An Assessment of
Economics Report 105
Food and Resourac Economic Department
Agricultua Experiment Stations
Institute of Food and Agricultural Sciences
University of Florida, Gainesville 32611
Timothy G. Taylor
J. Walter Milon
Clyde F. Kiker
A simulation model is developed to assess the economic feasibility
of utilizing photovoltaic arrays to power irrigation systems in Florida.
The model can be applied to any type of irrigation system. Furthermore,
a variety of economic and institutional scenarios can be specified by
means of user input variables. Simulation results for permanent over-
head systems irrigating citrus suggest that the use of photovoltaic
arrays to power irrigation systems may be economically feasible as
early as 1984.
Key words: solar energy, photovoltaic array, present value, simulation.
TABLE OF CONTENTS
ABSTRACT . . . . . . .
INTRODUCTION . . . . . .
BASIC CONCEPTS AND ASSUMPTIONS . . . .
Conventional System Costs . . . .
Photovoltaic Powered Irrigation System Costs . .
Economic Feasibility Criterion . . .
SIMULATION MODEL FOR ASSESSING THE ECONOMIC FEASIBILITY OF
PHOTOVOLTAIC POWERED IRRIGATION SYSTEMS. . .
Energy Requirement and Array Design Component. .
Annual Array Generation and Irrigation Energy Demand Cc
Economic and Institutional Component ... . .
Present Valuation Component. . . . .
AN APPLICATION TO CITRUS IRRIGATION. . . .
Economic and Technical Assumptions . ..
Simulation Results . . . . .
CONCLUSIONS . . . . . .
REFERENCES . . . . . .
APPENDIX A--PHOTOVOLTAIC SYSTEMS . . . .
APPENDIX B--CALCULATION OF PHOTOVOLTAIC SYSTEM
PRICES . . . . .
APPENDIX C--SAMPLE SIMULATION PROGRAM. ..
COSTS AND ELECTRIC
. . . .
LIST OF TABLES
1 Estimated cost per peak kilowatt of photovoltaic systems
1981-2000. . . . . ... ...... 16
2 Economic scenarios for the photovoltaic feasibility
simulation model . . . . ... .19
3 Estimated first year in which photovoltaic irrigation
systems are economically feasible. . . ... 20
LIST OF FIGURES
1 Basic flow diagram of photovoltaic powered irrigation
system feasibility simulation model. . . ... 12
2 Estimated differences in the discounted costs of
photovoltaic powered and conventional electric powered
irrigation systems for this optimistic scenario and
selected by back ratios. . . . . ... 21
3 Estimated differences in the discounted costs of
photovoltaic powered and conventional electric powered
irrigation systems for the base scenario and selected by
back ratios . . . . ... ... 23
4 Estimated differences in the discounted costs of
photovoltaic powered and conventional electric powered
irrigation systems for the pessimistic scenario and
selected by back ratios. . . . . ... 24
A-i Simplified schematic or a photovoltaic powered irrigation
system . .. . . . . .... 30
A-2 Mean, minimum and maximum hourly solar insolation levels
for Orlando/Herndon airport. . . . ... ..31
AN ASSESSMENT OF THE ECONOMIC FEASIBILITY OF POWERING
CITRUS IRRIGATION SYSTEMS IN FLORIDA WITH PHOTOVOLTAIC ARRAYS
Timothy G..Taylor, J. Walter Milon and Clyde Kiker
The use of supplemental irrigation has become an increasingly common
practice in the production of citrus in Florida. With relatively
inexpensive energy prices prior to the 1970s, and more intensive culti-
vation practices, irrigation has been a profitable operation for most
citrus producers. However, the rise in energy prices since 1970 has
threatened to reduce the economic benefits to citrus producers resulting
from irrigation. Anaman [1981,75] has estimated that the economic bene-
fits from irrigation could be completely dissipated if the price of
energy relative to citrus prices increases threefold from current 
The spectre of further increases in energy prices coupled with
shortages in the supplies of some fossil fuels has provided the impetus
to investigate the potential for utilizing fossil fuels more efficiently
and using alternative energy sources in agricultural production. One
source which appears to have considerable promise as a power supply for
irrigation is solar energy. The use of photovoltaic (PV) arrays to
produce electricity for powering irrigation pump motors is currently
technologically feasible [Matlin and Katzman, 1978]. The mere fact that
photovoltaic arrays can be used to power irrigation systems, however, is
not sufficient to conclude that such systems provide a viable alternative
to current conventional power sources. Economic feasibility must also
ISee Appendix A for a description of PV systems and their use
TIMOTHY G. TAYLOR and J. WALTER MILON are assistant professor of
food and resource economics. CLYDE KIKER is associate professor of
food and resource economics.
The purpose of this report is to describe the results of a study
on the economic feasibility of using photovoltaic arrays to power irri-
gation systems in Florida. For this analysis a photovoltaic system is
assumed to be economically feasible if the discounted cost of such a
system over a given period of time is less than the corresponding dis-
counted cost of currently used conventional systems. Following Matlin
and Katzman , the initial year in which photovoltaic ,co" will
be economically feasible is determined under a variety of economic and
The use of photovoltaic arrays for powering irrigation systems
represents a substantial change in the structure of irrigation energy
costs. The cost structure of powering irrigation systems with currently
used conventional fuels (e.g., electricity, diesel fuel, etc.) is one
that entails a moderate fixed cost in the pump-power unit, but rather
substantial variable fuel costs [Harrison, 1976]. Conversely, the cost
structure of irrigation systems powered by photovoltaic arrays is
characterized by a substantial fixed cost in the pump power-unit, but
very low (possibly negative) variable energy costs. This difference in
energy cost structure is significant in that farmers using photovoltaic
arrays reduce the direct impact of rising conventional fuel prices on
irrigation energy costs.
While such a shift in the composition of irrigation energy costs
may be desirable, the high fixed cost of photovoltaic systems is currently
prohibitive. At present, photovoltaic system costs are approximately
$10.75 per peak watt [Litka et al., 1981]. Thus, the fixed investment
cost of an array of sufficient size to power an irrigation system would
not be justified economically. System costs, however, are expected to
decline substantially as commercial production of these systems proceeds
The key factors in determining the economic feasibility of powering
irrigation systems with photovoltaic arrays are the cost of these systems,
the rate at which conventional energy prices increase and the rates
utilities pay for electricity purchased from dispersed energy systems.
2Dispersed energy systems denote systems which produce energy, in
this case electricity, at the site of use. Under Federal Energy
To analyze the effects of these factors on the economic feasibility of
photovoltaic systems several scenarios describing future economic condi-
tions are simulated.
