mechanics of fixed premium systems.
Figure 4: Subsidy systems in comparison
I show the mechanics of feed-in-tariffs under fixed and variable premium systems. Figure 4a shows the fixed premium system under which investors receive an additional premium to the current market price of electricity. Figure 4b documents the variable premium system under which investors are guaranteed a minimum level of compensation (K) for every production unit.
(a)Fixed premium
time P
SpotPt
Subsidy StF P Spot + Subsidy
(b) Variable premium
time P
Spot Pt
SubsidyStV P Floor K
The variable premium system one the other hand depends on the current level of electricity prices. In essence, investors are guaranteed a minimum price level of electricity. Whenever the current price of power exceeds the guaranteed price level, there are no distributions of additional subsidy compensations. When the price level of electricity is very low, however, the additional premium is high. The ability to always sell electricity at a minimum level can be considered as an option-like feature under which investors yield cash flows of
CtV P =
Pt+StV P ifPt< K Pt ifPt≥K,
(8)
where CtV P is the cash flow at time t under the variable premium system (V P). The minimum price level (floor) of electricity the investor is guaranteed is K, which one could think of as the strike. In the case wherePt< K, the cash flow at timetis determined by the sum of the electricity price StV P and the premium Pt, which always equals K (or put differently, the subsidy level at timet equals StV P =K−Pt). WheneverPt> K, the investor only yields the current level of Pt
for every MWh he sells; there is no additional compensation. Alternatively, the investor can think of the payoff at time t as CtV P = max[Pt, K].24 Figure 4b presents the fixed premium system graphically.25
Denmark, generally speaking, has adopted a type of a fixed premium system as their chosen subsidy to create incentives for investors to allocate capital to green energy. Both the old and the new system rely on the same mechanics but differ in their specifications with respect to levels, duration, and other constraints. One key objective of this study is to better understand the differences in risk and return dynamics in the change from the old to the new system.
Even though, this study focuses on a fixed premium system as observable in Denmark, one can adjust the framework to variable premium systems also. In the final section of the results, I apply a theoretical case of a variable premium system, in which case the definition of subsidy payoffs changes within the model and in line with Equation (8).
No uncertainty in subsidies
Referred to as the old subsidy compensation system, producers who commissioned projects until 20.02.2018 are compensated with 25øre/kWh (33.5€/MWh), represented byG, for 22.000 full load hours on top of 2.3øre/kWh (3.1€/MWh), denoted by B, balancing costs for electricity over the entire lifetime of the project. As discussed in the previous subsection, this is a type of a fixed premium system and can be defined as
StOld =
G+B if Ptj=1f(Vj)≤22.000h∗M Wmax
B if Ptj=1f(Vj)>22.000h∗M Wmax
(9)
Note that, in this definition, there is no consideration of uncertainty in subsidy distributions. In-vestors assume that they will be granted the full subsidy stream throughout the project’s eligibility, see Figure 5a.
The new subsidy system is that of a tender (but still a type of a fixed premium system).
Investors can place bids on receiving subsidies per MWh at yearly auctions. The lowest bids are granted to investors until funds for each tender are exhausted. The bids must not exceed 13øre/kWh (17.4€/MWh). If granted the tender bid, the subsidy premium is paid on top of the market price over a time horizon of 20 years (t= 20×365 = 7300 days):
24A policy maker might adjust this subsidy scheme in a number of ways. For example, there could be caps and floors to the premium level, so that the total premium at every time instance is constrained (e.g. sliding premium).
In this case, the total cash flow yielded at timetcould be belowK. Other constraints could, for example, relate to technological requirements, time limits, or total payouts of subsidies.
25For more information on feed-in-tariffs and feed-in-premiums see, for example, Kitzing and Ravn (2013), Kitzing (2014) or Farrell et al. (2017).
Figure 5: Subsidies under no uncertainty
Figure 5a depicts the old subsidy scheme in which investors are paid 33.5€/MWh until they have produced 22.000 full-load hours. It drops to 0€/MWh after, which is typically the case 5-7 years into the project.
Figure 5b exhibits the new subsidy tender system, under which investors place bids on the subsidy compen-sation they would like to receive for each MWh. The bids must not exceed 17.4€/MWh and are granted for a time horizon of 20 years. The lowest bids are accepted until the given budget runs out.
(a) Old subsidy system
0.0 33.5
0 5 10 15 20 25
Time in years
Subsidy in EUR/MWh
(b) New tender-based system
0.0 17.4
0 5 10 15 20 25
Time in years
Subsidy in EUR/MWh
StN ew =
SN ew ift≤7300
0 ift >7300 (10)
Formula (10) expresses the bid that investors place as SN ew. As in the old subsidy scheme, investors assume no uncertainty in this framework. They are entitled to their bid, if granted, over the project’s first 20 years and assume them to be distributed with certainty, see Figure 5b.
