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REAL OPTIONS ANALYSIS IN HYDRAULIC ENGINEERING
NGUYEN TAN THAI HUNG
DEPARTMENT OF CIVIL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
2008/2009
REAL OPTIONS ANALYSIS IN HYRAULIC ENGINEERING
NGUYEN TAN THAI HUNG
A THESIS SUBMITTED
FOR THE DEGREE OF BACHELOR OF ENGINEERING
DEPARTMENT OF CIVIL ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
i
ACKNOWLEDGEMENTS
First and foremost, the author would like to express his deepest gratitude to his supervisor,
Associate Professor Vladan Babovic, for his invaluable guidance and encouragement. It
would have been much harder to complete this project without the advice and motivation
from Professor Babovic.
Secondly, the author feels grateful to Mr. Zhang Xu, Stephen of the Singapore-Delft
Water Alliance for his consistent and helpful guidance during the last two semesters, as
well as his valuable comments and suggestions on the programming and debugging of the
MATLAB model.
Appreciation is also extended to Ms. Sally Teh, Mr. Albert Goedbloed and the Singapore-
Delft Water Alliance for the privileges that the author was provided during the period of
the project.
Acknowledgements are also attributed to those who have contributed to this research in
one way or another, and also to the authors of various papers and materiel referred to in
this thesis.
Last but not least, the author would like to thank his family for their support throughout
his years of education and to his many friends who had helped him in school works and
who had made his years in university memorable ones.
ii
TABLE OF CONTENTS
ACKNOWLEDGEMENTS .................................................................................................. i
TABLE OF CONTENTS..................................................................................................... ii
SUMMARY ......................................................................................................................... v
NOMENCLATURE............................................................................................................ vi
LIST OF TABLES ............................................................................................................ viii
LIST OF FIGURES.............................................................................................................. x
1. INTRODUCTION ........................................................................................................ 1
1.1 Background .......................................................................................................... 1
1.2 Objectives and scope of project ........................................................................... 1
2. LITERATURE REVIEW ............................................................................................. 3
2.1 Financial options .................................................................................................. 3
2.1.1 Definitions........................................................................................................ 3
2.1.2 Types of options ............................................................................................... 3
2.1.3 Examples .......................................................................................................... 4
2.2 Real options.......................................................................................................... 5
2.3 Monte Carlo simulation........................................................................................ 6
3. CASE STUDY – PARKING GARAGE....................................................................... 7
3.1 Is average a good approach? ................................................................................ 7
3.2 Dealing with uncertainties.................................................................................... 8
3.3 Case description ................................................................................................... 9
3.4 Planning with traditional Net-Present Value (NPV) model: ................................ 9
3.4.1 The model......................................................................................................... 9
3.4.2 Sensitivity analysis - What if demand changes? ............................................ 10
iii
3.5 Planning with randomized demand .................................................................... 13
3.5.1 Changing demand projection factors.............................................................. 13
3.5.2 Sensitivity analysis ......................................................................................... 15
3.6 Considering expansion option............................................................................ 17
3.7 Conclusion for the case study............................................................................. 18
4. SINGAPORE WATER – A PICTURE ...................................................................... 20
4.1 Demand .............................................................................................................. 20
4.1.1 Domestic demand........................................................................................... 20
4.1.2 Industrial demand........................................................................................... 24
4.2 Supply................................................................................................................. 24
4.2.1 The national four-tap model........................................................................... 25
4.2.2 The potential "fifth tap".................................................................................. 29
5. MONTE CARLO SIMULATION MODEL............................................................... 31
5.1 Demand model ................................................................................................... 31
5.1.1 Domestic consumption model........................................................................ 31
5.1.2 Total consumption model............................................................................... 34
5.2 Supply model...................................................................................................... 34
5.2.1 Configuration and risk premium .................................................................... 34
5.2.2 Imported water modelling .............................................................................. 35
5.2.3 Cost and payment modelling.......................................................................... 36
5.2.4 "Unit Tariff per Output" modelling................................................................ 40
5.2.5 "Two-part tariff" modelling............................................................................ 44
5.3 Risk modelling ................................................................................................... 44
6. RESULTS AND DISCUSSIONS............................................................................... 46
6.1 “Unit tariff” vs. “two part tariff” ........................................................................ 46
iv
6.2 Effects of the “fifth tap” ..................................................................................... 46
6.2.1 Mean NPV...................................................................................................... 46
6.2.2 Water security risks and water scarcity risks ................................................. 47
6.3 Effect of risk premium ....................................................................................... 48
6.4 Effect of β and m................................................................................................ 50
6.5 Recommendation for future researches.............................................................. 50
REFERENCES................................................................................................................... 51
APPENDIX A – CASE STUDY RESULTS ..................................................................... 53
APPENDIX B – POPULATION PROJECTION RESULTS............................................ 56
APPENDIX C– SIMULATION RESULTS ...................................................................... 59
v
SUMMARY
This dissertation aims to provide a framework for the planning of Singapore’s water
supply system in 40 years, using real options analysis with Monte Carlo simulation.
A hypothetical case study on a parking garage is conducted to examine the advantages of
real options analysis over the traditional Net-Present-Value model. The case study
remarked the value of flexibility, the ability to wait for more information before making
decision, and the sensitivity analysis is a guide to which kind of information worth
attending to. The case study also emphasized the strength of simulation in capturing
reality.
The review of Singapore’s water issues pointed out that there are a lot of uncertainties, a
lot of potential risks and opportunities that require a flexible management.
The Monte Carlo simulation model involving Singapore’s four national taps and a
potential fifth tap suggested that LNG-desalination is a valuable option with high chance
of exercising. The simulation model also studied the effect of different management
approaches and noted that flexibility is not always in favour. The model also examined the
effect of risk premium on imported water.
Keywords: real options, Monte Carlo simulation, MATLAB, water supply system, four-
tap model, expansion option, flexibility, risk premium
vi
NOMENCLATURE
β Proportion of break-even point volume to total capacity
DBOO Design-Build-Own-Operate
Df Final demand
DPM Deputy Prime Minister
D(t) Demand at time t
E Excessive amount of demand to supply
FC Fixed Cost
I Investment cost
kF Fixed Cost coefficient
kI Investment cost coefficient
LNG Liquid natural gas
m Economies of scale factors
O&M Operation & Maintenance
NPV Net Present Value
P The averaged unit cost of producing a unit volume of water
PM Prime Minister
PUB Public Utilities Board
pti Technical cost at year i
vii
pfi Energy cost at year i
Q Total capacity
q Break-even point volume
qe Expansion amount for capacity
qr Reduction amount for capacity
RO Reverse-Osmosis
RSP Required selling price
RV Revenue
S Saving
s Individual water consumption
TC Total Cost
TFR Total Fertility Rate
U Tap usage
u Unit production cost
x number of days Sinagpore can survive without imported
water
y year
viii
LIST OF TABLES
Table 3.1 – Summary of parking garage problem................................................................ 9
Table 3.2 - Sensitivity results for demand projection factors ............................................ 12
Table 3.3 - Mean NPV of randomized demands................................................................ 14
Table 3.4- Sensitivity results for initial demand’s volatility.............................................. 15
Table 3.5 - Sensitivity with respect to first year's volatility and with expansion option ... 17
Table 3.6- Case study summary ......................................................................................... 19
Table 4.1 - Domestic and individual water consumption................................................... 24
Table 4.2 -Break-down of Singapore's water consumption ............................................... 24
Table 4.3 - Major reservoirs............................................................................................... 26
Table 5.1 - Scenarios for 2011 Agreement ........................................................................ 35
Table 5.2 - Scenarios for 2061 Agreement ........................................................................ 35
Table 5.3 - Cost components.............................................................................................. 36
Table A.1 - Sensitivity results, demand by year 10 ........................................................... 54
Table A.2 - Sensitivity results, demand after year 10 ........................................................ 54
Table A.3 - Sensitivity results, volatility in year 10 demand............................................. 55
Table A.4 - Sensitivity results, volatility in demand after year 10..................................... 55
Table B.1 - Resident population projection ....................................................................... 56
Table B.2 - Non-resident population projection................................................................. 56
Table B.3 - Total population projection ............................................................................. 57
Table B.4 - Age-gender-specific population projection..................................................... 58
Table C.1 - Comparison between Unit tariff and two-part tariff, m = 1, β = 0.5............... 60
Table C.2 - m = 0.5, β = 0.5, two-part tariff....................................................................... 61
Table C.3 - Comparison between β = 0.5 and β = 0.75 (Unit tariff).................................. 62
ix
Table C.4 – Comparison between big and small LNG capacity ........................................ 63
x
LIST OF FIGURES
Figure 3.1 - The flaw of averages (from Savage, 2000) ...................................................... 7
Figure 3.2 - Hypothetical demand projection..................................................................... 10
Figure 3.3 - Different demand curves associated with different estimation of initial
demand ............................................................................................................................... 11
Figure 3.4 - Sensitivity results for demand projection factors ........................................... 12
Figure 3.5 - A typical demand scenario ............................................................................. 14
Figure 3.6 - Sensitivity results for different volatility........................................................ 16
Figure 4.1 - Average monthly water bill, inclusive of tax (in S$) 1980 - 2005 ................. 22
Figure 4.2 - Domestic Sector Breakdown, Singapore........................................................ 23
Figure 4.3 - The blue map of Singapore............................................................................. 25
Figure 4.4 - Contribution of four national taps with maximum capacity for local taps..... 29
Figure 5.1 - Individual water consumption model ............................................................. 33
Figure 6.1 – Effect of enlarging LNG capacity.................................................................. 47
Figure 6.2 - Mean NPV result ............................................................................................ 48
Figure 6.3 - Partial NPV curve from $0.00 to $0.50.......................................................... 50
Figure A.1 - Best, base and worst cases, demand by year 10 ............................................ 53
Figure A.2 - Base and worst cases, demand by year 10..................................................... 53
Figure A.3 - Base and best cases, demand by year 10 ....................................................... 54
Figure A.4 - Effect of volatility on net present value......................................................... 55
Figure C.1 - Unit tariff, m = 0.5, β = 0.5............................................................................ 59
Figure C.2 - Two part tariff, m = 1, β = 0.5 ....................................................................... 59
Figure C.3 - Unit tariff, m = 1, β = 0.5............................................................................... 60
Figure C.4 - Demand and supply spectra (100 simulation runs)........................................ 62
xi
Figure C.5 - A typical random walk for desalination variable costs.................................. 63
1
1. INTRODUCTION
1.1 Background
In project evaluation, the traditional discounted cash flow model, for which decision
making is based on net present value (NPV), has been widely practiced. However, this
model is a rigid approach and is incapable in risky projects that involve a high level of
uncertainty such as water supply system planning.
