GOING OFFSHORE: INVESTMENTS IN GERMAN WIND ENERGY UNDER UNCERTAINTY Yu-Fu Chen University of Dundee Michael Funke Hamburg University 2 nd October 2015, Brescia, Italy
Introduction (1) • Wind energy: the fastest-growing segment of green energy worldwide due to abundant and reliable wind resources. • Offshore wind is a relatively new form of renewable energy that has only recently spread beyond Europe to China and a handful of other countries. • By December 31, 2014, 258 offshore wind turbines in the German North Sea and Baltic Sea with a total capacity of 1,049.2 megawatts (MW). Another 220 foundations are currently under construction and further projects are in the pipeline. • See Green and Vasilakos (2011) for comprehensive overview 1
Introduction (2) • Germany’s roadmap for renewable deployment aims to redesign Germany’s energy system within the next few decades. • By 2022, all nuclear power plants are to be switched off. In addition, by 2050 about 80 percent of electricity is to come from renewable sources, compared with 22 percent now. • Furthermore, CO 2 emissions are supposed to fall from those in 1990 by 50 percent in 2030 and 80 percent by 2050. • The Renewable Energy Sources Act promised 20 years of guaranteed prices to wind, solar or other renewable sources. 2
Introduction (3) • One of the most ambitious elements is to build 6.500 MW of wind turbines off the North Sea and Baltic Sea coasts by 2020. (Due to anti-onshore wind farm protests on their size and the noise of their blades. • Offshore wind farms are more expensive but offer much higher energy yields. However, these potential gains of capturing economies of scale are counterbalanced by higher investment and maintenance expenditures. • With this background in mind, we analyze the investment in a German offshore wind farm bearing in mind the specific German support policy framework through the prism of a real options modelling framework. 3
The Analytical Framework (1) • Offshore investment decisions are option-rights and renewable energy investments can be seen as an application of real options. The Investment Incentives of the EEG Feed-In Tariff System • The EEG 2012 aimed to increase the share of renewable energy significantly within the next decades. • The operating company has the opportunity to receive initial remuneration of 19 ct/kWh for a shortened period of 8 years, provided that the wind farm is put into operation before 2018. • In short, 19 ct/kWh for a period of 8 years; 15 ct/kWh is for the extension period. Afterwards, a lower bound flat rate of 3.5 ct/kWh is guaranteed until the end of 20 years; and market prices for the last 5 years. 4
The Analytical Framework (2) Figure 1: Timeline of the Multi-Stage Offshore Wind Energy Feed-in Tariff Scheme τ : period of At t =0, the τ : period of 2 4 investment project m τ : period of guaranteed P , market prices guaranteed price decision is made 3 τ : period of received. medium guaranteed f and sunk cost P , if market 1 floor price m h P < P . guaranteed price price, where finished at t = 0 t . f P , prices fall below h P , higher f m h P < P < P . where guaranteed price. Time t =0 1 t 2 t 3 t 4 t t = t 0 t , the At 4 t , the At t = 0 windpark windpark starts to ceases operate, generating operations. cash flow. 5
The Analytical Framework (3) Figure 2: Electricity Prices Received in the Three Operating Phases Received nominal h P electricity prices Z Payoff over m P t three periods Market electricity Z = P prices are ( ) f Z = max P P , t t t t received f P time t t t t t 0 1 2 3 4 6
The Analytical Framework (4) Modelling of electricity prices • Assume that the wholesale electricity prices follow the mean- reverting stochastic process: � � − ��� � )�� + ��� ���� � = (��� � where � is the nominal electricity prices, � denotes the long-term constant prices, � is the parameter related to the mean-reverting speed of electricity � and prices returning to long-run equilibrium � � is the volatility parameter of the standard Wiener process � . 7
The Analytical Framework (5) • The investor’s problem is to maximize the discounted value of profit for the firm, � ��� , which is given by � � � ��� = (1 − �)� � ��(� � �� �)� ��(��� � ) �� � − �� �, � � where � is the constant tax rate on profits, � � �� � − �� � , � � is the electricity price received in various phases, � � is the maximum wind farm electricity output capacity per year, � is the capacity utilization rate, � is the constant annual maintenance per maximal output and � is the discount rate. 8
The Analytical Framework (6) • Pulling the deterministic parts out of the integral, � � � ��� = � � + � � + (1 − �)� � ���max�� � , � � � �� ��� ��(��� � ) �� � − �� � � � � � ��� �(���)(��� � ) �� +(1 − �)� � ���� � �� � − �� �, � � where � � �)�1 − � �(���)(� � �� � ) � (1 − �)(� � �� � − �� �)� ��(��� � ) �� � � = (1 − �) �(� � �� � − �� = � + � � � � � �)�� �(���)(� � �� � ) − � �(���)(� � �� � ) � (1 − �)(� � �� � − �� � � = (1 − �) �(� � �� �)� ��(��� � ) �� � − �� = . � + � � � 9
The Analytical Framework (7) • Approximate analytical solutions for period 3 and period 4 can be � � �� �max�� � , � � � �� � − obtained by numerical integration: � � � � ��� ��(��� � ) ��� & �� �� � �� ��� �(���)(��� � ) �� �� � − �� � � � • The real options are only related to the uncertain part of the integrals. Note that the duration � � of the third operating phase starts from � = � � and lasts until � � . The value-matching condition for the offshore wind farm at � = � � is denoted by � ��� =� � �sunk cost� + real options�max�� � (�; � � ), � � �, � � (�; � � ), sunk cost uncertainty�, where � ��� is denoted by equation (3). 10
The Analytical Framework (8) • Problem of mean-reverting of electricity prices uncertainty from markets: electricity prices uncertainty affect payoffs, but not real options: uncertainty is at 12 years away with fast mean-reverting. Value-matching implies that offshore investment is undertaken • This implies that only the sunk costs’ uncertainty exerts an influence upon the real options. �(sunk cost uncertainty) ≡ real options(sunk cost uncertainty). 11
The Analytical Framework (9) • The cost of electricity from offshore wind farms can be reduced by about one-third until 2023. • The costs for support structures and other components as well as for the installation will also decline. • A straightforward functional form for such declining sunk costs due to learning by doing and experimentation is � � ����� ����� = � � + � � �� � �� ��� , where � � denotes the sunk cost of the sophisticated state-of-the-art technology and � � �� � �� ��� represents the declining variable sunk costs over time with uncertain � � and h > 0 determines the cost reduction over time. 12
The Analytical Framework (10) • We assume sunk cost = � � + � � , where � � follows a geometrical Brownian motion with a negative trend. Thus, � � is governed by �� = −ℎ��� + � � ��� � , where � � is the uncertainty parameter for stochastic process � and � � is the standard Wiener process for � . • Real Options � + 1 � � � � � � � = −ℎ�� 2 � � �� , � � ��� � � � � � ��� � � � � � � � , �� �� �� �(�) = � � � 13
The Analytical Framework (11) • Value-matching condition and its corresponding smooth-pasting condition: � �� � � � ���� �� � ��� � � . � � � � � � � � �, �, �, � � , � � , � � � =� � + � + � � � � � ��� ��|� � �� � � � ���� �� � ��� � � 0 =1 − �− 1 2 − ℎ � + ��1 2 + ℎ + 2� � � � �� � � � � � � � � � � � � � � � . � � � � � � �1 + � � � �, �, �, � � , � � , � � �= � � + � . � ��� ��|� � � � � ��� � � � � � � ��� � � � � � � � �� �� �� � � 14
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