# Forecasting models for cost evolution of network components Risk analysis based on

```Forecasting models for cost
evolution of network components
and
Risk analysis based on
uncertainties in demand forecasts
and cost predictions
Kjell Stordahl
Telenor Networks
kjell.stordahl@telenor.com
19. okt. 2004
Telenor
1
Forecasting models for cost
evolution of network components
Kjell Stordahl
Telenor Networks
kjell.stordahl@telenor.com
19. okt. 2004
Telenor
2
Agenda
Write and Crawford’s learning curve model
The extended learning curve model
Discussion of different type of parameters in the
models
Examples
Conclusion on cost prediction models
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Learning curve
T. P. Wright proposed the concept of learning curves:
Tn= n-αα&middot;T0
where Tn is the average production time for n units, and
T0 is the time to complete the first unit.
J.R.Crawford applied the same formula, but interpreted Tn to
be the completing time for the nth unit in a series.
Let us assume that the component cost (price) Pn is
proportional to the production time Tn.
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Learning curve coefficient K
Pn= n-αα P0
Pn is the average cost for the nth unit.
The learning curve coefficient is defined by:
P2n= K &middot; Pn
Then
K= (2) -αα
α= −log2 K
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Relevant K values of different
network components
LearningCurveClass
CivilWorks
CopperCable
Electronics
SitesAndEnclosures
FibreCable
Installation (constant)
Installation (decresing)
OpticalComponents
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K_Value
100,00%
100,00%
80,00%
100,00%
90,00%
100,00%
70,00%
85,00%
80,00%
6
Learning curve prediction
Κ = 0,8 or α = 0,32
Learning curve predictions as a fuction of
number of produced units
1,2
1
Cost
0,8
0,6
0,4
0,2
0
1
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3
5
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7
9
11
13 15
17 19
7
21 23 25
27 29
What we need:
Cost as a function of time
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To combine the learning curves with volume forecasts
of components.
P(t) = n(t)−α P(0) = n(t)−log2K P(0)
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To combine the learning curves with volume forecasts
of components.
P(t) = n(t)−α P(0) = n(t)−log2K P(0)
(Olsen , Stordahl 1993) Extended learning curve
model is given by inserting a Logistic model into the
learning curve model
n(t)= M &middot; [1+ e(a+b&middot;t) ]–γγ
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Parameters in the model
K or α: Learning curve coefficient
P(0):
Production cost, unit no 1
M:
Saturation
a:
Parameter in the Logistic model
b:
Parameter in the Logistic model
γ:
Parameter in the Logistic model
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Reformulation of the parameters
The normalized Logistic model is:
nr (t) = n(t)/ M
The aggregated production volume the reference year, 0:
nr (0)
The growth period:
nr (t1) = 0,1
nr (t2) = 0,9
∆ T = t1 - t2
Interpretation of the parameters
1,2
1
0,8
0,6
0,4
nr(0)
0,2
0
t1
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0
∆T
t2
13
P( t ) = P( 0) ⋅ nr ( 0) −1 ⋅ 1 + e
−1 log 2 ⋅ K
2 ⋅ ln 9
−
1
⋅t
ln nr ( 0 ) − 1 −
∆T
The extended learning curve ( γ = 1)
P(0): Production cost the reference year (0)
nr(0): Relative accumulated production volume the
reference year
∆T: Time for the accumulated volume to grow from 10% to
20%
K:
Learning curve coefficient
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Cost as a function of Κ
nr (0)=0.1, ∆T=5
Relative cost
1
0.9
0.8
0.7
0.6
Relative
0.5
cost
0.4
0.3
0.2
0.1
0
0.9
0.5
0 1 2
3 4 5
Project year
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15
6
7
8
0.1
9
K
Cost as a function of nr(0)
∆T = 5, K = 0.8
Relative cost
1
0.9
0.8
0.7
0.6
Relative
0.5
cost
0.4
0.3
0.2
0.1
0
0.9
0.5
0 1 2
3 4 5
6 7 8
Project year
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0.1
9
nr (0)
Cost as a function of ∆T
nr (0) = 0.1, K = 0.8
Relative cost
1
0.9
0.8
0.7
0.6
Relative
0.5
cost
0.4
0.3
0.2
0.1
0
18
10
0 1 2
3 4 5
6 7 8
Project year
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2
∆T
Historical diffusions of selected
100
90
fixed telephone
80
70
Cable
60
50
VCR
40
PC
T elevision
30
Mobile
20
Internet
10
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19
99
19
97
19
95
19
93
19
91
19
89
19
87
19
85
19
82
19
75
19
66
19
62
19
56
19
53
0
Historical diffusions of selected
goods in Finland.
