Risk Analysis on Project
A Case Study by Using @Risk to
Wind Power Generation
William Zhu
WEL Networks Limited
P.O. Box 925
Hamilton, New Zealand
Abstract
A wind power generation project is valuated based on Discounted Free Cash Flow (DFCF)
methodology. Key risk factors, including revenue associated (eg, the amount of electricity
generated by wind and electricity spot prices), capital expenditure associated (eg, the NZ
exchange rate linked to the imported wind turbines), and operating expenditure associated (eg,
CPI and PPI fluctuation), are identified. Correlation constraints are added to capture the interrelationships among some of the risk factors. The @Risk Best Fit is used to find the proper
distributions for the key input factors. Interval (with certain confidence level) estimation on the
output factor (ie, Net Present Value --- NPV) is calculated. Both deterministic and stochastic (via
@Risk) sensitivity analyses are compared with each other. Advanced @Risk techniques, including
goal seek, stress and sequential analyses are utilized to further investigate the sensitivities of the
key input factors. Finally, the scenario results are summarized by using a simple decision tree
diagram. Excel Macros, which incorporates many @Risk functions, are widely used to display the
results and plot the graphs, so that users can run the model smoothly with little @Risk
knowledge. It is also easy to convert this case study into a general business valuation model with
minor modification.
Key Words:
Discounted Free Cash Flow
Stochastic versus deterministic sensitivity analyses
Visual Basic Application --- Excel Macros
@Risk V4.5 computer software
Precision Tree V1.0 computer software
July 2007
Presenter: William Zhu
2
Presentation Contents
• Brief Review of the Wind Farm Project
• Deterministic Discounted Free Cash Flow
Model (DFCF)
• Stochastic DFCF Model
• Sensitivity Analysis by Using @Risk
• Suggestions and Conclusions
July 2007
Presenter: William Zhu
3
Project Brief Review
• Background
• Investment Proposal
• Feasibility Studies
• Financial Analysis
‰
‰
‰
‰
Worth doing / Meet Required Rate of Return?
Likelihood to Earn / Lose Money
Major Risks and Their Impact
Decision Making
• Model Description
‰
‰
July 2007
Methodology --- Income Based DFCF Model + @Risk
software
Model Structure
Presenter: William Zhu
4
Building Blocks of the Model
@Risk
Tool
DFCF
Model
Sensitivity
Report
July 2007
Financial
Report
Presenter: William Zhu
5
Model Structure
Go Back
Valuation Model
Power Curve
Decision Tree
Price Path
INPUT
OUTPUT
Capex
Scenario Results
Statements
NPV Target
Proj basic info
Proj Detailed info
Graph Report
Valuation Report
Factor Impact Report
Sensiv (D)
Sensiv (S)
VBA Codes
Assumptions
DFCF
Data
IS
BS
Different Factors
MODEL STRUCTURE
July 2007
Presenter: William Zhu
6
Modeling Procedures
• Identification of Key factors
• Information Collection
• Deterministic DFCF Model
• Risk Specification
• Stochastic DFCF Model
• Sensitivity Analysis
• Decision Tree Diagram
• Reports
July 2007
Presenter: William Zhu
7
Deterministic DFCF Model
• Model Components
• Revenue
– Direct Revenue
– Indirect Revenue
• Cost
– Capital Expenditure (Capex)
– Operating Expenditure (Opex)
• Others
– Weighted Average Cost of Capital (WACC)
– Inflation (CPI) and etc.
July 2007
Presenter: William Zhu
8
Valuation Structure
Calculation of FCF
Category
Total Revenue
Energy Generation
Avoided Transmission Charges
Emmision Reduction Value
Less cost of Sales
Direct Cost
Grid connection charges
Grid services charge
Plant warranty costs
Total Cost of sales
Gross Profit ($k)
Gross Profit Ratio (%)
Less Operating Expenses
Mgt & Admin Costs incl insurance
Recurrent operating costs
Annualised non recurrent costs
Depreciation
Total Operating Expenses ($k)
EBITDA
EBIT
Less Interest Need to Pay
EBT
Less Taxation
Taxation
NPAT
Free Cash Flow Caculation
Add back
Depreciation
Interest Paid As A Shield
Less
Movement in Working Capital
Capital Expenditure
Capitalised Maintenance Cost
Free Cash Flow (FCF) Without TV
Free Cash Flow (FCF) With TV
July 2007
Year
Index
Unit\Year
-1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
$K
$K
$K
$K
-
-
4,388
3,747
230
412
4,563
3,907
235
421
4,769
4,099
240
430
4,935
4,250
245
439
5,335
4,635
251
449
5,320
4,604
256
459
5,319
4,588
262
469
5,721
4,974
268
479
5,730
4,966
274
490
5,926
5,145
280
501
6,129
5,331
286
512
6,339
5,524
292
523
6,557
5,724
299
535
6,784
5,932
305
546
7,018
6,148
312
558
7,262
6,373
319
571
7,514
6,605
326
583
7,776
6,847
333
596
8,048
7,098
340
609
8,330
7,359
348
622
$K
$K
$K
$K
$K
$K
$K
$K
$K
$K
$K
$K
$K
$K
$K
$K
$K
-
-
1,097
66
153
1,317
3,071
70%
1,141
68
157
1,365
3,198
70%
1,192
69
160
1,422
3,347
70%
1,234
71
164
1,468
3,467
70%
1,334
72
167
1,573
3,762
71%
1,330
74
1,404
3,916
74%
1,330
76
1,405
3,914
74%
1,430
77
1,508
4,213
74%
1,432
79
1,511
4,218
74%
1,481
81
1,562
4,363
74%
1,532
83
1,615
4,514
74%
1,585
84
1,669
4,670
74%
1,639
86
1,726
4,832
74%
1,696
88
1,784
5,000
74%
1,755
90
1,845
5,174
74%
1,815
92
1,908
5,354
74%
1,879
94
1,973
5,542
74%
1,944
96
2,040
5,736
74%
2,012
98
2,110
5,938
74%
2,082
100
2,183
6,147
74%
-
146
146
(146)
396
(542)
132
265
132
585
1,115
2,542
1,956
1,653
303
136
271
136
587
1,129
2,655
2,069
1,485
583
139
278
139
588
1,144
2,791
2,203
1,316
888
143
285
143
589
1,159
2,897
2,308
1,144
1,164
146
292
146
615
1,199
3,177
2,562
1,111
1,452
150
240
150
616
1,155
3,376
2,761
925
1,835
154
246
154
617
1,170
3,361
2,744
734
2,009
157
252
157
618
1,185
3,647
3,029
549
2,480
161
258
161
807
1,387
3,638
2,831
1,114
1,717
165
265
165
808
1,403
3,768
2,960
902
2,058
169
271
169
809
1,419
3,904
3,095
690
2,405
174
278
174
811
1,436
4,045
3,234
475
2,759
178
285
178
812
1,453
4,191
3,379
260
3,119
182
292
182
813
1,470
4,343
3,530
42
3,487
187
299
187
815
1,488
4,500
3,686
3,686
192
307
192
816
1,506
4,664
3,848
3,848
197
314
197
817
1,525
4,834
4,017
4,017
201
322
201
819
1,544
5,011
4,192
4,192
206
330
206
820
1,564
5,194
4,374
4,374
212
339
212
822
1,584
5,385
4,563
4,563
$K
$K
-
(179)
(363)
100
203
193
391
293
595
384
780
479
973
606
1,230
663
1,346
818
1,662
567
1,150
679
1,379
794
1,611
910
1,848
1,029
2,090
1,151
2,337
1,216
2,470
1,270
2,578
1,326
2,691
1,383
2,809
1,443
2,931
1,506
3,057
$K
-
146
396
585
1,653
587
1,485
588
1,316
589
1,144
615
1,111
616
925
617
734
618
549
807
1,114
808
902
809
690
811
475
812
260
813
42
815
-
816
-
817
-
819
-
820
-
822
-
5,855 17,565
(5,855) (17,386)
(5,855) (17,386)
20
2,421
2,421
21
2,442
2,442
21
2,477
2,477
1,000
22
1,491
1,491
22
2,676
2,676
23
2,748
2,748
23
2,674
2,674
7,500
24
(4,695)
(4,695)
24
3,047
3,047
25
3,064
3,064
25
3,085
3,085
26
3,108
3,108
27
3,135
3,135
27
3,165
3,165
28
3,256
3,256
28
3,366
3,366
29
3,480
3,480
30
3,598
3,598
30
3,721
3,721
31
3,848
21,546
$K
$K
$K
$K
$K
Presenter: William Zhu
9
Results of Deterministic Model
INPUT TABLE
OUTPUT TABLE
2007
2009
20
Start Year of Project
Start Year of Generation
Project Life
Generation Profile
Average
PRE Revenue Included?
