurer, and is authorized to
negotiate policies for Property, Terrorism, All-Risk Construction, Directors and Officers, Infidelity and
Financial Risk.
WhoAre
We Are
Who
We
JLT Re COLOMBIA is the first reinsurance brokerage company in Colombia with over 30 years of
experience in the reinsurance brokerage. JLT Re Colombia is the leader in the Colombian
reinsurance consultancy market for many industries including Oil & Gas, Energy Construction,
Aviation
and
Financial
Lines.
JLT RE Colombia is a subsidiary of Jardine Lloyd Thompson Group PLC (JLT Group PLC). JLT
Group PLC, based in London and founded in 1832, is a leader in risk management, insurance
and reinsurance brokerage and benefits. Through affiliated companies and subsidiaries, JLT has
over 100 offices world-wide in 36 countries and employs over 6,000 people.
Introduction
Budget Model is:
An in house development
A real time decision tool
An on going tool
What is the issue?
In the early planning and evaluation stages of a project it is fundamental to provide
an accurate determination of the budget in order to:
Define the project's viability from financial indicators (NPV, IRR)
Estimate funding required
Optimize procurement scheme
Estimation of the Probable Maximum Loss (PML) to insure the project
Define Insurance Policies
Estimation of the Cost of Risk
The cost assessment is hampered by uncertainty and risk conditions, which are
implicit in the quantities and unit cost of each item of budget estimations.
How do you solve it?
Commonly, the attempted solution for uncertainty and risk conditions in a budget is
through adding an additional percentage to costs in order to account for the unforeseen.
This is an inadequate process of estimation as these additional costs may not be appropriate
for the project, due to probability of these events not been considered. This can impact the
budget significantly and may lead to some projects going over budget – or some projects
not been undertaken due to excessive cost forecasts.
A better solution for estimating the budget is via a stochastic model based on uncertainty
and risk profiles for quantities and prices. From this, an accurate probability distribution can
be calculated for a budget.
The Project
This model can be applied to different projects– for the purpose of this presentation we
have used the construction of a hydroelectric power plant, because of high uncertainty
and risk implicit in underground construction.
Installed capacity :
307.5 MW
Annual energy :
1,642.50 GWh/year
Design flow:
58 m3/s
Gross head :
651 m
Type of dam:
RCC Rolled Compacted Concrete
High of the dam :
40 m
Tunnels and penstock: 8,174 m
Length of wells:
447 m
The Budget Model
Deterministic
Stochastic
Stochastic
(Risk)
Monte Carlo Simulation
The model is based on a Monte Carlo Simulation for the creation of possible scenarios where
prices and quantities change due to the implied variability and the risk of the Project.
Inputs (146)
Unit Prices
Triangular Distribution
Quantities
Risks
Triangular, Bernoulli and Discrete Distribution
Outputs (24)
Cost associated with different work streams, for example: Pre-Construction projects,
Infrastructure, Dams and Related Works, Surge tank, Penstock and tunnels, equipment, among
others.
The Budget Model (Inputs)
Minimum %
•
Mode%
•
stochastic Price%
• Maximum% •
The Budget Model (Inputs)
Graph of Quantities %
Minimum %
Mode
•
•
•
Mode
• Maximum •
stochastic Quantity
The Budget Model (Inputs)
Risks
Required to purchase more land
Disproportionate increase in
compensation
Landslides which affect the access
roads
Change of dumps site due to
environmental policy changes
PreInfrastruc
Construc
Machine Access
Trailrace
hall
Tunneles
X
X
X
X
Collapse of sections of road tunnels
during construction
Rising river that exceed the
protections
X
Occurrence of faults not identified
in the studies.
Collapsing of penstock and tunnels
during construction
Surgetank Penstock
X
Terrorist attacks and/or AMIT
affecting bridges.
Removing of alluvial deposits
thicker than identified in studies
Additional treatment to the rock
foundation of the dam
Dams
X
X
X
X
X
X
X
X
X
X
The Budget Model (Outputs)
Results show that there can be large differences between the simple deterministic model costs
and costs which are calculated considering variability and risk.
The Budget Model (Outputs)
The Budget Model (Outputs)
Model Results
USD
PREVIOUS ACTIVITIES
INFRAESTRUCTURE
DAMS AND RELATED WORKS
SURGETANK
PENSTOCK
MACHINE HALL
ACCESS AND AUX TUNNELS
TRAILRACE
EQUIPOS
ELECTROMECÁNICOS
TRANSMISION SYSTEM
CONNECTION
ENVIRONMENTAL COSTS
TOTAL
RISK
WITHOUT RISK
STOCHASTIC @RISK
STOCHASTIC @RISK
17.814.838
16.705.306
17.926.375
133.293.668
127.392.333
125.431.000
26.251.565
25.697.725
26.369.336
2.806.488
2.806.488
2.680.433
132.237.106
70.237.106
72.655.810
17.339.109
17.339.109
18.121.804
10.102.779
10.102.779
11.427.750
48.268.219
48.268.219
50.528.082
178.833.762
178.833.762
182.177.000
7.636.469
7.636.469
7.505.000
40.343.600
40.343.600
41.136.209
614.927.603
545.362.896
555.958.798
DETERMINISTIC
Results- Stochastic without risk/with risk
Mean: USD 561,471,075
Mean: USD 586,756,044
Conclusions
This stochastic approach provides a number of advantages over the commonly used
deterministic method, including:
Utilizes expert advice and judgment as well as historical statistical information for the
relevant variables.
