CEN Paper 03-2016Trommsdorff.pdf

                                     Constitutional
                                       Economics
                                        Network

                                    Working Paper
                                        Series
                                  ISSN No. 2193-7214

                                       CEN Paper
                                       No. 03-2016




          An Economic Analysis of Agrophotovoltaics:
          Opportunities, Risks and Strategies towards a
              More Efficient Land Use*

                 Maximillian Trommsdorff **
          **Department of Economic Policy and Constitutional Economic Theory,
                   University of Freiburg, Germany
                           &
               Fraunhofer Institute for Solar Energy Systems ISE
                   Division Electrical Energy Systems
               E-Mail: maximilian.trommsdorff@ise.fraunhofer.de

             *Developed at first as master thesis in cooperation with the
               Fraunhofer Institute for Solar Energy Systems ISE

                      December 30, 2016

University of Freiburg
Institute for Economic Sciences
Department of Economic Policy and Constitutional Economic Theory
Platz der Alten Synagoge / KG II D-79085 Freiburg
www.wipo.uni-freiburg.de
                     Für Johanna




                                  With friendly support of




University of Freiburg       Fraunhofer Institute
Department of Economic Policy and  for Solar Energy Systems ISE
Constitutional Economic Theory   Heidenhofstr. 2
Platz der Alten Synagoge      79110 Freiburg
79085 Freiburg
                Table of Contents
List of Figures                                           iii

List of Tables                                            iii

Acronyms and Abbreviations                                      iv

Nomenclature                                             vi

1 Introduction                                            1

2 Agrophotovoltaic – Dual Land Use Producing Food and Energy                     3

3 A Simple Model of Agrophotovoltaic                                 5
 3.1 Basic Set Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .       5
 3.2 Hybrid Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .        7
 3.3 Efficiency Criterion and Sensitivity Analyses . . . . . . . . . . . . . . . . . .         9

4 Dynamic Analysis of Revenues and Expenditures                           13
 4.1 Economics of Agriculture . . . . . . . . . . . . . . . . . . .  . . . . . . .  .  .  .  14
   4.1.1 Yield, Prices and Revenues . . . . . . . . . . . . . .   . . . . . . .  .  .  .  14
   4.1.2 Contribution Margin . . . . . . . . . . . . . . . . .   . . . . . . .  .  .  .  15
   4.1.3 Indirect Variable Costs, Fixed Costs and Net Profit     . . . . . . .  .  .  .  16
   4.1.4 WACC and NPV . . . . . . . . . . . . . . . . . . .     . . . . . . .  .  .  .  16
 4.2 Economics of Ground-Mounted Photovoltaic Systems . . .      . . . . . . .  .  .  .  19
   4.2.1 Earnings from Electricity Sales . . . . . . . . . . .   . . . . . . .  .  .  .  19
   4.2.2 Capital Expenditures . . . . . . . . . . . . . . . . .   . . . . . . .  .  .  .  20
   4.2.3 Operational Expenditures . . . . . . . . . . . . . .    . . . . . . .  .  .  .  20
   4.2.4 NPV, IRR and LCOE . . . . . . . . . . . . . . . .     . . . . . . .  .  .  .  21
 4.3 Economics of APV . . . . . . . . . . . . . . . . . . . . . .   . . . . . . .  .  .  .  22
   4.3.1 Parameter Changes and Further Effects in Terms of      Agriculture   .  .  .  22
   4.3.2 Parameter Changes and Further Effects in Terms of      PV . . . . .  .  .  .  24
   4.3.3 Results and Comparative Statics . . . . . . . . . .    . . . . . . .  .  .  .  29

5 Discussion                                            32

6 Conclusion                                            35

A Appendix                                              I
 A.1 First Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      I
 A.2 Second Part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .      II

B References                                             V

C Declaration of Authorship                                    VIII

                        ii
                List of Figures
1   Schematic illustration of an APV-system . . . . . . . . . . . . . . . . . . . .    3
2   LCOE of small scale PV and GMPV-systems . . . . . . . . . . . . . . . . . .      3
3   APV-system in Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   4
4   Graphical solution of optimal land allocation . . . . . . . . . . . . . . . . . .   6
5   Food produced by mono and hybrid technology . . . . . . . . . . . . . . . .      8
6   A rise in s leading to lower potential food contribution of the hybrid technology  10
7   Cost structures of agriculture and PV within APV production . . . . . . . .     29
8   Cost structures of APV production . . . . . . . . . . . . . . . . . . . . . . .   30
9   LCOE of small scale PV, GMPV and APV-systems . . . . . . . . . . . . . .       30




                 List of Tables
4.1  Financial parameters calculating the WACC . . . . . . . . . . . . . . . . . .    17
4.2  Financial parameters calculating the cost of equity  . . . . . . . . . . . . . .  17
4.3  Changes of agricultural parameters . . . . . . . . . . . . . . . . . . . . . . .   25
4.4  Expected changes of PV parameters . . . . . . . . . . . . . . . . . . . . . . .   28
A.1 Cost and revenue items of agriculture for baseline and APV scenario . . . . .      II
A.2 Cost and revenue items of agriculture for baseline and APV scenario . . . . .     III
A.3 CAPEX of the baseline and APV scenario . . . . . . . . . . . . . . . . . . .      III
A.4 OPEX of the baseline and APV scenario . . . . . . . . . . . . . . . . . . . .     IV




                      iii
         Acronyms and Abbreviations
Bavarian LfL   Bavarian State Research Center for Agriculture
Fraunhofer ISE  Fraunhofer Institute for Solar Energy Systems
a        Year
APV       Agrophotovoltaic
APV-RESOLA    AgroPhotoVoltaic RESOurce-efficient LAnd-use
BMEL       Federal Ministry of Food and Agriculture
BMWi       Federal Ministry for Economic Affairs and Energy
BOS       Balance of System
CAPEX      Capital Expenditures
CAPM       Capital Asset Pricing Model
CM        Contribution Margin
CO2       Carbon Dioxide
COP       Cost of Production
EEG       German Renewable Energy Act
FAOSTAT     Food and Agriculture Organization of the United Nations,
         Statistic Division
FIT       Feed-In Tariff
FOC       First Order Condition
GHI       Global Horizontal Irradiance
GMPV       Ground-Mounted Photovoltaic
ha        Hectare
IEA       International Energy Agency
IRR       Internal Rate of Return
KTBL       Association for Technology and Structures in Agriculture
kWh       Kilowatt hour




                     iv
LCOE  Levelized Cost of Electricity
LER  Land Equivalent Ratio
m2   Square meter
NP   Net Profit
NPV  Net Present Value
OPEX  Operational Expenditures
PV   Photovoltaic
RE   Renewable Energies
STC  Standard Test Conditions
StMELF Bavarian State Ministry for Nutrition, Agriculture and
    Forestry
Wp   Watt-peak
WACC  Weighted Average Cost of Capital




                    v
                  Nomenclature
C    Capacity of installed kWp per ha [kWp /ha]
Cd   Cost of dept [%]
Ce   Cost of equity [%]
D(·)  Difference between hypothetical and real mono production in the presence
    of hybrid production
E(·)  Electricity production function
F (·)  Food production function
N    Durability [a]
Pd   Share of dept [%]
Pe   Share of equity [%]
S    Annual insolation [kWh/ha]
W    Wealth
X    Total land area
α    Productivity of hybrid food production compared to mono technology [%]
β    Beta-factor
β    Productivity of hybrid food production compared to mono technology [%]
δ(·)  Difference between status quo electricity production and total electricity pro-
    duction in the presence of hybrid production
ˆ
xe   Status quo land allocation for electricity production
ˆ
xf   Land allocated for food production in the status quo
µ    System effectiveness [%]
d    Annual decline of efficiency [%]
d(·)  Difference between status quo food production and mono food production in
    the presence of hybrid production
dt   Quintile = decitonne
         ˆ




                       vi
rf  Market return risk-free [%]
rm  Market return historic [%]
s  Share of land allocated for hybrid production that in the status quo was
   allocated to food production [%]
xe  Land allocated for electricity production
xf  Land allocated for food production
xh  Land allocated for hybrid production




                      vii
1    Introduction
The way we produce food and generate energy substantially matters for major chal-
lenges of this century.1 Agricultural practices affect biopersity, human health and
quality of water; fossil-fuel power stations drive Carbon Dioxide (CO2 ) emissions exac-
erbating global warming; and efficiency of both sectors co-determines how many people
do have access to food and energy supply.2
  Seen in this light, it seems plausible that both sectors are – at least in most industrial
countries – widely regulated (see e.g. Sumner, Alston, and Glauber, 2010; Pearce,
2002). Indeed, externalities, public good characteristics, spillovers, and issues of just
distribution are frequently cited to justify regulations. In such an environment and
given rapid changes and developments of today’s energy and food branches, it is an
indispensable task of efficient governance to constantly monitor and assess technological
innovations, either with respect to their eligibility to get supported or with respect
to needs of restriction or prohibition. Recent examples of such a process entered the
public debate under the headings of genetically modified crops, promotion of Renewable
Energies (RE) or hydraulic fracturing.
  In Germany where this thesis focuses on, the recent legal environment with respect to
promotion of RE particularly urged for a thorough assessment of available technologies.
Year by year or even monthly the scope and amount of governmentally guaranteed
Feed-In Tariffs (FIT) changed, always chasing after latest technical and economical
developments. Most prominent example is PV, electricity generated by solar power.
Beneath the dramatic decline of overall PV-FITs, in 2010 systems of Ground-Mounted
Photovoltaic (GMPV) were excluded from receiving FITs. The debate accompanying
this decision was a highly controversial one. While on the one hand GMPV-systems
are the most cost-efficient way to generate PV-electricity, counterarguments frequently
entering the discussion targeted issues of land-use and competition between farmers
and investors with respect to available land.
  One possibility to overcome those conflicting goals is Agrophotovoltaic (APV), a
combined land-use of food and electricity production. This thesis analyses APV in
terms of economic efficiency. It develops a theoretic background to assess welfare impli-
cations and provides a detailed analysis of earnings and expenditures to assess economic
performance of an APV-system. Main findings of this thesis are (1) a welfare criterion
defining the productivity of an APV-system required to enhance social welfare; and (2)
that APV-plants operate profitable if FITs range between those of large GMPV-plants
  1
   Current major challenges of mankind as defined e.g. by the Milenium Project (Glenn, Gordon,
and Florescu, 2014).
  2
   Beneath efficiency, distributional aspects unquestionably operate as a further crucial determinant.




                                                  1
                                 1 INTRODUCTION


and small scale rooftop systems.
  After presenting the technology of APV in section2, section 3 introduces a simple
model of APV that illustrates land use competition and the opportunities APV might
offer in this context. Section 4 analyzes commercial efficiency of APV. Starting from
a dynamic analysis of revenues and expenditures, we first scrutinize agricultural farm-
ing processes before investigating in sales and cost of GMPV-systems. In a third step
we adjust relevant parameters to APV-specific levels. This is done based on estima-
tions, interviews with experts and data from an APV pilot project of the Fraunhofer
Institute for Solar Energy Systems (Fraunhofer ISE). Highlighting higher risks and
cost compared to conventional GMPV-plants, we apply the results estimating required
FITs as a political strategy to support APV. The last sections discuss results, further
implications, and conclude.