A better approach
1.2 Objectives and scope of project
This dissertation aims to provide a framework for the planning of Singapore’s water
supply system in 40 years, using real options analysis with Monte Carlo simulation.
The thesis consists of:
• a review on the theory of real options;
• a case study to demonstrate the advantages of the real options analysis compared
to traditional NPV;
• a summary of the current picture of the Singapore water supply and the
uncertainties involved;
• and an application of real options analysis to the planning of Singapore water
supply system.
2
As will be shown in the thesis, the planning for Singapore’s water supply system involves
not only many risks and uncertainties but also a lot of potential. As a framework, the
thesis will demonstrate how real options analysis can solve this problem, how it is better
compared to traditional method. To achieve that, a decision making model, involving
demand, supply and some expansion and reduction rules will be built and tested. This
thesis will be a start for subsequent researches towards a reliable decision making solution
for the planning works.
The time horizon for this project is 40 years from 2008 to 2047.
The programming language used in the case study is Microsoft Excel, and that for the
main model is Mathworks MATLAB.
3
2. LITERATURE REVIEW
2.1 Financial options
Since real options employs financial options theory but applies for real assets (hence the
name "real options"), it is beneficial to start our options understanding by going through
financial options theory.
2.1.1 Definitions
According the Australian Stock Exchange (2004), an option is a right, but not the
obligation, of the option holder to buy or sell a security with a specific price, called the
exercise or strike price, on or before a specific date in the future, called the expiry date.
Technically speaking, an option is a contract between two parties: the buyer of the right
(called the taker) and the seller (called the writer). The price for having this right is called
the option premium. Note that in options trading, the buyer and seller are not buying or
selling the underlying security directly. They are trading the right to buy or sell the
security. Clearly, there are two types of options: options to buy (call options) and options
to sell (put options).
2.1.2 Types of options
A call option gives the taker the right to buy the underlying security at an agreed price.
When the taker chooses to exercise the right, which means he decides to buy the security,
the writer has to sell the security at the agreed price, even if it is higher than the market
price. It is important to note that the taker does not have to exercise this right. Obviously,
the writer will choose to do so when the market price is higher than the agreed price.
4
Otherwise, if the market price is lower than the agreed price, the writer would rather buy
from the market. If the two prices are the same, the writer is indifferent.
Similarly, a put option gives the taker the right to sell the underlying security at an agree
price, and the taker has to buy the security once the right is exercised. Obviously, the taker
will sell the security to the writer when the agreed price is higher than the market price,
otherwise he would prefer to sell to the market. If the two prices are the same, the taker is
indifferent.
2.1.3 Examples
Example of call option: suppose share price of a particular firm is $5.00 each. If you
expect the price to rise, you take a $100 option to buy 1000 shares at $5.20 each in 3
months.
If 3 months later, share price rises to $5.50, and you buy at $5.20, you have made a profit
of ($5.50 - $5.20) x 1000 = $300, less the option premium $300 - $100 = $200. So, you
have achieved a capital gain of $200.
If, unfavourably, share price falls to $4.80, you will not buy the shares from the writer and
lose the option premium of $100. Should you have bought the share directly 3 months
earlier, you would have lost ($5.00 - $4.80) x 1000 = $200. So, the option limits your loss
to only $100.
Example of put option: suppose share price of a particular firm is $5.00 each. If you
expect the price to fall, you take a $100 option to sell 1000 shares at $4.80 each in 3
months.
5
If 3 months later, share price falls to $4.50, and you sell at $4.80, you have made a profit
of ($4.80 - $4.50) x 1000 = $300, less the option premium $300 - $100 = $200. So, you
have gained a profit of $200.
If, unfavourably, share price rises to $5.20, you will not sell the shares to the writer at
$4.80, and lose the option premium of $100. Should you have sold the share directly 3
months earlier, you would have suffered a capital lost ($5.20 - $5.00) x 1000 = $200. So,
the option limits your loss to only $100.
The examples show that options are a type of risk mitigation that limits loss over a
security to the option premium.
2.2 Real options
According to Wang (2003), Myers (1987) was one of the first authors to point out the
limitations of the traditional discount cash flow model. Then, Dixit and Pindyck (1994)
noted the irreversibility of investment decision making and the uncertainties involved.
Trigeorgis (1996) was attributed to have collected scattered knowledge about real options.
A few other authors wrote some introductory books and finally, the theory develops
rapidly at the beginning of this century. So, the theory of real options has just had a firm
ground in about 10 years.
Similar to financial option, a real option is the right (and not the obligation) to execute a
project. Unlike financial options which involve intangible assets (shares, securities), real
options often involve tangible assets: a factory, a patent etc – hence the name real options.
For example, a factory manager may have the right to expand his factory to meet new
productivity level. This right may be gained through a land acquisition - purchasing the
6
parcel of land next to his factory. With this parcel of land in possess, the factory manager
is technically taking a call option. He paid the option premium - the land acquisition cost.
Once market for his product turns good, he will exercise the option, expand the factory
and produce more products. If the market does not turn into his favour, he is not obliged to
expand the factory still.
Hence, with real option, the decision maker can wait until more information is available,
and then choose to execute if the situation is in favour, or abandon if not. The price for
this right to wait is the option premium, which is much smaller than the project execution
cost. Should the decision maker opt to abandon the project, the most loss suffered would
only be this premium, not the entire execution cost.
There are many ways to evaluate an option, the most common being Black-Scholes
model, decision tree analysis, and Monte Carlo simulation.
2.3 Monte Carlo simulation
Monte Carlo simulation is a process in which a large amount of random inputs (with an
assumed statistical distribution) are generated, and through a known model, converted to
outputs. It has some advantages over an analytical (mathematical) model. Usually an
analytical model requires simplification of the problem while a simulation can describe
the problem closely. As inputs are generated, it helps to save data acquisition time.
However, a simulation for a large problem may require significant computer resources
(Mun, 2006).
7
3. CASE STUDY – PARKING GARAGE
3.1 Is average a good approach?
In daily life circumstances, we tend to take an average of a quantity. For example, when
different clocks show different times and a standardized clock is unavailable, we take the
average of them.
However, an average is not always a good approach, especially when the quantities are
quite scattered, or even when there are some adverse situation where something might
happen far from the average. This situation is illustrated the case of a scientist who
drowned in a river that is of “average” 3 feet deep (see Figure 3.1) (Savage, 2000).
Figure 3.1 - The flaw of averages (from Savage, 2000) Cartoon by Jeff Danziger
8
A more technical example is the case of a car parking garage at a shopping centre. The
investor of the garage predicts that the average demand for parking in a particular area in
the next few years will be 750 spaces per year. He builds a facility to cater for 750 cars. In
the bad years when car parking demand is less than 750 spaces, he is not able to utilize
full garage capacity and may make a loss. In the good years when parking demand is more
than 750 spaces, he does not have sufficient facility to meet the entire demand. So he
cannot make extra profit to cover the bad years. Thus, even though demand averages up to
his correct estimate of 750 spaces per year, profit cannot average up. An average approach
of input does not lead to the average output. This is an expression of the so-called “The
Flaw of Average” (Savage, 2000).
3.2 Dealing with uncertainties
The moral of the story is that we need to pay attention to uncertainty. For the case of the
parking garage, demand is the main uncertainty. For various reasons, it is virtually
impossible to predict exactly how many parking slots will be demanded in a future year.
The Figure depends on how many people visiting the shopping centre, which in turn is
affected by economic conditions, consumers’ behaviour and other uncertainties. In
additions, it also changes due to infrastructure conditions such as public transport
availability, the overall development of the town in which the shopping centre is located
etc. In short, demand is an uncertainty input for the planning and using the average is not a
good strategy, as shown above. Therefore, a better strategy for decision making must be
adopted. In the following case study, we will examine the matter in greater details, with
numerical results.
9
3.3 Case description
The following case is adopted from de Neufville and Scholtes (2004).
Table 3.1 – Summary of parking garage problem
Inputs
Demand in year 1 750 spaces
Additional demand by year 10 750 spaces
Additional demand after year 10 250 spaces
Average annual revenue $5,000 per space used
Average operating costs $1,000 per space available
Land lease and other fixed costs $1,800,000 p.a.
Capacity cost $8,000 per space
10% growth per level for every level above 2
Capacity limit 200 cars per level
Time horizon 15 years
Discount rate 12%
An investor plans to construct a parking garage next to a commercial building in a
developing area. He forecasts that the immediate demand right after the car park is
constructed is 750 spaces and there will be a subsequent 750 spaces needed over the next
10 years. The revenue and cost associated with running the car park is summarized in
Table 3.1.
The site is large enough to accommodate 200 cars per level.
3.4 Planning with traditional Net-Present Value (NPV) model:
3.4.1 The model
In this model, demand is predicted as an exponential curve as shown in equation 3.1
t
f eDtD βα −−=)( (3.1).
10
The hypothetical demand curve is expressed graphically in Figure 3.2.