The scenarios differ in the degree to which future economic events
are conductive to establishing the economic feasibility of photovoltaic
powered irrigation systems. Thus, the optimistic scenario assumes a
rapid decline in the cost of photovoltaic arrays and a rapid rise in
conventional fuel prices. Conversely, the pessimistic scenario tsPumes a
very slow decline in array cost and no real increase in conventional
fuel prices. The base scenario assumes a moderate decline in array cost
and a moderate increase in fuel prices. For all scenarios, the ratio of
the price utilities pay for electricity relative to the prices at which
they sell electricity ("buyback" ratio) is varied over a range of values.
BASIC CONCEPTS AND ASSUMPTIONS
Any irrigation system is composed of two basic components. The
water dispersal system structure (e.g., pipes, sprinklers, support
structures) and a pump-power unit. A variety of energy sources can be
used to drive the pump-power unit. The two most common types of energy
used in Florida are diesel fuel and electricity [Stanley et al, 1980].
From a technical standpoint, the type of energy used to drive the pump-
power unit is, in most cases, independent of the type of system structure.
Thus, for example, a permanent overhead system can be powered by an
electric motor or a diesel engine [Stanley et al., 1980].
Given this independence between pump-power units and the corres-
ponding energy source, and water dispersal system structure, an assess-
ment of the economic feasibility of utilizing photovoltaic arrays to
power irrigation systems is fairly straightforward. If the discounted
cost of currently used conventional alternatives over the useful life
of the photovoltaic system, economic feasibility can be established.3
Regulation Commission (FERC) regulations, electric utilities are required
to purchase surplus electricity from dispersed producers.
3The discussion here, and that which follows, assumes that irrigation
as a cultivation practice is economically justified. Give this assumption
The estimation of discounted costs for conventionally powered and
solar powered pump-power units over some period of time requires a number
of assumptions regarding the behavior of energy prices and other economic
variables over time. Give that photovoltaic arrays are also dispersed
generators of electricity, issues involving the resale of electricity and
utility pricing policies must also be considered. The following discussion
outlines the basic manner in which the discounted pump-power unit and
energy costs are utilized to evaluate the economic feasibility of photo-
voltaic powered irrigation systems.
Conventional System Costs
The calculation of the discounted cost of a conventionally powered
irrigation system is straightforward. This discounted cost of an irri-
gation system with an investment life of T years is composed of a fixed
investment cost and a stream of variable energy costs.
The fixed cost investment of a irrigation system purchased in year
j can be represented by
ICC = SC + PPU j 1,...,J (1)
ICC = Fixed cost investment in year j
SC = cost of water dispersal system structures purchased in year j
PPUk cost of pump-power unit using fuel type K,
k = g (gasoline), e (electricity), d (diesel), 1 (1-p gas)
purchased in year j
Annual variable energy costs for a system using energy type k, k = g, e,
d, 1 are given by
and the fact that the use of photovoltaic arrays involves no change in the
way irrigation is practiced, the economic feasibility of these systems can
be assessed by only examining costs relating to the pump-power units and
commensurate energy costs.
A detailed discussion of the measurement and calculation of these
costs are contained in Appendix B.
k k k
VCECt = P E (2)
t t t
VCECt = variable energy cost of a conventionally powered system in
P = unit price of fuel type k in year t
E = amount of energy type k used for irrigation in year t
The discounted cost of an investment in an irrigation system powered by
fuel k can be written as
DCC. = SC + PPU. + E D (VCEC ) j = 1,...,J (3)
S3 J t t
DCC = discounted cost of a conventional irrigation system pruchased
in year j
D = discounting factor, D = (l+r)t and r denotes the real
Equation (3) provides a means of computing the discounted total cost
of irrigation over a period of T years assuming the initial investment
is made in year j, j + 1, and so on. While the theoretical construction
of equation (3) is relatively simple, obtaining values for the included
variables is a more difficult matter. Consider for example an invest-
ment life of 20 years (T = 20) and the investment can be undertaken in
any of 20 succeeding years (J = 20) beginning in 1980. Fixed investment
costs must be estimated for the next 20 years and energy prices and the
annual amount of irrigation must be estimated for the next 40 years.
Thus, the variables in equation (3) could have many different values
depending on one's forecasts about future prices.
Photovoltaic Powered Irrigation System Costs
Although the fixed cost structure of a photovoltaic powered irri-
gation system is similar to that of a conventionally powered system, the
variable energy cost structure is considerably different. The difference
is that a photovoltaic system can produce electricity. During periods
of time when irrigation is not needed, the electricity produced by the
system can be sold to the utility.5
The fixed cost investment for a photovoltaic powered irrigation
system purchased in year j can be written as
ICS = SC. + PPU3 + PC. j = 1,...,J (4)
ICS. = fixed investment cost of a photovoltaic irrigation system
purchased in year j
SC. = cost of water dispersal system structures purchased in year j
PPU. = cost of electric pump-power unit purchased in year j
PC. = cost of a photovoltaic system purchased in year j
The similarity of fixed investment costs between conventional and
photovoltaic powered systems can be seen by comparing equations (1) and
(4). If the conventional system is electrically powered, the fixed cost
structures are identical with respect to water dispersal system structures
cost and pump-power unit cost, differing only in that equation (4) con-
tains the additional fixed cost of the photovoltaic array. Even if the
systems are powered by different types of energy, the water dispersal
system structures cost will be identical. Therefore, the economic
feasibility of photovoltaic systems depends on whether the decrease in
variable energy costs and surplus electricity sold to the utility can
offset the additional fixed cost of the photovoltaic system.
The variable energy costs of a photovoltaic irrigation system can
be expressed by
VSECt Pe Ee RP SAG (5)
t t t t t
VSECt = variable photovoltaic system energy costs in year t
Electricity produced by the array can also be used for other on-
farm activities. In this report it is assumed that all surplus electri-
city produced by the photovoltaic system is sold to a utility grid.
This assumes that comparisons are being made for similar types
of irrigation systems (e.g., permanent overhead, etc.). No attempt is
made in this analysis to compare different types of irrigation systems.
P = unit price of electricity in year t
Ee = electricity purchased to supplement array production in
RPt = resale unit price of electricity paid to dispersed producers
for electricity in year t
SAGt = quantity of surplus electricity produced by the photovoltaic
array and sold to the utility in year t
The variable energy cost structure of a photovoltaic system differs con-
siderably from that of a conventional system. The first term on the
righthand side of equation (5) reflects the fact that a photovoltaic array
cannot supply all of the electricity necessary to power the irrigation
system at all times. This reflects the dependence of the output of a
photovoltaic system on incoming solar insolation levels (see Appendix A)
and the fact that irrigation may also occur during the night. In the
absence of battery storage of electricity, power must be purchased from
the utility to supplement the array power.