                                           2
2   Agrophotovoltaic – Dual Land Use Producing Food
   and Energy
APV describes dual usage of land for photovoltaic and agricultural production at the
same spot. Alternative terminologies frequently characterizing the same technology are
”Agrivoltaic” and ”Agrovoltaic” (see e.g. Dupraz et al., 2011; De Schepper et al.,
2012).
Originally, the idea was developed by
Goetzberger and Zastrow (1982) who
showed that, if Photovoltaic (PV) panels are
mounted at a sufficiently high level, about
two third of the solar radiation reaches the
surface below (see Fig. 1). Further the
authors illustrate that this radiation dis-
tributes almost uniformly over the day such
                         Figure 1: Schematic illustration of an APV-
that homogeneous plant growth could be re- system. Source: Goetzberger and Zas-
                         trow (1982)
alized.
  While in these early days the idea of generating electricity by large PV power plants
was a quite visionary one, the widespread existence of nowadays GMPV-systems sug-
gests that an efficient implementation of APV-systems might also become true. In
Germany 2014, GMPV accounts for 23% of total installed rated PV-output which is
5.1% of total installed RE or 1.3% of total electricity consumption (Statista, 2015).
                    0.16

                    0.14
           LCOE [Euro/kWh]




                    0.12

                     0.1

                    0.08

                    0.06

                    0.04

                    0.02


                        PV small   GMPV    PV small   GMPV
                        Low solar irradiance  High solar irradiance


     Figure 2: LCOE of small scale PV and GMPV-systems. Source: ISE (2013)


  Due to economies of scale, GMPV-systems typically generate electricity at lower
cost compared to other kinds of PV-systems (ISE, 2013). Fig. 2 illustrates this relation




                                                3
    2 AGROPHOTOVOLTAIC – DUAL LAND USE PRODUCING FOOD AND ENERGY


for regions with low and high solar irradiation, respectively, opposing the Levelized
Cost of Electricity (LCOE) of small PV-plants to those of GMPV.3
  Main benefit of APV-systems is a potential increase in land use efficiency (see e.g.
Obergfell, 2012; Dupraz et al., 2011). Given the constant rise in global demand for
food and energy4 , land use efficiency is a highly prevalent issue since it might ease the
growing pressure on available land currently endangering both biopersity and existing
forms of traditional land use. The relevance of those concerns became apparent through
recent debates about land-grabbing activities and biofuel policies (a.k.a. fuel vs. food
debates).
  Estimating the extent to which APV might contribute to mitigate land use conflicts,
the short run perspective essentially differs from the long run. Up to now, the total area
globally covered by PV-systems accounts for
far less than one per mil of arable land
(International Energy Agency (IEA),
2015) indicating that nowadays potential
contribution of APV to mitigate issues of
land use competition is rather limited. Ad-
ditionally, risks of a new technology and high
cost related to high elevation of AVP-panels   Figure 3: APV-system in Italy. Source:
are possible drawbacks of APV-systems. In    Ahlers (2014)

contrast, given the perspective of constantly falling cost and rising efficiency of PV-
cells and storage technologies, it seems likely that PV will play a major role within
future energy landscapes (Hernández-Moro and Martínez-Duart, 2013). This
seems particularly true with respect to PV and energy crops as competing parts of
tomorrows energy mix and their respective efficiency per unit of land: Today, average
energetic yield of PV-modules is about five times higher than the photosynthetic pro-
cess of energy crops (15% vs. 3%, see e.g. Dupraz et al., 2011). Moreover, the scope
for energy crops is limited due to scarcity of land: Taking Germany as an example,
energy crops already account for more than 18% of arable land (Schmidt, Maul, and
Haase, 2010) and its unfavorable consequences for biopersity and quality of soil and
ground water have intensively been discussed. Against this background, the long run
perspective suggests that PV in combination with storage technologies will win the race
against energy crops.

  3
  Low solar irradiation here refers to a Global Horizontal Irradiance (GHI) from 1000 to 1200 kilowatt
hours (kWh) per square meter (m2 ) and year (a), high solar irradiation to a GHI from 1450 to 2000
kWh/m2 /a.
 4
  Between 1973 and 2012 the total global food consumption and primary energy supply approxi-
mately doubled (Alexandratos, Bruinsma, et al., 2012; IEA, 2014).




                                                   4
3   A Simple Model of Agrophotovoltaic
This section develops a simple welfare model of APV. The first section presents the
general set up and underlying assumptions of competitive mono production technologies
using land as an input factor. That way we derive a status quo that will serve as point of
departure for introducing APV as a hybrid technology. Defining an efficiency criterion
we analyze productivity of the hybrid technology required to enhance social welfare.
  This section pursues two goals: First and foremost it provides a theoretic structure
shedding light on most important implications of the technology; second, it illustrates
land use competition and the mitigating role APV might play.


3.1   Basic Set Up
Generally, we follow the assumptions of a neoclassical welfare model considering food
(F ) and electricity (E) as the only consumption goods of society.5 Accordingly there are
two production technologies, F (·) and E(·), both depending on the same input factor
land, where xf and xe denote land used for food and electricity production, respectively,
with
               ∂F (xf )     ∂ 2 F (xf )
                    > 0 and       <0.
                ∂xf        ∂x2f

The same applies for electricity production. Since we regard a closed economy and full
use of resources, total available land X equals xf + xe . Further we assume social welfare
W to depend on the sum of produced food and electricity. This can be written as

                 W (xf ) = F (xf ) + E(X − xf ) .

Hence, society chooses an efficient allocation of available land if the optimal level of xf
solves the First Order Condition (FOC)

              ∂W (xf )  ∂F (xf ) ∂E(X − xf )
                  =     −      =0.                   (1)
              ∂xf    ∂xf    ∂xf

 In what follows we refer to optimal values of xf and xe given by (2) as the status quo
levels of the model and denote it with xf and xe . Fig. 4 provides a graphical solution
                    ˆ    ˆ
of the status quo. As shown in Fig. 4(a), social welfare is maximized if the slope of
the production possibility frontier equals the slope of iso-welfare levels.6 Figures 4(b)
  5
   Beneath full information and rational choice, main assumtion here is a benevolent dictator that
maximizes social welfare. Further we assume an inner solution with F, E > 0.
  6
   Iso-welfare lines here refer to areas of equal welfare levels. The analyzed situation implies that
society is indifferent between more food or more electricity while, with respect to available land,




                                                   5
                         3 A SIMPLE MODEL OF AGROPHOTOVOLTAIC


           Iso
      F       -W
              elf
                              F (xf )
               ar
                  eL
                   ev                  F (xf )
                    els

                               F (ˆf )
                                x

   (a)                                        (b)

                       Production
                       Possibility
                        Frontier

                        E           xf
                                    ˆ     xf
      xe
                        E(xe )




   (c)



      xe
      ˆ
              E(ˆe )
               x        E(xe )

Figure 4: Graphical solution of optimal land allocation. (a) Maximized welfare as defined by the
slope of iso-welfare levels. (b) Optimal food production. (c) Optimal energy production.



and (c) depict the optimal contribution of food and electricity production as well as the
required levels of xf and xe . Note that the graph in Fig. 4(c) follows an inverse shape
of the electricity production function in order to adjust axes to those of Fig. 4(a).




production is still feasible.




                                               6
                     3 A SIMPLE MODEL OF AGROPHOTOVOLTAIC


3.2  Hybrid Technology
Now we introduce a hybrid technology that produces both F and E without rivalry
of land. In return, we assume a lower productivity with respect to single good output
per unit of land. The reduction of productivity is determined by the parameters α
(food) and β (electricity), both [0,1]. Apart from reduced per unit output, the hybrid
technology follows the same production functions as mono technologies.
  Now, society can choose to reallocate some amount of land xh for hybrid technology
where X = xe + xf + xh . Further we denote s as the share of xh that in the status
quo was allocated for food production. Equally, the share of xh initially being used for
electricity production equals (1 − s)ˆf . Thus, total amount of reallocated land xh and
                   x
new levels of xf and xe can be written as

                  xh = sxh + (1 − s)xh ,
                  xf = xf − sxh , and
                     ˆ
                  xe = xe − (1 − s)xh .
                     ˆ

  Fig. (5) exemplarily illustrates total food output produced by mono and hybrid
technology. Compared to the status quo, there are two effects: On the one hand,
mono food production reduces from F (ˆf ) to F (xf ); on the other hand, the hybrid
                     x
technology contributes to total food production. This amount of food can be expressed
by the hypothetical output if land allocated to mono and hybrid production would
be used exclusively for mono food production: Since we assume the same production
function for both technologies, the difference between this hypothetical and real mono
production times α equals the hybrid food production. This is depicted by the red
elements in Fig. (5). In the following we refer to the difference between hypothetical
and real mono production as the potential contribution of the hybrid technology.
  With respect to land reallocation, the segments on the horizontal axis illustrate the
shares of xh which in the status quo were allocated to food and electricity production,
respectively. Hence, total food production can be written as

F (ˆf , xh ) = F (ˆf − sxh ) + α[F (ˆf ) − F (ˆf − sxh )] + α[F (ˆf + (1 − s)xh ) − F (ˆf )] , (2)
  x       x         x     x         x           x

which splits up into three parts: The first term refers to food produced by mono
technology; the second one concerns hybrid food production on land originally allocated
to mono food technology; and the third one deals with hybrid food production on land




                                                 7
                       3 A SIMPLE MODEL OF AGROPHOTOVOLTAIC


            F
                               F (xf )
       F (xf + xh )
          F (ˆf )
           x

          F (xf )
                               } α[F (x  f  + xh ) − F (xf )]




                 xf     xf
                      ˆ      xf + xh   xf

                   sxh

                         (1 − s)xh

          Figure 5: Food produced by mono and hybrid technology



originally allocated to mono electricity production. Simplifying (2) yields

      F (ˆf , xh ) = F (ˆf − sxh ) + α[F (ˆf + (1 − s)xh ) − F (ˆf − sxh )] .
       x       x         x           x              (3)

Since the same applies for electricity production, we can describe welfare in the presence
of hybrid production as

   W (ˆf , xe , xh ) = F (ˆf , xh ) + E(ˆe , xh )
     x ˆ         x       x
            = F (ˆf − sxh ) + α[F (ˆf + (1 − s)xh ) − F (ˆf − sxh )]
              x         x           x              (4)
            + E(ˆe − (1 − s)xh ) + β[E(ˆe + sxh ) − E(ˆe − (1 − s)xh )] .
              x           x       x




                                                 8
                   3 A SIMPLE MODEL OF AGROPHOTOVOLTAIC


3.3  Efficiency Criterion and Sensitivity Analyses
Evaluating efficiency of the hybrid technology, it appears helpful to set up an efficiency
criterion. One benchmark that comes naturally is to compare welfare of the status quo
with welfare if the hybrid technology is employed.

