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):

33 33.5 34 34.5 35 35.5 36 2006 2007 2008 €/MWh

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

• f 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

• Rivedal power plant at Dalsfjorden in western Norway
• Production started 2005
• 20 land owners
• 200 meters gross fall

~1,2 m3/s net inflow ~3,5 MW installed capacity ~13,5 km2 catchment area

Inlet dam Inlet Pipe Power station Grid Gross head Outlet

13

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

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 1 28 55 82 109 136 163 190 217 244 271 298 325 352 Day no. Inflow [m3/s] Mean Median Minimum

16

Inflow duration curve Rivedalselva

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

Loss Production

17

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

18

Principal solution

NPV large power plant NPV small power plant

19

Current equilibrium price: 231,7 NOK/MWh

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. 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

Geometric Brownian Motion

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
• Emphasizing technical choices with a

variable size and cost:

• turbine
• max. usable flow
• penstock (type and diameter)
• Cost of inlet dam, power house etc.

regarded as constant

• Physical relationships included

– gross head, pipe lengths, distance to grid, efficiency curves for all components, friction losses etc.

• Historical data on inflow: weekly 1931-2002
• Calculates investment cost as a function of

annual capacity Investment costs

1 2 3 4 5 13.5 14 14.5 15 15.5 Capacity (GWh/year)

• mill. €

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
• ption
• 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
• f investment opportunity

– Threshold is in terms of price (contribution margin) – American perpetual call option

24

Stochastic price model

• Geometric Brownian Motion for

long-term contribution margin

– = long term el.price – c – c is a small constant (”per unit variable cost”)

• d

= dt + σ dW : growth in the contribution margin

• σ: volatility of contribution margin
• Base case:
• = 0.69 %
• σ = 13 %

Forward prices on one-year contracts

10 20 30 40 2007 2008 2009 2010 2011 Delivery year Price (€/MWh)

Time series of one-year forwards traded 3 years in advance

10 20 30 40 2001 2002 2003 2004 Trading day Price (€/MWh)

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)

• V(m, )

Present value of operating cash flows (mill. €)

• V(m, ) = m

29

Model using math – Investment cost

• I(m)

Investment cost

• I(m) = Aebm

where A and b are constants

• Optimal investment size: Marginal

value equals marginal cost:

• Have found plant size as a function
• f the state variable

Ab b m m I m m V m ln 1 ) ( * ) ( ) , (

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 1

Ab

Ab Ae D

• 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]

10 20 30 40 50 60 0.1 0.2 0.3 0.4 0.5 sigma theta fixed m theta

32

Sensitivity wrt delta

Theta, trigger price

5 10 15 20 25 30 35 40 45 50

• 0.3
• 0.2
• 0.1

0.1 0.2 delta theta fixet m theta

33

New Renewable Electricity Capacity under Uncertainty: The Potential in Norway

• Annual electricity consumption Norway: ca 125 TWh
• Expansion of wind power and small hydropower in Norway,

– when there is a common green electricity certificate market in Norway and Sweden

• How much new power will come, and when?

– Hydropower: 25 TWh/yr, Norway – Hydropower: 26 TWh/yr, EU-25

• Methods and main elements:

– Net present value (NPV). – Real options analysis. – The technical and economic potential for expansion – Projects: Concession applied, granted, notified projects – An eligible project receives support for ten years – A stochastic two-factor model of electricity and green certificate prices

Cost curve

34

Electricity prices

• Model is based on two

stochastic factors ( og X), and a cosine term f(t) for seasonality.

• Parameters are estimated

from a time series of about 10 000 contracts traded on Nord Pool from 1996-2004.

Electricity price

50 100 150 200 250 300 350

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026

Year NOK/MWh Average 40 paths

1€ 8 NOK

t e X e t f T P F

t t * *

) 1 ( ) ( ) , (

52 2 ) ( cos ) , ( t T T t f

t t t

X t f P ) (

X X t t

dZ dt X dX ) ( dZ dt d

t

dt dZ dZ X

35

Electricity certificate prices

• Model is based on

STEM (2005) analyses using the long-term equilibrium model MARKAL.

• Two levels of political

ambition for the joint goal of the certificate policy for Norway and Sweden: 31 TWh/yr and 41 TWh/yr by 2017.

• This leads to two

different price scenarios

Electricity certificate price (sample paths)

50 100 150 200 250

2 7 2 8 2 9 2 1 2 1 1 2 1 2 2 1 3 2 1 4 2 1 5 2 1 6 2 1 7 2 1 8 2 1 9 2 2 2 2 1 2 2 2 2 2 3 2 2 4 2 2 5 2 2 6

Year NOK/MWh certifiable generation

31 TWh level of ambition 41 TWh level of ambition

1€ 8 NOK

36

Expected total price for a producer

• The level of

ambition is a TWh/yr target.