The second term on the righthand side of equation (5) represents
the revenue from sale of surplus electricity to the utility. This sur-
plus electricity is generated during time periods when no irrigation
occurs and, during irrigation, whenever the photovoltaic array produces
an amount of electricity greater than that required to power the pump
motor. If the value of this resale of surplus electricity is greater
than the value of purchased supplemental electricity, the variable energy
costs of a photovoltaic system will be negative.
The discounted cost of a photovoltaic powered irrigation system
purchased in year j and having an investment life of T years can be
expressed as the sum of equations (4) and (5).
DCS. = SC. + PPU + PC. + D (VSECt) J = 1,...,J (6)
3 3 3 3 t=jt
7The use of battery storage of electricity is not included in
the simulation model.
DCSj = discounted cost of a photovoltaic powered irrigation system
purchased in year j
D = a discounting factor, D = (1+r)t and r denoting the
This expression provides a means of computing the discounted cost of
purchasing and utilizing a photovoltaic powered irrigation system for
T years assuming the initial investment year occurs in years j, J+1, and
so on until year J.
As in computing the similar discounted cost for conventionally
powered systems, prices and costs must be estimated over a considerable
length of time. Estimation of prices for equation (6) is further com-
plicated by institutional factors affecting the price utilities will
pay for electricity produced by dispersed systems.
The price utilities are required to pay for electricity produced
by dispersed systems must reflect the "avoided cost"8 of producing an
equivalent amount of electricity. In addition, the Public Utilities
Regulatory Policies Act (PURRA) has provided the incentive for utilities
to move in the direction of pricing electricity according to the cost
of production in the form of time-of-use (TOU) rates [Milon, 1981].
Under TOU rates, electricity consumed during peak demand periods is more
expensive than that consumed during off-peak demand periods. Thus, the
increased cost of producing electricity during peak periods is reflected
in higher electric rates.
The implication for photovoltaic powered irrigation systems is that
if surplus electricity production occurs during peak electric demand
periods, avoided cost would be much higher than if surplus electricity
production occurred during off-peak periods. Thus, if the prices utili-
ties pay for electricity produced by dispersed systems reflect these
costs, the value of surplus electricity produced by photovoltaic arrays
will depend on the time period in which the surplus is produced. The
8The precise meaning of avoided cost is still unclear and currently
subject to litigation [Norman, 1981]. The notion of avoided cost is
intended to reflect the fact that dispersed energy systems, by producing
and selling electricity to electric utilities, enabled the utilities to
avoid incurring the cost of producing an equivalent amount of electricity.
exact rates utilities will pay for electricity from dispersed systems
unfortunately is still unclear [Norman, 1981].
Economic Feasibility Criterion
Equations (3) and (6) give expressions for obtaining the discounted
cost of purchasing and operating a conventionally powered and a photo-
voltaic powered irrigation system for T years assuming the initial
investment occurs in year j, j=l,...,J. Photovoltaic systems would be
an economically feasible investment in year j, if
DCS. < DCC j = 1,...,J (7)
The first year of economic feasibility will be that year in which the
discounted cost of a photovoltaic system is less than or equal to that
of a conventionally powered system. Substituting for DCS. and DCC
in equation (7) yields
SC + PPU + PC. + E Dt(VSECt) < SC. + PPU. +
t J J t t 3 3
E Dt(VCECt) (8)
where all terms retain their original definitions. Upon simplification
and rearranging terms, equation (8) can be rewritten as
k e T+j
-PC. + (PPU PPU.) + E D (VCEC VSEC ) > 0 (9)
3 t=j t t t -
j = 1,...,J
In this form, the importance of the revenue earned from the sale of
surplus electricity can be seen. Given the intermittent nature of
irrigation, the sign of VSECt (equation (5)) is almost surely negative.
Thus, the effect of this term in equation (9) is to offset the additional
fixed cost (-PC ) attributable to the photovoltaic system.
Equation (8) also facilitates the discussion of several additional
aspects involving photovoltaic system feasibility. First, the effects
of declines in the cost of photovoltaic arrays can be seen. The only
significant negative term in equation (9) is the PC. term. Given that
the cost of photovoltaic systems in the future is expected to decline,
equation (9) demonstrates that the rate of decline will be a significant
factor in determining when photovoltaic irrigation systems will be eco-
nomically feasible. In addition, VSEC and VCEC enter equation (9)
with a positive sign (note VSEC < 0 which implies -VSEC > 0). Thus,
increases in conventional fuel prices or the value of electricity sold
to the utility also offset the fixed array cost.
Examination of equation (9) also reveals that the fixed cost of
water dispersal system structures (SC.) drops out of the equation when
similar irrigation systems are being compared. This could also occur
if different system types have similar structure costs. In addition,
when the pump-power units being compared are both electric, ;he cost of
these units (PPUe) also drop out of equation (9). The economic feasi-
bility of photovoltaic systems then rests primarily on a comparison of
the discounted energy costs of irrigation over a fixed time horizon.
SIMULATION MODEL FOR ASSESSING THE ECONOMIC FEASIBILITY OF
PHOTOVOLTAIC POWERED IRRIGATION SYSTEMS
This section describes the computer simulation model used to deter-
mine the first year in which photovoltaic powered irrigation systems
will be economically feasible. Because the economic feasibility of these
systems depends on a number of assumptions regarding energy price increases,
photovoltaic system costs, irrigation levels, and other technical and
economic factors, the simulation model is designed to facilitate a wide
variety of assumptions via user specified input variables.
The model can be used to simulate a number of different types of
irrigation systems by appropriately specifying a set of technical input
variables. However, the model can only compare photovoltaic powered
systems with conventional electric powered systems. The simulation
model is composed of four basic components (Figure 1),whose functions
The term (PPUk PPUe) k = g,e,d,l is probably positive. However,
even if it is negative, the -PC. term would dominate this term in equa-
are discussed in the following sections. In addition, the underlying
economic and technical assumptions are discussed.
Energy Requirement and Array Design Component
The primary function of this component is to determine the pump
motor power requirements for a specific type of irrigation system and then
determine the size (m 2) of the photovoltaic array necessary to power the
system. The input variables for this component include acre inches of
water per application (gross), total acres irrigated, hours per day
irrigating, days to complete one irrigation and total dynamic head. Values
for these variables depend on the type of irrigation system, irrigation
strategy and geographic locations which can be obtained from Harrison
 and Stanley et al. .
Given values for these variables, simple engineering equations
[Harrison and Choate, 1969] are utilized to calculate the necessary
pumping rate (GPM) and the continuous brake horsepower (BHPC) required
at the pump shaft. These calculations assume a pump efficiency of 75
percent and a motor efficiency of 88 percent [Pair et al., 1975]. The
estimated BHPC is then converted to a continuous kilowatts (1KW) per hour
electrical demand using standard conversion values. Because the electri-
cal demand of the pump motor is uniform over time, this value provides an
estimate of continuous kilowatt hours (KWH) per hour required to power
the system. This estimate is utilized in obtaining the necessary size
of the photovoltaic array.