                W (ˆf , xe ) = W (ˆf , xe , xh )
                 x ˆ      x ˆ                  (5)

By this means we are now able to analyze the levels of α and β required for the hybrid
technology to be efficiency enhancing. Applying (4) and (5) and solving for α yields


    F (ˆf )−F (ˆf −sxh )+E(ˆe )−E(ˆe −(1−s)xh )−β[E(ˆe +sxh )−E(ˆe −(1−s)xh )]
     x    x       x    x           x      x
α=
                F (ˆf + (1 − s)xh ) − F (ˆf − sxh )
                  x           x
                                            (6)
  Scrutinizing this equation, we break it down into three differences. The first differ-
ence F (ˆf ) − F (ˆf − sxh ), here denoted as d(·), addresses food produced solely by mono
     x    x
technology. Subtracting mono food production in the presence of the hybrid technology
from the food production in the status quo, d(s) represents losses that occur if less land
is allocated to mono food production. Hence,

            for all s > 0 → d(s) > 0 , since
                      F (ˆf ) > F (ˆf − sxh ) .
                       x     x

Further, d(s) is strictly monotonic increasing in s.
  The second difference which we denote with δ(·) represents the change of total
electricity production that turns up if the hybrid technology is employed. Thus, δ(s, β)
corresponds to electricity production of the status quo less the electricity production in
the presence of both mono and hybrid technology, or, formally

               δ(s, β) = E(ˆe ) − E(ˆe , xh )
                     x    x                  (7)

which equals

δ(s, β) = E(ˆe ) − E xe − (1 − s)xh + β E(ˆe + sxh ) − E xe − (1 − s)xh
       x    ˆ          x       ˆ             . (8)

  In contrast to d(s), δ(s, β) can be both positive or negative, pointing at the fact
that we do not know whether electricity production exceeds the status quo level or not.
While a higher β clearly implies a fall of δ(s, β), at first glance the effect of s seems
unclear. All other variables remaining constant, a rise in s causes two effects: On the



                                             9
                     3 A SIMPLE MODEL OF AGROPHOTOVOLTAIC


                     E
                                      E(xe )
        E(xe + xh )
                E(xe + xh )

          E(xe )

                 E(xe )       (1 − s )xh   s xh




                        (1 − s)xh    sxh

                        xe     xe
                              ˆ   xe + xh    xe
                           xe        xe + xh

  Figure 6: A rise in s leading to lower potential food contribution of the hybrid technology.



one hand it implies that more land is reallocated from mono food to hybrid production
which in turn increases the share that remains for mono electricity production. On
the other hand an increase in s lowers the share of land allocated to hybrid electricity
production thus leading to less losses and a lower δ(s, β); on the other hand an increase
in s reduces the potential contribution of hybrid food production. In Equ. (8) this
lowers E(ˆe , xh ) and increases δ(s, β). This effect is visualized by Fig. (6). On the
     x
horizontal axis, a rise from s to s shifts land units allocated for hybrid production
to the right. This shift implies a lower potential contribution as shown by the red
intercept on the vertical axis. To shed light on the overall impact of s we derive the
first derivative of δ(s, β).

 ∂δ(s, β)   ∂E xe − (1 − s)xh
           ˆ          ∂E(ˆe + sxh )
                      x       ∂E xe − (1 − s)xh
                               ˆ
      = −            − β        + β
  ∂s         ∂s          ∂s         ∂s
           ∂E xe − (1 − s)xh
            ˆ         ∂E(ˆe + sxh )
                       x
      = (β − 1)          −β
              ∂s         ∂s
                                                  (9)

Dividing this expression in two parts, it becomes clear that the first one must be negative
since

                         β − 1 < 0 and
                ∂E xe − (1 − s)xh
                  ˆ
                             >0.
                     ∂s




                                                  10
                   3 A SIMPLE MODEL OF AGROPHOTOVOLTAIC


In contrast, the second part of (9) is always positive. Hence, the overall value is negative
indicating that δ(s, β) must be falling in s.
  The third difference of Equ. (6), denoted as D(·) represents potential contribution
of the hybrid technology to food output.

            D(s) = F xf + (1 − s)xh − F (ˆf − sxh )
                ˆ          x

  Alike decreasing marginal productivity that lowered the potential contribution of
electricity illustrated in Fig. 6, here a rise in s increases the potential contribution to
food production. Summarizing effects of the three differences we can rewrite Equ. (6)
as
                     +    − −
                    d( s ) + δ( s , β )
                  α=            ,
                         +
                        D( s )
where the superscripts indicate the sign of the marginal effect of s and β, respectively.
Evidentially, a high β lowers the required level of α that makes the employment of
the hybrid technology welfare enhancing. In contrast, consequences of a change of s
partially cancels out.
  For further analyses, it seems appropriated to treat s as an exogenous variable since
society is free to choose the level of s. For the sake of simplicity we set s equal to
1 assuming that all reallocated land stems from former food production. By that,
Equ. (6) reduces to
                    E(ˆe + xh ) − E(ˆe )
                     x       x
              α=1−β               .           (10)
                    F (ˆf ) − F (ˆf − xh )
                     x     x
  Due to decreasing marginal productivity we know that both the numerator and
denominator of the equation above must be greater than zero. This implies that the
fraction equals some positive number. To assess the magnitude of the fraction, it
appears helpful to assume xh being closed to zero. Here a xh of zero can be seen as
a situation in the status quo in which society asks for required levels of α and β that
makes a reallocation of one marginal land unit from xf to xh efficiency enhancing.
Analytically, this is done by analyzing the limits of the fraction as xh approaches 0.

                   E(ˆe + xh ) − E(ˆe )
                    x       x
                lim             .
                xh →0 F (ˆf ) − F (ˆf − xh )
                    x     x

  If we expand the fraction multiplying both the numerator and denominator with
x−1 we can apply Newton’s difference quotient (see e.g. Leithold, 1996).
h




                                             11
                   3 A SIMPLE MODEL OF AGROPHOTOVOLTAIC



                 E(ˆe +xh )−E(ˆe )
                  x      x     ∂E(ˆe )
                                x
                     xh         ∂ xe
                               ˆ
              lim x           =       .
              xh →0 F (ˆf )−F (ˆf −xh )
                      x       ∂F (ˆf )
                                x
                     xh         ∂ xf
                               ˆ

Thus, the numerator equals the marginal food productivity of the status quo and the
denominator equals the marginal electricity productivity of the status quo. From the
FOC of the status quo we know that

                 ∂E(ˆe )
                   x   ∂F (ˆf )
                        x
                     =     .
                  ˆ
                 ∂ xe    ˆ
                      ∂ xf

Consequently, the equation takes on a value of 1. For α in Equ. 10 this means that

                    α= 1−β ,

or, in other words, the hybrid technology enhances welfare if α and β sum up to more
than 1. In Appendix A.1 we show that the opposite case in which s = 0 results in the
same solution. Hence, as an efficiency rule for the hybrid technology we can write

                    α+β >1 .

This ruel is in line with the efficiency benchmark of the Land Equivalent Ratio (LER),
a common approach of measuring productivity of combined land use in agroforestry
(see e.g. Dupraz et al., 2011). In section 5 we discuss our efficiency rule with respect
to real life values.




                                           12
4     Dynamic Analysis of Revenues and Expenditures
In this section we analyze economic performance of APV with respect to commercial
usage. We describe and evaluate factors that determine the level of cost and revenues
and estimate the profitability of APV-systems by its expected Net Present Value (NPV)
and Internal Rate of Return (IRR). The first subsection illustrates this analysis for
common farming practices taking organic potatoes as an example. Providing a rough
overview about most relevant work processes and cost items we take this subsection as
a point of departure for linking agriculture to an APV-system. The second subsection
does the same analysis for standard GMPV-systems. Finally, the third subsection
combines both results by adjusting relevant parameters to APV-specific levels. This is
done based on estimations, interviews with experts and data from the APV-RESOLA
project led by Fraunhofer ISE.
  All assumptions concerning solar radiation, factor prices, and agricultural and finan-
cial parameters are based on regional data of south Germany in order to adjust the anal-
ysis to the APV-RESOLA pilot project in Heggelbach7 . With respect to the assumed
land size we regard an area of 2 hectares (ha) considering both the conditions of the
Heggelbach project and real plant sizes of GMPV-systems. With 0.5 ha the dimension
of the Heggelbach project is relatively small whereas nowadays GMPV-systems usually
require a minimum land size of approximately 20 ha to become competitive (Gimbel,
2015). According to the Heggelbach project, we further assume farming practices of
organic agriculture. Considering average durability of PV-systems, we regard a time
frame of 25 years.
  Since dynamic effects play a major role in assessing the economic performance over
time, one crucial parameter is the discount rate. To estimate an appropriate discount
rate, we employ the Weighted Average Cost of Capital (WACC) assuming the same
financial parameters in the farming and the energy sector. In doing so, we obtain
uniform and comparable results in both sectors. However, it should be noted that some
parameters considerably differ between the two branches, e.g. the equity ratio which
is traditionally much higher in the farming sector (Bavarian State Ministry for
Nutrition, Agriculture and Forestry (StMELF), 2014).8
  If not stated otherwise, all legal regulations like taxes, subsidies and fees follow the
current state of law in Germany 2014. As a default case we assume farmers and energy
producers being one economic entity. Large values are rounded up to whole e units.
All calculations are carried out using Microsoft ExcelTM .
  7
    Region Lake Constance upper Swabia.
  8
    See section 5 for a further discussion of these parameters.




                                             13
           4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


4.1   Economics of Agriculture
To perform a dynamic analysis of revenues and expenditures we first illustrate cash flows
of the base year regarding earnings, subsidies and a standardized Cost of Production
(COP) budget. Than we derive the WACC and employ the latter to discount all future
cash flows to their present value. The aim is to estimate an average NPV based on
common farming practices in order to draft a baseline scenario which we later adjust
to the case of APV.
  At first glance it might seem questionable that this inquiry focuses on organic farm-
ing practices. Indeed, with a 1% share of global agricultural land, today the certi-
fied organic farming sector is still relatively small compared to conventional farming
(Willer, Lernoud, and Home, 2013).
  However, this share is constantly growing. Further, in Germany and moreover in
Baden-Württemberg where this thesis focuses on, the share is considerably above av-
erage (6.8% and 8.5%, Federal Statistical Office, 2014; Federal Ministry
of Food and Agriculture (BMEL), 2014). Additionally – since mean farm size is
significantly smaller in the organic sector than in the conventional one – the share of
organic farms in Baden-Württemberg is already above 15%, with this figure set to in-
crease in future. (State Institute for the Environment, Measurements and
Conservation in Baden Württemberg (LUBW), 2014) Main reason why we take
organic potatoes as an example is, though, to adjust this analysis to the Fraunhofer
ISE project in Heggelbach, which follows organic farming practices.
  With respect to subsequent years, we assume no crop rotation. Quantities of agri-
cultural yield are given in quintiles (dt) which corresponds to 100 kg or one decitonne.
All other figures refer to one ha. Further, all assumptions concerning agricultural pro-
duction follow average values as recommended by the Bavarian State Research
Center for Agriculture (Bavarian LfL). A detailed list of cost and revenue
items can be found in Annex A2.