YES
NO
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Please Choose One of the Following Options
Using Weighted Average Price at Otahuhu
Using Weighted Average Price at Hayward
Not Using Weighted Average Price
Carbon Tax On?
NO
Electricity Price Profile
Otahuhu Avg
Terminal Value
Asset Based
Interest Tax Shield On?
YES
Capex
Case A - Base
Investment Type
Investment 1
($K)
OUTPUT
Key Measurement
NPV
PV
IRR
Pay Back Years
Average ROI
Average NPAT/Revenue
Initial Investment
Total Investment
Fixed Assets at the End
Equity at the End
Terminal Value
Total Dividend Paid
Total Cash at the End
Total Interest Paid
NPV (for EVA)
PV (for EVA)
Unit
$K
$K
%
Years
%
%
$K
$K
$K
$K
$K
$K
$K
$K
$K
$K
Selected
3,083
25,036
9.4%
12.6
7.0%
25.9%
23,420
32,427
17,698
18,144
17,698
9,010
23,971
12,795
(1,749)
4,106
Decision making Under Current
Scenario →
Cumulative Free Cash Flow (Excluding Terminal Value)
Instruction
SCENARIO
Median
Best
1,148
8,991
28,471
36,314
8.4%
11.2%
13.2
11.0
6.0%
9.8%
22.9%
30.5%
29,150
29,150
38,157
38,157
20,527
20,527
21,015
21,182
20,527
20,527
9,570
13,515
22,410
41,880
16,902
12,851
(6,306)
7,006
982
14,294
Profitability Measure
NPAT (LHS)
3500
30,000
Steps to Run the Model
1) Input/select parameter values in this sheet;
2) Fill in or change assumptions in the
"Assumption" sheet;
3) Go to the "Decision" sheet, make
selections and the press the button to start
the SCENARIO analysis;
4) Go to the sheets associated to perform the
following analyses, inclduing:
● NPV Target --- Individual
● NPV Target --- Group
● Sensitivity Analysis (Deterministic)
● Sensitivity Analysis (Stochastic)
5) Current case result is shown in the "Main"
sheet, while the overall expected result is
shown in the"Decision" sheet.
GREEN LIGHT ON --- The Project Is
Worth Doing
($K)
40,000
= INPUT data
= Pre-set value
= Make a selection
Worst
(6,990)
20,333
5.3%
17.1
1.1%
5.3%
29,150
38,157
20,527
20,777
20,527
5,078
(1,752)
24,037
(22,322)
(15,034)
ROI (RHS)
20%
3000
15%
20,000
2500
10,000
2000
10%
1500
0
5%
1000
(10,000)
500
0%
(20,000)
0
July 2007
-5%
Presenter: William Zhu
2028
2027
2026
2025
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
-500
2007
2028
2027
2026
2025
2024
2023
2022
2021
2020
2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
(30,000)
10
Financial Report (eg, Income Statement)
View Statement
Statement of Financial Position
Results Shown Only 10 Years
Statement of Financial Position (12 Years)
Category
2007
2008
$K
-
-
Opex Before Interest & Tax
$K
-
Interest Expenses
$K
Sales Revenue
EBIT
Taxation
NPAT
July 2007
Unit\Year
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
4,388
4,563
4,769
4,935
5,335
5,320
5,319
5,721
5,730
5,926
(146)
(2,432)
(2,495)
(2,566)
(2,627)
(2,773)
(2,559)
(2,575)
(2,692)
(2,899)
(2,965)
-
(396)
(1,653)
(1,485)
(1,316)
(1,144)
(1,111)
(925)
(734)
(549)
(1,114)
(902)
$K
-
(146)
1,956
2,069
2,203
2,308
2,562
2,761
2,744
3,029
2,831
2,960
$K
-
179
(100)
(193)
(293)
(384)
(479)
(606)
(663)
(818)
(567)
(679)
$K
-
(363)
203
391
595
780
973
1,230
1,346
1,662
1,150
1,379
Presenter: William Zhu
11
Further (Deterministic) Analyses
• 16 Financial Indicators
• NPV Target Analyses
Purpose --- Set output, how much should input
factor change to meet the target
ƒ Excel built in Goal Seek Function
ƒ Excel built in Solver Function
• Deterministic Sensitivity Analyses
Purpose --- Given factor changing certain amount
(eg, 10%), by how much will output change
ƒ Advantage --- clear economic meaning
ƒ Disadvantages --- static comparison, and not unit measure free
July 2007
Presenter: William Zhu
12
NPV Target Analyses
INPUT TABLE
1
2
Traget
New NPV ($K)
Maximise Target
5,000
NPAT
OUTPUT TABLE --- Individual
1
2
3
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
NPV Report
$K
Original
$K
New
$K
Difference
Category
Factor Name
Energy Generated
Revenue Revenue Multiplier
Factors Terminal Value
(Multiplier) Electricity Spot Price
Transmission Avoided
PRE Value
Grid Connection Charges
Plant Warrant Charges
Capex 1st Two Years
Cost
Capex 4th & 8th Years
Factors
Exchange Rate
(Multiplier)
Mgt & Insurance Costs
Recurrent Opex
Non Recurrent Opex
Direct Cost Ratio
PPI Growth
Other
CPI Growth
Factors
(Additive) WACC
Depreciation
July 2007
3,083
5,000
1,917
Grow/Drop to
110.9%
109.2%
154.5%
109.2%
268.7%
194.2%
-337.8%
-469.6%
86.6%
21.4%
117.2%
-114.6%
-24.0%
-114.6%
-5.96%
5.88%
-11.43%
-0.71%
-4.87%
Individual
Factor Impact
Group Factor
Impact
Instruction
Print Results
= INPUT Data
= Make a Selection
OUTPUT TABLE --- GROUP
33,767
40,456
6,690
Output
110.0%
102.2%
90.0%
Target Set = Maximum NPAT
33,767
33,767
33,767
39,418
33,975
36,665
5,651
208
2,898
Price
COG
Capex
33,767
34,744
977
Opex
110.0%
90.0%
96.9%
90.0%
90.0%
96.2%
90.0%
110.0%
90.0%
90.0%
90.0%
Presenter: William Zhu
Two constraints are made:
1) Factor growth is set to between 90% and 110%;
2) NPV = New settings.