The present model does not provide for battery storage of electri-
city produced by the photovoltaic system. Given the variation in solar
insolation level during the course of each day (see Appendix A) it is
not reasonable (in terms of cost) to design a system which could hypo-
thetically provide full power to the system during all sunlight hours.
Thus, the design rule used in the simulation model is that the average
hourly output of this photovoltaic array equals the continuous KWH
per hour demand of the pump motor.
Using the Orlando/Herndon Solmet data [U.S. National Climatic
Center, 1980], a mean hourly solar insolation profile was estimated.0
10The Solmet data contains hourly surfact meteorological readings on a
S Technical user
I# of irrigations Energy
Tot. dynamic head .array
S Frequency -
S Acres Irrigation
system and Dynam
Operating time --photovoltaic evalua
L----- ------ j array
IScenario key I ____ Economic
I I .and
t rate institutional
Discount rate I
I Resale price s-
Figure l.--Basic flow diagram of photovoltaic powered irrigation system feasibility simulation
Assuming a total photovoltaic system efficiency of .069 [Litka et al.,
1981] the average hourly output of the photovoltaic array was estimated
at .03418 KWH/m2. By setting this expression equal to the continuous
KWH demand of the pump motor and solving for m the size of the photo-
voltaic array is obtained. The peak kilowatt (KWP) output rating of the
array is determined by dividing the size of the array (m ) by 12.5 m
This calculation is based on the photovoltaic array in operation at the
Florida Solar Energy Center [Litka et al., 1981].
The assumptions utilized in determining the size of the photovoltaic
system imply that during a day in which the irrigation system is func-
tioning, there will be a period when the photovoltaic system's electri-
cal output must be supplemented by purchase electricity and a period of
time when the system is generating a surplus of electricity which can be
sold to the utility. In addition, if irrigation occurs at night, all of
the electricity used to power the system must be purchased. During time
periods when no irrigation is occurring, the entire output of electricity
produced by the photovoltaic system can be sold to the utility. Given
the intermittent nature of irrigation, it is expected that surplus gen-
eration sold to the utility will exceed supplemental electric purchases
during the year.
Annual Array Generation and Irrigation Energy Demand Component
The annual amount of electricity produced by the photovoltaic system
is obtained by multiplying the annual amount of solar insolation per m
by the estimated system operating efficiency (.069). This results in an
average expected system output of 118.1949 KWH/m2 annually. To obtain
total annual system output, the size of the photovoltaic system (m 2) is
multiplied by this value. For example, an 800 m array (64 KWP) would
annually produce approximately 94,556 KWH of electricity.
The amount of electricity needed for irrigation is estimated by
first determining the total number of KWH necessary to complete one
irrigation. This estimate is then multiplied by the number of
number of variables from 1952 to 1974. Data pertaining to global solar
radiation on a tilted surface were used in calculating the hourly solar
irrigations per year to obtain the annual quantity of electricity used
for irrigation. The annual number of irrigations per year is a user
specified input variable to the program.
Net generation of the photovoltaic system is calculated by sub-
tracting the annual electrical demand for irrigation from the annual
total electrical output of the system. It should be noted that measuring
net generation in this manner differs somewhat from the theoretically
"correct" measurement as implied by equation (5). The error resulting
from this approximation in the calculation of net generation can, however,
be shown to be very small.
Economic and Institutional Component
The function of this component is to estimate the change over time
in the economic variables used in calculating and comparing the discounted
energy cost of photovoltaic powered and conventional electric powered
irrigation systems. The basic input variables to this component are the
escalation rate of electricity KWH charges, the discount rate, the price
utilities must pay for electricity purchased from dispersed systems, and
the rate of decline in the cost ($/KWH) of photovoltaic arrays. All
prices and costs are expressed in terms of 1980 dollars and all rates of
change are in real terms. Furthermore, it is assumed that time-of-use
(TOU) electricity rate structures are in effect.
Electricity rates are assumed to escalate in an exponential fashion
with the real annual escalation rate specified by the user. The 1980
base price of electricity is set at $0.03604 per KWH. This price repre-
sents the off-peak price of purchased electricity. Under the assumption
that all irrigation occurs off-peak, the annual cost of electricity for
a conventional system is obtained by multiplying the annual quantity of
electricity used for irrigation by the corresponding "forecast price".
The rates utilities must pay for electricity purchased from dispersed
systems is assumed to be proportional (via the buy-back ratio) to the
price at which utilities sell electricity. The buy-back ratio is a user
specified variable which reflects institutional decisions regarding the
precise definition of avoided cost. Thus a buy-back ratio greater than
one implies that avoided costs are realized during peak periods.
Conversely, a buy-back ratio of less than one implies the institutional
decision that avoided costs were realized during off-peak periods.
Because the buyback price of electricity is tied to the price utilities
charge, it is assumed that this price increases over time at the same
rate as utility electricity prices.
This component of the model also contains three different time
paths along which the cost of photovoltaic systems may follow. Each
path reflects a differing view as to the rate at which technological
innovation and commercial production techniques will be reflected in
lower system costs. Costs under each scenario have a 1980 base cost of
$10,750 KWP [Litka et al., 1981] and are projected over a twenty year
period beginning in 1980 (Table 1).
Cost scenario I is obtained by splicing two exponential functions
such that the 1986 system cost is $2026.50/KWP and the year 2000 system
cost is $945.70/KWP (see Appendix B). Scenario II is also obtained by
splicing two exponential functions. Under this regime total system cost
declines to $8062.50/KWP 1986 and to $2026.50/KWP in the year 2000.
The final scenario (III) assumes a simple exponential decline to a total
system cost of $945.70/KWP. The 1986 system cost is $5184.50/KWP.
