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Power plant investments under uncertainty: Case studies and pricing models

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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  1. Power plant investments under uncertainty: Case studies and pricing models Stein-Erik Fleten Norwegian University of Science and Technology (NTNU) Trondheim, Norway

  2. 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, ...

  3. 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

  4. 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

  5. Before the license expires • Wait • Get more information (downside protection) • Save interest on investment cost • Invest • Receive cash flows

  6. 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

  7. 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

  8. 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.

  9. Net present value Base case NPV: 40 million NOK

  10. F(S*) = V(S*) –I

  11. Value of license Base case S* = 247 NOK/MWh

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

  13. 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/

  14. 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

  15. 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

  16. 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

  17. 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

  18. Norwegian cont. shelf pipeline network - there is also British network, etc.

  19. 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

  20. Data • Electricity: annual pattern • Gas: annual pattern • Spark spread: no seasonal pattern • Spark spread, electricity – KH·gas

  21. 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

  22. 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

  23. 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

  24. 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

  25. 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

  26. 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

  27. 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

  28. 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

  29. The value of CO2 capture technology(million NOK) Compare numbers with gas plant investment cost 2000, plus CO2 capture plant of additional 2000 - 3000

  30. 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:

  31. Kalman filter results

  32. Forward curve estimate

  33. 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

  34. 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!

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

  36. Small hydropower case • Rivedal power plant at Dalsfjorden in Sogn og Fjordane county • Under construction fall 2004 ~3,5 MW installed capacity

  37. 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

  38. 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

  39. Principal solution

  40. 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)

  41. 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

  42. 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

  43. 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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