Explanation
This sheet tries to answer 2 major questions.
1) Individual Factor Impact
Given NPV being set to a new value (in cell AD101),
what the factor ratio will it be (compared to the
original one) for each individual case?
Note for those factors measured by %, the result is
percentage point growth rather than the ratio (eg., if
original WACC = 9%, the WACC = -0.5% means that
WACC should decrease by 0.5 percentage point, so
the new WACC = 9%-0.5%=8.5%).
2)Group Factor Impact
The factors are classified into 5 groups:
Output, Price, Direct Cost, Capex and Opex.
Given the new NPV and the other groups unchanged,
what the growth combination should be for the tested
group to minimise the pay back years or to maximise
the total (cumulative) NPAT?
13
Deterministic Sensitivity Analysis
Description
Print Results
Deterministic Sensitivity means it compares the results under 2 status, ignoring the possibility of these 2 status occurring. It tries to answer the following question:
With certain percent (say, 1%) changes of a factor, what are the changes of the NPV and the other indices such as IRR and PBY?
Although it doesn't consider the likelihood of the percentage changes, the changes in NPV have clear economic meaning. Therefore, the results shown in the range
(S18:S45) in absolute values are used directly to construct the Tornado chart. This may differ from the results tested by the Stochastic Sensitivity Analysis since the
results shown there are indices instead of actual measures on changes in NPV.
Deterministic Sensitivity Analysis (Static Compariosn of NPV)
Instruction
Input growth rate below (Cell O16)
then press the "SA(D)" button
Growth Rate 10%
No
Factor
1 WACC
2 Electricity Spot Price
3 Revenue Multiplier
4 Energy Generated
5 Capex 1st Two Years
6 Exchange Rate
7 Depreciation
8 Terminal Value
9 Direct Cost Ratio
10 CPI Growth
11 Capex 4th & 8th Years
12 PPI Growth
13 PRE Value
14 Recurrent Opex
15 Transmission Avoided
16 Mgt & Insurance Costs
17 Non Recurrent Opex
18 Grid Connection Charges
19 Plant Warrant Charges
Original Measures ($K)
NPV
IRR
PBY
3,083
9.4%
12.6
New Measures ($K)
NPV
IRR
PBY
739
9.4%
12.6
5,178
10.2%
11.9
5,178
10.2%
11.9
4,844
10.1%
12.0
1,660
8.7%
13.1
4,267
10.0%
12.0
2,698
9.2%
12.3
3,435
9.5%
12.6
2,764
9.2%
12.7
2,777
9.2%
12.7
2,842
9.2%
12.8
3,321
9.4%
12.5
3,285
9.4%
12.5
2,930
9.3%
12.6
3,196
9.4%
12.5
2,994
9.3%
12.6
2,994
9.3%
12.6
3,040
9.3%
12.6
3,050
9.3%
12.6
Call William Zhu at 8410
Deterministic Sensitivity Analysis
Percentage change
Difference
∆ NPV
∆ IRR
(2,344)
0.0%
2,094
0.9%
2,094
0.9%
1,760
0.8%
(1,423)
-0.7%
1,184
0.6%
(385)
-0.1%
352
0.1%
(319)
-0.1%
(306)
-0.1%
(242)
-0.1%
238
0.1%
202
0.1%
(154)
-0.1%
113
0.0%
(89)
0.0%
(89)
0.0%
(43)
0.0%
(33)
0.0%
Any Enquery?
∆ PBY
(0.7)
(0.7)
(0.6)
0.5
(0.6)
(0.3)
0.1
0.1
0.2
(0.1)
(0.1)
0.1
(0.0)
0.0
0.0
0.0
0.0
Percentage change
Percentage change
WACC
Electricity Spot Price
Revenue Multiplier
Energy Generated
Capex 1st Two Years
Exchange Rate
Depreciation
Terminal Value
Direct Cost Ratio
CPI Growth
Capex 4th & 8th Years
PPI Growth
PRE Value
Recurrent Opex
Transmission Avoided
Mgt & Insurance Costs
Non Recurrent Opex
Grid Connection Charges
Plant Warrant Charges
July 2007
Presenter: William Zhu
14
Major Risk Factors
• Revenue Related
™ Electricity Generation --- Energy Related
™ Electricity Spot Prices --- Sales Price Related
™ Government Regulation --- Policy Related
• Cost Related
™ Capex Associated --- Exchange Rates, Budget
™ Opex Associated --- Inflation, Interest Rates, etc.
July 2007
Presenter: William Zhu
15
Key Features of Using @Risk
• Best Fit techniques to find proper
distributions for core input factors
• Correlation relationships among input
factors
• Stochastic vs. Deterministic sensitivity
analysis
• Advanced @Risk techniques
• A Decision Tree Diagram
July 2007
Presenter: William Zhu
16
Flow Chart of Using @Risk
Fit Distributions on
Input Factors
Correlation Matrix
& SimTable
@Risk Output
Distribution
Summary
Report
CDF
Curve
Percentile
Report
Histogram
Plot
Sensitivity
Analysis (O)
Sensitivity
Analysis (A)
Decision
Tree
Tornado
Chart
Scenario
Test
Multiple
Simulations
July 2007
L
e
v
e
L
1
L
e
v
e
L
2
L
e
v
e
L
3
Goal
Seek
L
e
v
e
L
4
Presenter: William Zhu
Stress
Analysis
Sequential
Analysis
17
Fit Distributions
•
•
•
Wind Speed
Electricity Spot Prices
NZ/US Exchange Rates
™ Wind Speed Distribution
‰
‰
‰
Empirical Studies --- Weibull (eg, Sathyajith Mathew and K. P. Pandey 2000)
Direct Regression Model --- Weibull
@Risk Fit Distribution Results --- Weibull
ƒ
ƒ
Excel Macros via @Risk are used to perform automatically
Top rank using χ2 statistics indicates Weibull(A,
Weibull(A, B)
‰ The fitted Weibull, together with power curve, determines annual energy generation
™ NZ Electricity Spot Prices
‰ Empirical Studies --- Log-logistic (eg, MICHAEL A. S. GUTH 2004)
‰ @Risk Fit Distribution Results --- Log-logistic
™ NZ/US Exchange Rates
‰ Empirical Studies --- Beta General (eg, Kai-Li Wang and Christopher Fawson 2001)
‰ @Risk Fit Distribution Results --- Beta General
• Demonstration @Risk results by using macros.