4.1.1  Yield, Prices and Revenues

Generally, total revenue of one produced commodity equals total yield times the average
price at which the commodity is sold. However, in case of organic potatoes out of total
yield only 70% are expected to be suitable for consumption, while 20% can be sold
for animal feed and 10% are waste. Additionally, farmers that are working according
to ecological guidelines receive subsidies for each ha of cultivated land. Thus, total




                                           14
            4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


revenues sum up to

    Total Revenues = (Yield × 0.7) × Pricecq + Yield × 0.2) × Pricef q + Subsidies

where Pricecq and Pricef q refer to potato market prices of consumption quality and
feedstuff quality, respectively. Both yield and prices of organic potatoes are relatively
volatile compared to other food crops.9 To account for this fact, we employ average
levels of yield and wages as recommended by Bavarian LfL (2015).
  To calculate revenues of subsequent years we assume per ha yield of organic potatoes
to increase by 25% less than the average rise of productivity of conventional potatoes
in Germany (1.36 instead of 1.81 %, see Food and Agriculture Organization
of the United Nations, Statistic Division (FAOSTAT), 2015). Based on annual
data from 1990 to 2013, we extrapolate future price levels of organic potatoes declining
by 0.56% per year compared to overall price levels (FAOSTAT, 2015). In our example,
first year’s total revenues amount to about e8,984.

4.1.2   Contribution Margin

Within the production process, standard agricultural cost accounting usually distin-
guishes between two types of costs: General expenses used in producing all commodi-
ties; and expenses related to the production of one specific commodity (Association
for Technology and Structures in Agriculture (KTBL), 2013). The latter
type is needed to calculate the Contribution Margin (CM) of a single production line,
i.e. the share that one commodity contributes to a farm’s operating result. Even though
potatoes are the only commodity in this analysis, we keep this structure calculating first
the contribution margin and in a second step the full cost of the production process.
By that we ensure that our analysis corresponds to the standard scheme of agricultural
cost accounting.
   The CM of a production process is defined by total revenues less the sum of variable
costs directly related to the production of the respective commodity.

           CM = Total Revenues −      Direct Variable Costs

Direct variable cost in the case of organic potatoes splits up in cost for seed potatoes,
fertilizers, direct machinery cost, sorting and grading, hail insurance, direct labor cost
and direct storage cost. With e1,613 seed potatoes account for more than half of the
  9
  Between 2008 and 2013, organic potato prices ranged from e29 to e63 reflecting ample fluctuations
in potato yields (see LfL, 2015; Gimbel, 2015).




                                                15
              4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


total direct variable cost. In total, variable cost sum up to e3,162 generating a CM of
e5,822.

4.1.3   Indirect Variable Costs, Fixed Costs and Net Profit

Machinery cost, cost for labor and storage, and other costs that are flexible but not
covered by the CM are generally considered as indirect variable costs (KTBL, 2013).
with e748 the largest share of indirect variable costs in the case of organic potatoes
are imputed labor cost. Whether machinery costs are already part of the CM or not
usually depends on the share of the machinery that is owned by the farmer. Here we
follow the recommendations of the Bavarian LfL assuming no own machines. Hence,
all machine cost are covered by indirect variable cost.
  Fixed costs in the case of organic potatoes are land cost and imputed costs of
capital, land and labor.10 In the first year, indirect variable cost and fixed cost amount
to e1,473. With respect to subsequent years and in contrast to yield and prices we
assume all future prices that affect the cost to develop proportionally to overall price
level.
  Finally, the Net Profit (NP) equals the difference between the CM and the sum of
indirect variable cost and fixed cost.

           NP = CM − (Indirect Variable Cost + Fixed Cost)

Hence, for the first year the NP per ha amounts to e4,349.

4.1.4   WACC and NPV

In case an investment comprises capital of both equity and dept, a standard approach
to discount future cash flows to their present value is to apply the WACC as a discount
factor (Brealey, Myers, and Franklin, 2006). Accordingly, the WACC consists of
the share of equity and dept and its respective prices. Additionally, the corporate tax
co-determines the WACC since it mirrors the tax advantage of dept capital if expenses
for interest payments reduce the tax base. Therefore, the WACC can be written as

                WACC = i = Pe Ce + Pd Cd (100 − t),

where Pe is the proportion of equity, Pd the proportion of dept, Ce and Cd its respective
costs, and t the corporate tax rate. For what follows we employ an equity ratio of
20% which meets the average figures of the last decades in Germany (Adenäuer and
10
   Imputed costs in this context refer to opportunity costs entering the accounting sheet.




                                                16
           4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


Haunschild, 2008). Following recent credit conditions of the German Kreditanstalt
für Wiederaufbau (KfW), we assume a Cd of 2.15 % (Gimbel, 2015). The average
corporate tax rate in Germany is given by approximately 30% (KPMG, 2015).

                 Share of    Share of    Cost of     Corporate
          WACC
                 equity     dept      dept      tax rate
  Parameter     i       Pe       Pd       Cd        t
           [%]      [%]       [%]      [%]       [%]
   Value     3.50      20       80       2.15      30

          Table 4.1: Financial parameters calculating the WACC


Tab. 4.1 provides an overview of all parameters and its values.
  In contrast to Cd and t which are usually given by the financial and legislative
environment, Ce can be derived endogenously employing the systematic risk of an in-
vestment (Frencha, 2003). This is typically done by the Capital Asset Pricing Model
(CAPM) which sets the expected return of an investment equal to a risk free interest
rate plus an investment specific risk premium. This relation can be expressed by the
formula
                Ce = rf + β(rm − rf )

in which rf is the risk free interest rate, β stands for the risk or, in other words, the
volatility of the expected return of the investment, and rm is the expected return of
the market. Generally, the level of rf can be approximated by governmental bonds –
here we employ a rf of 1.5%. With about 6.5% the rm is given by historic data of stock
markets (Fernádez and Campo, 2011). As a standard value for investment decisions
we apply a beta factor of 2 (Bordemann, 2015). All parameters of the CAPM are
listed in Tab. 4.2. By that, the cost of equity amounts to 11.5% and the WACC to
3.5%.

                 Market     Market
          Cost of                     Beta-      Risk
                 return     return
          equity                     factor     premium
                 risk-free    historic
  Parameter     Ce       rf       rm       β      rm − rf
           [%]      [%]       [%]      [-]       [%]
   Value     11.5      1.5       6.5       2        5

        Table 4.2: Financial parameters calculating the cost of equity


  Now the next step is employing the WACC to determine the NPV of the investment.
The NPV method aims to assess the economic efficiency on an investment and, hence,



                                               17
           4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


whether an investment should be done or not.
  A positive NPV indicates a profitable investment while a negative one suggests an
unfavorable one. Generally, the NPV equals the present value of all future cash flows.
For N time periods the NPV equals

                     N
                        NP
                NP V =       −n
                            .
                     n=1 (1 + i)


According to this formula and given the presumed cash flows and time frame, the NPV
of the investment amounts to e70,557 per ha. Although this figure already contains all
fixed cost related to the production process it should be noted that – since we regard
an already operating agricultural holding – it might neglect expenses related to initial
investment costs when dealing with a startup business. Further one should bear in
mind that this figure refers to a field size of 2 ha. Cultivating a smaller (larger) area
will, due to economies of scale, result in a lower (higher) NPV.




                                           18
           4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


4.2   Economics of Ground-Mounted Photovoltaic Systems
This subsection illustrates a NPV-analysis for common GMPV-systems. Similar to
section 4.1, we first take a look at earnings out of electricity sales before we focus on
the cost distinguishing between initial Capital Expenditures (CAPEX) and Operational
Expenditures (OPEX) representing costs over the life-time of the system. In a last step,
we calculate the NPV and the IRR and derive the average cost per unit of generated
kWh known as the LCOE. If not stated otherwise all applied figures stem from data
of the BayWa r.e. Solar Projects GmbH, a project partner of the Heggelbach project.
As mentioned in section 2, GMPV-systems typically generate electricity at lower cost
compared to other kinds of PV-systems due to economies of scale. However, with a size
of 2 ha the area we look at is relatively small compared to standard GMPV-plants and,
therefore, economies of scale effects are lower than on average.
  All figures concerning PV are given in Watt-peak (Wp ) which refers to nominal
power yields under Standard Test Conditions (STC). For instance, with 2 ha the field
size we look at encompasses a total installed capacity of 1,000 kWp , or 500 kWp per
ha.

4.2.1  Earnings from Electricity Sales

Normally, earnings are the amount of generated electricity times the price at which
electricity is sold. Today, however, realized earnings from PV electricity on the open
marked are not yet enough to cover the average cost of power generation. Thus, eco-
nomic performance still depends on governmental support – in our case the German
Renewable Energy Act (EEG). In its latest version from 2015, energy producers oper-
ating a GMPV-plant obtain FITs only if they successfully participate in a tendering
procedure (Federal Ministry for Economic Affairs and Energy (BMWi),
2014). Bidders agreeing to generate energy at the lowest price per kWh receive this
FIT for 20 years. Given the expectation that the auction will reveal entrepreneurs with
the lowest profit margin it seems reasonable to assume FITs being closed to the real
cost. With an average FIT of e0.0917 per kWh among successful bidders the first al-
location round lanced in April 2015 seems to confirm this trend (Federal Network
Agency, 2015b). Thus, in what follows we assume a successful participation in the
tendering procedure with a FIT of e0.0917 per kWh for 20 years. Since we regard a
life cycle of 25 years, we assume electricity of the remaining 5 years being sold at a
common market price of e0.05 per kWh (Gimbel, 2015).
  The amount of generated electricity depends on region-specific parameters – notably
annual insolation S – and physical performance of the PV-system. The latter includes




                                           19
           4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


durability N , system efficiency µ and an annual decline of efficiency d. Thus, over N
years total electrical yield in kWh per installed kWp follows the formula

                        N
              Electric Y ield =     Sµ(1 − d)n .
                        n=1


To obtain figures per ha we multiply electric yield with capacity of installed kWp per
ha (C) which here we assume to be 500 kWp . By that, over 25 years total earnings
sum up to about e1.27 million per ha.

4.2.2  Capital Expenditures

Fixed expenditures that incur once at the beginning of a project are typically labeled
as CAPEX. In the case of GMPV, CAPEX incorporate cost for solar panels and the
so called Balance of System (BOS) which encompasses all other costs. In earlier days,
solar panels contributed by far the larger share. But since learn effects of panel pro-
duction took place, the relative share of panel cost was constantly decreasing over time
(Hernández-Moro and Martínez-Duart, 2013). According to wholesale prices and
recommendations of BayWa r.e. Solar Projects GmbH we assume panel cost of e0.52
per Wp – which is 30% less than expenses on BOS.
  Components of the BOS include costs for inverters, mounting structures, racking
hardware components, combiner boxes and miscellaneous electrical components, fences,
the site preparation and system installations, grid connection, as well as system design,
management and administration and cost for tendering procedures, legal advice, due
diligence. For a detailed overview of all CAPEX see Tab. A.3 in Annex A2.

