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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. Overview. A wind power case Empirical analysis on spark spread Gas fired power plants and CO 2 capture

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Power plant investments under uncertainty: Case studies and pricing models

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Power plant investments under uncertainty case studies and pricing models l.jpg

Power plant investments under uncertainty: Case studies and pricing models

Stein-Erik Fleten

Norwegian University of Science and Technology (NTNU)

Trondheim, Norway


Overview l.jpg

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, ...


Slide3 l.jpg

Economic Analysis of a License to Build

a Wind Power Farm

Stein-Erik Fleten, NTNU

Kim Krossøy, NTNU -> D&F Group

Bernhard Kvaal, TrønderEnergi

Per-Christian Lysaker Torgersrud, NTNU ->

Statistics Norway

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


Slide4 l.jpg

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


Before the license expires l.jpg

Before the license expires

  • Wait

  • Get more information (downside protection)

  • Save interest on investment cost

  • Invest

  • Receive cash flows


Electricity prices l.jpg

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


Long term electricity prices forward prices sept 2003 l.jpg

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

S0 = 216 NOK/MWh

Yearly growth a = 4.4 NOK/MWh

Standard deviation parameter s = 10.1 NOK/MWh


Project data l.jpg

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.


Net present value l.jpg

Net present value

Base case NPV: 40 million NOK


Slide10 l.jpg

F(S*) = V(S*) –I


Value of license l.jpg

Value of license

Base case S* = 247 NOK/MWh


Discussion l.jpg

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/


Introduction l.jpg

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


The spark spread l.jpg

The spark spread

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

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

  • 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


Modelling spark spread l.jpg

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


Present value of gas plant l.jpg

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


Slide18 l.jpg

Norwegian cont. shelf pipeline network

- there is also British network, etc.


Slide19 l.jpg

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


Slide20 l.jpg

Data

  • Electricity: annual pattern

  • Gas: annual pattern

  • Spark spread: no seasonal pattern

  • Spark spread, electricity – KH·gas


Spark spread estimation l.jpg

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


Value of a base load plant l.jpg

Value of a base load plant

  • The present value of expected operating cash flows

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


Value of a peak load plant l.jpg

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


Only long term prices relevant l.jpg

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


Application l.jpg

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

Inv. cost probably too low, closer to 2000


Values and decisions l.jpg

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


Discussion27 l.jpg

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


Power plant with co 2 capture l.jpg

Power plant with CO2-capture

  • Kyoto agreement

  • National measures

  • Investment 2630 mill NOK

Quotas

Electricity

Steam

Compression

Separation

Exhaust

CO2

Electricity

Steam

Natural gas

Transport

Other exhaust

? other use

Storage

EOR


The value of co 2 capture technology million nok l.jpg

The value of CO2 capture technology(million NOK)

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


Empirical analysis of electricity prices l.jpg

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:


Kalman filter results l.jpg

Kalman filter results


Forward curve estimate l.jpg

Forward curve estimate


Other price modelling efforts l.jpg

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


Alternative to new domestic power capacity transmission cables l.jpg

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!


Conclusion l.jpg

Conclusion

  • Investment under power price uncertainty: There is value to waiting

    • Can explain slow investment behavior

    • not a form of market failure in itself


Small hydropower case l.jpg

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


Two alternatives l.jpg

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


Principal solution l.jpg

Principal solution


Stochastic price model l.jpg

Stochastic price model

  • Geometric Brownian Motion

  • dS =mSdt +σSdz

  • m: drift in long-term prices (forwards)

  • σ: volatility in long-term prices

  • Base case:

    - m = 1 %

    - σ = 5 % (should perhaps be larger)


Slide43 l.jpg

Changing volatility

Inputs

Base-case

m

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%

1.00%

2.50%

5.00%

7.50%

10.00%

12.50%

15.00%

σ

Results

no soln.

Sl

117.3

139.5

147.7

157.8

169.1

181.4

194.7

Sh

157.4

157.1

155.8

153.7

150.5

145.5

135.7

Ss

157.5

157.9

159.1

161.1

163.6

166.8

165.1

S*

121.8

144.8

153.3

163.8

175.5

188.3

202.1

Current equilibrium price: 231,7 NOK/MWh


Slide44 l.jpg

Changing drift parameter

Inputs

Base-case

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

m

r

6.25%

6.25%

6.25%

6.25%

6.25%

6.25%

6.25%

s

5.00%

5.00%

5.00%

5.00%

5.00%

5.00%

5.00%

Resulater

Sl

131.3

147.7

177.1

228.0

326.5

584.3

2909.8

Sh

156.8

155.8

161.2

158.3

157.9

157.8

157.7

Ss

158.1

159.1

155.0

156.7

157.0

157.2

157.2

S*

136.3

153.3

183.9

236.8

338.9

606.6

3021.1

Eqm price

245.0

231.7

219.0

206.9

195.2

184.1

173.4


Results l.jpg

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


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