• The example to

the right show the expected total price, from 2007 and 20 years on. ”Total” means sum of electricity price and electricity certificate price

1€ 8 NOK

Mean price (average of 2500 simulations)

100 200 300 400 500 Year NOK/MWh Scenario 1 Scenario 2

37

Wind resources in Norway

• Windpower projects are

categorized by average wind speed.

• Data is from ENOVA

and The Norw. Meteorological Institute, for sites in Finnmark (northernmost), Rogaland (southwest), Møre og Romsdal, Sør- Trøndelag and Nord- Trøndelag (lower middle).

Mean wind speed

2 4 6 8 10 12 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

m/s

Class 1 Class 2 Class 3 Mean C1 Mean C2 Mean C3

38

Small hydropower resources

• NVE: Small

hydropower is classified by investment cost (per annual generation in kWh) and winter generation as share

• f total generation.
• We used data from

four chosen real projects to set up hydro classes 1-3.

1eurocent 8 øre

Investment cost classification of remaining usable hydropower

100 200 300 400 500 600 700 10 20 30 40 50 60 70 80 90 100

Winter generation in % of total generation Investment cost (øre/kWh)

• Cl. 1

Cl 2 Cl 3 Four chosen real projects

1 2 3 4 5 6

39

Cost curve

• In total a technical potential
• f around 120 TWh/yr for

windpower and hydropower in Norway.

• The three cost classes of

small hydropower (12 TWh) are the least costly, before the substantial windpower potential takes over at a COE

• f just over 30 øre/kWh.
• Finnmark, the northernmost

county, is only in with 0,8 TWh/yr.

• Norway can fulfil a national

quota of up to around 20 TWh/yr at a COE below 33 øre/kWh.

• The return on capital after

taxes is around 5 to 6 %. Cost curve for windpower and small hydropower

0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 10 20 30 40 50 60 70 80 90 100 110 120

TWh NOK/kWh 6 % 5 %

Expansion path

40

Real options analysis

• Assumptions:

– An investor with a concession (license) has a right, but not the obligation, to invest. – The investment is irreversible. – Uncertainty in power prices, electricity prices.

• This can be seen as a

real option, where the investor commences the project when the the total price reaches a threshold, at which the net present value is much greater than zero.

Optimal trigger price

• 600
• 500
• 400
• 300
• 200
• 100

100 200 300 50 100 150 200 250 300 350 400 450 500

Trigger price (NOK/MWh) MNOK NPV Real option value

41

Trigger price small hydropower

Ambition level 1 (31 TWh) Ambition level 2 (41 TWh) ØK 1 ØK 2 ØK 3 ØK 1 ØK 2 ØK 3

ERT Vol 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7 4 5 6 7

5

236 261 287 313 329 365 403 444 422 471 522 575 265 291 319 348 368 408 449 493 473 526 581 639

10

262 289 318 348 364 405 447 492 468 522 579 638 317 348 382 416 440 488 537 589 565 628 695 764

15

298 329 361 395 414 460 508 559 532 593 658 725 378 416 455 499 525 582 641 703 675 750 830 912

20

341 377 414 453 475 527 583 641 609 680 754 830 449 494 541 591 625 692 762 836 802 892 986 1084

25

392 433 475 520 545 606 669 736 700 781 866 954 532 585 640 699 739 819 902 989 949 1055 1167 1283

30

450 497 545 597 625 695 768 844 803 896 993 1095 625 688 753 822 869 963 1061 1163 1116 1241 1372 1509

42

The path of expansion

• Ambition level 31 TWh:

– Windpower not very profitable, and only the ENOVA goal of ca 3 TWh will be built – Small hydropower has low

• ption value, and profitable

projects should be commenced as soon as possible for cost classes 1 and 2.

• Ambition level 41 TWh:

– Windpower projects have

• ption value, and projects in

wind class 1 will not be expected until the end of the escalation period for the electricity certificate arrangement. – The same applies to an extent also to small hydropower, but at a volatility of less than 20% much will be built early. Path of expansion in Norway 31 TWh/yr ambition

0,0 1,0 2,0 3,0 4,0 5,0 6,0 7,0 8,0 9,0 10,0 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

TWh Wind power Hydropower Total

Path of expansion Norway at 41 TWh/yr ambition

0,0 4,0 8,0 12,0 16,0 20,0 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016

TWh Wind Hydro Total

43

Conclusion

• A new way of applying real options analysis
• Able to quantify exected path of expansion
• Uses the informational efficiency of energy

derivatives markets

44

Conclusion

• Investment under power price uncertainty:

There is value to waiting

– Can explain slow investment behavior – not a form of market failure in itself

• Real options can serve as analysis

input/decision support for investors

– little use in practice (yet), herein lies a challenge – forward prices contain a lot of economic information, giving rise to market-based estimates of real option values