4.2.3  Operational Expenditures

In contrast to CAPEX, OPEX refer to running costs that incur during the lifetime of
a project. For GMPV, OPEX contain costs for land rent, mowing, cleaning, surveil-
lance, monitoring, commercial management, inverter replacement, cost for insurance,
provision of repair services and miscellaneous expenses. With more than 30%, cost of
commercial management accounts for the largest part of OPEX. With respect to total
cost of an GMPV-system, OPEX contribute only about 30% whereas CAPEX account
for 70% of total cost. However, over time relative importance of OPEX grew due to
above mentioned learn effects of PV-modules. Tab. A.4 in Annex A2 provides a list of
all cost items.




                                           20
           4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


4.2.4  NPV, IRR and LCOE

To estimate the NPV of a GMPV-system we apply the same financial parameters as in
the case of agriculture. With e2,226 per ha the NPV indicates that an investment in
this GMPV-system would be a profitable one.
  Closely connected to the NPV method, the IRR measures the required discount
factor to realize a NPV of zero.
                    N
                        NP
                NP V =       −n
                           =0
                    n=1 (1 + i)


In our example, a NPV of zero would be realized if instead of the calculated WACC of
3.5% we employ a slightly higher discount rate of 3.51% – which is, hence, the IRR of
the project. The lower the IRR the less attractive is an investment. If the WACC is
greater (lower) than the IRR the NPV is negative (positive). The fact that the IRR is
almost equal to the NPV illustrates that the analyzed GMPV-system operates on the
verge of profitability.
  Looking at the LCOE tells a similar story: With e0.0864 per generated kWh prof-
itability of an investment hinges on higher FIT in order to balance out low prices during
the last five years. A slight reduction of the assumed FIT from e0.0917 to e0.0912
would be enough to yield a NPV of zero. Formally, the LCOE are given by the CAPEX
and the present value of all OPEX over the present value of total electricity yield.
                          N  OP EX
                   CAP EX +   n=1 (1+r)n
             LCOE =       N
                       n=1
                        Sµ(1−d)n
                       (1+r)n




                                           21
           4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


4.3   Economics of APV
Based on previous findings, in this section we assess the change of parameters compared
to the baseline scenario if land is simultaneously used for farming and generation of
PV-electricity. While there are different approaches of how this dual land use can
be implemented, here we refer to the technology as developed by the APV-RESOLA
project of Fraunhofer ISE.
  In contrast to other approaches that stick to a maximization of electricity yields (see
e.g. Goetzberger and Zastrow, 1982; Dupraz et al., 2011) the ISE technology
allows to deviate from standard PV-panel configuration considering the agricultural
production process as an integral part of the optimization approach. Analyzing this
trade-off between agricultural and electricity yields, costs and earnings, the findings of
this section [this thesis] aim to contribute to this optimization process. Accordingly, the
inclination of and the distance between panel rows differ from those of GMPV-systems
obtaining both a higher and a more even distribution of solar radiation on the land
surface below. This causes a stronger and steadier plant growth while at the same time
electricity yields reduce (Obergfell et al., 2013). Further, with 5 to 6 meters above
ground the altitude of installed PV-panels guarantees that all kinds of mechanized field
works can be done.
  The next subsections present relevant effects and discuss their cause and their impact
on parameters and overall efficiency. We assess the magnitude of parameter changes in
the prevalent case and consider how these effects affect APV applications in general. A
last section summarizes the results and performs some comparative statics.

4.3.1  Parameter Changes and Further Effects in Terms of Agriculture

At first glance, a major concern of a dual land use is the limited availability of solar
radiation with its possible drawbacks for plant growth and, finally, agricultural yield.
While this is true for light-demanding plants, other plants remain unaffected or even
benefit from less sunlight. According to Obergfell et al. (2013) who distinguishe
agricultural crops with respect to their eligibility for an APV-system, there exist three
categories: Category Minus which shows adverse reactions if exposed to less insolation;
category Null which to a large degree remains indifferent; and category Plus to which
potatoes belong and which gains in terms of plant growth and yield. As Seidl (2010)
shows, if partially covered, Plus-class crops’ yield rises up to 12%. While less direct
insolation is likely to be one main driver, also micro-climatic effects might help to explain
this reaction. Therefore, in the present case we assume yield of potatoes to increase by
4% due to lower solar radiation while later discussing further micro-climatic effects.




                                             22
           4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


  The mounting system of PV-panels is another factor expected to reduce the area of
arable land and thus agricultural yield. Pillars and other racking hardware components
that are connected to the land surface curtail arable area by about 8% leading to a
decline of agricultural yield and all other variable cost items that depend on cultivated
field size. Indeed, the only cost items not affected by a change of arable land are "other
fixed cost" and "land cost". While a reduction of arable land applies to most agricultural
crops, fruit-growing farms and crops with larger row distances might rather remain
unaffected.
  Additionally, the mounting system restricts the availability of working tracks lead-
ing to a potential rise in travel distances and labor input. Therefore we assume fuel
consumption and labor effort to increase by 2% and 3%, respectively.
  Closely related to a rise in travel distances and labor input, restricted working
tracks also bear a higher risk of accidents and damages on machines and agricultural
equipment. We account for this issue regarding a rise of insurance cost. Since insurance
cost are no single cost item but covered by ”other fixed cost” we expect this item to
increase moderately by 2.5%.
  Regarding PV-panels, a wide range of more or less probable consequences are ex-
pected to alter the micro-climate below, with most of these effects being potentially
both beneficial and adverse. As the only exception that clearly enhances efficiency,
we suppose the balancing effect on local temperature fluctuation to foster agricultural
yield by 3%. Other effects like wind deflecting aspects or a higher local humidity un-
derneath PV-panels are ambiguous. On the one hand side crops are less exposed to
risks of wind or drought damage; on the other hand less wind and a higher humidity
might increase the risk of diseases as well as pest and fungal infestation. Thus, here
we assume pro and cons of these effects to perfectly cancel out. Though, in general,
notably regarding non-organic farming practices, it seems reasonable to expect a rise
in the use of pesticides and fungicides suppressing adverse effects with a slight overall
improvement of profitability. Moreover, beneficial micro-climatic effects are likely to be
achieved in regions or countries with low or unsteady precipitation, high temperature
fluctuation and fewer opportunities of artificial irrigation.
  With respect to PV-panels, a further issue is uneven rainwater distribution on
the surface below. Similar to the matter of limited solar radiation, the sign and the
magnitude of this effect depend on distinct needs of cultivated crops. Since potatoes
possess the ability to direct root growth towards regions of higher soil moisture (see
Obergfell, 2012, p.31) we expect no significant effect in our analysis. In general,
even though more research has to be done in this field, this effect has probably rather
negative implications on plant growth.



                                           23
           4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


  Furthermore, PV-panels potentially protect crops from hail damage. As we deal only
with partial protection we assume a decrease in hail insurance cost of 10% reflecting a
cost advantage of e15 per ha.



  Beside implications on agricultural production itself, there are aspects of APV that
affect overall economic performance of a farm. Among those are lock-in effects that
arise if, with respect to future business opportunities, farmers face a lack of flexibility
due to an APV investment decision. This is particularly true if – as in the case of APV
– the affected time horizon is large and unforeseen contingencies are likely to occur.
For instance, the restriction to Plus-class crops might cause opportunity cost if an
unexpected rise of Minus-class crops’ profitability opens up new business opportunities
that cannot be taken since they are not efficient anymore within an APV-system. To
account for lock-in effects we impute annual lump-sum costs of e50 per ha and year
which, following Schmid (2015), appears reasonable.
  Further, electricity yields affect economic performance of a farm since they generate
additional earnings and might lower expenses if own electricity is consumed instead
of external one. While from a farmer’s point of view these issues might be major
arguments for an APV-system, here we ignore them since we cover PV-specific aspects
in the next section.
  Tab. 4.3 aims to provide a complete list of relevant parameters and their expected
effect on efficiency of agriculture. The left (right) side of the table presents efficiency
enhancing (diminishing) effects each splitting up in four columns: The first describes
the cause or the origin of effect; the second names the effect itself; the third determines
which parameter are affected in the general case; and the last one quantifies the magni-
tude and sign at which the respective parameters change in the present case of organic
potatoes.

4.3.2  Parameter Changes and Further Effects in Terms of PV

With respect to the PV-system, most changes that affect earnings and cost originate
from higher elevation of PV-panels. First and foremost, this requires more and more
solid mounting frames and racking hardware components in order to obtain the desired
height and to meet increased operational demands due to a higher wind exposure.
This leads to a substantial rise in mounting cost. Relying on data from the APV-
RESOLA project, we assume both mounting cost and costs for site preparation and
system installation to more than double. More exact, expenses increase from e0.330




                                            24
            4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES




              Effects on Economic Efficiency of Agriculture
       Efficiency Enhancing              Efficiency Decreasing
               Affected                  Affected
Cause      Effect    Parame- Change   Cause    Effect  Parame-    Change
                 ter   [%]               ter    [%]
          Less                     Less
Mounting           Variable     Mounting
         arable         -8%         arable   Yield    -8%
system             cost       system
          land                     land
                              Restricted
          Hail     Hail      Mounting
PV-panels                -10%        working   Labor    +3%
        protection  insurance      system
                                tracks
        Less fluc-
                               Higher
        tuation in            Mounting        Insurance
PV-panels            Yield  +4%          risk of        +2%
        local tem-             system          cost
                              accidents
        perature
         Higher                    Lower
 Lower                      Lower
        growth of                  growth of
 solar             Yield  +5%    solar         Yield    ±0%
         Plus-                    Minus-
radiation                    radiation
         crops                     crops
                               Risk of
                                    Pesticides,
       Lower risk                   diseases
 Wind                       Wind         Insecti-
         of wind    Yield  ±0%         and pest         ±0%
deflection                    deflection         cides,
        damages                    infesta-
                                     yield
                                 tion
                               Higher
Higher    Lower risk             higher
                                risk of Fungicides,
 local       of     Yield  ±0%    local               ±0%
                              fungal in-  yield
humidity    droughts            humidity
                              festation
        Own con-
                               Uneven
        sumption    Fixed
Electricity                         rainwater
           of    energy  ±0%  PV-panels         Yield    ±0%
 yields                           distribu-
        produced     cost
                                 tion
        electricity
        Earnings              Time
                                    Opportu-
Electricity    from             horizon of  Lock-in
               Earnings  ±0%                nity    +e50
 yields    electricity             APV-    effects
                                      cost
          sales             system