Cost Scenario I is extremely optimistic in reference to the fact
that photovoltaic system costs decline substantially by 1986. This
scenario is very similar to Department of Energy (DOE) projections
[Smith, 1981]. There is considerable uncertainty in the rate at which
technological innovation and improved commercial production techniques
will be realized in the form of lower system costs, however. Thus,
scenarios II and III are included to admit several less optimistic array
cost paths over time. The inclusion of such diverse time paths for
photoltaic system costs enables an examination of the sensitivity of
the economic feasibility of these systems to cost behavior over time to
Present Valuation Component
This component of the model assimilates all of the information con-
tained in the program and evaluates an expression similar in form to
equation (9). Thus, assuming the investment in a photovoltaic system
cost per peak kilowatt of photovoltaic systems
Year I II III
1980 10,750.00 10,750.00 10,750.00
1981 8,140.13 10,246.73 9,519.75
1982 6,163.89 9,767.02 8,430.29
1983 4,667.43 9,309.77 7,465.52
1984 3,534.28 8,873.93 6,611.15
1985 2,676.24 8,458.49 5,854.55
1986 2,026.50 8,062.50 5,184.55
1987 1,552.03 4,972.36 4,591.22
1988 1,494.00 4,640.62 4,065.80
1989 1,438.14 4,331.01 3,600.50
1990 1,384.36 4,042.06 3,188.45
1991 1,332.60 3,772.38 2,823.56
1992 1,282.78 3,520.70 2,500.43
1993 1,234.81 3,285.81 2,214.27
1994 1,188.64 3,066.59 1,960.87
1995 1,144.20 2,861.99 1,736.46
1996 1,101.42 2,671.05 1,537.74
1997 1,060.24 2,492.85 1,361.76
1998 1,020.59 2,326.53 1,205.92
1999 982.43 2,171.31 1,067.91
2000 945.70 2,062.50 945.70
Costs are expressed in 1980 dollars.
is made in succeeding years from 1980 to 2000, the discounted cost of
photovoltaic systems are compared with the discounted energy cost of a
conventional electric powered irrigation system. Economic feasibility
is said to be established in the first year in which an investment in a
photovoltaic system has a discounted cost less than the corresponding
cost of a conventional electric powered system.
From the above discussion it should be apparent that most of the
technical variables entered into equation (9) such as the number of
irrigations per year, and the overall irrigation strategy remain fixed
over time. Given the variation in weather and other factors over time,
it is highly unlikely that any of these technical variables are in fact
constant. Similarly, escalation rates in electricity prices almost
certainly vary from year to year rather than exhibiting some constant
real rate of increase. However, when evaluating an investment over
a considerable length of time, detailed information on the behavior of
technical and economic variables can seldom be known with a high degree
of certainty. In such circumstances, the decision maker must formulate
expectations concernin g how factors affecting the investment decision
will change over time. Within the present context, the fixed nature of
the technical variables and rates of change in the economic variables
can be construed as representing a given set of expectations. Thus,
the economic feasibility criterion estimated in this component can be
considered as based on various technical and economic expectations
specified in terms of the simulation program's input variables.
AN APPLICATION TO CITRUS IRRIGATION
The simulation model was utilized to examine the economic feasibility
of utilitizing photovoltaic arrays to power permanent overhead citrus
irrigation systems in the Ridge area of central Florida.1 The initial
investment year was varied from 1980 to 2000 assuming an investment life
of 20 years. The choice of a permanent overhead type system rests mainly
on the fact that about 90 percent of the acreage utilizing these systems
11Counties located in the Ridge area of Florida can be found
in Stanley et al. [1980, p. 4].
use electricity to power the pump motor [Stanley et al., 1980]. A
sample simulation program is presented in Appendix C.
Economic and Technical Assumptions
Utilizing data contained in Harrison , a hypothetical per-
manent overhead system irrigating 40 acres of citrus was modeled. Each
irrigation application was defined as two acre inches (gross of water
applied in a period of six days with the system operating 18 hours per
day. A total of six applications per year was assumed (12 acre-inches
per year) and held constant throughout the program. Assuming a total
dynamic head of 250 feed [Stanley et al., 1980], the motor size necessary
to power the system was estimated to be 32 HP. When in operation, the
motor required a continuous electrical load of approximately 24 KWH/H.
Based on the photovoltaic system design rules discussed previously,
the array size necessary to power the irrigation system was calculated
to be approximately 766 m2 (61KWP). Under average solar insolation con-
ditions this system is estimated to produce about 89,865 KWH of electri-
city annually. The estimated annual amount of electricity needed for'
irrigation is approximately 15,510 KWH, yielding a net generation of
electricity for resale to the utility of 74,355 KWH.
Three basic economic scenarios were simulated for the irrigation
system described above (Table 2). The scenarios (base, optimistic, and
pessimistic) differ primarily on the basis of expectations regarding the
rate at which the cost of photovoltaic systems declines over time and
the real rate of increase in electricity KWH rates over time. The
scenarios also differ in the degree to which economic and technical
assumptions are amenable to establishing the economic feasibility of
photovoltaic powered irrigation systems. For each of these scenarios
the buy-back ratio linking the price of resale electricity to utility
rates is varied from 0.25 to 1.5 in 0.25 increments.
For each of the three economic scenarios presented in Table 2, a
total of six simulations were run. This resulted in a total of 18
different model scenarios. In all but two cases, the discounted cost
scenarios for the photovoltaic feasibility simulation
Buy-back Discount Fuel escalation
Scenario Target costs ratio rateb rateb
ratio rate rate
Base 1986; 4,740/KWP 0.25-1.50 .06 .06
Optimistic 1986: 2,026.50/KWP 0.25-1.50 .06 .06
Pessimistic 1986: 8,062.50/KWP 0.25-1.50 .06 .00
aFor each scenario, the buy-back ratio is varied between these
limits in increments of 0.25.
The discount rate and annual rate of increase in electricity rates
are expressed in real terms.
of using photovoltaic arrays to power irrigation systems became less
than the discounted cost of purchasing electricity for powering irriga-
tion systems before the year 2000 (Table 3).
Table 3.--Estimated first year in which photovoltaic
irrigation systems are economically feasible
Scenario 0.25 0.50 0.75 1.0 1.25 1.50
Optimistic 1990 1987 1986 1985 1985 1984
Base 1997 1985 1993 1992 1991 1990
Pessimistic 2000+ 2000+ 1998 1997 1995 1994
Simulation results for the optimistic scenario, which assumed a
rapid decline in photovoltaic system costs and a significant increase
in electricity rates, indicated the first year of economic feasibility
could occur as early as 1984 if the buy-back ratio was 1.50. Generally,
each increase of 0.25 in the buy-back ratio moved the initial year of
economic feasibility toward the present by 1 to 2 years. Increasing the
buy-back ratio from 0.25 to 0.50 changed the initial year of feasibility
from 1990 to 1987 whereas increasing the buy-back ratio from 1.25 to 1.50
changed the initial year of economic feasibility from 1985 to 1984. The
estimated differences in the discounted costs of photovoltaic powered
and conventional electric powered systems assuming the investment is
made in succeeding years from 1980 to 2000 are plotted in Figure 2 for
several buy-back ratios.