Figure 3.2 - Hypothetical demand projection
Based on this demand projection, the revenue and cost for each year is then calculated.
After that, the net present value of the whole investment is computed. The process is
repeated for each different capacity of the garage in order to find out the best investment.
For this particular problem, building 6 levels is the best investment strategy, with an NPV
of $3,119,208.
3.4.2 Sensitivity analysis - What if demand changes?
As mentioned above, it is very unlikely that demand will be the same as prediction due to
its high level of uncertainty.
The investment’s outcome depends heavily on demand, which is an interpolation based on
three factors, the value of which are the investor’s estimation.
- Initial demand at year 1
- Demand at year 10
11
- Additional demand after year 10
Now, the investor expects that each of the above factors can be 50% higher or lower than
his prediction. The former is called the “best case”, the latter the “worst case” and his
prediction is called the “base case”. The investor carried out a sensitivity analysis in which
each of the factors is set as their best and worst cases in order to compare with their base
case. The different demand curves associated with different estimation of initial demand is
shown in Figure 3.3. For the complete set of Figures for all different values of the factors,
see Appendix A – Case study results.
0
500
1000
1500
2000
2500
0 5 10 15 20 25
Year
De
man
d (
space
s)
Base case
Worst case
Best case
Figure 3.3 - Different demand curves associated with different estimation of initial
demand
The different estimations and results are summarized in Table 3.2.
12
Table 3.2 - Sensitivity results for demand projection factors
Year 1 Additional by Year
10
Additional demand
after Year 10
Spaces NPV Spaces NPV Spaces NPV
Worst case 375 -$5,575,322 375 -$649,900 125 $3,528,689
Base case 750 $3,118,834 750 $3,118,834 250 $3,118,834
Best case 1125 $6,929,612 1125 $4,349,167 375 $2,865,465
The change in NPV with respect to different values of demand factors is plotted in Figure
3.4. It can be seen that the NPV changes for year 1 demand is significantly large, for year
10 is moderate and for demand after year 10, the change in NPV is very small.
-$8,000,000
-$6,000,000
-$4,000,000
-$2,000,000
$0
$2,000,000
$4,000,000
$6,000,000
$8,000,000
Worst case Base case Best case
NP
V
Year 1
Year 10
After year 10
Figure 3.4 - Sensitivity results for demand projection factors
Each factor affects demand in a different way. It is seen that the most sensitive factor is
the initial demand. This is reasonable because the demand curve is very steep at first and
13
getting flatter towards the future. So any change in the early proportion of the curve will
affect the entire curve more significantly than the latter part.
3.5 Planning with randomized demand
3.5.1 Changing demand projection factors
We have seen different possible results for the best cases and worst cases. So which
Figure should the investor use for his project? Should he take an aggressive one and hope
for the best, or should he be defensive and prepare for the worst? Can he take somewhere
in between? If so, which one?
In real life, demand can be much different from the predicted figures, which leads to
various possible outcomes, some of which are disastrous. In other words, the predicted
demand is only an average of the many possible situations. Therefore, the reliability of the
analysis based on this average demand is questionable.
To capture a more realistic picture, a randomized demand model is created.
Firstly, the investor expects demand to rise or fall 50% away from his prediction, with 5%
volatility in demand growth. Figure 3.5 shows a typical demand scenario, among the
various possible.
14
Demand
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
1 3 5 7 9 11 13 15 17 19
Time (years)
Demand (spaces)
Demand projection
Demand scenario
Figure 3.5 - A typical demand scenario
A Monte Carlo Simulation is programmed in Excel and performed with 100,000 runs. The
mean NPV for different capacities are shown in Table 3.3.
Table 3.3 - Mean NPV of randomized demands
Capacity Mean NPV Static NPV
4 -$38,200 $615,996
5 $1,681,600 $2,615,732
6 $1,996,800 $3,119,208
7 $620,100 $2,022,130
Although the optimum capacity is still 6 levels, the expected net present value is much
smaller than that in the static model ($2.0 million versus $3.2 million). This represents the
flaw of the average: “The result of average of input is not necessarily the same as the
average results of input” (Savage, 2000). In this case, when demand is higher than the car
15
park’s capacity, the profit is not realized. Therefore, the mean NPV is lower than that from
the static model, which did not capture this characteristic of demand.
3.5.2 Sensitivity analysis
In the above simulation, demand is expected to fall 50% on either side of the projection.
This percentage indicates how reliability the estimation is. What if there is more
information which leads to a more convincing projection, so that demand will only fall
within 10% away from its expected value? Or what if development in the area becomes
volatile and demand can differ as much as 75% away from the projection? The sensitivity
of the expected NPV with respected to different volatility levels is examined through
simulations with various values for the demand estimation parameters. The results with
respect to initial demand at year 1 are shown numerically in Table 3.4 and graphically in
Figure 3.6. For entire results, see appendix A.
Table 3.4- Sensitivity results for initial demand’s volatility
Capacity 10% 25% 50% 75%
4 $594,741 $288,809 -$38,200 -$711,709
5 $2,438,317 $2,418,779 $1,681,600 $710,959
6 $2,720,151 $2,434,126 $1,996,800 $1,085,276
7 $1,344,570 $1,216,553 $620,100 -$173,881
16
Sensitivity - Demand at year 1
-$1,000,000
$0
$1,000,000
$2,000,000
$3,000,000
$4,000,000
0% 20% 40% 60% 80%
4 levels
5 levels
6 levels
7 levels
Figure 3.6 - Sensitivity results for different volatility
As we can see in the results, the higher the volatility, the less the expected profit. In
addition, the slopes of the NPV curves are steeper towards the larger volatility, which
means that NPV is more sensitive with volatility as it grows larger. This is because the
higher the volatility, the smaller demand can be compared to the projection, hence the
larger unused capacity there is. On the other hand, there is also higher chance that demand
will be much higher than expected, but there are not enough spaces to be utilized then.
Therefore, “the flaw of averages” is more prominent in markets with high volatility.
The results show that with different volatility, year 1 demand is still the most sensitive
factor, followed by year 10 demand and that after year 10. In addition, expected NPV also
decreases with increasing volatility. This is in alignment with the analysis we have
mentioned above.
This information is very valuable since it guides the investor as where should he put effort
to find out more market information.
17
We also examine the sensitivity of NPV with respect to the volatility in demand growth
while keeping those of demand projection constant as 50%.
3.6 Considering expansion option
It is not necessary that the investor must have a big garage right from the start to cater for
the demand in 20 years. In fact, he may choose to build a small garage in the early years
when demand is small, and expand one or a few more levels in the subsequent years when
demand increases.
A simulation with this expansion option is performed with 100,000 runs. In this model,
the investor will build additional floors when demand has exceeded capacity in the
previous two years. Sensitivity analysis is also incorporated into the model. The mean
NPV corresponding to 50% volatility of all demand factors is $5,309,424, which is
significantly higher than both static NPV and randomized demand models. The common
decision rule is to build 4 levels first and expand 1 each time. The sensitivity results in
regards of first year demand’s volatility is shown in Table 3.5.
Table 3.5 - Sensitivity with respect to first year's volatility and with expansion option
As expected, the common strategy is to start with a small capacity and build up additional
capacity later rather than going for a big facility right at the start.
Volatility 10% 25% 50% 75%
Mean NPV $5,937,170 $5,832,101 $5,309,424 $4,521,155
Initial levels 4 4 4 4
Additional levels
each expansion 1 1 1 1
18
The results are significantly higher than those obtained without the expansion option. This
is because with the option, the investor is able to capture the whole demand curve. When
it was low, he has a small facility so he does not suffer lost from unused spaces and when
it grows, he is able to expand his capacity to cater for that demand.
We can also see that even though the NPV is still sensitive to the volatility in the same
way as in the case without expansion option (i.e. most sensitive to demand at year 0 and
least to demand after year 10), the magnitude of sensitivity is less.
High volatility still decreases the profit. As volatility is high, the good period is short and
hence cannot totally make up for the bad period.
Without the expansion option, the investor has to make decision before the project is
implemented. Thus, he does not have sufficient information about future demand. When
he has the option to expand, he can choose to wait until more information is available and
his decision is more accurate. He is faced with less risk and hence the volatility has less
effect.
3.7 Conclusion for the case study
From the results of the three different models (static NPV, randomized demand without
expansion option, randomized demand with expansion option), it can be seen that the
model with expansion option is the best approach, being the most realistic model and
yielding the highest NPV (see Table 3.6).
19
Table 3.6- Case study summary
Model NPV Decision rule
Static NPV $3,119,208 Build 6 levels (and maintain)
Randomized demand
$1,996,800 Build 6 levels (and maintain)
With expansion option
$5,309,424 Build 4 levels and expand 1 level when demand is higher than supply for 2 consecutive years (can end up with 4, 5, 6 or 7 levels)
The different NPVs resulted from different models reflect the value of information
(demand in this case), thus they reflect the value of the option to wait and decide when
there is more information. Therefore, it is the amount the investor is willing to pay for the
right to wait for more information.
In this case the expansion option offers the investor more flexibility in making his
decision. Rather than making a single decision, he can, from time to time, make
continuous decisions when the situation changes and more information is available. This
is very important when there is a lot of uncertainty and the market is volatile. In such
circumstances, the investor is able to response correctly. If the demand is not as good as
expected, he can choose not to exercise the right to expand. In this case what he has lost is
just the option premium, rather than the construction cost of the excessive facility.
The case study also showed that the option’s value depends on the volatility of the market.
The higher the volatility is, the higher the option’s value is. However, it has different
sensitive level with respect to different factors, which guides the decision maker on where
to put efforts to find more information.
20
4. SINGAPORE WATER – A PICTURE
4.1 Demand
Currently, Singapore’s demand for water is 1.3 million m3/day. Its total land area is 697
km2 with a population of 4.5 million and annual rainfall of 2400mm (Tan, 2007).