100
Color T V
90
Freezer
80
Microwave
70
PC
60
Mobile
50
Video recorder
40
Dishwasher
Internet
30
20
CD player
10
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19
20
02
20
00
19
98
19
90
19
80
19
76
0
Recommended values on the
parameters when cost time series are
not available
LearningCurveClass
CivilWorks
CopperCable
Electronics
SitesAndEnclosures
FibreCable
Installation (constant)
Installation (decresing)
OpticalComponents
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VolumeClass
Emerging_Fast
Emerging_Medium
Emerging_Slow
Emerging_VerySlow
Mature_Fast
Mature_Medium
Mature_Slow
Mature_VerySlow
New_Fast
New_Medium
New_Slow
New_VerySlow
Old_Fast
Old_Medium
Old_Slow
Old_VerySlow
Straight Line
K_Value
100,00%
100,00%
80,00%
100,00%
90,00%
100,00%
70,00%
85,00%
80,00%
20
nr(0)
0,001
0,001
0,001
0,001
0,1
0,1
0,1
0,1
0,01
0,01
0,01
0,01
0,5
0,5
0,5
0,5
0,1
∆T
5,00
10,00
20,00
40,00
5,00
10,00
20,00
40,00
5,00
10,00
20,00
40,00
5,00
10,00
20,00
40,00
1000,00
Forecasts for ADSL line costs. Estimation:
P(2000)= 212 Euro, ∆T=8, n(2000)=0,1%,K=0,736
Forecast model for ADSL line costs
250
Model
Data
Euro
200
150
100
50
0
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
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Forecasts for STM equipment costs. Estimation:
P(2000)=1188 Euro, ∆T=8, n(2000)=7,4%, K=0,756
Forecast model for STM equipment costs
1400
Model
1200
Data
Euro
1000
800
600
400
200
0
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
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Logistic model with different γ values
1,2
1
0,3
0,8
0,5
0,6
1
2
0,4
4
0,2
10
0
-10
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-0,2
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0
5
10
23
15
20
ln δ
−1 +
⋅t
∆T
P(t ) = P(0) ⋅ n (0) − 1 ⋅ 1 + e
r
− γ log 2 ⋅ K
ln n (0)
r
−1
y
The extended learning curve (diff γ)
P(0): Production cost the reference year (0)
nr(0): Relative accumulated production volume the reference year
∆T: Time for the accumulated volume to grow from 10% to 20%
K:
Learning curve coefficient
γ:
Parameter asymmetry
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Use of the the Extended learning
curve model
RACE 2087/TITAN 1992-1996
AC 226/OPTIMUM1996-1998
AC364/TERA1998-2000
IST-2000-25172 TONIC2000-2002
ECOSYS / CELTIC 2004Many Eurescom projects
– P306, P413, P614, P901 etc
Within Telenor and other project partners organizations
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learning curve model
The model makes forecasts of component costs
(predictions as a function of time
The model has the possibility to include both a priori
knowledge and statistical information at the same time
The model can be used to forecast component costs
evolution even if no cost observations are known
The model can be used to forecast component costs based
on estimation of the parameters when historical costs are
available
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Risk analysis based on
uncertainties in demand forecasts
and cost predictions
Kjell Stordahl
Telenor Networks
kjell.stordahl@telenor.com
19. okt. 2004
Telenor
27
Agenda
Business case: Roll out of ASDL2+/VDSL
Evaluation of 6 different roll out scenarios
Calculation of net present values for the roll out scenarios
Framework for risk analysis
Modelling dependency between variables in risk analysis
Results from risk analysis
Conclusions
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roll out
Competition (Same technology and other technologies)
Size of the access area
Distribution of the copper line length
Standardisation of network technology/components
Component price and functionality
Maintenance costs
Expected ARPU (Average revenue per user)
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Adoption rate as a function of delayed
introduction
35,0 %
30,0 %
Alone
25,0 %
0 Year delay
20,0 %
1 year delay
2 year delay
15,0 %
3 year delay
10,0 %
4 year delay
5 year delay
5,0 %
6 year delay
0,0 %
2004
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2005
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2006
2007
2008
30
2009
2010
Market segmentation
Market segment
Area 1
Area 2
Area 3
Area 4
Area 5
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Exchange size N
15.000 &lt; N
10.000 &lt; N =&lt; 15.000
5.000 &lt; N =&lt; 10.000
2.000 &lt; N =&lt; 5.000
N =&lt; 2.000
31
Percent households
10 %
15 %
20 %
20 %
35 %
Generic case study
Population and coverage
60 000 000
2,4
25 000 000
Population
Persons per Household (HH)
total number of HH
Distribution of HHs
Averagen number of HHs per CO
Coverage level
HH (in %) within 2 km
Coverage (HP)
Total number of HHs in covered echanges
Number of HHs in areas without deployment
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Area 1
14 %
12 000
Area 2
21 %
8 000
Area 3
29 %
2 600
Area 4
23 %
1 400
Area 5
13 %
400
100 %
10 %
15 %
20 %
15 %
0%
60 %
75 %
2 500 000
3 333 333
278
166 667
75 %
3 750 000
5 000 000
625
250 000
75 %
5 000 000
6 666 667
2 564
583 333
75 %
3 750 000
5 000 000
3 571
750 000
32
15 000 000
7 038
3 250 000
The 6 scenarios studied
Scenario 1 – Market equality, no overlap
Scenario 2 – Market equality, 50% overlap
Scenario 3 – Market equality, 75% overlap
Scenario 4 – Incumbent 2 years delayed
Scenario 5 – Incumbent 1 years delayed
Scenario 6 – Incumbent offensive roll out
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Scenario 1
”Market equality, no overlap”
Year
Incumb.