Supports decisions with quantifiable justifications and with greater certainty
Allows for accurate planning of procurement schemes, design control, negotiation of
policies and determining the technical and economic feasibility of the project.
Optimize financing obtained in the capital market.
SUMMING UP
Unit Prices
(Distribution)
Deterministic Budget
Budget Distribution
Quantities
(Distribution)
(stochastic)
MODEL
Budget Distribution
(stochastic with Risks)
Risks
Making-Decision:
Project Viability(NPV,IRR)
Funding requirements
Procurement Scheme
PML
Insurance Policies
What is next?
Promoting the consideration of risk and variability in determining the budget
and decision making.
Build databases with unit price information that allows them to fit probability
distribution functions.
Find econometric relationships between unit prices and different
characteristics of the project and quantities of work, location, among others.
¡Thanks!
The Budget Model (Deterministic)
Return
The Budget Model (Stochastic)
Return
The Budget Model (Stochastic Risk)
Return
The Budget Model (Pre-Construction Risk)
Return
The Budget Model (Pre-Construction Risk)
Return
The Budget Model (Infrastructure Risk)
Return
The Budget Model (Infrastructure Risk)
Return
The Budget Model (Penstock Risk)
Return
The Budget Model (Penstock Risk)
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The Budget Model – Infrastructure
Summary Statistics for INFRAESTRUCTURA Sin Riesgo / Summary
Estocastico
Statistics
@RISKfor INFRAESTRUCTURA / Estocastico @RISK
Statistics
Percentile
Statistics
Percentile
Minimum 117.134.028
5% 122.565.437
Minimum
117.156.633
5% 123.720.470
Maximum 143.804.025
10% 123.843.353
Maximum
153.011.997
10% 125.228.503
Mean
129.217.196
15% 124.856.183
Mean
131.505.302
15% 126.204.165
Std Dev
4.144.338
20% 125.600.046
Std Dev
5.030.403
20% 127.093.193
Variance 1,71755E+13
25% 126.286.498
Variance
2,5305E+13
25% 127.874.744
Skewness 0,109668589
30% 126.895.499
Skewness 0,30308954
30% 128.645.577
Kurtosis
2,703289798
35% 127.442.442
Kurtosis
3,042129035
35% 129.318.861
Median
129.192.158
40% 127.963.134
Median
131.212.680
40% 129.976.294
Mode
127.577.689
45% 128.595.298
Mode
129.809.059
45% 130.625.455
Left X
122.565.437
50% 129.192.158
Left X
123.720.470
50% 131.212.680
Left P
5%
55% 129.710.536
Left P
5%
55% 131.943.922
Right X
136.222.877
60% 130.201.717
Right X
140.285.181
60% 132.591.500
Right P
95%
65% 130.753.533
Right P
95%
65% 133.268.059
Diff X
13.657.439
70% 131.398.925
Diff X
16.564.710
70% 133.953.462
Diff P
90%
75% 132.031.979
Diff P
90%
75% 134.795.532
#Errors
0
80% 132.777.889
#Errors
0
80% 135.697.411
Filter Min Off
85% 133.712.064
Filter Min Off
85% 136.829.215
Filter Max Off
90% 134.734.864
Filter Max Off
90% 138.058.118
#Filtered 0
95% 136.222.877
#Filtered 0
95% 140.285.181
Return
The Budget Model- Surgetanck
Summary Statistics for ALMENARA Sin Riesgo / Estocastico
@RISK
Summary
Statistics for ALMENARA / Estocastico @RISK
Statistics
Percentile
Statistics
Percentile
Minimum
2.313.628
5% 2.486.290
Minimum
2.313.628
5%
2.487.390
Maximum
3.024.928
10% 2.527.324
Maximum
3.422.204
10%
2.529.075
Mean
2.667.847
15% 2.557.673
Mean
2.687.978
15%
2.560.348
Std Dev
108.524
20% 2.577.513
Std Dev
142.452
20%
2.580.240
Variance 11777429687
25% 2.593.732
Variance
20292620051
25%
2.597.111
Skewness -0,08250855
30% 2.610.953
Skewness 1,080592374
30%
2.614.561
Kurtosis
2,909989497
35% 2.626.914
Kurtosis
5,677025678
35%
2.631.176
Median