Singapore's water demand comprises of domestic and non-domestic sectors (Table 4-2).
Since domestic demand is the larger proportion and involves more uncertainties, it will be
viewed as the product of population and individual water consumption, and will be
examined down to that level.
4.1.1 Domestic demand
4.1.1.1 Population
The more people the more the water consumption. It is important to study the future
population in order to plan for water supply.
As of June 2008, the population of Singapore is 4,839,400, of which 3,642,700 are
residents (Department of Statistics).
The population growth rate is estimated as 1.135% (CIA World Fact Book, 2008) but
there are many uncertain factors that obstruct population prediction.
The high proportion of non-resident population (1,196,700 people) which contributes
24.7% of the total population indicates a fluctuation to some extent of the total number of
people living on the island. There are a large flow of transient foreign workers.
21
On average, there are 52,500 PRs and 12,800 new citizens granted every year from 2004.
In 2007 there were 63,600 PRs and 17,300 new citizens (DPM, 2008).
A general picture of the population is sketched out by PM Lee in his National Day Rally
Speech. There are significant decreases in the population trend. Total Fertility Rate (TFR),
which is the average number of children per woman over her life time, is only 1.29, far
lower than the replacement level of 2.1. When times are hard, people tend to have fewer
babies and there were more babies born in the years of the dragon (Lee, 2008). The recent
financial crisis has great impact on Singapore and this can strongly affect the population in
the near future.
In order to increase the fertility rate, the government is encouraging couples to get married
and have children. They have created special agencies for this purpose. In addition, a
series of policies such as child care leave, extended maternity leaves, baby bonuses are
and will be implemented (Lee, 2008).
The effectiveness of these policies will affect the population and thus the water demand.
4.1.1.2 Individual water consumption
As a result of appropriate demand management, individual water consumption has kept
decreasing from 176 lit/day in 1994 to 158 lit/day in 2006 (Tan, 2007).
Tortajada (2006) remarked that various demand management schemes from PUB such as
water tariff and water conservation tax has helped to convey and reinforce the water
conservation message to the households. Average monthly bill, in general, has been
increasing in the period 1980 - 2005 (Figure 4.1). Consequently, there are disincentives
for households to consume more water.
22
Figure 4.1 - Average monthly water bill, inclusive of tax (in S$) 1980 - 2005
(from Tortajada, 2006)
Beside increasing tax, a better tariff structure involving a targeted subsidy for the poor and
eliminating the case that commercial and industrial users subsidize domestic users, and a
penalty for households that use more than 40m3/month, helped to address the problem
without creating pressure on those who cannot afford the high water bill to meet their
basic needs. Campaigns to raise awareness such as the "10 litre a day" programme also
contributed to the decrease in consumption per capita. The fact that the average monthly
bill slightly decreased in the period 2000-2005 (Figure 4.1), but the consumption per
capita also decreased in that period has proved the success of the demand management
scheme.
Individual water consumption can be further reduced by targeting its major components
such as shower and flushing system (Figure 4.2).
23
Figure 4.2 - Domestic Sector Breakdown, Singapore
In Australia, water-efficient showerhead and smart flushing system (including no-flush
system) have been used in order to target the two large segments of water demand. It is
possible that these measures will be adopted in Singapore. In fact, the no-flush system has
been adopted in ViVo City, one of the largest shopping centers on the island.
4.1.1.3 The results
As individual consumption declines, the effect of increasing population on domestic water
consumption is less prominent (see Table 4.1).
24
Table 4.1 - Domestic and individual water consumption
4.1.2 Industrial demand
Industrial water demand has remained about 43% of the total water demand.
Table 4.2 -Break-down of Singapore's water consumption
2002 2003 2004 2005 2006 2007
Domestic 687 690 686 694 702 725
Industrial 572 534 517 512 528 521
Total 1259 1224 1203 1206 1230 1246
% Industrial 45.43% 43.63% 42.98% 42.45% 42.93% 41.81%
4.2 Supply
Singapore’s water supply system is solely managed by the Public Utilities Board (PUB).
The Board has envisioned Singapore to be the ASEAN hydro hub, and has conFigured the
nation’s water supply system with four “national taps”: local catchment, imported water
from the State of Johor, Malaysia, NEWater, and desalinated water (PUB).
Year 2002 2003 2004 2005 2006 2007
Population 4,176,000 4,114,800 4,166,700 4,265,800 4,401,400 4,588,600
Domestic water
consumption
(1000 m3/day)
687 690 686 694 702 725
Individual 165 168 165 163 159 158
25
4.2.1 The national four-tap model
4.2.1.1 Water catchment
With the completion of the Marina Barrage in 1 November 2008, two-third of the island’s
area is now catchment area (PUB) (See Figure 3-2. In 2005, around 680,000 m3 of water
was drawn from these catchment areas (Lee, 2005).
Figure 4.3 - The blue map of Singapore
(from Young, 2008)
Some of the major reservoirs and their capacities are listed in Table 4.3.
26
Table 4.3 - Major reservoirs
Name of reservoir Year completed Storage capacity (million m3)
MacRitchie 1867 (*1894) 4.2
Lower Pierce 1912 2.8
Selatar 1935 (*1969) 24.1
Upper Pierce 1974 27.8
Kranji/Pandan 1975 22.5
Western Catchment 1981 31.4
Bedok/Sungei Selatar 1986 23.2
Total 142.0
* Year when the reservoir is enlarged
There are totally 15 reservoirs in commission, and 2 more in progress (PUB). Therefore, it
can be predicted that more water will be drawn from the reservoirs in the future.
4.2.1.2 Imported water
About 40% of Singapore’s water supply is imported from Malaysia, following the 1961
and 1962 Water Agreements that end in 2011 and 2061 respectively. The first agreement
allows Singapore to draw 391,000 m3 of raw water per day from Malaysia. The second
one in allows Singapore to draw 1,136,500 m3 of raw water per day from Johor, but it also
requires Singapore to sell 168,200 m3 of treated water per day back to Johor (Lee, 2003),
hence the maximum capacity is 1,359,300 m3/day.
Singapore is no longer depending extremely on imported water, and in fact, can become
self-sufficiency (Lee, 2003). However, the Singapore government has “expressed the view
that it would like to continue to purchase water, under fair terms, from Malaysia or any
other country willing to be its long-term supplier” (Lee, 2003).
27
The price revision and the future of these agreements when they come to lapse have been
brought to the political front of the two countries for many years. Lee (2003) described in
details the political and historical background of this matter. His paper showed that these
conflicts pose great uncertainties to the planning of future water supply system for
Singapore.
4.2.1.3 NEWater
According to the PUB website,
“NEWater is high-graded re is high-grade reclaimed water produced from treated
used water that is purified further using advanced membrane technologies, making
the water ultra-clean and safe to drink.”
NEWater has passed thousands of scientific tests and well surpasses WHO and USEPA
standards. Water reclamation was first mentioned in 1970s but was hindered due to
technological limitations as well as high cost at that time. With the latest membrane
technology and decreasing membrane prices, NEWater proved to be more feasible. A
board of expert initiated NEWater study in 1998 and NEWater was born in 2003.
NEWater is pioneered and directed by the PUB to become a “key pillar” in Singapore’s
water supply system.
At the moment, there are 4 NEWater plants: Bedok (7 mgd), Kranji (12 mgd), Seletar (5
mgd) and Ulu Pandan (32 mgd). They contribute totally 56 mgd, about 20% of
Singapore’s water demand. The promising future of NEWater has triggered early
construction of the fifth NEWater factory at Changi, with capacity 50mgd (Lee, 2005).
NEWater’s contribution to total water supply was set to increase to 30% by 2012. There is
28
potential to expand existing plants (e.g. the Ulu Pandan plant was expanded from 25 mgd
to 32 mgd) and build more plants.
4.2.1.4 Desalinated water
Singapore has commissioned its first desalination plant in Tuas with capacity 30 mgd
(136,380 m3/day) in 2005.
Recently, desalinated water has seen much technological advancement. Multi Stage Flash
(MSF) and Multi-Effect Distillation (MED) can be combined with Reverse-Osmosis (RO)
to reduce cost (Methnani, 2006). Advanced technology has made membranes cheaper,
modern technology in pre-treatment and design have led to “better performance, lower
capital and operating costs” ("Cover story: Singapore shines at desalination conference,"
2005).
However, there are considerable uncertainties involved in the process of desalination.
Firstly, the reverse-osmosis technology that desalination employed requires a fairly large
amount of energy, ranging from 30% to 50% of the total cost (Methnani, 2006). Since fuel
price fluctuates significantly from year to year, desalination cost is expected to change
accordingly. Secondly, technology, even though advancing rapidly now, is a noTable
unknown, and “making it [desalination] economically viable is something of an art”
("Cover story: Singapore shines at desalination conference," 2005).
4.2.1.5 Summary on the four-tap model
The three local taps (catchment, NEWater, desalination) can contribute up to 236 mgd
(1,072,856 m3/day or 82.5% of the total demand). Only 50 mgd (227,300 m3/day or 17.5%
of the total demand) is dependent on the imported tap (see Figure 4.4). However,
29
desalination is still an expensive source, with the Tuas plant’s tender price of $0.78/m3,
more than three times as expensive as imported water ($0.25/m3) (Lee, 2005), and
NEWater is also 20% more expensive than imported water ($0.3/m3 for the latest Ulu
Pandan and Changi plants). Therefore, it is not economically feasible to rely only on the
local sources. In order to become self-sufficient, given the above potential and
uncertainties, water supply system planning needs special attention. New researches, both
on planning and on technology, are of critical importance.
17.48%
19.58%
10.49%
52.45%
Foreign reliance
NEWater
Desalinated water
Catchment water
Figure 4.4 - Contribution of four national taps with maximum capacity for local taps
4.2.2 The potential "fifth tap"
Shaik, Ooi and Pehkonen (2006) outlined a promising future for desalination using liquid
natural gas (LNG) as a heat sink instead of the traditional RO method. The authors
remarked that 70% of Singapore's electricity originated from natural gas. Currently,
natural gas is imported into Singapore as its gaseous form through a system of pipelines.