Other Overlap Incumb. Other
Incumb. Other Incumb. Other Incumb. Other
Area 1 Area 1 Area 2 Area 2 Area 3 Area 3 Area 4 Area 4
2004
2,5 %
2,5 %
0,0 % 2,5 % 2,5 %
2005
7,5 %
7,5 %
0,0 % 2,5 % 2,5 % 2,5 % 2,5 %
2006 12,5 % 12,5 %
0,0 %
2007 17,5 % 17,5 %
0,0 %
5,0 % 5,0 %
2008 22,5 % 22,5 %
0,0 %
5,0 % 5,0 %
2009 27,5 % 27,5 %
0,0 %
5,0 % 5,0 %
2010 30,0 % 30,0 %
0,0 %
2,5 % 2,5 %
Sum
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5,0 % 5,0 %
5,0 %
Telenor
5,0 %
34
7,5 % 7,5 % 10,0 % 10,0 % 7,5 %
7,5 %
Scenario 4
”Incumbent 2 years delayed”
Year
Incumb.
Other Overlap Incumb. Other
Incumb. Other Incumb. Other Incumb. Other
Area 1 Area 1 Area 2 Area 2 Area 3 Area 3 Area 4 Area 4
2004
0,0 %
5,0 %
0,0 %
5,0 %
2005
0,0 % 15,0 %
0,0 %
5,0 %
2006 10,0 % 25,0 %
5,0 % 5,0 %
5,0 %
5,0 % 5,0 %
2007 22,5 % 37,5 % 15,0 % 5,0 %
5,0 %
5,0 % 7,5 % 7,5 %
2008 35,0 % 45,0 % 27,5 %
5,0 %
2,5 % 5,0 % 5,0 % 2,5 %
2009 45,0 % 50,0 % 37,5 %
5,0 %
2,5 % 2,5 % 2,5 % 2,5 %
2010 47,5 % 52,5 % 45,0 %
Sum
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7,5 %
10,0 %
Telenor
10,0 % 15,0 % 15,0 % 20,0 % 20,0 % 7,5 %
35
2,5 %
7,5 %
Demand for the Telecommunications
Services
Risk Assessment
DB
Services
Architectures
Geometric
Model
OA&amp;M
Costs
Revenues
Investments
FirstInstalled
Installed
First
Cost
Cost
LifeCycle
Cycle
Life
Cost
Cost
Cash flows,
Profit &amp; loss accounts
Economic
Inputs
Year 0
NPV
NPV
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Year 1
Year n
IRR
IRR
36
...
Year m
Payback
Payback
Period
Period
Net present values for the roll out
scenarios
700
600
NPV [ mill. EUR]
500
400
300
200
100
0
-100
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Sc. 1
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Sc. 2
Sc. 3
37
Sc. 4
Sc. 5
Sc. 6
Conclusions
A framework for analysing ADSL2+/VDSL rollout has been
developed
The first step is to enter the market with a cherry picking
strategy
Delay in roll out causes significant loss
The best strategy is to enter the areas as the first operator
starting with the largest areas
But what about the uncertainty and the risks?