2.667.982
40% 2.640.681
Median
2.673.777
40%
2.645.183
Mode
2.669.182
45% 2.654.110
Mode
2.640.833
45%
2.659.882
Left X
2.486.290
50% 2.667.982
Left X
2.487.390
50%
2.673.777
Left P
5%
55% 2.680.688
Left P
5%
55%
2.688.497
Right X
2.843.140
60% 2.696.088
Right X
2.930.716
60%
2.705.918
Right P
95%
65% 2.712.728
Right P
95%
65%
2.722.554
Diff X
356.850
70% 2.728.007
Diff X
443.326
70%
2.739.172
Diff P
90%
75% 2.743.995
Diff P
90%
75%
2.756.480
#Errors
0
80% 2.760.036
#Errors
0
80%
2.776.575
Filter Min Off
85% 2.780.595
Filter Min Off
85%
2.802.792
Filter Max Off
90% 2.805.998
Filter Max Off
90%
2.841.428
#Filtered 0
95% 2.843.140
#Filtered
0
95%
2.930.716
Return
The Budget Model-Dams and Related Works
Summary Statistics for PRESA Y OBRAS ANEXAS Sin Riesgo
Summary
/ Estocastico
Statistics@RISK
for PRESA Y OBRAS ANEXAS / Estoca
Statistics
Percentile
Statistics
Percentile
Minimum
19.791.145
5%
22.605.169
Minimum
20.455.552
5%
23.600.596
Maximum 40.270.528
10%
23.578.361
Maximum
44.602.551
10%
24.593.718
Mean
28.809.863
15%
24.415.573
Mean
29.879.111
15%
25.396.411
Std Dev
4.134.643
20%
25.137.795
Std Dev
4.249.668
20%
26.049.812
Variance 1,70953E+13
25%
25.679.837
Variance
1,80597E+13
25%
26.664.498
Skewness 0,308480289
30%
26.231.718
Skewness 0,360715793
30%
27.273.299
Kurtosis
2,412617812
35%
26.807.490
Kurtosis
2,559526814
35%
27.788.547
Median
28.357.022
40%
27.296.027
Median
29.387.064
40%
28.313.547
Mode
28.203.557
45%
27.833.645
Mode
28.786.368
45%
28.825.448
Left X
22.605.169
50%
28.357.022
Left X
23.600.596
50%
29.387.064
Left P
5%
55%
28.925.649
Left P
5%
55%
29.991.699
Right X
36.191.179
60%
29.607.919
Right X
37.457.364
60%
30.670.625
Right P
95%
65%
30.244.049
Right P
95%
65%
31.339.730
Diff X
13.586.010
70%
30.969.126
Diff X
13.856.768
70%
32.034.362
Diff P
90%
75%
31.735.332
Diff P
90%
75%
32.836.118
#Errors
0
80%
32.549.950
#Errors
0
80%
33.643.066
Filter Min Off
85%
33.580.312
Filter Min Off
85%
34.658.715
Filter Max Off
90%
34.748.556
Filter Max Off
90%
35.865.787
#Filtered 0
95%
36.191.179
#Filtered
0
95%
37.457.364
Return
The Budget Model-Penstock and Tunnels
Summary Statistics for CONDUCCIÓN Sin Riesgo/ Estocastico
Summary
@RISK
Statistics for CONDUCCIÓN / Estocastico @RISK
Statistics
Percentile
Statistics
Percentile
Minimum 58.381.906
5% 62.701.259
Minimum
58.381.906
5%
63.919.316
Maximum 75.926.193
10% 63.934.264
Maximum
136.754.447
10%
65.378.059
Mean
68.618.219
15% 64.846.386
Mean
88.985.176
15%
66.586.775
Std Dev
3.303.700
20% 65.633.546
Std Dev
26.095.116
20%
67.634.041
Variance 1,09144E+13
25% 66.292.416
Variance
6,80955E+14
25%
68.611.120
Skewness -0,41198881
30% 66.902.116
Skewness 0,580366866
30%
69.452.131
Kurtosis 2,528652767
35% 67.465.773
Kurtosis
1,448882213
35%
70.219.742
Median
69.068.914
40% 68.037.943
Median
72.489.209
40%
70.903.640
Mode
69.462.182
45% 68.577.254
Mode
70.955.951
45%
71.627.783
Left X
62.701.259
50% 69.068.914
Left X
63.919.316
50%
72.489.209
Left P
5%
55% 69.491.699
Left P
5%
55%
73.500.831
Right X
73.379.967
60% 69.926.125
Right X
127.512.499
60%
78.246.249
Right P
95%
65% 70.321.681
Right P
95%
65%
93.991.901
Diff X
10.678.708
70% 70.755.276
Diff X
63.593.184
70% 119.962.104
Diff P
90%
75% 71.175.205
Diff P
90%
75% 122.038.031
#Errors
0
80% 71.592.427
#Errors
0
80% 123.608.229
Filter Min Off
85% 72.072.503
Filter Min Off
85% 124.867.222
Filter Max Off
90% 72.638.814
Filter Max Off
90% 126.171.715
#Filtered 0
95% 73.379.967
#Filtered 0
95% 127.512.499
Return