The base model scenario was characterized by a moderate decline in
the cost of photovoltaic systems over time. Similarly, the annual
increase in utility electric rates was also moderate, increasing at an
annual real rate of 2 percent. As with the optimistic scenario, as the
buy-back ratio increased, the first year of economic feasibility moved
closer to the present. With the buy-back ratio at 0.25, the initial
year of feasibility was 1997, whereas a buy-back ratio of 1.50 resulted
in photovoltaic systems being economically feasible in 1990. In general,
each 0.25 increase in the buy-back ratio moved the initial year of
0 :------ *: l Year
84 8 92 96 2000
Figure 2.--Estimated differences in the discounted costs
of photovoltaic powered and conventional electric
powered irrigation systems for this optimistic
scenario and selected by back ratios
feasibility up to one to two years. Figure 3 plots the estimated differ-
ence in the discounted cost of the two systems for each investment year
beginning in 1980.
A very slow decline in photovoltaic system costs characterized the
pessimistic scenario. Furthermore, no real increase in utility electric
rates was allowed. Under this scenario, the first year of economic
feasibility for buy-back ratios of 0.25 and 0.50 does not occur until
after year 2000. With a buy-back xatio of 0.75 the initial year of
feasibility is 1998. The effect of increasing the buy-back ratio on the
initial year of economic feasibility is similar to the preceding scenarios.
Each 0.25 increase in the ratio moves the initial year of feasibility up
by one to two years. For each investment year, the difference is dis-
counted costs of the two systems under comparison is plotted in Figure 4.
The importance of the cost behavior of photovoltaic systems over
time can also be inferred from the results of the simulation. For given
buy-back ratios, the base model cost projections result in initial
feasibility occurring an average of five years sooner than if system
costs follow the pessimistic cost projections. Similarly, optimistic
cost projections result in the initial economic feasibility of photovoltaic
systems occurring an average of six years sooner than if base cost pro-
jections held. These results imply that the effects of commercializing
the manufacture of photovoltaic arrays, and the ensuing cost declines,
have a significant impact on when photovoltaic powered irrigation systems
are economically viable.
Overall, the results of the simulation model appear internally
consistent. Changes in the buy-back ratio generally have the same effect
on the initial year of economic feasibility for a wide range of changes
in system costs over time. Furthermore, the effects of changing the
cost projections for system cost generate similar responses in the initial
year of feasibility for differing buy-back ratios. Because the analysis
of these types of problems require considerable abstraction and assumptions
in the absence of any statistical measures, such consistency is extremely
significant in giving the above results considerable credence.
S ; -1 Year
85 90 95 2000
Figure 3.--Estimated differences in the discounted costs
of photovoltaic powered and conventional electric
powered irrigation systems for the base scenario
and selected by back ratios
Figure 4.--Estimated differences in the discounted costs
of photovoltaic powered and conventional electric
powered irrigation systems for the pessimistic
scenario and selected by back ratios
Agricultural production in Florida is very energy intensive. Be-
cause of this, the need to investigate means of countering the rising
costs of energy are paramount. It appears that the solution to the
problem rests in either altering production practices to utilize less
energy with greater efficiency or finding alternative sources of energy
which can be used in agricultural production activities. In .:egards to
the latter possibility, the results of this analysis have shown photo-
voltaic systems to have considerable promise as a means of providing
electricity to power irrigation systems.
The feasibility of utilizing photovoltaic systems for such purposes
does not rest on the development of technology which can produce electri-
city from sunlight. Adequate technology already exists. The results of
the simulations have shown that the cost of producing these systems has
a significant effect on when photovoltaic systems will be economically
feasible. If commercial production of photovoltaic systems results in
a rapid decline in cost, these systems will be economically feasible in
the mid- to late 1980s. Tf however, commercial production is slow to
develop or the cost of photovoltaic systems declines slowly, economic
feasibility is not likely until the mid- to late 1980s.
The cost of such systems is only one factor which will have an
effect on when photovoltaic powered irrigation systems will be economi-
cally viable. Institutional factors such as the buy-back ratio also have
been shown to have a significant impact on when these systems will be
economically viable. Decisions as to what rates utilities must pay for
electricity generated and sold by small decentralized producers can
change the first year of economic feasibility by as much as seven years.
The analysis presented here i not to be construed as definitive
in concluding that the use of Elhtovoltaic arrays to power irrigation
systems is a future certaiti: The promise of these systems, based
on the preceding results, is considerable. However, energy costs and
technological impediments may prevent photovoltaic irrigation systems,
or even irrigation as a cultivation practice, from being justified as
a sound economic practice in agricultural production,
Anaman, Jehu Asomanin. 1981. "Optimal Irrigation Strategies for
'Valencia' Citrus Crop in Florida." Unpublished MS. thesis, Food
and Resource Economics Department, Univ. of Fla.
Cheremisinoff, Paul N. and Thomas C. Regino. 1978. Principles & Appli-
cations of Solar Energy. Ann Arbor: Ann Arbor Science Publishers,
Harrison, Dalton S. 1976. Energy Management in Irrigation. Univ. of
Fla. Coop. Ext. Svc. Energy Conservation Fact Sheet EC-12.
1978. Irrigation Systems for Crop Production in Florida.
Univ. of Fla. Water Resource Council Bulletin WRC-8.
and Rush E. Choate. 1969. Selection of Pumps and Power
Units for Irrigation Systems in Florida. Univ. of Fla. Coop. Ext.
Sve. Cir. 330.
Katzman, Martin T. and Ronald W. Matlin. 1978. "The Economics of Adopt-
ing Solar Energy Systems for Crop Irrigation," American Journal of
Agricultural Economics 60(Nov.): 648-654.
Litka, Arthur, Robert Walker, Mukesh Khattar and Craig Maytrott. 1981.
"The FSEC Photovoltaic Residence: Initial Operational Performance."
Paper presented at AS/ISES Meeting, May 26-30, 1981.
Milon, J. Walter. 1981. "Alternative Energy Systems and Electric Rate
Reform," Public Utilities Fortnightly (June 4): 15-20.
Norman, Collin. 1981. "Renewable Power Sparks Financial Interest,"
Science 212(June 26): 1479-1481.
Pair, ClaudeH., Walter W. Hinz, Crawford Reid, and Kenneth R. Frost.
1975. Sprinkler Irrigation. Silver Springs, The Irrigation
Smith, Jeffrey L. 1981. "Photovoltaics," Science 212(June 26): 1972-
Stanley, James M., Clifton Taylor, William R. Summerhill, Jr. and Lionel
J. Beaulieu. 1980. "Citrus Energy Survey-Use Estimates and Con-
servation." Univ. of Fla. IFAS Energy Report No. 2.
U.S. National Climatic Center. 1980. "Hourly Solar Radiation Surface
Meteorological Observation." Solmet Users Manual, Vol. 1-~TD-9724).
