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Power plant investments under uncertainty: Case studies and pricing models

Stein-Erik Fleten

Norwegian University of Science and Technology (NTNU)

Trondheim, Norway

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Overview

• A wind power case• Empirical analysis on spark spread• Gas fired power plants

– and CO2 capture

• Empircial analysis on electricity prices• Renewables in Norway

– If time: small hydropower, new transmission cables, ...

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Economic Analysis of a License to Build a Wind Power Farm

Stein-Erik Fleten, NTNUKim Krossøy, NTNU -> D&F Group Bernhard Kvaal, TrønderEnergiPer-Christian Lysaker Torgersrud, NTNU ->

Statistics Norway

Fleten, Economic Analysis of a License to Build a Wind Power Farm

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Economic Analysis of a License to Build a Wind Power Farm

– Uncertain electricity prices

– Net present value of the farm varies with electricity prices

– A license is right, but not an obligation, to invest before the license expires

Fleten, Economic Analysis of a License to Build a Wind Power Farm

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Before the license expires

Invest• Receive cash flows

Wait• Get more information (downside protection)

• Save interest on investment cost

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Electricity prices

• Higher in winter– also true for wind speeds

• What is the expected future electricity prices received for selling windpower during the lifetime of the wind farm?– long term price level is uncertain, so profitability is uncertain

– short term prices even more uncertain, but do not influence windfarm profitability!

Movie

100

140

180

220

260

1 7 13 19 25 31 37 43 49

Week

[NO

K/M

Wh]

1,0

1,5

2,0

2,5

3,0

%

Average local el. price 1996-2003

Share of annual generation

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Long-term electricity prices(forward prices Sept. 2003)

200

210

220

230

240

250

260

270

0 2 4 6 8 10

Ye ars

Pri

ce [

NO

K/M

Wh]

dS dt dz S0 = 216 NOK/MWh

Yearly growth = 4.4 NOK/MWh

Standard deviation parameter = 10.1 NOK/MWh

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Project data

• Bessakerfjellet windpower farm, TrønderEnergi, 50 MW• Average wind speed of 8.44 m/s • Green certificate price 150 NOK/MWh • Cost of capital r = 8%

– not adjusted for price risk!

• Investment cost 8 million NOK/MW, I = 400 million NOK• Lifetime 20 years• OM cost 47.5 NOK/MWh • Taxes, balancing cost, compensation to property owner etc.

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Net present value

Green cert. price NOK/MWh

-300

-200

-100

0

100

200

300

200 250 300

Long term el. price

NP

V,

mil

l. N

OK 0

50

100

150

200

250

Base case NPV: 40 million NOK

10

rFdt E dF

212 ''( ) '( ) '( )dF F S F S dt F S dz

212 ''( ) '( ) ( ) 0F S F S rF S

1 21 2( ) S SF S A e A e

2 212 0r

11( ) SF S A e

F(S*) = V(S*) – I 1 *

1 *SA e aS b 1 1 1*

1( , *) ( * )S S SF S S A e e aS b I e

1

1 ( )*

b IS

a

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Value of license

-20

0

20

40

60

80

100

120

140

170 220 270

Long-term electricity price [NOK/MWh]

Val

ue

[mill

ion

NO

K]

V(S) - I

F(S)

Base case S* = 247 NOK/MWh

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Discussion

• Have assumed license does not expire• Learning effect not accounted for

• Conclusion: Wait for better prices!– Lognormal model gives same conclusion

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Gas fired power plants

• Investment timing, operating flexibility and abandonment– joint work with E. Näsäkkälä, HUT

– available: http://www.sal.hut.fi/Personnel/Homepages/ErkkaN/thesis/

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Introduction• A firm holds a license, i.e. an option, to build a gas fired

power plant• The cash flows from the plant depend on the spark spread

– Defined as the difference between the unit price of electricity and cost of gas

• Electricity is produced when the spark spread exceeds emission costs– Otherwise, if it is a peak plant, the plant is ramped down and held idle

• The plant can be abandoned – The salvage value of the plant is realized

• We compute – The value of the plant

– Entry and exit thresholds for the spark spread

– The value of installing CO2 capture technology eliminating emission costs

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The spark spread

• We consider a two-factor model for the spark spread

• Two-factor model (see e.g. Schwartz and Smith, 2000)