             Table 4.3: Changes of agricultural parameters




                                            25
              4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


to e0.696 per kWp which equals a rise of 109% compared to conventional GMPV-
systems. Also related to higher elevation of PV-panels we expect expenses for system
design, management, and administration to rise by 30% due to higher complexity of
the system. Jointly, these changes account for a rise in CAPEX of about one third
from e1.248 to e1.632 per kWp . This change implies large consequences on efficiency:
Disregarding earnings from agriculture, the NPV of the project drops from e362 to a
loss of e154,650.
  A further consequence of higher panel elevation is a rise in OPEX if maintenance
works and cleaning of PV-panels demand higher efforts compared to ground-mounted
systems. Accordingly we expect provision of repair services and cost of cleaning to rise
by 5% and 25%, respectively.
  Additionally to more complex cleaning operations, also the frequency of the latter is
affected by the height of PV-panels. The higher the elevation above ground the lower is
the amount of dust and other air particles – hence, less cleaning operations have to be
undertaken over time. On average, it is efficiency enhancing to clean PV-panels each
10 years (Gimbel, 2015). With respect to higher elevation of APV-panels we assume
this time horizon to extend by 20% or 2 years.
  Another side-effect of elevated PV-panels is protection against theft. Taking this
matter into account we consider a decline of insurance cost by 25%.
  As mentioned above, deviations from standard PV-panel configuration lead to lower
electricity yield. This is with respect to two features: Row distances and sun exposure
of PV-panels. Greater row distances allowing more direct insulation to reach the agri-
cultural surface below cause a drop in installed capacity per ha of about 32%. With
respect to the angle of incidence, the south-east or south-west exposure of PV-panels
reduces system effectiveness by 5% (Obergfell, 2012).
  Agricultural work affects efficiency through several channels. Among those, three
effects can be identified that reduce efficiency: Higher risk of accidents and thus damages
of the PV-system leading to a rise of insurance cost (+30%); higher air pollution in
terms of dust and other air particles shortening the time periods between cleaning
operations (-80% or 8 years); and, since free accessibility for machines implies no fences
on the site boundaries, a greater risk of theft drives insurance cost (+10%). On the
other hand, though, agricultural work indirectly fosters efficiency. No continuous fence
unquestionably implies less fence cost (-90%)11 and in contrast to common GMPV-
systems need of weed controls only remains underneath mounting elements where no
crops are cultivated. This reduces cost of mowing by 60%.
  Concerning earnings from market sales, prices of electricity are likely to change due
 11
    No complete elimination of fence cost since combiner boxes still require some kind of boundary.




                                                  26
             4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


to time differentials in feeding electricity into the grid. If prices vary over the day, the
deviation of a pure south exposure of PV-panels leads to a shift in electricity generation
peaks thus affecting the level of earnings. At which time prices rise or fall depends on
the level of demand and supply for electricity. Even though peak demand usually occurs
around midday, nowadays the supply also peaks around this time due to high shares of
PV-electricity in Germany. Recently, excessive supply of PV even depresses electricity
prices shifting the price peak to morning and evening hours. On average, the price
differential between morning and evening peaks and midday low is about 15% to 20%
(ISE, 2015). Thereby, the future trend of this phenomenon seems clear: The more
installed PV-capacity the larger this price differential will be. However, yield peaks of
APV-systems do not perfectly coincident with price peaks. Instead, here we presume
a time shift of about two hours which results in a price advantage of about 10%.12
  With respect to land cost, major differences exist dependent on the kind of land
use and the status of the tenant. For an average farmer, land rents per ha and year
approximately amount to e360 whereas energy investors usually budget e1,500 (Gim-
bel, 2015). Reasoning behind this differential is a kind of monopoly rent on the part
of farmers: Due to local land use plans the choice of qualified areas is limited and
strong bargaining positions of land owners – commonly farmers – raise land rents if
energy investors are restricted to few available areas. However, since land cost already
appeared within the agricultural production budget, here we disregard any additional
expenses.13



  The same applies for earnings out of agricultural production. While generally addi-
tional earnings might affect economic performance of GMPV-systems, here we ignore
this issue since we already covered agricultural earnings in the previous section. Tab. 4.4
provides a list of relevant parameters and their expected effect on efficiency in terms of
PV. As in the case of agriculture, the left (right) side of the table presents effects that
improve (reduce) efficiency.




 12
   Note that this effect is lower than it might seem since market prices only step in when FITs expire,
which in our case is after 20 years.
 13
   Additional expenses in case the investor and the farmer are no economic entity we wil discuss in
section 5.




                                                  27
            4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES



               Effects on Economic Efficiency of PV
       Efficiency Enhancing              Efficiency Decreasing
              Affected                   Affected
Cause     Effect   Parame- Change     Cause    Effect  Parame-   Change
               ter    [%]                 ter   [%]
                                    Mounting
                         Higher   Higher  cost, Site
 Agri-    No need   Mainte-
                        elevation  material  prepara-
cultural   of weed   nance    –50                     +109
                          of   and labor  tion and
 work     controls   cost
                        PV-panels    cost  system in-
                                    stallation
                                     System
                                     design,
Higher   Decreasing              Higher   Higher
                                    manage-
elevation    risk of  Insurance       elevation  labor and
                    –25              ment and    +30
  of     module    cost          of    planning
                                    adminis-
PV-panels    theft             PV-panels    cost
                                     trative
                                     costs
                                More
Higher     Lower               Higher
                               complex
elevation   pollution  Cleaning       elevation        Cleaning
                   +2 years        cleaning         +25
  of       of    cost          of           cost
                                 of
PV-panels   PV-panels            PV-panels
                              PV-panels
Accessibi-                           More
                         Higher
lity for                          complex   Mainte-
        Reduced             elevation
agricul-         Fence cost  –90          mainte-   nance    +5
         fence               of
  tural                            nance    cost
                        PV-panels
 work                             works
                         Higher
                               Less ab-
                          row         Required
Farmer as   No land    Land              sorption
                    –100   distance        area per   +32
investor     cost    Rent               of solar
                          of           kWp
                              radiation
                        PV-panels
No entire                   No entire
       Peak shift                   Less ab-
 south           Market        south         System
          of                    sorption
exposure          price of   +10   exposure        effective-   –5
       generated                    of solar
  of          electricity        of           ness
       electricity                  radiation
PV-panels                   PV-panels
       Additional
 Agri-    earnings              Agri-   Higher
                                    Insurance
cultural   from agri-  Earnings   –    cultural   risk of         +30
                                      cost
 yields    cultural              work   accidents
         sales
                               Higher
                          Agri-
                               pollution Cleaning
                         cultural              –8 years
                                 of    cost
                         work
                              PV-panels
                               Higher
                         Free ac-       Insurance
                               risk of         +10
                        cessibility         cost
                                theft

            Table 4.4: Expected changes of PV parameters




                                            28
               4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


4.3.3    Results and Comparative Statics

Given the assumptions made with respect to revenues and expenses, an investment
in an APV-system seems not to be profitable. This is indicated by a negative NPV
of e84.858 per ha. Accordingly, with 1.94% the IRR is 1.57 percentage points below
WACC. Main driver for these results is cost related to high elevation of PV-panels.
  The NPV of the project splits up in a surplus of e73,812 contributed by agriculture
and a loss of e154,650 on the part of PV. Hence, profitability of agriculture is about 5%
higher than under mono production. These efficiency gains mainly result from lower
variable cost at almost stable yield and earnings. Indeed, there are also gains with
respect to PV: Keeping other variables constant, the elimination of land cost reduces
OPEX by about 12% alleviating total losses by almost 30%. However, all these benefits
are not large enough to balance out the fierce rise in CAPEX. A graphical overview
of most relevant cost items is given by Fig. 7. The pie chart on the left shows the
structure of agricultural costs within the APV-system whereas the right one depicts
this structure for PV-related costs.
        Cost of agriculture14                 Cost of PV
                                 Commercial
                                 management
  Indirect                        OPEX
variable cost    16%                         8%
           16%                 22%
    34%      Other
           indirect
                                  14%
             cost                   14%
                                 Other
                   34%               OPEX       41%
         18%       Seed potatoes                    Mounting
        18%
       Imputed labor                            structures etc.
                 66%               Other 12%
                                 CAPEX     78%
               32%                     25%
            Other direct cost   Direct
                                     PV-panels
                      variable cost                   CAPEX
                         66%                      78%
       Figure 7: Cost structures of agriculture and PV as parts of APV production


  With respect to scope and added economic value, total sales of around e1.1 million
per ha split up in e0.17 million from agriculture and e0.93 million from PV. This
means, sales from PV are about 5.5 times more worth than those from agriculture.
This relation is also prevalent in terms of cost. Fig. 8 illustrates this by the structure
of APV cost incorporating agricultural and PV cost of Fig. 7.
  Considering potential learn effects related to high elevation of PV-panels, it might
be interesting to know the maximum rise of expenses on mounting structures etc. to
still attain an equal NPV as expected by the mono PV project. As it turns out, a
 14
    Figures refer to first year’s budget




                                                   29
            4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


                        Cost of APV
             Agricultural cost
                Direct
                    11%        Indirect
                              variable cost
                variable cost
                           4%
               Commercial        4%
               management     7%
                        7%
             OPEX       7%
              20%                  37%
                   Other
                    20%           Mounting
                   OPEX          structures etc.
                        13%

                        10%  89%
                    Other
                    CAPEX     25%
                           PV-panels
                                      CAPEX
                                        69%

             Figure 8: Cost structures of APV production



rise up to 42% could be compensated by efficiency gains and additional earnings from
agriculture. Put differently, if cost in terms of elevation of PV-panels rise only by 42%
instead by 109%, a PV investor would be indifferent between a conventional GMPV
project and an APV project.15
  As another point of interest, a comparison of LCOE of different PV-systems seems
fruitful to asses economic performance of APV-systems. Fig. 9 depicts LCOE of APV
                         together with those of small scale and
   0.14
                         GMPV-systems. In line with findings
   0.12                    above, average costs of APV are higher
LCOE [Euro/kWh]




   0.1                    than those of GMPV. In contrast, com-
   0.08                    pared to LCOE of small scale PV-plants
                         electricity from APV-systems is likely to
   0.06
                         be cheaper than if produced by rooftop
   0.04
                         systems.
   0.02                      If governmentally supported, the re-
                         lation of different LCOE also mirrors so-
       PV small GMPV    APV
                         cial cost linked to different technologies.
Figure 9: LCOE of small scale PV, GMPV and
APV-systems for a GHI between 1,450 and 2,000  Today, PV-systems below 10 kWp re-
    2
kWh/m /a. Source: Own representation based on  ceive a FIT of e0.1234 (Federal Net-
ISE (2013)
                         work Agency, 2015a). Following our
    15
  Note, though, that this constellation would require further adjustments of parameters since it
deviates from our default case in which the farmer is also the investor.




                                                30
          4 DYNAMIC ANALYSIS OF REVENUES AND EXPENDITURES


calculations, an APV-system is expected to work cost-effective already at a FIT of
e0.1154. Taking into account economies of scale, also FITs below e0.10 are probably
enough to ensure efficient operation of larger APV-systems.