Photovoltaic systems convert the energy in sunlight to electrical
energy. This conversion is accomplished by using "solar cells" which
are semiconductors constructed of cadmium or silicon. While a single
solar cell can produce only a small amount of electricity, these cells
may be interconnected to form large photovoltaic arrays capable of
producing a considerable amount of electrical energy [Cheremisnoff and
Regino, 1978]. Figure A-1 presents a basic schematic diagram of a
photovoltaic system which is being used to power an irrigation pump
motor. When sunlight (solar insolation) is received on the photovoltaic
array (solar cells) a direct current (DC) of electricity is produced.
This DC electricity is fed into an inveter which transforms the electri-
city from DC to alternating current (AC). The inverter also upgrades
the waveform of electricity produced by the array to be compatible with
the utility grid current and regulates current flows. During periods
when the electricity demand of the pump motor is greater than array
output, the inverter feeds supplemental power from the utility to the
pump motor. During periods when array generation exceeds the pump motor
demand, surplus electricity is routed into the utility grid.
Becuase photovoltaic systems rely on solar insolation to produce
electricity, the output of these systems will vary with the movement of
the sun both hourly and seasonally. Figure A-2 presents the average
hourly insolation for a solar day. The insolation profile shown in this
figure was estimated using the Orlando/Herndon Solmet Data [National
Climatic Center, 1980]. On average, a positive level of solar insolation
(KWH/m2) occurs between solar hours 6 and 19. This however varies
seasonally. As would be expected, the greatest insolation levels occur
at solar noon.
The shape of the insolation curve shown in Figure A-2 demonstrates
why an array with no electricity storage capabilities must use supple-
mental electricity purchased from the utility at certain times. Assume
that operation of the pump motor requires an array output of electricity
equivalent to .35 KWH/m2 of array. It can be seen that array output
per m is below this level during several hours of the day. During
per m is below this level during several hours of the day. During
A.C. KWH D.C. ELECTRICITY
TO/FROM AC A.C. TO PUMP
UTILITY ELECTRICITY ELECTRICITY MOTOR
Figure A-1.--Simplified schematic or a photovoltaic powered irrigation system
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Figure A-2.--Mean, minimum and maximum hourly solar insolation levels for Orlando/Herndon
these time periods, electricity must be purchased to supplement the
array output. During the remaining time periods the array output is
greater than required to power the pump and the surplus power is sold
to the utility grid. Furthermore, when no irrigation occurs, the entire
output of the photovoltaic system can be sold to the utility grid.
Given the intermittent nature of irrigation, a substantial amount of
surplus electricity can be generated and sold to the utility grid.
CALCULATION OF PHOTOVOLTAIC SYSTEM COSTS AND ELECTRIC PRICES
Photovoltaic system cost is calculated for a 20 year time period.
Cost is expressed in terms of $1980 per peak Kilowatt (KWP). The pro-
gram contains three distinct cost scenarios representing different rates
and magnitudes of array cost declines. All scenarios have a 1980 base
cost of $10,750/KWP.
The "pessimistic" cost scenario assumes that cost decreases will
come about very slowly, with costs declining less than 25 percent by
1986. Under this scenario, array cost is estimated by using a spliced
CKWPT(t) = d* 10750*EXP(-0.0479*(t-1)) + (1-d)*8062.5*EXP(-0.069
CKWP(t) = estimated photovoltaic systems cost ($/KWP) in year t
and d is a Kronecker Delta equal to 1 for t < 7 and 0 for t > 7. Thus,
the splice occurs in 1986 (t=7).
The "optimistic" cost scenario is also estimated by using a spliced
exponential function. This scenario assumes a rapid and significant de-
cline in photovoltaic system costs. By 1986, system cost is assumed to
decline by more than 75 percent. The estimated equation for this scenario
is given by
CKWP(t) = d*10750*EXP(-0.2781*(t-l)) + (1-d)*2026.5*EXP(-0.0381*
where all terms are defined as above.
The third cost scenario is characterized by a moderate decline in
the cost of photovoltaic systems. This scenario is moderate in that it
is approximately mid-way between the above two rather extreme cost pro-
jections. The moderate photovoltaic system cost decline is approximated
by the exponential function
CKWP(t) = 10750*EXP(-0.1215(t-1)) (B3)
where all terms retain their previous definitions. For all cost scenarios
the total system cost is estimated by multiplying the estimated cost per
PKW by peak kilowatt rating of the system.
The cost of electricity purchased from the utility C$/KWH) was
estimated over a 40 year time period (1980-2020). This was also true
for the rates utilities are required to pay for electricity produced
and sold by dispersed systems. Since this price is tied to utility rates
via the buyback ratio, it is only necessary to discuss the estimation
of the former prices.
The 1980 base price used in estimating future utility KWH rates is
$.03604/KWH. This rate is assumed to correspond to the off-peak KWH
charge for electricity. Estimation of KWH rates was accomplished using
the exponential function
PB(t) = 0.03604*EXP(n(t-1)) t = 1,...,41 (B4)
PB(t) = Estimated price per KWH of electricity in year t
n = Annual (real) rate of escalation in utility KWH rates. As
with the system cost estimates, all future estimates of the utility KWH
rates are expressed in term of $1980.
This appendix has presented the basic equations used to estimate
future photovoltaic system costs and electricity prices. The interface
of these equations with the user specified input variables and other
model components is depicted in the sample program contained in Appendix
SAMPLE SIMULATION PROGRAM
C THIS PROGRAM CALCULATES THE NET PRESENT VALUE OF INVESTING IN A SCLAR
C PHCTOVCLTAIC POWERED IRRIGATION SYSTEM IN YEAR J. THIS VERSION OF THE
C PFOGRAA CONSID=ES MAKING TH;- INVESTMENT IN EACH YEAR FROM 1990 TO
C YEAR 2000. THERE ARE TWO SETS OF VARIABLES WHICH MUST BF SPECIFIED BY
C THE USER: I RRI';ATION SUBMO EL VARILLES AND ECONOMIC VALUATIfN
C SUSMCDEL VAfIA.LES
C THE IRRIGATION SJROODEL VARIABLES ARE:
C AI=INCH=S OF VATER APPLIED PER IRRIGATION (GROSS)
C A=TOTAL ACRES TO 9E IRRIGATLD
C H=HCURS PER CAY IN NHICH IRRIGATION OCCURS
C D=0AYS TO COMPLETE ONE IRRIGATION (THIS SHOULD NOT EXCEED 75
C PERCENT OF THE IRRIGATION FREQUENCY)
C TOH=TCTAL DYNAMIC HEAD GF THE SYSTEM (FEET)
C TIR=NUMqER OF IRRTATTIONS PER YEAR.
C THE ECONOMIC SU3MODEL VARIABLES ARE:
C PRB=9ASE OF PERIOD MARKET PRICE OF ELECTRICITY (DOLLARS PER KWH)
C ASSUMING TIME OF DAY UTILITY RATES. IN THIS PRCGPAM. PRB IS A
C WEIGHTED AVERAGE PRICE OF THE PEAK AND OFF PEAK RATES.
