electricity capacity in Norway Stein-Erik Fleten, NTNU 2 Overview - PowerPoint PPT Presentation

1 Real options analysis of new electricity capacity in Norway Stein-Erik Fleten, NTNU

2 Overview • Empircial analysis of electricity prices • Small hydropower • If time: The potential for new hydropower and windpower in Norway

3 Electricity derivatives • Forward: contract for delivery in a specified future time interval at an agreed price • Futures: Same as forward, but changes in the contract price are settled daily • Standardized • Market’s informed consensus on future spot prices – adjusted for risk

4 Long term energy contracts • Nord Pool: Year contracts for the next three years, after 1.1.2005 one listed ENOYR-08 (in € /MWh) • Basesload prices 7 NOV 2005 (bid-ask and latest): 36 35.5 35 €/MWh 34.5 34 33.5 33 2006 2007 2008

5 What are the contracts use for? • NB! A producer making investment decisions do not need to trade these contracts, only know the current price – Do not need perfect liquidity as long as one gets good price information, but good liquidity gives a smaller difference between buyer and seller price • The prices are used in contributing to portray the expected risk-adjusted value of future energy exchange

6 Power value = FWprice/(1+r) T • To have this power value locked in: • Sell 1 MWh now f.ex. FWYR-06 to 252,5 NOK/MWh (disregards least contract size 1 MW) – No money change hands now! • Loan 252,5/(1+r) T NOK to risk free interest rate r • This must be the power value , since we in 2006 can deliver 1 MWh, receive the spot price, get payoff of 252,5 NOK minus spot price on the forward contract, use the 252,5 NOK we are left with to pay back the loan

7 Uncertainty • Long term price gives us exact value now, on future delivery – No uncertainty in value now • Long term prices will change – Uncertainty about future values • Spot prices, weather, external conditions etc. will still be uncertain – If the project can be altered/can react to development in such uncertain factors, this flexibility must be accounted for and valued – Deterministic analyses/tools (e.g. sensitivity analysis) will not do the job • Long term prices are just as useful under uncertainty as when you know parts of the future

8 Empirical analysis of electricity prices • Two-factor model, log-based and with seasonality:

9 Kalman filter results

10 Forward curve estimate

11 Only long-term prices relevant • When long-term commodity projects are valued, standard one-factor models 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

12 Small hydropower case Inlet dam Inlet Pipe Power station Grid Gross head Outlet • Rivedal power plant at Dalsfjorden in western Norway • Production started 2005 • 20 land owners • 200 meters gross fall ~1,2 m 3 /s net inflow ~3,5 MW installed capacity ~13,5 km 2 catchment area

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14 External economic conditions • No green certificates – start of construction Sept. 2003 • Most important inputs: - Nominal interest rate 5,8 % (long term loan) - 10-year forward 245 kr/MWh

15 Inflow over the year river Rivedal 1929-2003 3.50 3.00 Inflow [m3/s] 2.50 Mean 2.00 Median 1.50 Minimum 1.00 0.50 0.00 1 28 55 82 109 136 163 190 217 244 271 298 325 352 Day no.

16 Inflow duration curve Rivedalselva 300 Inflow [% of mean] Loss 250 200 150 100 Production 50 0 0 % 6 % 12 % 18 % 23 % 29 % 35 % 41 % 46 % 52 % 58 % 64 % 69 % 75 % 81 % 87 % 92 % 98 % Time [% of year]

17 Two alternatives • Under construction: - max. usable flow: 1,9 m 3 /s - ductile cast-iron pipe, diameter: 0,7 m - Pelton turbine - Investment: 18,4 mill NOK • Our alternative: - max. usable flow: 2,3 m 3 /s - fibre glass pipe, diameter: 0,95 m - Pelton turbine - Investment: 21,1 mill NOK

18 Principal solution NPV large power plant NPV small power plant

19 Geometric Brownian Motion Changing volatility Inputs 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. S l 117.3 139.5 147.7 157.8 169.1 181.4 194.7 S h 157.4 157.1 155.8 153.7 150.5 145.5 135.7 S s 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