July 2007
Presenter: William Zhu
18
Results of @Risk Fit Distribution
Distribution of Wind Speed (Rank by Chi Sq)
Weibull(2.2371, 9.0801) Shift=-0.28030
BetaGeneral(3.8331, 12.075, -1.0505, 35.523)
Gamma(8.3584, 1.3239) Shift=-3.3027
InvGauss(16.574, 311.470) Shift=-8.8112
Pearson5(36.670, 802.91) Shift=-14.745
Lognorm(16.686, 3.8243) Shift=-8.9221
ChiSq
3,536
3,834
3,928
3,988
4,070
4,317
A-D
14.56
14.48
19.57
20.39
21.44
20.92
K-S
0.0139
0.0153
0.0153
0.0153
0.0165
0.0157
Distribution of Elec Spot Price (Rank by Chi Sq)
LogLogistic(-9.1411, 56.691, 3.8650)
Pearson5(7.9535, 567.33) Shift=-26.642
ExtValue(41.090, 22.989)
Lognorm(66.498, 32.817) Shift=-11.516
InvGauss(69.937, 313.820) Shift=-14.481
Gamma(3.0791, 18.481) Shift=-1.4503
ChiSq
234
371
434
440
481
589
A-D
8.64
24.81
30.95
31.18
38.74
52.51
K-S
0.0349
0.0514
0.0716
0.0594
0.0697
0.0823
Distribution of Daily Exchg Rate (Rank by Chi Sq)
BetaGeneral(2.0136, 1.7190, 0.38657, 0.74440)
Triang(0.36853, 0.64280, 0.74551)
Weibull(5.8117, 0.43296) Shift=+0.18190
Normal(0.582191, 0.081363)
Logistic(0.585034, 0.047586)
Uniform(0.39208, 0.74427)
ChiSq
748
752
1,047
1,082
1,479
1,600
A-D
23.75
23.14
19.37
26.30
27.19
188.88
K-S
0.0547
0.0622
0.0417
0.0464
0.0480
0.1602
July 2007
Presenter: William Zhu
Start Fit Process
(Tick Box Below ↓)
Find Best Fit
Start Fit Process
(Tick Box Below ↓)
Find Best Fit
Start Fit Process
(Tick Box Below ↓)
Find Best Fit
19
Comparable Results of Weibull Distrib
Linear Regression
(Find Directly the
Parameters of Weibull
Distribution)
Actual Histogram
Weibull Curve
Weibull Curve @Risk
5%
4%
0.5
30
3%
OUTPUT TABLE
Regression Results
Value
Slope
2.20
Intercept
-4.80
R2
1.00
F-value
64094
σSlope
0.01
t-value of Slope
253.2
Sample Size
55
Weibull Parameters
Shape parameter (α)
2.20
Scale parameter (β)
8.86
Mean of Weibull
7.84
Stdev of Weibull
3.77
2%
1%
Wind Energy Distribution
30%
25%
25.0 < X ≤ 25.5
30
60
5%
5%
90
0%
240
120
270
90
0%
240
150
120
210
180
July 2007
20%
10%
10%
210
25%
15%
300
60
15%
270
22.5 < X ≤ 23.0
0
330
30
20%
300
20.0 < X ≤ 20.5
Wind Energy Distribution
0
330
17.5 < X ≤ 18.0
15.0 < X ≤ 15.5
12.5 < X ≤ 13.0
10.0 < X ≤ 10.5
7.5 < X ≤ 8.0
5.0 < X ≤ 5.5
0.0 ≤ X ≤ 0.5
0%
2.5 < X ≤ 3.0
INPUT TABLE
Speed Interval Size
Direction Interval Size
Add @Risk WB Curve
Wind Speed Distribution
6%
150
180
Presenter: William Zhu
20
Power Curve of Wind Turbine
(kW)
Power Curve of Wind Turbine (KW)
3500
3000
2500
2000
1500
1000
500
0
4
July 2007
6
8
10
12
14
16
Presenter: William Zhu
18
20
22
24
(m /s)
21
Define @Risk Input Factors
• Distributions for Other Factors
• Growth trend is added for some factors
• @Risk distribution functions are built
directly into Excel (as @Risk input factors)
• Lists of Input Factors
July 2007
Presenter: William Zhu
22
@Risk Input Table
NO
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
Factor Distribution ((@Risk Input Variables 1 --- Differ in Years)
Year
Energy SpotPrice RevMutiple PPI
CPI
ExRate Capex
2007
5855
2008
0.68 17565
2009
52
67.9
1.07
2.2%
2.5%
2010
52
70.8
1.07
2.2%
2.5%
2011
52
74.3
1.07
2.2%
2.5%
2012
52
77.0
1.07
2.2%
2.5%
0.62
1000
2013
52
84.0
1.07
2.2%
2.5%
2014
52
83.4
1.07
2.2%
2.5%
2015
52
83.1
1.07
2.2%
2.5%
2016
52
90.1
1.07
2.2%
2.5%
0.58
7500
2017
52
90.0
1.07
2.2%
2.5%
2018
52
93.2
1.07
2.2%
2.5%
2019
52
96.6
1.07
2.2%
2.5%
2020
52
100.1
1.07
2.2%
2.5%
2021
52
103.7
1.07
2.2%
2.5%
2022
52
107.5
1.07
2.2%
2.5%
2023
52
111.4
1.07
2.2%
2.5%
2024
52
115.5
1.07
2.2%
2.5%
2025
52
119.7
1.07
2.2%
2.5%
2026
52
124.1
1.07
2.2%
2.5%
2027
52
128.6
1.07
2.2%
2.5%
2028
52
133.4
1.07
2.2%
2.5%
2029
2030
2031
2032
2033
Spearman RkOder Correl Matrix
SpotP
PPI
CPI
SpotP 1.00
0.30
0.30
PPI
0.30
1.00
0.95
CPI
0.30
0.95
1.00
July 2007
Simple SpotP, PPI & CPI Correl Matrix
SpotP
PPI
CPI
SpotP
1.00
0.38
0.34
PPI
0.38
1.00
0.97
CPI
0.34
0.97
1.00
Factor Distribution (@Risk Input Variables 2)
Parameters used for factor distribution 1
NO
Factor
Factor
Distribution Parameter Value
1
Energy
Energy
Normal
µ
51.64
2
SpotPrice
σ
15.29
3
RevMutiple
α
4.09
4
PPI
β
58.36
5
CPI
γ
-10.46
6
ExRate
θ
0.77
7
Capex
SpotPrice Log-Logistic
New α
4.09
8
Pk Avoid
225
New β
9.46
9
PRE
403
New γ
-10.46
10
Plant Warrant Charges
150
New θ
0.77
11
Direct Cost Ratio
25%
Mean
0.00
12
Grid connection
65
Stdev
5.31
13
Mgt & Admin Costs
2.50 RevMultip
Normal
µ
1.07
14
Recurrent Opex
0.00
σ
0.25
15
Non Recurrent Costs
2.50
PPI
Normal
µ
2.2%
16
Terminal Value
17698
σ
0.01
17
WACC
8.0%
CPI
Normal
µ
2.5%
18
Depreciation
2.5%
σ
0.01
α1
2.48
α2
2.11
1
Capex & ExRate Correlation
-0.66
Min
0.37
1
Mean Generation Change
1
Max
0.76
1
Truncated Spot Price Mean
4.43
EX Rate
Beta(G)
New α1
2.48
New α2
2.11
New Min
0.43
Sensitivity Result (@Risk Output Variable)
New Max
0.74
3,083
1
NPV Result
Mean
0.60
Stdev
0.07
Min
80%
CapexNY1
Pert(B)
Most Lkly
100%
Other Parameters/Assumptions
Max
120%
Assumed Stdev
5%
Base %
65%
52
Available Energy (GWh/yr)
Capex
Discrete
Worse %
20%
Revenue Multiplier
1.07
Yr 0
Distribution Worst %
5%
Best %
10%
Presenter: William Zhu
Summary
Distribution of Input factors
1) Wind Speed --- Weibull Distribution
2) Energy --- Normal Distribution
3) Spot Prices --- Log-Logistic Distribution
4) Exchange Rates --- Beta General Distribution
5) Capex --- Pert General Distribution
6) Other factors --- Normal Distributions
Correlation Relationships
1) Exchange Rates and Capex
2) Spot Prices, CPI, and PPI Correlation Matrix
Go to SenS Results
23
Correlation Relationships
• Correlation exists
ƒ Negative relationship between Exchange rate and Capex
ƒ Positive relationships among Spot Price, PPI and CPI
• 2 groups of @Risk Correl Functions Used
ƒ
ƒ
ƒ
InDec() used for Exchange Rates (Independent variable)
Dec() used for Capex (Dependent variable)
Correlation matrix (Defined as Spearman Rank Order
Coeffs.) is defined in an Excel range and CorrelMat() is
used for Spot Price, PPI, and CPI.