However, it is more economical to import natural gas in liquid form, as it only occupies
30
1/600th of its gaseous volume, can be shipped easily by tankers and is easier to store. As
natural gas demand is expected to exceed the current level of supply, the Singapore
Energy Market Authority is investigating the potential to build an LNG terminal.
The drawback of LNG, however, is that it has to be regasified before use, and this process
consumes a huge amount of energy.
It has been known in literature since the 1960s that LNG regasification process, since
taking in large amount of energy, can be made use of as a heat sink for another process,
such as refrigeration (Shaik et all, 2006). Researchers such as Shwartz and Probstein
(1969), Cravalho et al (1977) analyzed the use LNG regasification to freeze seawater in
order to separate salt from it. Shaik et al (2006) applied mass-enthalpy balance and
economic considerations within Singapore context to examine the potential of a linked
LNG-desalination terminal with capacity 34,000m3/day (2.6% of Singapore's total water
demand). Their calculation showed that the required selling price (RSP) for the
desalinated water as a result of this process is $0.53/m3, which is favourably comparable
to RO desalinated water ($0.78/m3) and NEWater ($0.3/m3). Although the authors noted
the key constraint of limited LNG terminal capacity (6mtpa), they recommended that LNG
regasification-desalination should be further studied so that its potential can be explored,
the process can be improved and the capacity can be increased (Shaik et al, 2006).
This thesis will consider this new LNG-desalination technology as an option and examine
its value.
31
5. MONTE CARLO SIMULATION MODEL
5.1 Demand model
5.1.1 Domestic consumption model
Domestic consumption is the product of total population and individual water
consumption. These two factors will be examined in details.
5.1.1.1 Population model
Resident population: As suggested by Hashmi and Hui (2002), previous studies on
Singapore's population such as Saw (1987), Shantakumar (1996) are outdated because
they did not include migration in the projection, and their base years were only as latest as
1990. Hashmi and Hui pointed out that immigration and total fertility rate (TFR) will be
the key parameters contributing to Singapore's population in the future. They provided a
new population projection which allowed for migration and used 1999 as the base year.
However, as their assumptions for migration are outdated at the moment, and the base
year 1999 is far ago, an improvement to Hashmi and Hui's projection is performed with
aids of the PDE Projection software (PDE), using 2007 as the base year. The data are
provided in the Population Year Book 2008 by the Department of Statistics.
The projection uses the component method. The total population is divided into 2 genders,
male and female. Each gender group is then divided into 5-year age groups: 0-4, 5-9, 10-
14 and so on. The oldest age group is 85 and above (85+). Age-specific data such as
migration rate, fertility rate and mortality rate are entered into PDE for the base year. The
40-year analysis horizon is also divided into 5-year periods. The population of age group
32
(x to x + 4) at period (t to t + 5) is calculated based on the migration rate and mortality
rate of age group (x - 5 to x - 1) at period (t-5 to t). The population of age group (0 to 4) is
calculated based on the age specific fertility rate of all the female from 14 to 44 years of
age in the previous period (Saw, 1983 and PDE manual). All calculations were performed
by PDE.
In this projection, a total fertility rate is assumed to increase 10% each year, from 1.29 in
2007 to 1.39 in 2047. Migration rate is also assumed to increase 10% each year, starting
from 36,500 males and 44,483 females.
To take uncertainty into account, each year's population is randomized as a normal
distribution with the mean being the PDE's estimated value and standard deviation 4,200.
The standard deviation will ensure that the randomized population is within 50,000 away
from the mean, according to Chebyshev’s theorem.
Non-resident population: the base projection is calculated as a linear regression line to
the historical data. Then it is randomized with mean is the base projection and standard
deviation 10% of mean.
Total population: is the sum of resident and non-resident population.
5.1.1.2 Individual water consumption model
According to the analysis in section 4.1.1.2, it is reasonable to assume that water
consumption per capita will continue to decrease, but with a decreasing rate, and will
remain constant at a steady state.
One way to describe this nature is to use an exponential curve with negative power, and
the following equation is used:
33
caes by += − (5.1)
where s is consumption per capita (litre/day), y is the year (from 0 to 40) and a, b, c are
constants.
Consumption is 158 litre/day in year 0 (2007).
Since it took 4 years (from 2003 to 2007) to reduce consumption by 10 litre/capita/day
(Table 4-1), it can be assumed that another 10 litre reduction will take 8 years into the
future. That means consumption per capita will be 148 litre/day by year 8 (2015).
It is also reasonable to let the consumption per capita be 140 litre/day at its steady state at
the end of the analysis period, year 40 (2047).
Substituting the above values to equation 5.1, and perform Goal Seek in Excel, we obtain
641.139359.18 098.0 += − yes (5.2)
The resulted consumption per capita each year is plotted in Figure 5.11.
138
140
142
144
146
148
150
152
154
156
158
160
2007 2012 2017 2022 2027 2032 2037 2042 2047
Figure 5.1 - Individual water consumption model
34
To consider uncertainty, each year's Figure will be randomized within 0.5 litres away from
the projected value, according to a uniform distribution.
5.1.2 Total consumption model
From Table 4-2, it can be calculated that industrial demand takes up an average of 43.21%
the total demand, or in other words, domestic demand takes up 56.79% of the total. The
standard deviation of this percentage is calculated as 0.012466. Therefore, total water
consumption will be calculated as follow:
• Generate a random number x following a normal distribution with mean 0.5679
and standard distribution 0.012466.
• Total water consumption = Domestic water consumption / x
5.2 Supply model
5.2.1 Configuration and risk premium
Each year, facing with a demand and different water prices from the four taps, PUB has to
configure the contribution of the four taps to minimize the cost of supplying water. The
key strategy is to choose the tap with cheapest unit cost, use as much as possible, and then
move on to use the next cheapest tap.
It is obvious that currently, the import tap is the second cheapest and should be utilized as
much as possible. However, if PUB takes the cost of imported water as its face value, it is
omitting the potential risks that this tap is cut off. Therefore, a risk premium should be
incorporated into the cost of imported water when compared with other taps. How much
this risk premium should be is an unknown. This study will assign values from $0.00 to
35
$3.50 with an increment of $0.10 to the risk premium to see the effect of different
considerations.
5.2.2 Imported water modelling
For the Agreement ending 2011, the Singapore government has expressed the intention to
let it lapse (Lee, 2003). However, there are possibilities that a revision be made in 2011.
The following scenarios are adopted for the purpose of this study (Table 5.1).
Table 5.1 - Scenarios for 2011 Agreement
Description Probability
Lapse 0.7 Renew at $0.25 (same price) 0.1 Renew at $1.00 (unfavourable) 0.1 Renew at $3.45 (Very unfavourable) 0.1
For the Agreement ending 2061, its expiry date is out of our study horizon; therefore we
need not consider the revision. However, as the capacity of water in this Agreement is
very high, the small likelihood of it being disrupted will lead to severe consequences.
Therefore, we have to take into account the risk of it being broken out. The following
scenarios are to be examined:
Table 5.2 - Scenarios for 2061 Agreement
Description New unit price ($/m3) Probability
Unchanged Same as the value of 2011 revision 0.97 Cut off 0.01 Quantity reduced by half Same as the value of 2011 revision 0.01 Price doubled Twice the value of 2011 revision 0.01
36
5.2.3 Cost and payment modelling
5.2.3.1 Cost components
There are 3 components of cost in the simulation: investment cost, fixed cost (operation
and maintenance), variable costs (production cost). The initial proportion of each
component for desalination, NEWater and LNG desalination are shown in Table 5.3. The
proportion for desalination is based on Methnani (2006) and Zhang (2006). The Figures
for NEWater is an adjustment from desalination and based on Zhang (2006). The Figures
for LNG desalination is based on Shaik et al (2006)
Table 5.3 - Cost components
Desalination NEWater LNG-Desalination
Components % % Components Cost ($
million)
Energy (variable) 46.90% 23.45% Capital charge 1.65
Investment 29.50% 42.53% Investment 5.67
O & M (fixed) 17.90% 25.80% O & M (fixed) 2.93
Technical (variable) 5.70% 8.22% Variable costs 1.41
For desalination and NEWater, since they employ reverse-osmosis technology which
consumes a large amount of energy, the variable cost is broken down to energy cost and
technical cost, each of which follows a different random walk:
Technical cost: as efforts are made to increase efficiency, the technical cost at year i is
rptpt ii ×= −1 (5.4)
where r is a random number following a normal distribution of 0.926 and standard
deviation 0.0926. This means that generally, technical cost is declining over time. But in
37
some certain simulation run, it can be either declining or increasing from one year to
another.
Energy cost: due to the high uncertainty involved in the crude oil prices, energy cost at
year i is
rpepe ii ×= −1 (5.5)
where r is a random number following a normal distribution of mean 1 and standard
deviation 0.5.
Technical cost and energy cost add up to unit (variable) production cost, which does not
depend on capacity.
O&M cost and investment cost depends on capacity and they remain unchanged if there is
no change in capacity. When there is an expansion, both investment and O&M will
increase. When there is a reduction, O&M will decrease while investment remains
unchanged because it is considered sunk cost.
5.2.3.2 Economies of scale
The new investment and O&M cost after expansion or reduction is assumed the following
cost curve:
C = kQm (5.6)
where C is the cost at capacity Q, k is a constant and m is the economies of scale factor.
• When m > 1, we have economies of scale. An increase in capacity will lead to
smaller averaged unit cost and expansion is favourable.
38
• When m < 1, we have diseconomies of scale. An increase in capacity will lead to
larger averaged unit cost and expansion is not favourable.