20 Results • Base case: - no value of waiting (”deep in the money”) - also for volatility of 10 % • The project Rivedal is robustly profitable • Should have been built larger

21 Engineering model for general case • Developed spreadsheet-based software Investment costs • Emphasizing technical choices with a variable size and cost: 5 - turbine 4 - max. usable flow mill. € 3 - penstock (type and diameter) 2 - Cost of inlet dam, power house etc. 1 regarded as constant 0 • Physical relationships included 13.5 14 14.5 15 15.5 – gross head, pipe lengths, distance to grid, Capacity (GWh/year) efficiency curves for all components, friction losses etc. • Historical data on inflow: weekly 1931-2002 • Calculates investment cost as a function of annual capacity

22 Modelling assumptions • The owner of the property has an exclusive right to invest and can postpone the investment • Maximize market value • Assume an uncertain future electricity-price – Only uncertain factor modelled • New: Can choose between continuous capacity alternatives • Mutually exclusive investment – Can only build one plant size • No changes in inflow pattern

23 Investment timing model • The value of the investment opportunity is a real option • With an uncertain price it can be worth more than the expected net present value of building now • Our model follows T. Dangl (Eur J Op Res 1999) • Choose capacity to maximize net present value – Get capacity as a function of long-term price (contribution margin) • Choose price investment threshold to maximize value of investment opportunity – Threshold is in terms of price (contribution margin) – American perpetual call option

24 Stochastic price model Forward prices on one-year • Geometric Brownian Motion for contracts long-term contribution margin 40 Price (€/MWh) 30 – = long term el.price – c 20 – c is a small constant (”per unit variable 10 cost”) 0 • d dt + σ = dW 2007 2008 2009 2010 2011 Delivery year : growth in the contribution margin Time series of one-year forwards traded 3 years in advance • σ : volatility of contribution margin 40 • Base case: Price (€/MWh) 30 - = 0.69 % 20 - σ = 13 % 10 0 2001 2002 2003 2004 Trading day

25 External economic conditions • Variable cost – c = 1.19 € /MWh • Nominal discount interest rate 5.8 % – (approximately the risk free rate ...) • Project life 30 years • Current long-term price 32.7 € /MWh • No green certificates sales – Policy makers do not find small hydro ”green” enough

26 Case conclusion • The project Rivedal is robustly profitable • No value of waiting to build • Should have been built larger

27 Main results • We find an investment threshold for the long-term contribution margin * – Below * it is optimal to wait, even though NPV may be positive – Should current be higher than *, invest as soon as possible using the capacity that maximizes NPV with the current • A real-options based decision support system, combining finance and hydro engineering • Have made a spreadsheet-based program – Thor Bøckman uses this professionally

28 Model using math – Present value • Long-term contribution margin ( € /MWh) • Growth in contribution margin • Estimated discount interest rate • – = Lease rate (rate of return shortfall), i.e. correct discount interest rate for revenue cash flows = [ 1 – ( 1 + ) – T ]/ • capitalization factor • T Project life (years) • m Plant size to be chosen (MWh/year) • Present value of operating cash flows (mill. € ) V ( m , ) • V ( m , ) = m

29 Model using math – Investment cost • I ( m ) Investment cost • I ( m ) = A e bm where A and b are constants V ( m , ) I ( m ) m m • Optimal investment size: Marginal 1 value equals marginal cost: m * ( ) ln b Ab • Have found plant size as a function of the state variable

30 Model using math – Investment strategy • Using standard financial theory we know that the value of the investment opportunity, the real option: • F ( ) = D • where is a known function of , , and • When the investment decision is made, we have value matching and smooth pasting giving * exp 1 Ab Ae Ab D 1 • The threshold contribution margin * is the absolute lower limit for investing in the project. At lower contribution margins one waits, and at higher margins one invests with capacity m *( )

31 Sensitivity wrt uncertainty Theta, trigger price [€/MWh] 60 50 40 theta 30 fixed m theta 20 10 0 0 0.1 0.2 0.3 0.4 0.5 sigma