Uncertainty in subsidies
In this section, I add uncertainty in subsidy distributions over time to conduct additional sensitivity analyses. Specifically, I assume that with a given probability, policy makers impose subsidy cuts, affecting the expected cash flows from the investment and therefore its risk exposure. In detail, I redefineSOld and SN ew as the updated processes that incorporate a risk parameter calledλ.
In particular, the old subsidy scheme as in Equation (9) changes in a way thatGt, now depen-dent on time, is considered to be uncertain in the future:
St+1Old =
max[Gt−ε˜t(Nt+1−Nt); 0] +B if Pt+1j=1f(Vj)≤22.000h∗M Wmax
B if Pt+1j=1f(Vj)>22.000h∗M Wmax
(11)
I assume that investors predict future cuts in these subsidies, meaning that the state will not respect its commitment to compensate them as agreed. The variable Gt, under this new assumption, follows a jump process, whereNt+1 is defined as
Nt+1=Nt+
1 with probabilityλOld∆t 0 with probability 1−λOld∆t
(12)
The probabilities are defined as
P rob(Nt+1=Nt+ 1) =P rob(z1t≤zα) =λOld∆t (13)
P rob(Nt+1=Nt) =P rob(z1t> zα) = 1−λOld∆t (14) The parameter of ˜εtcaptures the magnitude of the jump that is realized if triggered and is computed as
˜
εt=|uo+u1z2t|, (15)
whereu0 depicts the constant average jump in subsidies. The parameter of u1, another constant, is multiplied by a standard normally distributed variable of z2t and thereby adds uncertainty to the jump’s magnitude. The jump value of Equation (15) is strictly positive, meaning that subsidy compensations cannot increase but only decrease over time. Furthermore, there is no uncertainty in the constant of B. G0 in Equation (9) equals 25øre/kWh (33.5€/MWh) as the old subsidy scheme’s starting point.
I redefine the new subsidy compensation system and incorporate uncertainty through
St+1N ew =
maxhStN ew−υ˜t(Mt+1−Mt); 0i ift <7300
0 ift≥7300 (16)
The likelihood of future cuts in the subsidy level investors were granted at the auction follows the same process as in Equation (13) and (14):
Mt+1=Mt+
1 with probabilityλN ew∆t 0 with probability 1−λN ew∆t
(17)
The probabilities follow
P rob(Mt+1=Mt+ 1) =P rob(z3t≤zα) =λN ew∆t (18)
P rob(Mt+1 =Mt) =P rob(z3t> zα) = 1−λN ew∆t (19) I assume the magnitude of the jump ˜υt to be
˜
υt=|qo+q1z4t|, (20)
whereq0 depicts the constant average jump under the new subsidy system andq1 adds uncertainty to the jump’s magnitude by being multiplied with the standard normally distributed variable of z4t. Starting off,S0N ew is 17.4€/MWh, which represents the maximum bid in the new tender-based system.
The variables ofz1t, ..., z4tare standard normally distributed random variables ofzit∼N(0,1).
Furthermore, ∆tequals 3651 , so that λOldt and λN ewt document yearly probabilities.
Figure 6 shows what a subsidy cut path could look like in the model. Investors yield lower income in the future if subsidy cuts materialize, lowering the present value, i.e. returns, of their investment.
Figure 6: Subsidies under uncertainty
Both graphs represent sample paths of subsidy compensation streams under uncertainty. The yearly proba-bility of subsidy cuts, denoted byλOld andλN ew, equals 10%. In Figure 6a, investors are subject to the old subsidy system with 33.5€/MWh at timet= 0. Thereafter, StOld depends on how subsidies develop under uncertainty. Investors are then compensated withStOld at each time instance t until they have produced 22.000 full-load hours. It drops to 0€/MWh thereafter, which is typically the case 5-7 years into the project.
Figure 6b exhibits the new tender-based subsidy compensation scheme, under which investors place bids on the subsidy compensation they want to receive for every MWh. These bids must not exceed 17.4€/MWh and are granted for a time horizon of 20 years. This scenario assumes investors are compensated with the maximum bid of 17.4€/MWh att= 0 but are exposed to subsidy cuts thereafter.
(a)The old subsidy system
0.0 10.0 20.0 33.5
0 5 10 15 20 25
Time in years
Subsidy in EUR/MWh
(b)The new tender-based system
0.0 5.0 10.0 15.0 17.4
0 5 10 15 20 25
Time in years
Subsidy in EUR/MWh