( ) ( ) ( )S t t t ( ) ( ) ( )d t t dt dB t ( ) ( )d t dt dB t

• The changes in spark spread are normally distributed– the spark spread can be either negative or positive

• Spark spread is mean reverting and also has long-term uncertainty

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Modelling spark spread• Usually as two separate processes: Realistic but complex

• Here the spread is modelled directly

• Simpler – one indicator of profitability

• The variance of the spark spread is not necessarily realistic at all combinations of electricity and gas prices

– with direct modelling of the spread it is difficult to capture the true dynamics if electricity and gas follow two distinct, nonintegrated processes

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Present value of gas plant

• Solid lines: using the two-factor model presented

• Dashed lines: using separate models for electricity and gas

• Present value as a function of short- and long term volatility

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Norwegian cont. shelf pipeline network

- there is also British network, etc.

Norwegian cont. shelf pipeline network

- there is also British network, etc.

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Data

• Nord Pool electricity– Nearest 1-month forward and

year contracts 2-3 years ahead

• IPE gas – Nearest 1-month forward and

year contracts 3 years ahead

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Data

• Spark spread, electricity – KH·gas

• Electricity: annual pattern• Gas: annual pattern• Spark spread: no

seasonal pattern

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Spark spread estimation

• Kalman filter• Long-term drift estimated

from long-term forwards 30.1.2004

• Current (Jan.04) and chosen so that forward curve is matched

• Grey: Estimated time series

• Black: Estimated time series

Parameter 0 0

UnitNOK/ MWh

NOK/ MWh

NOK/ MWh

NOK/ MWh

NOK/ MWh

Value2.6

2.18-0.21

382.2 47.8 62.3 52.9

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Value of a base load plant

• The present value of expected operating cash flows

( )

( ) ( )

( , ) ( ) |

( ) ( ) ( )

Tr s t

L t

t

Tr s t s t

t

V e C E S s F E G ds

e C e t t E s t G ds

• where E is emission costs and G is fixed cost of running the plant

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Value of a peak load plant• The gas plant at time t can be replicated with t-maturity

European call options with strike price equal to the emission costs E

• As the changes in the spark spread are normally distributed, finding the value is straightforward by integration

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Only long-term prices relevant• When long-term commodity projects are valued, models

with constant convenience yield give practically the same investment decision results as models using stochastic convenience yield (see e.g. Schwartz, 1998)

• Thus we assume investment decisions are made on the basis of equilibrium prices only

• Option to invest, (to shut down temporarily), to abandon– values and trigger levels found simultaneously

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Application• Norwegian authorities have given three licenses to build gas

fired power plant– The costs of building and running a combined cycle gas plant in Norway are

estimated by Undrum, Bolland, Aarebrot (2000) for a 415 MW plant

Parameter

W C G I D

Unit MNOK/year MMwh/year MNOK/year MNOK MNOK

Value 2.5 3.27 50 1620 570

Inv. cost probably too low, closer to 2000Inv. cost probably too low, closer to 2000

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Values and decisions

• Building threshold H

– No abandonment:

[46.3; 165.3] NOK/MWh.– Abandonment included: [43.8;

134.3] NOK/MWh, • Abandonment threshold:

[-362.8; -131.6] NOK/MWh

• DCF investment threshold: [-178.2; 8.7] NOK/MWh

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Discussion • It is not optimal to exercise the option to build a base load

gas fired power plant– Regardless, the reality may be different

• 2004 data, base load 800 MW: NPV for building now 0. Value of investment opportunity = value of waiting 2800 mill NOK (not considering expiry of the license)

• Naturkraft sept. 2004: “We’re building!”• There are several possible explanations why our results

differ from the apparent policies of the actual investors – License expires (but not from society point of view)– The preemptive effect of early investment gives the license holders an

incentive to build the plant (see e.g. Smets, 1991) – We have used the UK market as a reference for gas– There is also a tax issue that has not been considered

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Power plant with CO2-capture

Oth

er

exhaust

Oth

er

exhaust

? other use? other use

ExhaustExhaust

Steam Steam ElectricityElectricity CO2CO2 T

ransp

ort

Tra

nsp

ort

Natu

ral gas

Natu

ral gas

SeparationSeparation CompressionCompression

Ele

ctri

city

Ele

ctri

city

S

team

S

team

Storage EOR

Quotas• Kyoto agreement• National measures• Investment 2630 mill

NOK

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The value of CO2 capture

technology (million NOK)Plant value based on linear forward price paths on electricity and gas