July 2007
Presenter: William Zhu
24
Estimated Distribution of NPV
• Define Target --- RiskOutput() + NPV
• Start Simulation(s)
• Characteristics
Automatically Running via Macros
A Built in CDF Graph (variant template)
Interval Probability is calculated and shown
Sensitivity graph is grouped by similar factors
and plotted with a custom style
™ Standard @Risk template is built for saving key
results
™
™
™
™
July 2007
Presenter: William Zhu
25
Key Stochastic Analysis Results
Description
Stochastic Sensitivity Analysis (SSA) uses "Monte Carlo" statistical technique to let computer do simulation by
randomly selecting many scenarios (sample size is set to 10,000). This is different from the deterministic sensitivity
analysis (DSA) which only compares 2 cases (static, so it is called deterministic). The main advantage of SSA
against DSA lies in it provides the distribution of NPV (ie., it is easy to find what the chance will be for NPV sitting
between say, 50K to 100K). There are some disadvantages though. The sensitivity ranking in SSA is an index
rather than the actual changes in NPV, so it is a relative measure which hasn't got intuitive economic meaning. In
addition, the SSA results are sensitive to the assumptions used in the input factor distributions. Finally, to launch
SSA successfully, you have to install a computer software called "@Risk".
Instruction
Make sure "@Risk" is installed. Fill in Lower & Upper Bands in Cells Q14 and Q15 (green color), then press the
b tt
INPUT PARAMETERS ($K)
Lower Band ($K)
Upper Band ($K)
Click Here
30,000
→
Sensitivity
Analysis
Generation
Simulation
Print
Results
KEY OUTPUT
Probability of $K 0 <= NPV <= $K 30000
78.1%
Any Enquery? Contact William Zhu at Extn 8410
Stochastic Sensitivity Analysis and Cumulative probability Distribution of NPV
Stochastic Sensitivity Analysis
Cumulative Probability Distribution of NPV
Stochastic Sensitivity Index
WACC
1.000
-0.701
Mean=2834.662
ExRate
0.189
Capex
-0.160
0.800
SpotPrice
0.135
Depreciation
-0.116
Direct Cost Ratio
-0.107
0.600
Energy
0.081
RevMutiple
0.078
CPI
0.000
Grid connection
0.000
Mgt & Adm in Costs
0.000
Non Recurrent Costs
0.000
Pk Avoid
0.000
Plant Warrant Charges
0.000
PPI
0.000
PRE
0.000
Recurrent Opex
0.000
Term inal Value
0.000
-0.8
0.400
0.200
0.000
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
-10
-5
0
10
15
20
Values in Thousands
0.1
0.2
0.3
5%
90%
-3.0019
July 2007
5
Presenter: William Zhu
5%
9.1497
26
Templates for Other Key Results
Descriptive Results
Statistic
Value
Mean
$2,835
Minimum
($9,020)
Maximum
$17,070
StdDev
$3,712
Skewness
0.24
Kurtosis
3.27
Percentile Distribution
Percentile
Value
1th Percentile
($5,391)
5th Percentile
($3,002)
10th Percentile
($1,727)
25th Percentile
$344
50th Percentile
$2,676
75th Percentile
$5,200
90th Percentile
$7,564
95th Percentile
$9,150
99th Percentile
$12,470
@RISK graph
Description
This template uses some @Risk statistical graph functions to generate useful information from
the simulation. The percentile table results on the left hand side can be compared with the
results (ie., NPV > 0) shown in the "SensivS" sheet; while the original tornado graph shown
below can be comapred with the modified one in the "SensivS" sheet. Note also no cumulative
distribution is displayed in this sheet since it has already been created in the "SensivS" sheet.
@RISK graph
--- Histogram
--- Tornado Chart
Histogram
NPV
Tornado ofofNPV
Distribution
for SenS
NPV/N29
(Sim#1)
Distribution
for SenS
NPV/N31
3.000
1.200
-.701 -.513
ExRate/I6
SpotPrice/E7
SpotPrice/E7
Terminal Value/N20
Energy/D7
SpotPrice/E14
Energy/D8
Energy/D12
Energy/D11
ExRate/I14
RevMutiple/F7
Energy/D10
Energy/D9
Energy/D10
RevMutiple/F7
Energy/D14
Energy/D9
Energy/D15
Energy/D8
RevMutiple/F9
Energy/D12
RevMutiple/F7
Energy/D11
Energy/D14
Energy/D7
RevMutiple/F8
Energy/D13
Energy/D12
RevMutiple/F10
RevMutiple/F12
RevMutiple/F9
Energy/D14
RevMutiple/F14
Mean=2693.374
Mean=2834.662
Values in 10^ -4
2.500
1.000
2.000
0.800
1.500
0.600
1.000
0.400
0.500
0.200
0.000
-4
-10
-2-5
0 0
2
5
4
10 6
158
10
20
-1
-0.75
Values in Thousands
5%
5%
90%90%
-.9607
-3.0019
July 2007
-.301
-.247
-.291
-.116
-.107
-0.5
WACC/N21
.428
.285 .426
.305
Capex/J6
Capex/J6
.161 .281
.232
.216
Depreciation/N22
.174
.187
.108
.164
.163
Direct Cost Ratio/N15
.151
.161
.093
.148
.155
.093
.148
.151
.088
.148
.147
.085
.147
.084
.143
.145
.084
.141
.144
.083
.137
.138
.083
.135
.137
.083
-0.25
0
Std b Coefficients
0.25
0.5
0.75
1
5% 5%
9.14976.4629
Presenter: William Zhu
27
Brief Discussion on Results
• Basic statistics of NPV (eg, mean = 2835)
• 90% Confidence Interval (-3002, 9150)
• Interval Probability (NPV > 0 : 78.1%)
• Percentile (See Results in the Template)
• Others (See Results in the Template)
July 2007
Presenter: William Zhu
28
Stochastic Sensitivity Analysis (O)
• Tornado Graph
ƒ Own style
ƒ Succinct by grouping similar factors together
ƒ Key results --- Identifying sensible factors
WACC, Exchange rate, Capex, Spot Price, Energy
ƒ Comparison with the Deterministic Results
‰ Rank orders similar for WACC, Capex and Spot Price
‰ Rank orders differ for Energy, Exchange Rate, Depreciation
• Scenario Analysis
• 3 Multiple Simulations --- RiskSimTable()
‰ Energy level set to 100%, 110%, and 90%.