                                        31
5   Discussion
This section discusses main findings of section 3 and 4 and sets them in relation to each
other. First we challenge some underlying assumptions of the theoretic model; then we
consider possible drawbacks and limitations of the methodology applied for the dynamic
analysis of the previous section, reconsidering our standard investor-farmer constellation
and briefly touching welfare implications. Finally, we discuss the results with respect
to the efficiency criterion developed in section 3 and address future developments and
further possible applications of APV.
  As a crucial assumption, in section 4 we applied an additive social welfare function
to derive optimal allocation of land. Arguably, one could also advocate a multiplicative
welfare function since an additive type implies that food and electricity are perfect
substitutes for which the marginal rate of substitution is always constant. However, in
such a situation society would be indifferent between food and electricity and willed to
substitute at the same rate even when it comes to the last unit of food. This seems little
realistic. Yet, formally this sort of corner solution is unlikely to occur. As we based
the model on production functions with decreasing marginal productivity, the highest
productivity exists for the first production units hence simulating a similar optimization
behavior as in the case of a multiplicative welfare function. Against this background,
the additive and much handier type seems more eligible.
  Another assumption that might be questionable is full information. Various regula-
tions of food and energy sectors are motivated by environment issues, notably climate
change. Time lags and uncertainties, though, play a major role in explaining why
agreements on climate change policies are so hard to obtain. Thus, with incomplete
information optimal levels of food and electricity production are much harder to define
as the model may suggest.
  Likewise, the model completely ignores political decision making and the role of
interest groups. In agriculture and energy branches in which public debates, lobbying,
and various layers of legislative competences are integral parts of daily life, there is no
doubt that a thorough analysis also needs to address these issues.
  With respect to the dynamic analysis of earnings and expenditures in section 4, a
major methodological drawback is the absence of crop rotation. If potatoes are culti-
vated on the same field in consecutive years, yield reduces considerably due to plant
diseases and pest infestations (Agricultural Chamber of North-Rhine West-
phalia, 2012). Hence, the recommended crop-specific rotation period is at least four
years. With respect to organic farming methods, a rotation period of seven years is
common practice (Schmid, 2015). In the context of this thesis crop rotation is particu-




                                            32
                                       5 DISCUSSION


larly important since average earnings from potatoes are substantially above earnings of
other crops leading to an overestimation of the agricultural NPV in section 4. Roughly,
we speculate this overestimation to range between 20% and 40%. When performing
the calculations with 30% less agricultural earnings, the required FIT to maintain prof-
itability of APV rises from e0.1047 to e0.1133. Still, a detailed analysis including crop
rotation seems like a meaningful task for further research.
  As a further limitation of APV calculations performed in this thesis, economies of
scale are not sufficiently considered. Surely, larger APV-plants perform more efficient.
Hence, more specific investigations appear desirable to assess the scope of scale effects
and required FITs to support larger plants.
  Regarding assumptions about financial parameters, we already mentioned the dif-
ferent equity shares prevalent within farming and energy sectors. This matter is excep-
tionally important since the share of equity serves as a main driver for the WACC. In
turn, the level of WACC has dramatic consequences on the NPV. The average equity
capital in the farming sector is about four times higher than in the energy sector.16
Employing the farming sector’s equity ratio rises the WACC from 3.5% to 9.5%. How-
ever, we argue that the reasoning behind the difference of equity ratios lies rather in
the nature of the investment and not in the origin of the investor. A farmer, usually
dealing with high own equity shares with respect to farm investments might face com-
pletely different financing opportunities when considering a PV investment. However,
it remains to specify whether this holds in reality or not.
  Closely related to this issue is the assumption about the investor-farmer constella-
tion. Similar to equity ratio, parameters like land cost, the ownership of land or the
legal status are likely to alter if deviating from our default case, and, hence, should be
addressed by further investigations.
  Estimating the relevance of the APV calculations with respect to the efficiency cri-
terion derived in section 3, the results are little comparable since the calculations do
not encompass any welfare effects. However, the fact that productivity of agriculture
almost remains constant (referring to an α closed to 1) and productivity of PV only
drops by 28% (referring to a β of 0.72) implies that the sum of both parameters is far
beyond our efficiency benchmark.17 A verification of these figures requires a detailed
welfare analysis including a quantitative assessment of relevant factors. Partially, this
is done by Zangl (2012) who analyzes land use conflicts and APV as a mitigation
strategy. Additionally, two other aspects are expected to cause major external effects
 16
   Comparing equity shares, with 25% vs. 400% the difference appears to be even larger (StMELF,
2014).
 17
   Note that these figures only refer to output per ha and do not reflect involved cost.




                                               33
                                   5 DISCUSSION


and thus need further research. First, since APV would significantly affect the char-
acter of landscape, assessments of social acceptance seem indispensable if it comes to
policy implications. Second, as a parameter of sustainability, an assessment of the en-
vironmental footprint of APV is required in order to illuminate the ecological impact
of APV compared to GMPV. Notably, this seems relevant regarding higher resource
input related to high elevation of PV-panels. As life cycle assessments of Jungbluth,
Tuchschmid, and Wild-Scholten (2008) estimate, mounting structures and hard-
ware components of rooftop systems account for approximately 15% of the system’s
CO2 emissions. Comparing the amount of installed materials, it appears probable that
CO2 emissions per installed Wp in the case of of APV-systems are significantly higher
compared to GMPV or rooftop systems. Incorporating those welfare effects into the
parameter α and β would be task for further research.




                                          34
6  Conclusion
In this thesis, we analyzed economic performance of APV with respect to land use ef-
ficiency, earnings and cost. After presenting the technology as such, we first developed
a simple welfare model to provide a theoretic structure of land use competition and
technological opportunities. In what followed we examined efficiency of APV with re-
spect to commercial usage performing a dynamic analysis of earnings and expenditures.
This was done in three steps: (1) we examined agricultural farming processes, (2) we
investigated in earnings and cost of GMPV-systems, and (3) we adjusted relevant pa-
rameters to APV-specific levels. By that we emphasized on higher risks represented
by rising cost compared to GMPV-systems and estimated FITs required for a political
strategy to support APV. Finally we discussed main findings reconsidering underlying
assumptions and methodologies as well as possible drawbacks and limitations.
  Main finding of the thesis is that APV-plants are expected to operate profitable
if FITs lie between those of large scale GMPV-plants and small rooftop systems. For
Germany, August 2015, the respective figures are e0.0917 and e0.1234 with APV
ranging between e0.10 and e0.12. Concerning theory of land use efficiency, a further
finding defines a welfare criterion with respect to productivity of APV as a hybrid
technology. Referring to respective mono technologies, the welfare criterion states that
the application of the hybrid technology enhances social welfare if it is at least half as
productive as the respective mono technology. Applying this result to the analysis of
earnings and expenditures suggests that – neglecting any external welfare effects – the
employment of APV enhances land use efficiency and thus social welfare. This is in
line with findings of Dupraz et al. (2011).
  In the context of long term projects like the German Energiewende, the results of
this thesis suggest that APV has the potential to be part of future energy landscape.
Despite existent drawbacks and open questions discussed further above, APV possibly
lowers cost of the energetic transition while at the same time does not consume any
additional land. An explicit policy implication, though, requires a public debate about
arguments that speak in favor or against APV. This is particularly important in order to
clarify which reasons led to an exclusion of GMPV from FITs since two frequently cited
arguments point in completely different directions with respect to APV: If aesthetical
reasons were responsible APV might even worsen the situation since it affects landscape
more than GMPV. However, if competition to common farming is the reason then APV
might be an appropriate technology to solve this problem.




                                            35
A   Appendix
A.1   First Part
In this part of the Appendix we provide the derivation of the efficiency rule as done in section
3.1 with the only difference that here s = 0 instead of s = 1. As in section 3.1 we start from
Equ. 6 which is

   F (ˆf ) − F (ˆf −sxh ) + E(ˆe ) − E(ˆe −(1−s)xh ) − β[E(ˆe + sxh ) − E(ˆe −(1−s)xh )]
     x     x       x    x           x      x
α=                                             .
                 F (ˆf + (1 − s)xh ) − F (ˆf − sxh )
                   x          x

Setting s to 0 yields

               E(ˆe ) − E(ˆe − xh ) − β[E(ˆe ) − E(ˆe −xh )]
                x    x        x    x
            α=                         .
                    F (ˆf + xh ) − F (ˆf )
                      x       x
Now we bracket the term E(ˆe ) − E(ˆe −xh ) in the numerator of the fraction such that
             x    x

                        E(ˆe ) − E(ˆe −xh )
                          x     x
                α = (1 − β)              .         (11)
                        F (ˆf + xh ) − F (ˆf )
                          x       x
As in section 3.1 we focus on the fraction analyzing the limits as xh approaches 0.

                     E(ˆe ) − E(ˆe −xh )
                       x     x
                   lim             .
                  xh →0 F (ˆf + xh ) − F (ˆf )
                       x       x

Again, first we expand the fraction multiplying both the numerator and denominator with
x−1 . Then we apply Newton’s difference quotient.
h

                    E(ˆe )−E(ˆe−xh )
                      x    x       ∂E(ˆe )
                                   x
                        xh         ∂ xe
                                   ˆ
                  lim x           =       .
                 xh →0 F (ˆf +xh )−F (ˆf )
                            x     ∂F (ˆf )
                                   x
                        xh         ∂ xf
                                   ˆ

Thus, the numerator and denominator equal the marginal productivities of the status quo
from which we know that they equal each other. Consequently, the equation takes on a value
of 1 and all that remains from Equ. (11) is

                       α= 1−β

which leeds us to the same efficiency rule as in section 3.1.




                         I
                                       A APPENDIX


A.2   Second Part
This section provides detailed figures of cost and revenue items as employed in section 4. Tab.
A.1 presents cost and revenue items of agriculture as applied in section 4.1. Additionally,
the last collumn shows the corresponding APV figures after the change of parameters as
described in section 4.3.1. Changes are highlighted in bold type.

                   Yield, prices and revenues
   Item                    Unit Baseline scenario    APV scenario
   Agricultural yield             dt/ha       246.60      244.10
   Producer price               e/ha        35.50       35.50
   Subsidies for agricultural farming     e/ha        230.00      230.00
   Total revenues               e/ha      8,984.30     8,896.76
                     Contribution margin
   Seed potatoes               e/ha       1,613.20      1,484.14
   Fertilizer                 e/ha        509.89       464.41
   Direct machinery cost           e/ha        470.30       432.67
   Sorting and grading            e/ha        224.16       221.92
   Hail insurance               e/ha        153.20       136.50
   Direct labor cost             e/ha        100.30       92.28
   Direct storage cost            e/ha        91.24       90.33
   Contribution margin            e/ha      5,822.01      5.974.50
                 Indirect variable cost and fixed cost
   Indirect machinery cost          e/ha        747.89       710.50
   Storage space               e/ha        164.61       162.96
   Land cost                 e/ha        220.00       220.00
   Imputed costs of capital, land and labor e/ha         243.91       292.60
   Other fixed cost              e/ha        96.60       99.02
   Total cost                 e/ha      4,635.30      4,407.33
                       Net profit
   NP                     e/ha      4,349.00      4,489.43
                     Net present value
   Annual growth yield             %         1.36        1.36
   Annual growth price             %         -2.36        -2.36
   Annual Inflation               %         1.92        1.92
   WACC                     %         3.50        3.50
   NPV (25 periods)              e/ha     70,556.87      73,811.84

      Table A.1: Cost and revenue items of agriculture for baseline and APV scenario




                       II
                                        A APPENDIX


  The following tables provide figures with respect to PV-related cost and revenue items.
Tab. A.2 shows an overview of electrical yield and earnings.

