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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

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 CO2 capture
- Empircial analysis on electricity prices
- Renewables in Norway
- If time: small hydropower, new transmission cables, ...

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

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

- Wait
- Get more information (downside protection)
- Save interest on investment cost

- Invest
- Receive cash flows

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)

S0 = 216 NOK/MWh

Yearly growth a = 4.4 NOK/MWh

Standard deviation parameter s = 10.1 NOK/MWh

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

Base case NPV: 40 million NOK

Value of license

Base case S* = 247 NOK/MWh

Discussion

- Have assumed license does not expire
- Learning effect not accounted for
- Conclusion: Wait for better prices!
- Lognormal model gives same conclusion

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

- 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

- 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

- 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

- 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

Norwegian cont. shelf pipeline network

- there is also British network, etc.

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

Data

- Electricity: annual pattern
- Gas: annual pattern
- Spark spread: no seasonal pattern

- Spark spread, electricity – KH·gas

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

- 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

- 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

- 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

- 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

- 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

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 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 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

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

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

- 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

- 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

- Rivedal power plant at Dalsfjorden in Sogn og Fjordane county
- Under construction fall 2004

~3,5 MW installed capacity

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

- 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

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)

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

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

- 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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