July 2007
Presenter: William Zhu
29
Tornado Graph Comparison
Stochastic Sensitivity Analysis
Deterministic Sensitivity Analysis
Percentage change
WACC
Electricity Spot Price
Revenue Multiplier
Energy Generated
Capex 1st Tw o Years
Exchange Rate
Depreciation
Terminal Value
Direct Cost Ratio
CPI Grow th
Capex 4th & 8th Years
Percentage change
Percentage change
Stochastic Sensitivity Index
WACC
-0.701
ExRate
0.189
Capex
-0.160
SpotPrice
0.135
Depreciation
-0.116
Direct Cost Ratio
-0.107
Energy
0.081
RevMutiple
0.078
CPI
0.000
Grid connection
0.000
Mgt & Admin Costs
0.000
PPI Grow th
Non Recurrent Costs
0.000
PRE Value
Pk Avoid
0.000
Recurrent Opex
Plant Warrant Charges
0.000
Transm ission Avoided
PPI
0.000
Mgt & Insurance Costs
PRE
0.000
Non Recurrent Opex
Recurrent Opex
0.000
Grid Connection Charges
Terminal Value
0.000
Plant Warrant Charges
July 2007
-0.8
Presenter: William Zhu
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
30
Three Multi-simulations
@RISK Output Details Report
Output Statistics
Outputs
Simulation
Statistics / Cell
Minimum
Maximum
Mean
Standard Deviation
Variance
Skewness
Kurtosis
Number of Errors
Mode
5.0%
10.0%
15.0%
20.0%
25.0%
30.0%
35.0%
40.0%
45.0%
50.0%
55.0%
60.0%
65.0%
70.0%
75.0%
80.0%
85.0%
90.0%
95.0%
Filter Minimum
Filter Maximum
Type (1 or 2)
# Values Filtered
Scenario #1
Scenario #2
Scenario #3
July 2007
X1 Energy
X1.1 Energy
X0.9 Energy
SenS_NPV
1
$N$29
SenS_NPV
2
$N$29
SenS_NPV
3
$N$29
-
-
-
9,020
17,070
2,835
3,712
13,782,612
0.238
3.273
6
1,438
3,002
1,727
877
218
344
876
1,323
1,750
2,211
2,676
3,138
3,575
4,078
4,644
5,200
5,892
6,645
7,564
9,150
7,357
19,920
4,792
3,913
15,307,963
0.264
3.267
6
5,060
1,348
38
849
1,567
2,160
2,698
3,193
3,633
4,129
4,608
5,098
5,568
6,091
6,673
7,275
7,982
8,804
9,816
11,513
0
>75%
<25%
>90%
10,666
14,244
907
3,518
12,374,937
0.209
3.279
6
902
4,651
3,444
2,621
1,979
1,445
935
511
84
326
775
1,212
1,617
2,084
2,617
3,136
3,781
4,540
5,404
6,802
0
>75%
<25%
>90%
Presenter: William Zhu
0
>75%
<25%
>90%
31
Scenario Analysis Results
@RISK Scenario Report (Simplified Sensitivity Report)
Scenario Report
Cell
Name
Select Index
MedianSD
Sim 1 >75%
-
Sim 1 <25%
-0.715
1.476
-
MedianSD
Sim 1 >90%
0.595
-
Sim 2 >75%
-
Sim 2 <25%
-0.693
-
MedianSD
MedianSD
Sim 2 >90%
0.562
-
Sim 3 >75%
0.502
-
Sim 3 <25%
-0.752
1.476
-
Sim 3 >90%
$J$5
Capex
0.615
$I$6
ExRate
$J$6
Capex
$D$7
Energy
$E$7
SpotPrice
$F$7
RevMutiple
$G$7
PPI
$H$7
CPI
$D$8
Energy
$E$8
SpotPrice
$F$8
RevMutiple
$G$8
PPI
$H$8
CPI
$D$9
Energy
$E$9
SpotPrice
$F$9
RevMutiple
$G$9
PPI
$H$9
CPI
$D$10
Energy
$E$10
SpotPrice
$F$10
RevMutiple
$G$10
PPI
$H$10
CPI
$I$10
ExRate
$J$10
Capex
$D$11
Energy
…………………………………………………………………………………………………………………………………………………………………………………………………………………………
$E$21
SpotPrice
$F$21
RevMutiple
$G$21
PPI
$H$21
CPI
-0.919
0.812
-1.378
-0.944
0.832
-1.378
-0.908
0.792
-1.377
$N$21
WACC
$D$22
Energy
$E$22
SpotPrice
$G$26
PPI
$H$26
CPI
July 2007
Presenter: William Zhu
32
Stochastic Sensitivity Analysis (A)
Using @Risk Advanced Techniques to do
the following 3 Important Analyses
™ Goal Seek
™ Stress Analysis
™ Sequential Analysis
July 2007
Presenter: William Zhu
33
Interface of Sensitivity Analysis (A)
Stochastic Goal Seek
On average, by how much should a factor change to
meet the new target (eg; new NPV)?
Energy Generated
Stress Analysis
Impact of input factors on the target NPV under special cases,
that is, stress input distributions (restricts samples) between
a specified pair of percentiles.
Lower Percentile
Upper Percentile
Individual Report
SpotPrice
All those 3 advanced analyses remain testing the sensitivities of the target variable
to the changes of input factors. However, unlike the ordinary @risk sensitivity test,
the results here have explicit economic meaning, since they directly measure the
changes of the target variable rather than ranking the β coefficients.
Energy
SpotPrice
1.0%
1.0%
5.0%
5.0%
10.0%
10.0%
25.0%
25.0%
50.0%
50.0%
75.0%
75.0%
90.0%
90.0%
95.0%
95.0%
99.0%
99.0%
July 2007
ExRate
1.0%
5.0%
10.0%
25.0%
50.0%
75.0%
90.0%
95.0%
99.0%
Capex
1.0%
5.0%
10.0%
25.0%
50.0%
75.0%
90.0%
95.0%
99.0%
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Energy SpotPrice
36.5
-20.0
40.0
-15.0
43.5
-10.0
47.0
-5.0
50.5
0.0
54.0
5.0
57.5
10.0
61.0
15.0
64.5
20.0
ExRate
0.56
0.59
0.61
0.64
0.66
0.69
0.71
0.74
0.76
1
Capex
15000
16500
18000
19500
21000
22500
24000
25500
27000
Factor Year
2009
See Value Distrib
See Value Distrib
-15
15
INPUT TABLE for SenS Goal Seek
9
Values for Distributions
75%
100%
NO
Value in Exel Table
Sequential
Analysis
# of Steps/Sim in Sequential Analysis
Percentile of Distributions
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Stress Analysis
ExRate
Sequential Analysis --- ie; Advanced Sensitivty Analysis in @Risk
A batch mode auto-reports of target, given input factors follow a
certain type of changes (comparable with Stress Analysis and
Multi # Simulation, but with greater flexibility)
Assumptions Used for Sequential Analysis
Goal Seek
Target
New NPV ($K)
5,000
OUTPUT TABLE for SenS Goal Seek
1
2
3
No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Presenter: William Zhu
NPV Report
$K
Original
3,083
$K
New
5,000
$K
Difference
1,917
Category
Factor Name
Chg to/by
# Sim
Energy Generated
112.25%
5
110.30%
5
Revenue Revenue Multiplier
Terminal Value
158.10%
6
Factors
110.30%
5
(Multiplier) Electricity Spot Price
Transmission Avoided
290.19%
8
PRE Value
206.31%
7
Grid Connection Charges -393.6%
9
Plant Warrant Charges
-549.10%
9
Cost
Capex 1st Two Years
85.23%
5
Factors Capex 4th & 8th Years
11.83%
11
(Multiplier) Exchange Rate
118.81%
7
Mgt & Insurance Costs
-141.47%
8
Recurrent Opex
-39.64%
7
Non Recurrent Opex
-141.51%
8
Direct Cost Ratio
-6.71%
7
Other
PPI Growth
6.35%
8
Factors
CPI Growth
-14.38%
13
(Additive) WACC
-0.78%
8
Depreciation
N/A
N/A
Compared
with
Deterministic
Goal Seek
Results
Chg to/by
110.89%
109.15%
154.52%
109.15%
268.65%
194.21%
-337.85%
-469.58%
86.62%
21.36%
117.23%
-114.57%
-23.97%
-114.57%
-5.96%
5.88%
-11.43%
-0.71%
-4.87%
34
Goal Seek
• Goal Seek
™ Purpose --- same as in the deterministic case, but
under stochastic environment
™ Feature --- Macro based automatic search
™ Results Compared to the deterministic case
• Results
™ Most of the results are close each other
™ Grid, Warranty, Mngt, and Non-Rec-opex Differ
™ No result for Depreciation
July 2007
Presenter: William Zhu
35
Stress Analysis
• Purpose of Stress Analysis
™ Intuitive Explanation --- optimistic vs.