• When m = 1, the cost curve is linear. An increase in capacity will lead to a
proportional increase in fixed costs. Therefore, whether expansion is favourable
depends on other factors.
It is difficult to estimate the correct m value. In practice, m also depends on the operators.
For instance, if all the desalination plants are operated by one company, they can take
advantage of the common resources and there will be economies of scale.
For the purpose of this study, m will be assigned values of 0.5, 0.8 and 1.
5.2.3.3 Ownership and payment scheme simulation
The three latest water treatment plants in Singapore, namely Tuas Desalination Plant, Ulu
Pandan NEWater Plant, and Changi NEWater Plant, have undertaken a PPP (Public-
Private-Partnership) scheme, in which the project procurement followed the DBOO
(Design-Build-Own-Operate) model (Sanmuganathan, 2008). Accordingly, private
companies will bid to be PUB's water supplier. The tender will include a first year's
selling price and an adjustment formula with respect to inflation, energy cost, taxes and so
on. Once a company is awarded the contract - since then called the "concession company"
(Sanmuganathan, 2008) - it will employ subcontractors to design, build and operate the
plant, and it is the concession company that owns the project, not PUB.
The reasons behind this is to "offer a win-win solution" for both the public and private
sectors as well as the services users - members of the public. This strategy also helps to
utilize the strength of both the public and private sectors (Sanmuganathan, 2008). Besides,
39
by involving the private sector, PUB will be offered a more competitive price, and
competition in the private sector will also help to increase efficiency, optimize technology
configuration and keep cost affordable (Sivaraman, 2006).
Under DBOO scheme, there are three possible payment structures that PUB can adopt
(Sanmuganathan, 2008):
• "Unit Tariff per Output" structure: PUB is not obliged to purchase any minimum
amount of water; therefore this structure offers the highest flexibility. However, in
terms of financing for the project, the concession company cannot get a bank loan
because there is no security against the loan; hence it is harder to implement the
project of this type.
• "Take or Pay" pay structure: PUB agrees to pay at least a minimum of money to
cover the capital charge for the concession company, even though it does not need
to buy the equivalent amount of treated water. This minimum purchase amount can
be used as a security for a bank loan, thus procurement for the project of this type
is easier. However, it does not offer as much flexibility.
• "Two-part tariff" structure is the hybrid of the previous two and is the one adopted
in all three DBOO plants. Under this structure, PUB pays the fixed costs to cover
the project capital, thus partially reduce the risks for the concession company. On
the other hands, variable payments are dependent on production and the
concession company still faces market risks.
40
As the "two-part tariff" structure is being used and the "unit tariff per output" structure can
offer high flexibility, they will be simulated in the model. The "take or pay" structure will
not be addressed.
Whilst all the current DBOO plants are following the third structure, it is possible that
some future plants will follow the first scheme. It is also important to note that the first
three NEWater plants are self-operated by PUB. However, it is very complicated to
simulate this composition, as it requires the model to track the process to the plant level,
while the purpose of this research is to examine the impact only at the "tap" level.
Therefore, in the Monte Carlo simulation model, the two payment structures will be
modelled separately.
As we are not interested in modelling to the plant level, where each plant can be operated
by a different concession company, we will consider that there are two sides in the
transaction: one single concession company who operates the plants and sell water to
PUB, and PUB as the buyer, and we are interested in the cost born by PUB.
5.2.4 "Unit Tariff per Output" modelling
This model employs the "break even point" concept in economics.
The treatment of water will require the concession company to pay some fixed cost
(investment, fixed operation and maintenance cost, staff salary etc) and some variable
cost, which depends on the unit cost per unit volume of water treated.
After treatment, the company will then sell the treated water to PUB at a required selling
price (RSP). This is the price that PUB will buy water from the concession company.
41
5.2.4.1 Selling price
Let q (m3) be the volume of water treated.
The cost of treating q m3 of water is
IFCquTC ++×= (5.7)
where TC is the Total Cost ($), u is the unit variable cost ($/m3), FC is the Fixed Cost ($)
and I is the Investment cost or Capital charged ($).
The revenue (RV, in $) of selling q m3 of water is
qRSPRV ×= (5.8)
At break-even point where revenue equals cost and the company does not gaining any
profit or suffering any loss
TCRV = (5.9)
qRSPIFCqu ×=++× (5.10)
q
I
q
FCuRSP ++= (5.11)
Let Q be the total capacity that can be supplied by the concession company, so
Qq β= (5.12)
where β is the break-even point coefficient and 0 < β ≤ 1. This means β is the proportion
of the break-even quantity to the total capacity.
Substituting (5.12) to (5.11)
Q
I
Q
FCuRSP
ββ++= (5.13)
42
Applying economies of scale; let
m
IQkI = (5.14)
where
I ($) is the capital needed to invest in having the total capacity Q
kI is a capital cost coefficient
m is the economies of scale factor.
Similarly, let
m
FQkFC = (5.15)
where
FC ($) is the fixed cost needed to operate the total capacity Q
kF is a fixed cost coefficient
m is the economies of scale factor.
Note that for simplicity, we have assumed that I and FC have the same economies of scale
factor.
Substituting (5.14) and (5.15) into (5.13)
β
1
)(−
++=m
IF
QkkuRSP (5.16)
In this simulation model, two values β = 0.5 and β = 0.75 will be examined.
5.2.4.2 Expansion
When a tap is in full capacity for 5 consecutive years and its price is the cheapest of all the
taps that are expandable, PUB will consider expanding its capacity by inviting the
concession company to build a new plant or expanding existing plant.
In that case, the concession company will have to put in more investment cost and fixed
cost to operate the larger facility.
43
If the capacity is expanded an amount qe, the new RSP will then be
β
1)()(
−+++=
m
eIFnew
qQkkuRSP (5.17)
Supposed the tap will be in full capacity after expanding, hence, PUB can save money Q
m3 at the new price and the additional qe m3 is used to replace the amount previously
bought through the more expensive taps. Let S be the saving, then
∑≠
−+−=ij
jnewenew RSPRSPqRSPRSPQS )()( (5.18)
where
i is the tap of interest
j is any tap that is more expensive than i
If in a year there are more than one expandable taps, then the one with the highest saving
will be expanded.
Note that as the unit variable cost of each tap changes over time, in calculating the RSP
values in (5.18), we use u as the average of the previous 5 years.
5.2.4.3 Reduction
If a tap has been running below its break-even point for 5 consecutive years, then the
concession company may decide to shut down some part of the plants to save operating
and maintenance cost. The amount of reduction would be (1 - β) Q and the capacity after
reduction is βQ.
However, it has to resume its original capacity quickly since this is the contractual
obligation that it has to provide the full capacity upon request.
44
In reducing capacity, the concession company can save the fixed cost but cannot recover
the investment costs, as they are considered sunk cost. The new cost after reduction would
be:
Q
Qk
Q
QkuRSP
m
I
m
F
βββ
β++=
)(
)( (5.19)
If the new RSP is too high, the product will become less competitive, and then PUB
and/or the concession company may choose to shut down the source completely and wait
for favourable demand. In this study the threshold is set at $2.00.
5.2.5 "Two-part tariff" modelling
This model is similar to the "Unit tariff per output" model, but the Investment cost term is
not presented. On the other hand, the investment cost is considered in the tap ranking
when PUB decides how much of each tap is used, and the savings when expansion takes
place must make up for the additional investment expense.
5.3 Risk modelling
Apart from economic consideration when calculating net present value, it is inadequate to
consider economic values only. In this model, we propose two types of risk:
• Water security risk: is when the averaged unit cost of supplying a unit volume of
water for a particular year is greater than $1.50. The averaged unit cost of
supplying water is calculated as:
TWC
URSP
Pi
i
i ×
=∑
(5.20)
where
45
i denotes the tap
Ui is the usage of tap i in that year
TWC is total water consumption in that year.
• Water scarcity risk: how many days Singapore can survive without the import tap.
If for a particular year, the total available capacity is greater than total water consumption,
then clearly there is no risk.
Otherwise, let E be the excessive amount per day that consumption has more than supply.
This amount will have to be met by the water stored in the reservoir. But we have already
taken out catchment water to consider in the total supply capacity, so, let x be the number
of days we can survive,
CapacityCatchment
capacity storageReservoir
+=
Ex (5.21).
If x is greater than 365 then there is no risk. Otherwise risk is calculated as the difference
between x and 365 days.
These two risks will be calculated in the simulation.
46
6. RESULTS AND DISCUSSIONS
6.1 “Unit tariff” vs. “two part tariff”
On average, the “unit tariff” approach helps to reduce NPV by 7.29% for the case without
LNG and 7.35% for the case with LNG (Table C.2), because under the “unit tariff”
structure, project cost is part of the variable purchase costs. Hence, PUB does not always
have to bear this cost, but only when it purchases some water. On the other hand, for the
“two-part tariff” structure, this payment is fixed so PUB always has to pay. However, the
difference between the two structures is small because the proportion of investment cost is
moderate. In addition, PUB has the option to expand when needed in stead of having to
pay capital upfront. Therefore, it does not have excessive capacity and wasted capital.
The result suggests that the savings from the “unit tariff’ does not justify the difficulties in
financing the projects of its type. Therefore, in the future, PUB should continue on the
“two-part tariff” structure. In this case the dispatch flexibility cannot balance the
procurement costs.
6.2 Effects of the “fifth tap”
6.2.1 Mean NPV
Table () showed that by keeping the prospective LNG-desalination terminal capacity at
$34,000 m3/day as the current limit, LNG as the “fifth tap” can only help to save about
$3.50 - $3.60 million SGD in terms of NPV for the lower range of political risk premium
($0.00 to $1.50) and about $6.50 million for the higher range. However, if we can make
the capacity three times bigger (up to 102,000 m3/day) the saving would increase
47
significantly, to $29.3 million for the lower range and $47.0 million for the higher range,
which means 6 to 8 times the original savings.