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Risk analysis principles
Variable 1
0,68
0,74
0,80
0,86
0,92
10 000 Trials
1,09
1,54
2,00
2,46
2,91
0,55
0,78
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1,00
1,23
1,45
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52 Outliers
,027
269
,020
201,7
,013
134,5
,007
67,25
,000
0
-3000
Variable 3
NPV
Frequency Chart
-1000
1000
kECU
3000
5000
Frequency
Probability
Variable 2
Evaluation of the output distribution
Suppose Net Present Value is the output distribution
Alternative measures:
Mean value
Confidence interval
10% percentage
5% percentage
Percentage of observations below NPV=0
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Fitting of probability densities for
the input variables
The probability densities have the ability not to give negative
values.
The following input are convenient for defining the probability
densities:
Default value
Minimum value
5% percentile
95% percentile
Maximum value
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Beta function and the fitting
1
α −1
β −1
p( y ) =
( y − a ) (b − y )
α + β −1
Β(α , β )(b − a )
Γ(α )Γ(β )
Β(α , β ) =
Γ(α + β )
The parameters/variables a, b, α and β in the Beta function
are found base on the shown input
Solver is used in the calculations
The distribution is multiplied with the default value to map
the real distribution
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Definition of probability functions
for critical variables
Variable
Name
Monthly
ARPU
Line Card
Price
Sales Costs
Provisioning
Costs
Equipment
Price
Reduction
Rate
Rate, final
year
Customer
Installations
Cost
Content Costs
Smart Card
Costs
Customer
Operations &amp;
Maintenance
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α
β
124.7
5.11
11.16
1,800
2,000
4.94
4.94
30%
32.5%
35%
4.94
4.94
60
65
70
80
11.77
11.77
5%
8%
10%
12%
15%
8.02
8.02
26%
29%
32%
37%
42%
4.02
6.04
100
110
120
130
140
4.95
4.95
50%
55%
60%
65%
70%
4.95
4.95
20
25
30
35
40
4.94
4.94
15
20
25
30
35
4.95
4.95
Minimum
Value
5%
percentile
Default
Value
95%
percentile
Maximum
Value
90
95
100
108
1,200
1,400
1,600
25%
27.5%
50
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Demand for the Telecommunications
Services
Risk Assessment
DB
Services
Architectures
Geometric
Model
OA&amp;M
Costs
Revenues
Investments
FirstInstalled
Installed
First
Cost
Cost
LifeCycle
Cycle
Life
Cost
Cost
Cash flows,
Profit &amp; loss accounts
Economic
Inputs
Year 0
NPV
NPV
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Year 1
Year n
IRR
IRR
44
...
Year m
Payback
Payback
Period
Period
Net present values for the roll out
scenarios
700
600
NPV [ mill. EUR]
500
400
300
200
100
0
-100
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Sc. 2
Sc. 3
45
Sc. 4
Sc. 5
Sc. 6
Net present value results from risk
analysis. Different simulations
10 variables simulated
Scenario
5% perc.
95%
perc.
σ
simulated
95%
5% perc.
σ
perc.
5% perc.
95%
perc.
σ
Sc. 1
-48.5
1 155.7
364.1
-5.1
1 114.5
339.5
58.6
928.4
263.4
Sc. 2
-70.6
1 138.4
365.7
-27.4
1 097.3
341.2
37.6
909.7
265.6
Sc. 3
-102.3
1 108.3
366.4
-58.9
1 066.1
341.9
4.3
882.5
266.6
Sc. 4
-376.4
438.5
264.8
-341.4
408.4
227.6
-287.4
261.6
166.7
Sc. 5
-212.0
830.8
315.9
-174.2
795.8
293.8
-112.9
624.9
224.1
Sc. 6
-50.6
1 561.9
487.7
6.0
1 507.2
455.9
90.6
1 256.9
356.1
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5% percentile for NPV for the scenarios
for different correlation between demand
and ARPU
400
5% percentiles of NPV [mill. EURO]
300
200
100
no corr.
-0.25 corr.
0
Sc. 1
Sc. 2
Sc. 3
Sc. 4
-100
-200
-300
-400
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Sc. 5
Sc. 6
-0.50 corr.
-0.75 corr.
Conclusions
The risk framework has been developed through the
European programs RACE, ACTS and IST, by the projects
RACE 2087/TITAN, AC 226/OPTIMUM, AC364/TERA and
IST-2000-25172 TONIC.
The presentation shows how risk analysis is applied on a
specific business case for evaluation of the economic risks.
The methodology for fitting the probability densities of
critical variables in the business case is described
The analysis also show the effect by modelling dependency
between ARPU and demand in the risk simulations
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Time for Questions &amp;