pessimistic likelihood on input factors
™ Statistical Explanation --- constrain
distribution by “stressing” it to a pre-defined
range so that Monte Carlo simulations only
sample data from that range
• Stress Analysis on 4 Key Input Factors
Energy, Spot Price, Exchange Rate, and Capex
• Stress Results
July 2007
Presenter: William Zhu
36
Results of Stress Analysis
• Key Results
Stress Results (Range 0% ~ 25%. For Capex, the range corresponds to 75% ~ 100%)
Mean (B)
Mean (S)
90% CI (B)
90% CI (S)
Prob NPV>0 (B)
-3616
(-8168, 1533)
1950
(-3911, 8240)
3083
(-3002, 9150)
78.1%
1011
(-5034, 7448)
2482
(-3849, 9302)
Stress Results (Range 75% ~ 100%. For Capex, the range corresponds to 0% ~ 25%)
Mean (B)
Mean (S)
90% CI (B)
90% CI (S)
Prob NPV>0 (B)
9517
(2509, 17428)
4411
(-2312, 11420)
3083
(-3002, 9150)
78.1%
4483
(-1117, 10437)
3203
(-3041, 9922)
Factor
Energy
Sport Price
Exchge Rate
Capex
Factor
Energy
Sport Price
Exchge Rate
Capex
Prob NPV>0 (S)
9.4%
75.6%
59.6%
77.6%
Prob NPV>0 (S)
99.1%
87.3%
92.6%
83.4%
• Some Graphs (See the Excel file for details)
NPV CDF --- Energy Distribution Stressed to upper quartile
NPV CDF --- Energy Distribution Stressed to lower quartile
CDF Summary
CDF Summary
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
Baseline
0.1
Baseline
0.1
Stressed Simulation
Stressed Simulation
0
-12000
July 2007
-7000
-2000
3000
8000
13000
0
-10000
-5000
0
Presenter: William Zhu
5000
10000
15000
20000
25000
37
Sequential Analysis
• Purpose of Sequential Analysis
™ Intuitive Explanation --- testing different scenarios as
input factors changes steadily
™ Statistical Explanation --- Sampling input distributions
(rather than “stressing” them) sequentially so that
allows multiple Monte Carlo simulations to step
through each case. This is comparable to what
RiskSimTable() function does but with more
flexibilities.
• Sequential Analysis on 4 Key Input Factors
Energy, Spot Price, Exchange Rate, and Capex
• Sequential Results
July 2007
Presenter: William Zhu
38
Results of Sequential Analysis
Key Results of Sequential Analysis
Factor
Spot Price (yr 09)
Exchange Rate (08)
Capex (yr 08)
Energy (yr 09)
Value change
+/- $20 around its trend
US 0.56c → 0.76c
$27m → $15m
36.5 GWh → 64.5 GWh
NPV Changes in 90% Conf. Interval
(-3745, 8931) → (2860, 9300)
(-3134, 8512) → (-64, 10968)
(-17469, -1867) → (-5556, 7245)
(-3582, 9064) → (-2960, 9626)
Cumulative Distributions of N31 for Changing Values of SpotPrice E7
1
1
0.9
0.9
SpotPrice/2009(2)
0.7
SpotPrice/2009(3)
0.6
SpotPrice/2009(4)
SpotPrice/2009(5)
0.5
SpotPrice/2009(6)
0.4
SpotPrice/2009(7)
0.3
SpotPrice/2009(8)
0.2
SpotPrice/2009(9)
0.1
ExRate/2008(3)
0.6
ExRate/2008(4)
ExRate/2008(5)
0.5
ExRate/2008(6)
0.4
ExRate/2008(7)
0.3
ExRate/2008(8)
0.2
ExRate/2008(9)
-5000
0
5000
10000
0
-10000
15000
1
1
0.9
0.9
Capex/2008(2)
0.7
Capex/2008(3)
0.6
Capex/2008(4)
Capex/2008(5)
0.5
Capex/2008(6)
0.4
0
5000
10000
15000
20000
Capex/2008(7)
0.3
Capex/2008(8)
0.2
Capex/2008(9)
Values for Energy
D7
Energy/2009(1)
0.8
Cumulative Probability
Values for Capex
J6
Capex/2008(1)
0.8
-5000
Cumulative Distributions of N31 for Changing Values of Energy D7
Cumulative Distributions of N31 for Changing Values of Capex J6
Cumulative Probability
ExRate/2008(2)
0.7
0.1
0
-10000
Energy/2009(2)
0.7
Energy/2009(3)
0.6
Energy/2009(4)
Energy/2009(5)
0.5
Energy/2009(6)
0.4
Energy/2009(7)
0.3
Energy/2009(8)
0.2
Energy/2009(9)
0.1
0.1
0
-20000
Values for ExRate
I6
ExRate/2008(1)
0.8
Cumulative Probability
Values for SpotPrice
E7
SpotPrice/2009(1)
0.8
Cumulative Probability
Cumulative Distributions of N31 for Changing Values of ExRate I6
-15000
July 2007
-10000
-5000
0
5000
10000
15000
0
-10000
-5000
Presenter: William Zhu
0
5000
10000
15000
39
A Simple Decision Tree
• Reasons to Use Decision Tree
™ Many cases/scenarios exist
™ Easy to get lost without condensing them together
™ Try to find the overall expected value of NPV
• Factors/Cases for Building Decision Tree
™ Investment Types --- 3 decision nodes;
™ Energy generation --- 3 chance nodes;
™ Policy issue --- 2 chance nodes;
™ Spot price due to load growth --- 3 chance nodes.
So in total, there are 3 X 3 X 2 X 3 = 54 cases
• The NPVs for these 54 cases are calculated (via a VBA)
in the model, and together with the probabilities for
those 8 nodes, are linked directly into the decision tree.
July 2007
Presenter: William Zhu
40
Interface of Calculating 54 Cases
← Press the Button
Explanation
NPV Result ($K)
544
Terminal Value Asset Based
Tax Shield
YES
Price Node
Otahuhu
Capex
The scenario analysis tries to calculate different NPVs under different options and/or assumptions that a user chooses.
Because there are too many options/selections in this model, ONLY centain key risk related factors (or options) are chosen for the scenario
test. They are:
● Investment Decisions (3 options)
● Electricity Generation Profile/Probability (3 possible results)
● Carbon Tax On/Off Profile/Probability (2 possible results)
● National Electricity Load Growth Profile (3 possible results)
Therefore, there are 3 X 3 X 2 X 3 = 54 scenarios in total. It is these 54 cases that form the basis for the best, median and worst scenarios in
the "Main" sheet. They are also used for building the Decision Tree (in a seperate Excel workbook --- somehow, it seems not to work if built
within this workbook, might be due to the reason that we only have a trial version of Precision Tree software).