Figure 6.1 – Effect of enlarging LNG capacity
This suggests that Singapore is in the situation of holding a call option – and Singapore
should invest in a research on LNG-desalination and realize its potential economic value.
The research’s success provide Singapore the right to implement LNG-desalination in the
future. Table () suggests that the funding for the research should be around $2.0 million,
and it is also the option premium. Once Singaopre has the technology in hand, it has
another option – to enlarge the capacity by three times. This option to expand is called
“option on option”.
6.2.2 Water security risks and water scarcity risks
48
The fifth tap, due to its small capacity, does not contribute significantly to reducing the
water security and scarcity risks.
6.3 Effect of risk premium
Figure 6.2 shows the mean NPV versus political risk premium, with m = 0.8 for
desalination and NEWater, LNG's maximum capacity set as 34,000 m3/day.
Figure 6.2 - Mean NPV result
The results showed that the mean NPV of the total water supply cost over the analysis
period is very sensitive with risk premiums valued from $0.00 to $1.50. Beyond $1.50, the
NPV curve flattens.
It is interesting to note that, generally, the mean NPV increases as the risk premium
increases. However, between $0.00 and $0.10, NPV actually decreases. A finer simulation
for the range from $0.00 to $0.50 with $0.05 increment proved this (Figure 6.3).
49
Figure 6.3 - Partial NPV curve from $0.00 to $0.50
This is because the risk premium of $0.10 makes imported water generally more
expensive than NEWater. Therefore, the model chooses to expand NEWater and use less
imported water. As this is the case where economies of scale exist (m = 0.8), the
expansion of NEWater is beneficial and helps to save cost. The same result is obtained
when m = 0.5 (Figure C.1). However, political cost is still not too high to make
desalination more favourable than imported water. Therefore, the cost of supplying is still
low. As the risk premium goes higher, less imported water is used, more desalinated water
is produced and this increases the cost of supplying water.
50
6.4 Effect of β and m
From the various tables in appendix C, we can see that the model is not quite sensitive to β
and m. In fact, from Table C.2, changing from β = 0.75 to β = 0.5 only decreases NPV by
less than 2%.
6.5 Recommendation for future researches
This study has not examined the water supply system to the plant level. In further
research, the problem should be addressed to that level of details to be realistic.
In addition, in this study, the time step is one year each. Therefore, we take averaged daily
consumption as the constant consumption for every day in a year. To have a more realistic
simulation, further researches should also take a daily time step so that the reaction to
disruption can be captured more accurately.
51
REFERENCES
• DPM’S SPEECH ON POPULATION AT COMMITTEE OF SUPPLY (2008).
http://www.nps.gov.sg/files/news/DPM%27s%20speech%20on%20population%20at
%20COS%2027%20Feb%202008.pdf. D. P. s. Office.
• Department of Statistics (2008). Yearbook of Statistics 2008.
• Deparment of Statistics (2008). Population if Brief 2008.
• Department of Statistics (2008). Population Trends 2008.
• de Neufville, R., Scholtes, S (2004 ). Designing a parking garage.
• Australian Stock Exchange (2004). Options - Understanding Options trading.
• Hashmi, A. R., Hui, W. T. (2002). Population and Labour Force Projections for
Singapore (1999 - 2049). IUSSP Conference on Southeast Asia's Population in a
Changing Asian Context. Bangkok, Thailand.
• Lee, P. O. (2003). "The Water Issue between Singapore and Malaysia: No Solution in
Sight?" Economics and Finance 1: 1-29.
• Lee, P. O. (2005). Water Management Issue in Singapore. Water In Mainland
Southeast Asia. Siem Reap, Cambodia.
• Methnani, M. (2007). "Influence of fuel costs on seawater desalination options."
Desalination 205(1-3): 332-339.
• Mun, J. (2006). Real Options Analysis: Tools and Techniques for Valueing Strategic
Investment and Decisions. Hoboken, New Jersey: John Wiley & Sons Inc.
52
• Sanmuganathan, D. (2008). PUB Singapore's Experience in Public-Private-Partnership
(PPP) Projects. CAPAM Biennial Conference.
• Saw, S.-H. (1983). Population Projections for Singapore 1980 - 2070.
• Seah, H. (2008). "PUB's NewWater Programme."
• Shaik, S. O. T., Ho; Pehkonen Simo, O (2006). Potential for Seawater Desalination in
Singapore using LNG Regasification as a Heat Sink. UltraPure Water Asia.
• Sivaraman, A. (2006). Desalination and Ulu Pandan NEWater DBOO Project, PUB's
Experience. Capacity Building Workshop. Bangkok.
• Tan, N. S. (2007). Integrated Urban Water Management in Singapore. Urban
Sustainability Conference.
• Tortajada, C. (2006). "Water Management in Singapore." Water Resource
Development 22(2): 227-240.
• Young, J. C. (2008). "Meeting the challenges of sustainable water supply - Integrated
water resource management."
53
APPENDIX A – CASE STUDY RESULTS
Results without expansion option
0
500
1000
1500
2000
2500
0 5 10 15 20 25
Base case
Year 10 - Worst
Year 10 - Best
Figure A. 1 – Best, base and worst cases, demand by year 10
0
200
400
600
800
1000
1200
1400
1600
1800
0 5 10 15 20 25
Base case
> yr 10 - Worst
Figure A. 2 – Base and worst cases, demand after year 10
54
Figure A. 3 – Base and best cases, demand after year 10
Table A. 1- Sensitivity results, demand by year 10
Capacity 10% 25% 50% 75%
4 $31,263 $5,966 -$38,200 -$172,296
5 $1,910,019 $1,815,273 $1,681,600 $1,329,153
6 $2,246,297 $2,226,523 $1,996,800 $1,455,020
7 $1,094,273 $1,057,458 $620,100 $167,421
Table A. 2 – Sensitivity results, demand after year 10
Capacity 10% 25% 50% 75%
4 -$84,534 -$62,990 -$38,200 -$46,314
5 $1,644,533 $1,685,499 $1,681,600 $1,732,331
6 $1,887,795 $1,973,699 $1,996,800 $2,000,341
7 $708,070 $706,963 $620,100 $700,847
55
Results with expansion option
Table A. 3 - Sensitivity result, volatility in year 10 demand
10% 25% 50% 75%
Max Profit $5,529,409 $5,420,879 $5,321,847 $5,600,358
Initial levels 4 4 5 4
Additional levels 1 1 1 2
Table A.4 – Sensitivity result, volatility in demand after year 10
Figure A.4 – Effect of volatility on net present value
10% 25% 50% 75%
Max Profit $5,481,395 $5,443,167 $5,294,556 $5,031,332
Initial levels 4 4 4 4
Additional levels 1 1 1 1
56
APPENDIX B – POPULATION PROJECTION RESULTS
Table B.1. Resident population projection
Year Population Year Population Year Population Year Population
2007 3,583,200 2017 3,887,131 2027 4,151,326 2037 4,337,086
2008 3,615,064 2018 3,914,503 2028 4,172,564 2038 4,348,906
2009 3,646,929 2019 3,941,876 2029 4,193,803 2039 4,360,726
2010 3,678,793 2020 3,969,248 2030 4,215,041 2040 4,372,547
2011 3,710,658 2021 3,996,621 2031 4,236,280 2041 4,384,367
2012 3,742,522 2022 4,023,993 2032 4,257,518 2042 4,396,187
2013 3,771,444 2023 4,049,460 2033 4,273,432 2043 4,407,492
2014 3,800,366 2024 4,074,926 2034 4,289,345 2044 4,418,796
2015 3,829,287 2025 4,100,393 2035 4,305,259 2045 4,430,101
2016 3,858,209 2026 4,125,859 2036 4,321,172 2046 4,441,405
2047 4,452,710
Table B.2. Non-resident population projection
Year Population Year Population Year Population Year Population
2007 941,322 2017 1,259,458 2027 1,577,593 2037 1,895,729
2008 973,135 2018 1,291,271 2028 1,609,407 2038 1,927,543