Deterministic cash flow

Market value based on real options. Gas volatility resp. 25%, 30%, 35%

Alt 1 "Base Case" 892 2 769 3 199 3 628

Alt 2 CO2-quotas 200 NOK -2 021 1 800 2 278 2 758 Alt 3: With CO2 capture plant

-516 2 217 2 687 3 155

Alt 3b: Capture plant+ sale for EOR 50 NOK/ton CO2

211 2 497 2 950 3 401

Compare numbers with gas plant investment cost 2000, plus CO2 capture plant of additional 2000 - 3000Compare numbers with gas plant investment cost 2000, plus CO2 capture plant of additional 2000 - 3000

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Empirical analysis of electricity prices

• For the purpose of valuing long-term generation assets• Same two-factor model as before, but log-based and

with seasonality added:

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Kalman filter results

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Forward curve estimate

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Other price modelling efforts

• Long-term electricity forward prices– how to combine long-term info on supply and demand with high-

resolution info on e.g. fuel prices

– Joint work with Martin Povh

• Short-term electricity spot prices– For bidding, short term generation planning etc

– Considering ARFIMA, GARCH etc.

– Joint work with Trine K. Kristoffersen

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Alternative to new domestic power capacity: transmission cables• Statnett: ”NSI is (social-) economically profitable”

– Norsk Hydro agreed– Statistics Norway, Elkem: ”Not profitable”

• NPV= -I + capacity*discounted sum of exp. price difference Norway-UK

– depends on variations in price level, interest rates and exchange rates

• Decision rules – NPV >= 0– NPV – value of waiting >= 0

• What about NorNed? 700 MW, I = 2600 million NOK, NPV = 2000 mill NOK

– not a word about option value, value of waiting for better information etc. in the reports!

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Conclusion

• Investment under power price uncertainty: There is value to waiting – Can explain slow investment behavior– not a form of market failure in itself

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Small hydropower case

• Rivedal power plant at Dalsfjorden in Sogn og Fjordane county

• Under construction fall 2004~3,5 MW installed capacity

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External economic conditions

• No green certificates– start of construction Sept. 2003

• Most important inputs:- Nominal interest rate 6,25 % (long term loan)

- 10-year forward 245 kr/MWh

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Two alternatives

• Under construction:- max. usable flow: 1,9 m3/s- ductile cast-iron pipe, diameter: 0,7 m- Pelton turbine- Investment: 18,4 mill NOK

• Our alternative:- max. usable flow: 2,3 m3/s- fibre glass pipe, diameter: 0,95 m- Pelton turbine- Investment: 21,1 mill NOK

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Principal solution

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Stochastic price model

• Geometric Brownian Motion• dS = Sdt + σSdz

• : drift in long-term prices (forwards)

• σ: volatility in long-term prices

• Base case:

- = 1 %

- σ = 5 % (should perhaps be larger)

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Current equilibrium price: 231,7 NOK/MWh

Changing volatilityInputs Base-case 0.00% 1.00% 1.00% 1.00% 1.00% 1.00% 1.00%r 6.25% 6.25% 6.25% 6.25% 6.25% 6.25% 6.25%σ 1.00% 2.50% 5.00% 7.50% 10.00% 12.50% 15.00%Results no soln.Sl 117.3 139.5 147.7 157.8 169.1 181.4 194.7Sh 157.4 157.1 155.8 153.7 150.5 145.5 135.7Ss 157.5 157.9 159.1 161.1 163.6 166.8 165.1S* 121.8 144.8 153.3 163.8 175.5 188.3 202.1

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Changing drift parameterInputs Base-case 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00%r 6.25% 6.25% 6.25% 6.25% 6.25% 6.25% 6.25% 5.00% 5.00% 5.00% 5.00% 5.00% 5.00% 5.00%ResulaterSl 131.3 147.7 177.1 228.0 326.5 584.3 2909.8Sh 156.8 155.8 161.2 158.3 157.9 157.8 157.7Ss 158.1 159.1 155.0 156.7 157.0 157.2 157.2S* 136.3 153.3 183.9 236.8 338.9 606.6 3021.1Eqm price 245.0 231.7 219.0 206.9 195.2 184.1 173.4

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Results

• Base case: - no value of waiting (”deep in the money”)- also for volatility of 10 %

• Option has no value before at least 3% drift

• The project Rivedal is robustly profitable • Should have been built larger