Case A - Base
Electricity Price
Assumed Grth
After 2017
PRE Revenue
NO
Included?
Note however, the NPV calculation is also associated with the other options/assumptions, which are listed on the left hand side of this sheet.
These options themselves (5 for TV, 2 for TS, 2 for PN, 4 for capex, 2 for EPA, and 2 for PRE) combined have 5 X 2 X 2 X 4 X 2 X 2 = 320
outcomes. If they were included in the scenario analysis, it would lead to 54 X 320 = 17280 cases! To avoid losing consentration and to allow
the decision tree to be reasonablly readible, the model constructor deliberately seperates these options from the major scenario analysis, and
lets users to decide which options he/she wants to use beforeahnd.
FINAL DECISION
Based on those 6 options being chosen, the expected NPV under those 54 scenarios discussed above is $K 544. Therefore, it arrivals the final decision ---
GREEN LIGHT ON --- The Project Is Worth Doing
July 2007
Presenter: William Zhu
41
Decision Tree --- Target
Decision
NPV
+
July 2007
$544
Presenter: William Zhu
42
Decision Tree --- 1st Layer
InvtTyp 1
NPV
TRUE
Generation
+
Decision
$544
$544
InvtTyp 2
InvtTyp 3
FALSE
Generation
+
FALSE
Generation
+
July 2007
Presenter: William Zhu
-$264
$512
43
Decision Tree --- 2nd Layer
Average
InvtTyp 1
TRUE
60.0%
Carbon Tax On ?
+
Generation
$879
$544
10.0%
High
0
30.0%
Low
NPV
Carbon Tax On ?
+
+
Decision
$2,595
Carbon Tax On ?
-$809
$544
Average
InvtTyp 2
FALSE
60.0%
Carbon Tax On ?
+
Generation
-$25
-$264
10.0%
High
0
30.0%
Low
+
Average
InvtTyp 3
FALSE
Carbon Tax On ?
+
60.0%
-$1,237
Carbon Tax On ?
+
Generation
$1,221
Carbon Tax On ?
$920
$512
High
10.0%
0
Low
30.0%
Carbon Tax On ?
+
+
July 2007
Presenter: William Zhu
$2,988
Carbon Tax On ?
-$1,130
44
Decision Tree --- 3rd Layer (Part)
Average
+
Carbon Tax On ?
60.0%
National Load Growth
10.0%
Yes
$1,949
$879
InvtTyp 1
TRUE
National Load Growth
90.0%
No
+
Generation
$760
$544
Carbon Tax On ?
10.0%
High
0
Low
30.0%
+
$2,595
Carbon Tax On ?
-$809
NPV
Decision
$544
InvtTyp 2
+
FALSE
Generation
-$264
+
InvtTyp 3
FALSE
Generation
$512
+
July 2007
Presenter: William Zhu
45
Decision Tree --- 3rd Layer (Full)
10.0%
Yes
Average
60.0%
National Load Growth
+
Carbon Tax On ?
$1,949
$879
90.0%
No
InvtTyp 1
TRUE
National Load Growth
+
Generation
$760
$544
10.0%
Yes
0
10.0%
High
Carbon Tax On ?
0
30.0%
$3,782
$2,595
No
90.0%
Yes
10.0%
0
Low
National Load Growth
+
National Load Growth
+
$2,464
National Load Growth
+
Carbon Tax On ?
$139
-$809
90.0%
No
NPV
National Load Growth
+
Decision
-$915
$544
10.0%
Yes
Average
60.0%
National Load Growth
+
Carbon Tax On ?
$757
-$25
90.0%
No
InvtTyp 2
FALSE
National Load Growth
+
Generation
-$112
-$264
10.0%
Yes
0
10.0%
High
Carbon Tax On ?
0
30.0%
$2,099
$1,221
No
90.0%
Yes
10.0%
0
Low
National Load Growth
+
National Load Growth
+
$1,124
National Load Growth
+
-$539
Carbon Tax On ?
-$1,237
90.0%
No
10.0%
Yes
Average
60.0%
National Load Growth
+
-$1,314
National Load Growth
$2,206
+
Carbon Tax On ?
$920
90.0%
No
InvtTyp 3
FALSE
National Load Growth
$777
+
Generation
$512
10.0%
Yes
0
High
10.0%
Carbon Tax On ?
0
No
90.0%
Yes
10.0%
0
30.0%
$4,419
$2,988
0
Low
National Load Growth
+
Carbon Tax On ?
National Load Growth
+
$2,829
National Load Growth
+
$15
-$1,130
No
90.0%
0
July 2007
National Load Growth
+
Presenter: William Zhu
-$1,257
46
Decision Tree --- 4th Layer (Part)
70.0%
Avg
2393
10.0%
Yes
4.2%
$2,393
National Load Growth
$1,949
Low
15.0%
0.9%
-3552
-$3,552
15.0%
High
5379
Average
60.0%
0.9%
$5,379
Carbon Tax On ?
$879
Avg
90.0%
No
70.0%
37.8%
1065
$1,065
National Load Growth
$760
Low
High
15.0%
8.1%
-4588
-$4,588
15.0%
4686
InvtTyp 1
TRUE
8.1%
$4,686
Generation
$544
10.0%
High
0
30.0%
Low
NPV
Carbon Tax On ?
+
+
Decision
$2,595
Carbon Tax On ?
-$809
$544
Average
InvtTyp 2
FALSE
60.0%
Carbon Tax On ?
+
Generation
-$25
-$264
10.0%
High
0
30.0%
Low
InvtTyp 3
FALSE
+
$1,221
Carbon Tax On ?
-$1,237
Generation
+
July 2007
Carbon Tax On ?
+
$512
Presenter: William Zhu
47
Project Summary
• Fifty-four cases exist for the project, but the overall NPV (ie., the expected
•
•
•
•
•
NPV) reaches $544K. It therefore, confirms that the project worth doing.
The NPV for the Case Selected equal $3,083K.
For the case selected, there are 90% chance that the NPV sits between $3,002K ~ $9,150K, with 78.1% chance it is greater than zero.
Factor analyses show that WACC, Exchange Rates, and Capex are most
sensible to the NPV, with Spot Prices and Energy Generation followed by.
To raise the current NPV up from $3,083K to $5,000K, it need to either
generate more energy by 12% or to push the electricity spot price up by
10%.
If, say the NZ exchange rates fall into the upper quartile of the forecast
range, the chance of NPV > 0 will rise from 78.1% to 92.6%. Alternatively,
it will drop to 59.6% if the exchange rates move to the opposite direction
(ie., the lower quartile of the forecast range).
July 2007
Presenter: William Zhu
48
Conclusion
™Presentation Review
‰ An income based FCF model is discussed for a
proposed wind farm project
‰ Risk factors are identified and analyzed by using
@Risk software
‰ Stochastic vs. deterministic sensitivity analyses are
discussed and compared
‰ Advanced stochastic sensitivity analysis is explored
‰ A simple decision tree is provided for summarizing
different scenario results
‰ Excel macros are built into the model so that users
can run the associated tests without knowing much
about @Risk
July 2007
Presenter: William Zhu
49
Conclusion
™Further Extension
‰ Target more @Risk output factors (eg, IRR)
‰ Incorporate @Risk Optimizer into the model
‰ Investigate in detail on the Decision Tree
‰ Randomize other factors (eg, interest rates)
‰ Add more financial features (eg, hedge)
™Suggestions and Questions
July 2007
Presenter: William Zhu
50