2009 1,004,949 2019 1,323,085 2029 1,641,221 2039 1,959,357
2010 1,036,762 2020 1,354,898 2030 1,673,034 2040 1,991,170
2011 1,068,576 2021 1,386,712 2031 1,704,848 2041 2,022,984
2012 1,100,390 2022 1,418,526 2032 1,736,661 2042 2,054,797
2013 1,132,203 2023 1,450,339 2033 1,768,475 2043 2,086,611
2014 1,164,017 2024 1,482,153 2034 1,800,289 2044 2,118,425
2015 1,195,830 2025 1,513,966 2035 1,832,102 2045 2,150,238
2016 1,227,644 2026 1,545,780 2036 1,863,916 2046 2,182,052
2047 2,213,865
57
Table B.3. Total population projection
Year Population Year Population Year Population Year Population
2007 4,524,522 2017 5,146,589 2027 5,728,919 2037 6,232,815
2008 4,588,199 2018 5,205,774 2028 5,781,971 2038 6,276,449
2009 4,651,878 2019 5,264,961 2029 5,835,024 2039 6,320,083
2010 4,715,555 2020 5,324,146 2030 5,888,075 2040 6,363,717
2011 4,779,234 2021 5,383,333 2031 5,941,128 2041 6,407,351
2012 4,842,912 2022 5,442,519 2032 5,994,179 2042 6,450,984
2013 4,903,647 2023 5,499,799 2033 6,041,907 2043 6,494,103
2014 4,964,383 2024 5,557,079 2034 6,089,634 2044 6,537,221
2015 5,025,117 2025 5,614,359 2035 6,137,361 2045 6,580,339
2016 5,085,853 2026 5,671,639 2036 6,185,088 2046 6,623,457
2047 6,666,575
58
Table B
.4. Age-gen
der-specific population pro
jection
59
APPENDIX C– SIMULATION RESULTS
Figure C.1 – Unit tariff, m = 0.5, β = 0.5
Figure C.2. – Two part tariff, m = 1, β = 0.5
60
Figure C.3 – Unit tariff, m = 1, β = 0.5
Table C.1 – Comparison between Unit tariff and Two-part tariff. m = 1, β = 0.5
Unit tariff Two part tariff Percentage different
Risk premium
Without LNG With LNG
Without LNG With LNG
Without LNG
With LNG
$0.00 $3,015,533 $3,008,627 $3,272,130 $3,270,173 7.84% 8.00% $0.10 $3,027,891 $3,023,089 $3,301,439 $3,299,574 8.29% 8.38% $0.20 $3,049,612 $3,044,994 $3,312,934 $3,311,012 7.95% 8.03% $0.30 $3,060,626 $3,055,942 $3,334,274 $3,331,475 8.21% 8.27% $0.40 $3,078,751 $3,073,727 $3,386,621 $3,382,838 9.09% 9.14% $0.50 $3,115,894 $3,110,825 $3,417,319 $3,413,273 8.82% 8.86% $0.60 $3,185,308 $3,180,380 $3,432,941 $3,429,744 7.21% 7.27% $0.70 $3,212,544 $3,207,580 $3,441,390 $3,438,934 6.65% 6.73% $0.80 $3,225,455 $3,220,251 $3,448,328 $3,446,043 6.46% 6.55% $0.90 $3,232,320 $3,226,898 $3,455,083 $3,452,267 6.45% 6.53% $1.00 $3,236,426 $3,230,846 $3,461,502 $3,457,759 6.50% 6.56% $1.10 $3,238,967 $3,233,239 $3,466,929 $3,462,645 6.58% 6.63% $1.20 $3,240,808 $3,234,855 $3,472,728 $3,467,742 6.68% 6.72% $1.30 $3,242,245 $3,236,005 $3,477,780 $3,472,148 6.77% 6.80% $1.40 $3,243,341 $3,236,889 $3,481,756 $3,475,793 6.85% 6.87% $1.50 $3,244,118 $3,237,510 $3,485,512 $3,479,392 6.93% 6.95% $2.00 $3,246,284 $3,239,049 $3,494,710 $3,488,046 7.11% 7.14% $2.50 $3,247,224 $3,239,718 $3,496,567 $3,489,672 7.13% 7.16% $3.00 $3,247,625 $3,240,002 $3,496,907 $3,489,836 7.13% 7.16% $3.50 $3,247,878 $3,240,169 $3,497,080 $3,489,769 7.13% 7.15%
Average 7.29% 7.35%
61
Table C.2 m = 0.5, β = 0.5, Two-part tariff
mean NPV mean water security risk
mean water scarcity risk (days)
Risk premium
Without LNG
With LNG Savings Without
LNG With LNG
Without LNG
With LNG
$0.00 $2,894,257 $2,891,995 $2,262 0.0098 0.0094 796.54 796.00 $0.10 $2,882,516 $2,880,622 $1,895 0.0014 0.0014 128.68 128.73 $0.20 $2,890,272 $2,888,341 $1,931 0.0008 0.0008 53.64 53.42 $0.30 $2,909,638 $2,907,571 $2,067 0.0008 0.0008 25.46 21.45 $0.40 $2,961,849 $2,959,125 $2,724 0.0006 0.0006 11.81 9.81 $0.50 $2,992,541 $2,989,739 $2,802 0.0006 0.0006 4.67 3.39 $0.60 $3,010,187 $3,007,705 $2,482 0.0006 0.0006 3.00 2.07 $0.70 $3,020,616 $3,018,120 $2,496 0.0006 0.0006 2.38 1.93 $0.80 $3,027,899 $3,025,130 $2,768 0.0006 0.0006 2.08 1.72 $0.90 $3,034,004 $3,030,722 $3,281 0.0006 0.0006 1.94 1.70 $1.00 $3,039,130 $3,035,221 $3,909 0.0006 0.0006 1.88 1.61 $1.10 $3,043,679 $3,039,002 $4,678 0.0006 0.0006 1.80 1.59 $1.20 $3,047,564 $3,042,206 $5,358 0.0006 0.0006 1.72 1.52 $1.30 $3,050,324 $3,044,595 $5,729 0.0006 0.0006 1.66 1.54 $1.40 $3,052,697 $3,046,717 $5,980 0.0006 0.0006 1.61 1.52 $1.50 $3,054,178 $3,048,019 $6,158 0.0006 0.0006 1.55 1.46 $2.00 $3,055,381 $3,049,511 $5,870 0.0006 0.0006 1.36 1.36 $2.50 $3,055,578 $3,049,544 $6,033 0.0006 0.0006 1.36 1.36 $3.00 $3,055,461 $3,049,264 $6,197 0.0006 0.0006 1.36 1.36 $3.50 $3,055,253 $3,048,873 $6,380 0.0006 0.0006 1.36 1.36
62
Table C.3 Comparison between β = 0.5 and β = 0.75 (Unit tariff)
m = 0.8 β = 0.75 m = 0.8 β = 0.5 Difference
Without LNG With LNG Without
LNG With LNG Without
LNG With LNG
$0.00 $3,009,991.0 $3,004,592.4 $2,984,145 $2,967,281 0.86% 1.24%
$0.10 $2,986,255.7 $2,981,542.5 $2,954,483 $2,943,342 1.06% 1.28%
$0.20 $3,002,009.8 $2,998,249.8 $2,969,547 $2,958,694 1.08% 1.32%
$0.30 $3,011,314.2 $3,006,763.6 $2,979,408 $2,968,560 1.06% 1.27%
$0.40 $3,028,231.6 $3,023,122.4 $2,994,851 $2,983,551 1.10% 1.31%
$0.50 $3,064,618.2 $3,058,980.3 $3,028,315 $3,016,630 1.18% 1.38%
$0.60 $3,133,300.5 $3,127,272.5 $3,094,548 $3,084,250 1.24% 1.38%
$0.70 $3,160,034.6 $3,153,487.1 $3,117,049 $3,105,888 1.36% 1.51%
$0.80 $3,172,819.7 $3,165,646.2 $3,127,051 $3,115,160 1.44% 1.59%
$0.90 $3,180,402.0 $3,172,414.9 $3,132,172 $3,119,624 1.52% 1.66%
$1.00 $3,185,154.8 $3,176,289.9 $3,135,240 $3,122,245 1.57% 1.70%
$1.10 $3,188,414.9 $3,178,833.2 $3,137,622 $3,124,271 1.59% 1.72%
$1.20 $3,191,146.9 $3,180,772.8 $3,139,878 $3,125,900 1.61% 1.73%
$1.30 $3,193,047.1 $3,182,078.7 $3,142,035 $3,127,427 1.60% 1.72%
$1.40 $3,194,413.7 $3,182,924.0 $3,144,017 $3,128,836 1.58% 1.70%
$1.50 $3,195,723.7 $3,183,783.2 $3,146,178 $3,130,258 1.55% 1.68%
$2.00 $3,200,357.6 $3,186,833.7 $3,152,335 $3,134,884 1.50% 1.63%
$2.50 $3,202,043.6 $3,187,878.0 $3,154,202 $3,136,537 1.49% 1.61%
$3.00 $3,202,774.0 $3,188,303.5 $3,154,954 $3,137,278 1.49% 1.60%
$3.50 $3,203,275.9 $3,188,567.0 $3,155,348 $3,137,663 1.50% 1.60%
Figure C.4 – Demand and supply spectra (100 simulation runs)
63
Table C.4 – Comparison between big and small LNG capacity
Figure C.5 – A typical random walk for desalination variable cost
LNG = 34,000 LNG = 102,000
Without
LNG With LNG Savings Without
LNG With LNG Savings
$0.00 $2,894,257 $2,891,995 $2,262 $3,276,045 $3,272,484 $3,561 $0.10 $2,882,516 $2,880,622 $1,895 $3,302,558 $3,296,086 $6,472 $0.20 $2,890,272 $2,888,341 $1,931 $3,313,832 $3,300,735 $13,097 $0.30 $2,909,638 $2,907,571 $2,067 $3,335,355 $3,317,620 $17,734 $0.40 $2,961,849 $2,959,125 $2,724 $3,388,161 $3,366,512 $21,649 $0.50 $2,992,541 $2,989,739 $2,802 $3,417,727 $3,394,917 $22,810 $0.60 $3,010,187 $3,007,705 $2,482 $3,433,078 $3,409,945 $23,133 $0.70 $3,020,616 $3,018,120 $2,496 $3,442,436 $3,417,591 $24,845 $0.80 $3,027,899 $3,025,130 $2,768 $3,449,889 $3,422,157 $27,733 $0.90 $3,034,004 $3,030,722 $3,281 $3,456,252 $3,424,860 $31,392 $1.00 $3,039,130 $3,035,221 $3,909 $3,463,418 $3,426,714 $36,705 $1.10 $3,043,679 $3,039,002 $4,678 $3,469,649 $3,428,201 $41,448 $1.20 $3,047,564 $3,042,206 $5,358 $3,474,729 $3,429,535 $45,194 $1.30 $3,050,324 $3,044,595 $5,729 $3,479,512 $3,430,722 $48,790 $1.40 $3,052,697 $3,046,717 $5,980 $3,483,255 $3,431,801 $51,454 $1.50 $3,054,178 $3,048,019 $6,158 $3,486,500 $3,432,998 $53,503 $2.00 $3,055,381 $3,049,511 $5,870 $3,496,031 $3,440,315 $55,717 $2.50 $3,055,578 $3,049,544 $6,033 $3,498,750 $3,448,423 $50,328 $3.00 $3,055,461 $3,049,264 $6,197 $3,499,259 $3,455,689 $43,570 $3.50 $3,055,253 $3,048,873 $6,380 $3,499,352 $3,460,885 $38,467