                 Electricity yield, prices and revenues
     Item               Unit   Baseline scenario  APV scenario
     Electricity yield (first year) kWh/kWp          1,200      1,140
     FIT               e/kWh        e0.0917     e0.0917
     Market price electricity     e/kWh         e0.05      e0.055
     Total              e/kWp         e2,537     e2,437

      Table A.2: Cost and revenue items of agriculture for baseline and APV scenario


  Tab. A.3 lists all CAPEX of the baseline and APV scenario. Note that values per ha
change even though the actual parameter does not since the installed capacity per ha changes
(compare collumns three and five).

                       CAPEX
                              Baseline scenario      APV
 Item
                             in e/Wp in e/ha    in e/Wp in e/ha
 Solar panels                        0.520  260,000    0.520 197,600
 Inverter                          0.075  37,500    0.075  28,500
 Mounting structures and racking hardware components     0.080  40,000   0.167  63,523
 Combiner box                        0.015   7,500    0.015  5,700
 Miscellaneous electrical components             0.015   7,500    0.015  5,700
 Site preparation and system installation          0.255  127,500   0.533 202,478
 Fence                            0.020  10,000   0.002    760
 System design, management and administrative costs     0.125  62,500   0.163  47,500
 Due diligence                        0.025  12,500    0.025  9,500
 Legal advice                        0.013   6,250    0.013  4,750
 Grid connection                       0.100  50,000    0.100  38,000
 Cost for tendering procedure (fees, risk premia etc.)    0.005   2,500    0.005  1,900
 Total                           1.248 623,750     1.632 605,910

            Table A.3: CAPEX of the baseline and APV scenario




                       III
                                    A APPENDIX


                      OPEX
                     Baseline scenario      APV
     Item
                    in e/kWp in e/ha   in e/kWp in e/ha
     Land cost              3.00   1,500    0.00   0
     Mowing               1.80    900    0.72  274
     Surveillance            2.20   1,100    2.20  836
     Monitoring             3.00   1,500    3.00 1,140
     Commercial management        7.89   3,945    7.89 2,998
     Inverter replacement reserve    1.50    750    1.50  570
     Insurance              0.39    195    0.39  148
     Insurance (APV-sensitive)      0.97    485    1.12  424
     Provision of repair services    2.00   1,000    2.10  798
     Cleaning              0.65    327    1.95  740
     Miscellaneous expenses       1.46    730    1.46  555
     Total               24.86 12,432     22.32 8,483

          Table A.4: OPEX of the baseline and APV scenario


Tab. A.4 provides all OPEX of the baseline and APV scenario.




                     IV
B   References
Adenäuer, C. and L. Haunschild (2008). Anmerkungen zur Eigenkapitalquote im deutschen
 Mittelstand – ein Arbeitspapier. (German). Working Paper 02/08. Institute for Small
 Business Research.
Agricultural Chamber of North-Rhine Westphalia (2012). Kartoffelanbau. Ratge-
 ber 2012. (German). [Online] https://www.landwirtschaftskammer.de/landwirtschaft/acker-
 bau/kartoffeln. 09/08/2015.
Ahlers, J.-G. (2014). Welche Größe ist denn großgenug? (German). [Online] landund-
 forst.agrarheute.com. 07/31/2015.
Alexandratos, N., J. Bruinsma, et al. (2012). World agriculture towards 2030/2050: the
 2012 revision. ESA Working Paper 3.
Association for Technology and Structures in Agriculture (KTBL) (2013).
 Ökologischer Feldgemüseanbau. Betriebswirtschaftliche und produktionstechnische Kalku-
 lationen. (German). Niestetal.
Bavarian State ministry for Nutrition, Agriculture and Forestry (StMELF)
 (2014). Bayrischer Agrarbericht 2014. (German). [Online] http://www.agrarbericht-2014.
 bayern.de/landwirtschaft-laendliche-entwicklung.html. 07/23/2015.
Bavarian State Research Center for Agriculture (2015). LfL-Deckungsbeiträge
 und Kalkulationsdaten - Öko-Speisekartoffeln. (German). [Online] https://www.stmelf.bay-
 ern.de/idb/ oekospeisekartoffeln.html. 07/24/2015.
Bordemann, H.-G. (2015). Betafaktoren für Wirtschaftssektoren. (German). Onvalue GmbH
 & Co. KG. Bad Neuenahr-Ahrweiler.
Brealey, R. A., S. C. Myers, and A. Franklin (2006). Principles of Corporate Finance.
 8th edition. Patterson, S. M. New York.
De Schepper, E. et al. (2012). “Combining photovoltaics and sound barriers–A feasibility
 study”. In: Renewable Energy 46, pp. 297–303.
Dupraz, C et al. (2011). “Combining solar photovoltaic panels and food crops for optimising
 land use: Towards new agrivoltaic schemes”. In: Renewable Energy 36.10, pp. 2725–2732.
Federal Ministry for Economic Affairs and Energy (BMWi) (2014). Verordnung
 zur Ausschreibung der finanziellen Förderung für Freifächenanlagen. (German). Berlin.
Federal Ministry of Food and Agriculture (BMEL) (2011). Nationaler Strate-
 gieplan der Bundesrepublik Deutschland für die Entwicklung ländlicher Räume 2007 -
 2013. (German). Berlin.




                     V
                                  B REFERENCES


Federal Network Agency (2015a). Bestimmung der Förderssätze für Fotovoltaikanla-
  gen § 31 EEG 2014 für die Kalendermonate Juli 2015, August 2015 und September 2015.
  (German). Bonn.
— (2015b). Ergebnisse der ersten Ausschreibungsrunde für Photovoltaik (PV) - Freiflächenan-
  lagen. (German). Bonn.
Federal Statistical Office (2014). Land- und Forstwirtschaft, Fischerei. Betriebe mit
  ökologischem Landbau. (German). Wiesbaden.
Fernádez, P. and d. J. Campo (2011). Market Risk Premium Used in 2010 by Analysts
  and Companies: A Survey with 2,400 Answers. University of Navarra. Working Paper
  WP-912.
Food and Agriculture Organization of the United Nations, Statistic Divi-
  sion (FAOSTAT) (2015). Potatoe Yield: Germany 1973 – 2012. [Online] http://faostat3.
  fao.org/faostat-gateway/go/to/download/p/*/e. 07/27/2015.
Fraunhofer-Institute for Solar Energy Systems (ISE) (2013). Stromgestehungs-
  kosten Erneuerbare Energien. (German). [Online] http://www.ise.fraunhofer.de/de/daten-
  zu-erneuer-baren-energien/daten-zu-erneuerbaren-energien. 07/27/2015.
— (2015). Electricity production and spot prices in Germany. [Online] https:// www. energy-
  charts.de. 04/08/2015.
Frencha, C. W. (2003). “The Treynor capital asset pricing model”. In: Journal of Invest-
  ment Management 1.2, pp. 60–72.
Gimbel, E. (2015). Expert Interview with Edgar Gimbel. BayWa re Solar Projects, Freiburg
  im Breisgau. 06/23/2015.
Glenn, J. C., T. J. Gordon, and E. Florescu (2014). State of the Future. American
  Council for the UN University.
Goetzberger, A. and A. Zastrow (1982). “On the Coexistence of Solar-Energy Con-
  version and Plant Cultivation”. In: International Journal of Solar Energy 1.1, pp. 55–
  69.
Hernández-Moro, J and J. Martínez-Duart (2013). “Analytical model for solar PV
  and CSP electricity costs: Present LCOE values and their future evolution”. In: Renewable
  and Sustainable Energy Reviews 20, pp. 119–132.
International Energy Agency (2014). Key World Energy Statistics 2014. [Online]
  https://www.iea.org/publications/freepublications/publication/key-world-energy-statistics-
  2014.html. 06/23/2015.
— (2015). 2014 Snapshot of Global PV Markets. [Online]http://www.iea-pvps.org/index.php.
  06/23/2015.



                     VI
                                   B REFERENCES


Jungbluth, N., M. Tuchschmid, and M. de Wild-Scholten (2008). Life Cycle Assess-
  ment of Photovoltaics: Update of ecoinvent data v2.0. Working Paper. Energy research
  Centre of the Netherlands, Unit Solar Energy. Petten.
KPMG (2015). Corporate Tax Rates Table. [Online] https://home.kpmg.com/xx/en/home/
  services/tax/tax-tools-and-resources/tax-rates-online/corporate-tax-rates-table.html.
  04/08/2015.
Leithold, L. (1996). The calculus of a single variable. HarperCollins College Publishers.
  New York.
Obergfell et al. (2013). “Combining PV and Food Crops to Agrophotovoltaic – Optimiza-
  tion of Orientation and Harvest”. In: EU PVSEC. 5AV.2.25, pp. 4096–4100.
Obergfell, T. (2012). Agrovoltaik: Landwirtschaft unter Photovoltaikanlagen. (German).
  Master thesis, University of Kassel.
Pearce, D. (2002). Energy policy and externalities: an overview. Paper prepared for OECD
  Nuclear Energy Agency.
Schmid, T. (2015). Expert Interview with Thomas Schmid. Hofgemeinschaft Heggelbach.
  07/28/2015.
Schmidt, M, A Maul, and E Haase (2010). Statistisches Jahrbuch über Ernährung, Land-
  wirtschaft und Forsten. Wirtschaftsverlag NW GmbH Bremerhaven.
Seidl, F. (2010). Auswirkungen von Baumstreifen auf Ertrläge und Bodenerosion. Vortrag
  bei der Tagung Agroforstsysteme – eine Chance flür Bewirtschafter, Natur und Land-
  schaft. (German). University of Freiburg. [Online] http://www.agroforst.multifunktion.uni-
  freiburg.de/vortraege.php. 04/08/2015.
State Institute for the Environment, Measurements and Conservation in
  Baden Württemberg (LUBW) (2015). Ökologische Landwirtschaft. (German). [On-
  line] https:// www.lubw.baden-wuerttemberg.de/servlet/is/221850/. 07/24/2015.
Statista (2015). Anteil der Photovoltaik an der Bruttostromerzeugung in Deutschland in
  den Jahren 2002 bis 2014. [Online] http://de.statista.com/statistik/daten/studie/250915/
  umfrage/anteil-der-photovoltaik-an-der-stromerzeugung-in-deutschland. 07/28/2015.
Sumner, D. A., J. M. Alston, and J. W. Glauber (2010). “Evolution of the economics of
  agricultural policy”. In: American Journal of Agricultural Economics 92.2, pp. 403–423.
Willer, H., J. Lernoud, and R. Home (2013). The World of Organic Agriculture: Statistics
  and Emerging Trends 2013. International Federation of Organic Agriculture Movements
  (IFOAM).
Zangl, I. (2012). Land-use conflicts at the food-energy nexus. Institutional analysis, sustain-
  ability appraisal and Agrophotovoltaic as a mitigation strategy. Master thesis, University
  of Freiburg.


                     VII