C R=DISCOUNT FACTOR
C BR=EJY BACK CONSTRAINT OF PRGP3OTIONALITY FOR ELECTRICITY RESCLD TO
C THE UTILITY GRID
C TU=EXPECTED LLNG TERM ESCALTION RATE (ANNJAL) OF KWH CHANGES.
C Z=AERAY COST OUTLOOK. Z=I IMPLIES A PESSIMISTIC VIEW. Z=2
C IMPLIES AN OPTIMISTIC VIEW(D.O.Ee PROJECTIONS). Z=3 OEONOTES
C A MCCERATE COST DECLINE.
1 INTEGER Z
2 DIMENSION PK'P(21).PR(41)*P3(41),VRS(41A)TPE(41I)
C ENTER TME USER SPECIFIED VARIABLES AT THIS POINT
14 DC 5 1=1.21
16 5 CONTINUE
C THIS PCRTICN OF THE PROGRAM DEFINES THE PHYSICALL SYSTEM DESIGN CN THE
C BASIS CF SIMPLE ENGINEERING EQUATIONS GIVEN IN HARRISON AND CHOATE
C (196 ) AND UTILIZED THE ORLANOO/HERNOCN SOLMET DATA TAPE.
C THE PUMPING RATE IN GALLONS PER MINUTE IS GIVEN HY
C THE CCNTINUCUS 3RAKE HORSEPOWER REQUIRED IS CALCULATED BY
C THIS CALCULATICE ASSUMES A PUMP EFFICIENCY CF .75 AND MOTOR
C EFFICIENCY OF -55.
C THE CCTINrUOUS Kd DEMAND OF THE MOTOR IS GIVEN BY
C THE FCLLC.ING EQUATIONS CALCULATE THE PV ARRAY SIZE AND KWP
C RATING. THE CALCULATION IS: AZ(4**2)=(I/0.03143)-CKWe*
C THIS IS EQUIVALENT TO AZ=31.7L(2e*CKW.
C (NQTE:SYSTEM EFFICIENCY IS ASSUMED TO BE 0.069).
C THE FCLLC#ING EQUATIONS CALCULATE TOTAL ARRAY OUT'UT (TAO)
C (KWH). ELECTRICITY UTILIZED FOR INRIGATION(EDIR) AND NET ARRAY
C GENERATION FOR RESALE TO THE UTILITY GRID (AQN)
C NOTE: ANNUAL ARRAY GENERATION IS 116.1949KWH/(M*m*.).
23 EDI= (CKdI*r()f(D)*(TIRj
25 P 'IT 1OS5
26 105 FCFMAT(5X. 3HGPMF.5X.HHtHPC.9X3MHCKWg9X2HAZ.IOX,3HPKW,9Xs3TAQ)
27 WRITE(6, 1 04) O;nM HPC.CKW AZ.PKW.TAQ
2d 104 FCFuAT(FL3.2,2X.F10.2.2Xe.F 1.2.ZA.FIO.2.2X.rlo.22X.FIO.2e2XI
21 P ['RI1TI05
39 106 FCl'.AT (4X, HE IRGX, 3HAQNI
31 FRITE(6.1 7) EDIR.AON
J2 IC7 FCRV4T(F103.2.2X.FL0.2.2X)
C THE FCLLC'I:IG STATEMENTS GErNERATE THE ARRAYS UTILIZED IN THE
C ECONOMIC VALUATION' PORTION iF THE POGCRAYM
33 GC TO(50.60.701.Z
34 50 DC 100 J=1.2t
38 PKI (J) a( D*10750EXP( -0. 047947*M
I 9 (-0)8062.5*EXP(-0.069047M*4))
100 TAC( JI=PKW*PKWP(J)
CC TO 500
60 DC 200 J=t.21
PKP ( J )=(010750*EXP(-0.278099*M))
1 *( -0D)(206.5XP(-O.028 107*M) )
200 TAC( J)=lPKk*PKWP(J
GC TO 500
70 DC 300 J=1.21
PKPI( J )-L0750*EXP(-0.125 37*M)
300 TAC(J)=PK 'PKWP(J)
DC 101 1=1.41
00 102 1=141
PB( I =0.03604*EXP(TU*N
C THE FCLLC'ING SECTION COMPUTES THE NET PRESENT VALUE CP AN INVESTMENT
C IN YEAR J.
CC 110 J=1.21
DC 120 I=1.K
PR INT 103
108 FCFMAT(2Xl1HJ 6X.4HPKWP.9Xe3HTAC.9X2MHPV)
00 109 J=1.21
109 tRITE(6,11)t J.PKWP(J).TAC(J);PV(J)
111 FC;MAT(2X. 12o IXFIO.22ZX.FOe.2.2XeFIO.2s2X)
112 FCFMAT(2X. HI e7X2HPR O1Xe.2HPB
DO 113 1=1.41
113 w;ITE(6.l14) I. PR(I).PB(I)
4 4667 .4
10 143. 1
12 1332 (
16 1144. ,
17 1131 3 .
6 .3 1220
) 0 .9134
!0 695;6. 19
i9 62077. a
10 0 031040
17 0 054591
1C 0.104505 0.061845
11 3.110S67 0.065669
12 0.1i1729 0.069730
13 0.125115 0.074042
14 0.132552 0.073620
15 C.141067 0.033432
lu 0.149790 0.0Sd644
17 0.159052 0.094126
Id 0.168687 0.099946
19 3.179331 0.136126
20 0.1,0420 0.112659
21 0.2J2195 0.11S657
22 0.214698 0.127056
23 0.227974 0.134913
24 0.242071 0.143255
? 0.257040 0.152114
26 0.272;35 0.161520
27 0.23)812 0.171508
28 0.307733 0.132113
29 0.326762 0.1;3374
30 0.346968 0.205332
31 0.363423 0.213029
32 0..391205 0.231511
33 0.415356 0.245e27
34 0.4410 3 0.261028
35 0.463358 0.277169
36 0.497319 0.294309
37 0.528C72 0.212508
s3 0.560726 0.331832
39 0.595400 0.352351
40 0.632217 0.374139
41 0.671311 0.397275
STATEMENTS EXECUTED= 2527
CORE USAGE CBJECT COOE= 3680 BYTESeARRAY AREA= 908 BYTESTOTAL AREA
DIAGNOSTICS bUM8ER OF ERRORS= O0 NUMBER OF WARNINGS= O NUMBER
COMPILE TIME= 0.05 SEC.EXECUTION TIMEa 0.05 SEC. .1034.19 TUESDAY
Copies of this program are available from the authors on request.